Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2

Percentage Accurate: 95.0% → 97.5%

Time: 23.0s

Alternatives: 33

Speedup: 0.5×

• 36.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

Alternative 1: 97.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;t_1 \leq \infty:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (+ (+ x (* z (- 1.0 y))) (* a (- 1.0 t))) (* b (- (+ t y) 2.0)))))
   (if (<= t_1 INFINITY) t_1 (+ x (* t (- b a))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((t + y) - 2.0));
	double tmp;
	if (t_1 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = x + (t * (b - a));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((t + y) - 2.0));
	double tmp;
	if (t_1 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = x + (t * (b - a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((t + y) - 2.0))
	tmp = 0
	if t_1 <= math.inf:
		tmp = t_1
	else:
		tmp = x + (t * (b - a))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(x + Float64(z * Float64(1.0 - y))) + Float64(a * Float64(1.0 - t))) + Float64(b * Float64(Float64(t + y) - 2.0)))
	tmp = 0.0
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(t * Float64(b - a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((x + (z * (1.0 - y))) + (a * (1.0 - t))) + (b * ((t + y) - 2.0));
	tmp = 0.0;
	if (t_1 <= Inf)
		tmp = t_1;
	else
		tmp = x + (t * (b - a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(x + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b)) < +inf.0

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))

   1. Initial program 0.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 0.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 0.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 0.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 0.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 0.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 0.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 0.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 0.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 0.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 0.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 53.8%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in z around 0 62.3%

      \[\leadsto \color{blue}{x - t \cdot \left(a - b\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(t + y\right) - 2\right) \leq \infty:\\ \;\;\;\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 2: 97.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma a (- 1.0 t) (fma (+ y (+ t -2.0)) b (fma z (- 1.0 y) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma(a, (1.0 - t), fma((y + (t + -2.0)), b, fma(z, (1.0 - y), x)));
}

Julia

function code(x, y, z, t, a, b)
	return fma(a, Float64(1.0 - t), fma(Float64(y + Float64(t + -2.0)), b, fma(z, Float64(1.0 - y), x)))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(a * N[(1.0 - t), $MachinePrecision] + N[(N[(y + N[(t + -2.0), $MachinePrecision]), $MachinePrecision] * b + N[(z * N[(1.0 - y), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.9%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Step-by-step derivation

   1. sub-neg 94.9%

      \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. +-commutative 94.9%

      \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   3. associate-+l+ 94.9%

      \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

   4. *-commutative 94.9%

      \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   5. distribute-rgt-neg-in 94.9%

      \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   6. +-commutative 94.9%

      \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

   7. fma-def 96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

   8. neg-sub0 96.5%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

   9. associate--r- 96.5%

      \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

   10. neg-sub0 96.5%

       \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

   11. +-commutative 96.5%

       \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

   12. sub-neg 96.5%

       \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

   13. fma-def 97.3%

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

   14. sub-neg 97.3%

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

   15. associate-+l+ 97.3%

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

   16. metadata-eval 97.3%

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

   17. sub-neg 97.3%

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

   18. +-commutative 97.3%

       \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

3. Simplified 97.3%

   \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

4. Final simplification 97.3%

   \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right) \]

Alternative 3: 97.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (fma (+ t (- y 2.0)) b (- x (fma (+ y -1.0) z (* a (+ t -1.0))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return fma((t + (y - 2.0)), b, (x - fma((y + -1.0), z, (a * (t + -1.0)))));
}

Julia

function code(x, y, z, t, a, b)
	return fma(Float64(t + Float64(y - 2.0)), b, Float64(x - fma(Float64(y + -1.0), z, Float64(a * Float64(t + -1.0)))))
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(t + N[(y - 2.0), $MachinePrecision]), $MachinePrecision] * b + N[(x - N[(N[(y + -1.0), $MachinePrecision] * z + N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 94.9%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Step-by-step derivation

   1. +-commutative 94.9%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

   2. fma-def 96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]

   3. +-commutative 96.5%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\left(t + y\right)} - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   4. associate--l+ 96.5%

      \[\leadsto \mathsf{fma}\left(\color{blue}{t + \left(y - 2\right)}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]

   5. sub-neg 96.5%

      \[\leadsto \mathsf{fma}\left(t + \left(y - 2\right), b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)}\right) \]

   6. associate-+l- 96.5%

      \[\leadsto \mathsf{fma}\left(t + \left(y - 2\right), b, \color{blue}{x - \left(\left(y - 1\right) \cdot z - \left(-\left(t - 1\right) \cdot a\right)\right)}\right) \]

   7. fma-neg 96.9%

      \[\leadsto \mathsf{fma}\left(t + \left(y - 2\right), b, x - \color{blue}{\mathsf{fma}\left(y - 1, z, -\left(-\left(t - 1\right) \cdot a\right)\right)}\right) \]

   8. sub-neg 96.9%

      \[\leadsto \mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(\color{blue}{y + \left(-1\right)}, z, -\left(-\left(t - 1\right) \cdot a\right)\right)\right) \]

   9. metadata-eval 96.9%

      \[\leadsto \mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y + \color{blue}{-1}, z, -\left(-\left(t - 1\right) \cdot a\right)\right)\right) \]

   10. distribute-lft-neg-in 96.9%

       \[\leadsto \mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y + -1, z, -\color{blue}{\left(-\left(t - 1\right)\right) \cdot a}\right)\right) \]

   11. distribute-lft-neg-in 96.9%

       \[\leadsto \mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(-\left(-\left(t - 1\right)\right)\right) \cdot a}\right)\right) \]

   12. remove-double-neg 96.9%

       \[\leadsto \mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]

   13. sub-neg 96.9%

       \[\leadsto \mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot a\right)\right) \]

   14. metadata-eval 96.9%

       \[\leadsto \mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y + -1, z, \left(t + \color{blue}{-1}\right) \cdot a\right)\right) \]

3. Simplified 96.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y + -1, z, \left(t + -1\right) \cdot a\right)\right)} \]

4. Final simplification 96.9%

   \[\leadsto \mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right) \]

Alternative 4: 48.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := a \cdot \left(1 - t\right)\\ t_3 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+88}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-220}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-262}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-104}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-73}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-43}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+19}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* a (- 1.0 t))) (t_3 (* y (- b z))))
   (if (<= y -3.2e+88)
     t_3
     (if (<= y -2.1e-28)
       t_1
       (if (<= y -3.9e-110)
         t_2
         (if (<= y -4.2e-128)
           (* b (- t 2.0))
           (if (<= y -9.6e-220)
             (+ a z)
             (if (<= y -5.8e-298)
               t_2
               (if (<= y 3.1e-262)
                 (+ a z)
                 (if (<= y 4.2e-224)
                   t_1
                   (if (<= y 1.4e-104)
                     (+ a x)
                     (if (<= y 8.2e-73)
                       (* t b)
                       (if (<= y 6.2e-43)
                         (+ a z)
                         (if (<= y 8e+19) (+ a x) t_3))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = a * (1.0 - t);
	double t_3 = y * (b - z);
	double tmp;
	if (y <= -3.2e+88) {
		tmp = t_3;
	} else if (y <= -2.1e-28) {
		tmp = t_1;
	} else if (y <= -3.9e-110) {
		tmp = t_2;
	} else if (y <= -4.2e-128) {
		tmp = b * (t - 2.0);
	} else if (y <= -9.6e-220) {
		tmp = a + z;
	} else if (y <= -5.8e-298) {
		tmp = t_2;
	} else if (y <= 3.1e-262) {
		tmp = a + z;
	} else if (y <= 4.2e-224) {
		tmp = t_1;
	} else if (y <= 1.4e-104) {
		tmp = a + x;
	} else if (y <= 8.2e-73) {
		tmp = t * b;
	} else if (y <= 6.2e-43) {
		tmp = a + z;
	} else if (y <= 8e+19) {
		tmp = a + x;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = a * (1.0d0 - t)
    t_3 = y * (b - z)
    if (y <= (-3.2d+88)) then
        tmp = t_3
    else if (y <= (-2.1d-28)) then
        tmp = t_1
    else if (y <= (-3.9d-110)) then
        tmp = t_2
    else if (y <= (-4.2d-128)) then
        tmp = b * (t - 2.0d0)
    else if (y <= (-9.6d-220)) then
        tmp = a + z
    else if (y <= (-5.8d-298)) then
        tmp = t_2
    else if (y <= 3.1d-262) then
        tmp = a + z
    else if (y <= 4.2d-224) then
        tmp = t_1
    else if (y <= 1.4d-104) then
        tmp = a + x
    else if (y <= 8.2d-73) then
        tmp = t * b
    else if (y <= 6.2d-43) then
        tmp = a + z
    else if (y <= 8d+19) then
        tmp = a + x
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = a * (1.0 - t);
	double t_3 = y * (b - z);
	double tmp;
	if (y <= -3.2e+88) {
		tmp = t_3;
	} else if (y <= -2.1e-28) {
		tmp = t_1;
	} else if (y <= -3.9e-110) {
		tmp = t_2;
	} else if (y <= -4.2e-128) {
		tmp = b * (t - 2.0);
	} else if (y <= -9.6e-220) {
		tmp = a + z;
	} else if (y <= -5.8e-298) {
		tmp = t_2;
	} else if (y <= 3.1e-262) {
		tmp = a + z;
	} else if (y <= 4.2e-224) {
		tmp = t_1;
	} else if (y <= 1.4e-104) {
		tmp = a + x;
	} else if (y <= 8.2e-73) {
		tmp = t * b;
	} else if (y <= 6.2e-43) {
		tmp = a + z;
	} else if (y <= 8e+19) {
		tmp = a + x;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = a * (1.0 - t)
	t_3 = y * (b - z)
	tmp = 0
	if y <= -3.2e+88:
		tmp = t_3
	elif y <= -2.1e-28:
		tmp = t_1
	elif y <= -3.9e-110:
		tmp = t_2
	elif y <= -4.2e-128:
		tmp = b * (t - 2.0)
	elif y <= -9.6e-220:
		tmp = a + z
	elif y <= -5.8e-298:
		tmp = t_2
	elif y <= 3.1e-262:
		tmp = a + z
	elif y <= 4.2e-224:
		tmp = t_1
	elif y <= 1.4e-104:
		tmp = a + x
	elif y <= 8.2e-73:
		tmp = t * b
	elif y <= 6.2e-43:
		tmp = a + z
	elif y <= 8e+19:
		tmp = a + x
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(a * Float64(1.0 - t))
	t_3 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -3.2e+88)
		tmp = t_3;
	elseif (y <= -2.1e-28)
		tmp = t_1;
	elseif (y <= -3.9e-110)
		tmp = t_2;
	elseif (y <= -4.2e-128)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= -9.6e-220)
		tmp = Float64(a + z);
	elseif (y <= -5.8e-298)
		tmp = t_2;
	elseif (y <= 3.1e-262)
		tmp = Float64(a + z);
	elseif (y <= 4.2e-224)
		tmp = t_1;
	elseif (y <= 1.4e-104)
		tmp = Float64(a + x);
	elseif (y <= 8.2e-73)
		tmp = Float64(t * b);
	elseif (y <= 6.2e-43)
		tmp = Float64(a + z);
	elseif (y <= 8e+19)
		tmp = Float64(a + x);
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = a * (1.0 - t);
	t_3 = y * (b - z);
	tmp = 0.0;
	if (y <= -3.2e+88)
		tmp = t_3;
	elseif (y <= -2.1e-28)
		tmp = t_1;
	elseif (y <= -3.9e-110)
		tmp = t_2;
	elseif (y <= -4.2e-128)
		tmp = b * (t - 2.0);
	elseif (y <= -9.6e-220)
		tmp = a + z;
	elseif (y <= -5.8e-298)
		tmp = t_2;
	elseif (y <= 3.1e-262)
		tmp = a + z;
	elseif (y <= 4.2e-224)
		tmp = t_1;
	elseif (y <= 1.4e-104)
		tmp = a + x;
	elseif (y <= 8.2e-73)
		tmp = t * b;
	elseif (y <= 6.2e-43)
		tmp = a + z;
	elseif (y <= 8e+19)
		tmp = a + x;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+88], t$95$3, If[LessEqual[y, -2.1e-28], t$95$1, If[LessEqual[y, -3.9e-110], t$95$2, If[LessEqual[y, -4.2e-128], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.6e-220], N[(a + z), $MachinePrecision], If[LessEqual[y, -5.8e-298], t$95$2, If[LessEqual[y, 3.1e-262], N[(a + z), $MachinePrecision], If[LessEqual[y, 4.2e-224], t$95$1, If[LessEqual[y, 1.4e-104], N[(a + x), $MachinePrecision], If[LessEqual[y, 8.2e-73], N[(t * b), $MachinePrecision], If[LessEqual[y, 6.2e-43], N[(a + z), $MachinePrecision], If[LessEqual[y, 8e+19], N[(a + x), $MachinePrecision], t$95$3]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if y < -3.1999999999999999e88 or 8e19 < y

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -3.1999999999999999e88 < y < -2.10000000000000006e-28 or 3.0999999999999998e-262 < y < 4.20000000000000013e-224

   1. Initial program 96.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 96.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 96.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 96.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 96.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 96.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 96.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 96.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 96.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 96.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 96.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 55.1%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -2.10000000000000006e-28 < y < -3.9e-110 or -9.6000000000000006e-220 < y < -5.8000000000000003e-298

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 62.3%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -3.9e-110 < y < -4.2000000000000002e-128

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 100.0%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 100.0%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 100.0%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 100.0%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in b around inf 80.2%

      \[\leadsto \color{blue}{\left(t - 2\right) \cdot b} \]

   if -4.2000000000000002e-128 < y < -9.6000000000000006e-220 or -5.8000000000000003e-298 < y < 3.0999999999999998e-262 or 8.20000000000000032e-73 < y < 6.1999999999999999e-43

   1. Initial program 94.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 94.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 94.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 94.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 94.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 94.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 94.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 94.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 94.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 94.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 94.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 94.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in a around inf 74.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]
   6. Step-by-step derivation

      1. associate-*r* 74.7%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

      2. neg-mul-1 74.7%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   7. Simplified 74.7%

      \[\leadsto \color{blue}{\left(-a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   8. Taylor expanded in y around 0 74.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right) - \left(-1 \cdot z + -1 \cdot a\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 74.7%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(-1 \cdot z + -1 \cdot a\right) \]

      2. mul-1-neg 74.7%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(-1 \cdot z + -1 \cdot a\right) \]

      3. distribute-lft-out 74.7%

         \[\leadsto \left(-a\right) \cdot t - \color{blue}{-1 \cdot \left(z + a\right)} \]

   10. Simplified 74.7%

       \[\leadsto \color{blue}{\left(-a\right) \cdot t - -1 \cdot \left(z + a\right)} \]

   11. Taylor expanded in t around 0 61.6%

       \[\leadsto \color{blue}{a + z} \]

   if 4.20000000000000013e-224 < y < 1.4e-104 or 6.1999999999999999e-43 < y < 8e19

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.2%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 97.2%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 97.2%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 97.2%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 97.2%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 97.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 97.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 97.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 97.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 97.2%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 97.2%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 73.2%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   6. Taylor expanded in z around 0 56.4%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   7. Step-by-step derivation

      1. sub-neg 56.4%

         \[\leadsto \color{blue}{x + \left(--1 \cdot a\right)} \]

      2. mul-1-neg 56.4%

         \[\leadsto x + \left(-\color{blue}{\left(-a\right)}\right) \]

      3. remove-double-neg 56.4%

         \[\leadsto x + \color{blue}{a} \]

   8. Simplified 56.4%

      \[\leadsto \color{blue}{x + a} \]

   if 1.4e-104 < y < 8.20000000000000032e-73

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 100.0%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 100.0%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 100.0%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 100.0%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in b around inf 80.4%

      \[\leadsto \color{blue}{\left(t - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf 80.4%

      \[\leadsto \color{blue}{t \cdot b} \]
3. Recombined 7 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-28}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-110}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-128}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -9.6 \cdot 10^{-220}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-298}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-262}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-224}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-104}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-73}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-43}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+19}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 5: 48.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.25 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-35}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-131}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-159}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-297}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-262}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-104}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-73}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-42}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+19}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -1.25e+88)
     t_2
     (if (<= y -1.65e-35)
       t_1
       (if (<= y -9.5e-121)
         (* a (- 1.0 t))
         (if (<= y -1.6e-131)
           (* b (- t 2.0))
           (if (<= y -1.25e-159)
             (+ a z)
             (if (<= y -1.1e-297)
               (- x (* a t))
               (if (<= y 3.2e-262)
                 (+ a z)
                 (if (<= y 9.2e-225)
                   t_1
                   (if (<= y 9.4e-104)
                     (+ a x)
                     (if (<= y 8.5e-73)
                       (* t b)
                       (if (<= y 1.18e-42)
                         (+ a z)
                         (if (<= y 8e+19) (+ a x) t_2))))))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.25e+88) {
		tmp = t_2;
	} else if (y <= -1.65e-35) {
		tmp = t_1;
	} else if (y <= -9.5e-121) {
		tmp = a * (1.0 - t);
	} else if (y <= -1.6e-131) {
		tmp = b * (t - 2.0);
	} else if (y <= -1.25e-159) {
		tmp = a + z;
	} else if (y <= -1.1e-297) {
		tmp = x - (a * t);
	} else if (y <= 3.2e-262) {
		tmp = a + z;
	} else if (y <= 9.2e-225) {
		tmp = t_1;
	} else if (y <= 9.4e-104) {
		tmp = a + x;
	} else if (y <= 8.5e-73) {
		tmp = t * b;
	} else if (y <= 1.18e-42) {
		tmp = a + z;
	} else if (y <= 8e+19) {
		tmp = a + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-1.25d+88)) then
        tmp = t_2
    else if (y <= (-1.65d-35)) then
        tmp = t_1
    else if (y <= (-9.5d-121)) then
        tmp = a * (1.0d0 - t)
    else if (y <= (-1.6d-131)) then
        tmp = b * (t - 2.0d0)
    else if (y <= (-1.25d-159)) then
        tmp = a + z
    else if (y <= (-1.1d-297)) then
        tmp = x - (a * t)
    else if (y <= 3.2d-262) then
        tmp = a + z
    else if (y <= 9.2d-225) then
        tmp = t_1
    else if (y <= 9.4d-104) then
        tmp = a + x
    else if (y <= 8.5d-73) then
        tmp = t * b
    else if (y <= 1.18d-42) then
        tmp = a + z
    else if (y <= 8d+19) then
        tmp = a + x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.25e+88) {
		tmp = t_2;
	} else if (y <= -1.65e-35) {
		tmp = t_1;
	} else if (y <= -9.5e-121) {
		tmp = a * (1.0 - t);
	} else if (y <= -1.6e-131) {
		tmp = b * (t - 2.0);
	} else if (y <= -1.25e-159) {
		tmp = a + z;
	} else if (y <= -1.1e-297) {
		tmp = x - (a * t);
	} else if (y <= 3.2e-262) {
		tmp = a + z;
	} else if (y <= 9.2e-225) {
		tmp = t_1;
	} else if (y <= 9.4e-104) {
		tmp = a + x;
	} else if (y <= 8.5e-73) {
		tmp = t * b;
	} else if (y <= 1.18e-42) {
		tmp = a + z;
	} else if (y <= 8e+19) {
		tmp = a + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -1.25e+88:
		tmp = t_2
	elif y <= -1.65e-35:
		tmp = t_1
	elif y <= -9.5e-121:
		tmp = a * (1.0 - t)
	elif y <= -1.6e-131:
		tmp = b * (t - 2.0)
	elif y <= -1.25e-159:
		tmp = a + z
	elif y <= -1.1e-297:
		tmp = x - (a * t)
	elif y <= 3.2e-262:
		tmp = a + z
	elif y <= 9.2e-225:
		tmp = t_1
	elif y <= 9.4e-104:
		tmp = a + x
	elif y <= 8.5e-73:
		tmp = t * b
	elif y <= 1.18e-42:
		tmp = a + z
	elif y <= 8e+19:
		tmp = a + x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.25e+88)
		tmp = t_2;
	elseif (y <= -1.65e-35)
		tmp = t_1;
	elseif (y <= -9.5e-121)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= -1.6e-131)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (y <= -1.25e-159)
		tmp = Float64(a + z);
	elseif (y <= -1.1e-297)
		tmp = Float64(x - Float64(a * t));
	elseif (y <= 3.2e-262)
		tmp = Float64(a + z);
	elseif (y <= 9.2e-225)
		tmp = t_1;
	elseif (y <= 9.4e-104)
		tmp = Float64(a + x);
	elseif (y <= 8.5e-73)
		tmp = Float64(t * b);
	elseif (y <= 1.18e-42)
		tmp = Float64(a + z);
	elseif (y <= 8e+19)
		tmp = Float64(a + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.25e+88)
		tmp = t_2;
	elseif (y <= -1.65e-35)
		tmp = t_1;
	elseif (y <= -9.5e-121)
		tmp = a * (1.0 - t);
	elseif (y <= -1.6e-131)
		tmp = b * (t - 2.0);
	elseif (y <= -1.25e-159)
		tmp = a + z;
	elseif (y <= -1.1e-297)
		tmp = x - (a * t);
	elseif (y <= 3.2e-262)
		tmp = a + z;
	elseif (y <= 9.2e-225)
		tmp = t_1;
	elseif (y <= 9.4e-104)
		tmp = a + x;
	elseif (y <= 8.5e-73)
		tmp = t * b;
	elseif (y <= 1.18e-42)
		tmp = a + z;
	elseif (y <= 8e+19)
		tmp = a + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.25e+88], t$95$2, If[LessEqual[y, -1.65e-35], t$95$1, If[LessEqual[y, -9.5e-121], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e-131], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.25e-159], N[(a + z), $MachinePrecision], If[LessEqual[y, -1.1e-297], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e-262], N[(a + z), $MachinePrecision], If[LessEqual[y, 9.2e-225], t$95$1, If[LessEqual[y, 9.4e-104], N[(a + x), $MachinePrecision], If[LessEqual[y, 8.5e-73], N[(t * b), $MachinePrecision], If[LessEqual[y, 1.18e-42], N[(a + z), $MachinePrecision], If[LessEqual[y, 8e+19], N[(a + x), $MachinePrecision], t$95$2]]]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if y < -1.24999999999999999e88 or 8e19 < y

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -1.24999999999999999e88 < y < -1.65e-35 or 3.2e-262 < y < 9.1999999999999995e-225

   1. Initial program 96.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 96.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 96.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 96.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 96.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 96.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 96.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 96.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 96.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 96.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 96.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 55.1%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -1.65e-35 < y < -9.4999999999999994e-121

   1. Initial program 99.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 99.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 99.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 99.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 99.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 99.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 53.6%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -9.4999999999999994e-121 < y < -1.6e-131

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 100.0%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 100.0%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 100.0%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 100.0%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in b around inf 100.0%

      \[\leadsto \color{blue}{\left(t - 2\right) \cdot b} \]

   if -1.6e-131 < y < -1.25000000000000008e-159 or -1.0999999999999999e-297 < y < 3.2e-262 or 8.4999999999999996e-73 < y < 1.17999999999999995e-42

   1. Initial program 92.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 92.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 92.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 92.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 92.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 92.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 92.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 92.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 92.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 92.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 92.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 92.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in a around inf 78.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]
   6. Step-by-step derivation

      1. associate-*r* 78.7%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

      2. neg-mul-1 78.7%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   7. Simplified 78.7%

      \[\leadsto \color{blue}{\left(-a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   8. Taylor expanded in y around 0 78.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right) - \left(-1 \cdot z + -1 \cdot a\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 78.7%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(-1 \cdot z + -1 \cdot a\right) \]

      2. mul-1-neg 78.7%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(-1 \cdot z + -1 \cdot a\right) \]

      3. distribute-lft-out 78.7%

         \[\leadsto \left(-a\right) \cdot t - \color{blue}{-1 \cdot \left(z + a\right)} \]

   10. Simplified 78.7%

       \[\leadsto \color{blue}{\left(-a\right) \cdot t - -1 \cdot \left(z + a\right)} \]

   11. Taylor expanded in t around 0 67.8%

       \[\leadsto \color{blue}{a + z} \]

   if -1.25000000000000008e-159 < y < -1.0999999999999999e-297

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 83.1%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in z around 0 68.8%

      \[\leadsto \color{blue}{x - t \cdot \left(a - b\right)} \]

   6. Taylor expanded in a around inf 65.7%

      \[\leadsto x - \color{blue}{a \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 65.7%

         \[\leadsto x - \color{blue}{t \cdot a} \]

   8. Simplified 65.7%

      \[\leadsto x - \color{blue}{t \cdot a} \]

   if 9.1999999999999995e-225 < y < 9.4e-104 or 1.17999999999999995e-42 < y < 8e19

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.2%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 97.2%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 97.2%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 97.2%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 97.2%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 97.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 97.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 97.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 97.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 97.2%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 97.2%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 73.2%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   6. Taylor expanded in z around 0 56.4%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   7. Step-by-step derivation

      1. sub-neg 56.4%

         \[\leadsto \color{blue}{x + \left(--1 \cdot a\right)} \]

      2. mul-1-neg 56.4%

         \[\leadsto x + \left(-\color{blue}{\left(-a\right)}\right) \]

      3. remove-double-neg 56.4%

         \[\leadsto x + \color{blue}{a} \]

   8. Simplified 56.4%

      \[\leadsto \color{blue}{x + a} \]

   if 9.4e-104 < y < 8.4999999999999996e-73

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 100.0%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 100.0%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 100.0%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 100.0%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in b around inf 80.4%

      \[\leadsto \color{blue}{\left(t - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf 80.4%

      \[\leadsto \color{blue}{t \cdot b} \]
3. Recombined 8 regimes into one program.

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-35}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-121}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-131}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-159}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-297}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-262}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-225}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 9.4 \cdot 10^{-104}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-73}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-42}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+19}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 6: 48.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-33}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-301}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-263}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-224}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-103}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-73}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-42}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+21}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))))
   (if (<= y -2.1e+88)
     t_2
     (if (<= y -1.6e-33)
       t_1
       (if (<= y -9e-301)
         (* a (- 1.0 t))
         (if (<= y 7.2e-263)
           (+ a z)
           (if (<= y 4.5e-224)
             t_1
             (if (<= y 1.08e-103)
               (+ a x)
               (if (<= y 7.8e-73)
                 (* t b)
                 (if (<= y 1.18e-42)
                   (+ a z)
                   (if (<= y 1.35e+21) (+ a x) t_2)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -2.1e+88) {
		tmp = t_2;
	} else if (y <= -1.6e-33) {
		tmp = t_1;
	} else if (y <= -9e-301) {
		tmp = a * (1.0 - t);
	} else if (y <= 7.2e-263) {
		tmp = a + z;
	} else if (y <= 4.5e-224) {
		tmp = t_1;
	} else if (y <= 1.08e-103) {
		tmp = a + x;
	} else if (y <= 7.8e-73) {
		tmp = t * b;
	} else if (y <= 1.18e-42) {
		tmp = a + z;
	} else if (y <= 1.35e+21) {
		tmp = a + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = y * (b - z)
    if (y <= (-2.1d+88)) then
        tmp = t_2
    else if (y <= (-1.6d-33)) then
        tmp = t_1
    else if (y <= (-9d-301)) then
        tmp = a * (1.0d0 - t)
    else if (y <= 7.2d-263) then
        tmp = a + z
    else if (y <= 4.5d-224) then
        tmp = t_1
    else if (y <= 1.08d-103) then
        tmp = a + x
    else if (y <= 7.8d-73) then
        tmp = t * b
    else if (y <= 1.18d-42) then
        tmp = a + z
    else if (y <= 1.35d+21) then
        tmp = a + x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -2.1e+88) {
		tmp = t_2;
	} else if (y <= -1.6e-33) {
		tmp = t_1;
	} else if (y <= -9e-301) {
		tmp = a * (1.0 - t);
	} else if (y <= 7.2e-263) {
		tmp = a + z;
	} else if (y <= 4.5e-224) {
		tmp = t_1;
	} else if (y <= 1.08e-103) {
		tmp = a + x;
	} else if (y <= 7.8e-73) {
		tmp = t * b;
	} else if (y <= 1.18e-42) {
		tmp = a + z;
	} else if (y <= 1.35e+21) {
		tmp = a + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -2.1e+88:
		tmp = t_2
	elif y <= -1.6e-33:
		tmp = t_1
	elif y <= -9e-301:
		tmp = a * (1.0 - t)
	elif y <= 7.2e-263:
		tmp = a + z
	elif y <= 4.5e-224:
		tmp = t_1
	elif y <= 1.08e-103:
		tmp = a + x
	elif y <= 7.8e-73:
		tmp = t * b
	elif y <= 1.18e-42:
		tmp = a + z
	elif y <= 1.35e+21:
		tmp = a + x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -2.1e+88)
		tmp = t_2;
	elseif (y <= -1.6e-33)
		tmp = t_1;
	elseif (y <= -9e-301)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= 7.2e-263)
		tmp = Float64(a + z);
	elseif (y <= 4.5e-224)
		tmp = t_1;
	elseif (y <= 1.08e-103)
		tmp = Float64(a + x);
	elseif (y <= 7.8e-73)
		tmp = Float64(t * b);
	elseif (y <= 1.18e-42)
		tmp = Float64(a + z);
	elseif (y <= 1.35e+21)
		tmp = Float64(a + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -2.1e+88)
		tmp = t_2;
	elseif (y <= -1.6e-33)
		tmp = t_1;
	elseif (y <= -9e-301)
		tmp = a * (1.0 - t);
	elseif (y <= 7.2e-263)
		tmp = a + z;
	elseif (y <= 4.5e-224)
		tmp = t_1;
	elseif (y <= 1.08e-103)
		tmp = a + x;
	elseif (y <= 7.8e-73)
		tmp = t * b;
	elseif (y <= 1.18e-42)
		tmp = a + z;
	elseif (y <= 1.35e+21)
		tmp = a + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e+88], t$95$2, If[LessEqual[y, -1.6e-33], t$95$1, If[LessEqual[y, -9e-301], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-263], N[(a + z), $MachinePrecision], If[LessEqual[y, 4.5e-224], t$95$1, If[LessEqual[y, 1.08e-103], N[(a + x), $MachinePrecision], If[LessEqual[y, 7.8e-73], N[(t * b), $MachinePrecision], If[LessEqual[y, 1.18e-42], N[(a + z), $MachinePrecision], If[LessEqual[y, 1.35e+21], N[(a + x), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -2.1e88 or 1.35e21 < y

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -2.1e88 < y < -1.59999999999999988e-33 or 7.2000000000000001e-263 < y < 4.5000000000000004e-224

   1. Initial program 96.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 96.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 96.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 96.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 96.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 96.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 96.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 96.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 96.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 96.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 96.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 55.1%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -1.59999999999999988e-33 < y < -9.00000000000000039e-301

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 52.4%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -9.00000000000000039e-301 < y < 7.2000000000000001e-263 or 7.79999999999999963e-73 < y < 1.17999999999999995e-42

   1. Initial program 92.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 92.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 92.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 92.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 92.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 92.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 92.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 92.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 92.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 92.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 92.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in a around inf 76.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]
   6. Step-by-step derivation

      1. associate-*r* 76.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

      2. neg-mul-1 76.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   7. Simplified 76.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   8. Taylor expanded in y around 0 76.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right) - \left(-1 \cdot z + -1 \cdot a\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 76.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(-1 \cdot z + -1 \cdot a\right) \]

      2. mul-1-neg 76.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(-1 \cdot z + -1 \cdot a\right) \]

      3. distribute-lft-out 76.1%

         \[\leadsto \left(-a\right) \cdot t - \color{blue}{-1 \cdot \left(z + a\right)} \]

   10. Simplified 76.1%

       \[\leadsto \color{blue}{\left(-a\right) \cdot t - -1 \cdot \left(z + a\right)} \]

   11. Taylor expanded in t around 0 63.9%

       \[\leadsto \color{blue}{a + z} \]

   if 4.5000000000000004e-224 < y < 1.0799999999999999e-103 or 1.17999999999999995e-42 < y < 1.35e21

   1. Initial program 97.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.2%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 97.2%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 97.2%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 97.2%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 97.2%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 97.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 97.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 97.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 97.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 97.2%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 97.2%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 73.2%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   6. Taylor expanded in z around 0 56.4%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   7. Step-by-step derivation

      1. sub-neg 56.4%

         \[\leadsto \color{blue}{x + \left(--1 \cdot a\right)} \]

      2. mul-1-neg 56.4%

         \[\leadsto x + \left(-\color{blue}{\left(-a\right)}\right) \]

      3. remove-double-neg 56.4%

         \[\leadsto x + \color{blue}{a} \]

   8. Simplified 56.4%

      \[\leadsto \color{blue}{x + a} \]

   if 1.0799999999999999e-103 < y < 7.79999999999999963e-73

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 100.0%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 100.0%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 100.0%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 100.0%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in b around inf 80.4%

      \[\leadsto \color{blue}{\left(t - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf 80.4%

      \[\leadsto \color{blue}{t \cdot b} \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-33}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-301}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-263}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-224}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{-103}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-73}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.18 \cdot 10^{-42}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+21}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 7: 63.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := a + \left(\left(z + x\right) + -2 \cdot b\right)\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-221}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-297}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{-260}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-233}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t (- b a))))
        (t_2 (* y (- b z)))
        (t_3 (+ a (+ (+ z x) (* -2.0 b)))))
   (if (<= y -1.7e+88)
     t_2
     (if (<= y -6.5e-77)
       t_1
       (if (<= y -3.2e-221)
         t_3
         (if (<= y -5.6e-297)
           (- x (* a (+ t -1.0)))
           (if (<= y 1.48e-260)
             t_3
             (if (<= y 7.4e-233) t_1 (if (<= y 1.15e+21) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double t_2 = y * (b - z);
	double t_3 = a + ((z + x) + (-2.0 * b));
	double tmp;
	if (y <= -1.7e+88) {
		tmp = t_2;
	} else if (y <= -6.5e-77) {
		tmp = t_1;
	} else if (y <= -3.2e-221) {
		tmp = t_3;
	} else if (y <= -5.6e-297) {
		tmp = x - (a * (t + -1.0));
	} else if (y <= 1.48e-260) {
		tmp = t_3;
	} else if (y <= 7.4e-233) {
		tmp = t_1;
	} else if (y <= 1.15e+21) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (t * (b - a))
    t_2 = y * (b - z)
    t_3 = a + ((z + x) + ((-2.0d0) * b))
    if (y <= (-1.7d+88)) then
        tmp = t_2
    else if (y <= (-6.5d-77)) then
        tmp = t_1
    else if (y <= (-3.2d-221)) then
        tmp = t_3
    else if (y <= (-5.6d-297)) then
        tmp = x - (a * (t + (-1.0d0)))
    else if (y <= 1.48d-260) then
        tmp = t_3
    else if (y <= 7.4d-233) then
        tmp = t_1
    else if (y <= 1.15d+21) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double t_2 = y * (b - z);
	double t_3 = a + ((z + x) + (-2.0 * b));
	double tmp;
	if (y <= -1.7e+88) {
		tmp = t_2;
	} else if (y <= -6.5e-77) {
		tmp = t_1;
	} else if (y <= -3.2e-221) {
		tmp = t_3;
	} else if (y <= -5.6e-297) {
		tmp = x - (a * (t + -1.0));
	} else if (y <= 1.48e-260) {
		tmp = t_3;
	} else if (y <= 7.4e-233) {
		tmp = t_1;
	} else if (y <= 1.15e+21) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * (b - a))
	t_2 = y * (b - z)
	t_3 = a + ((z + x) + (-2.0 * b))
	tmp = 0
	if y <= -1.7e+88:
		tmp = t_2
	elif y <= -6.5e-77:
		tmp = t_1
	elif y <= -3.2e-221:
		tmp = t_3
	elif y <= -5.6e-297:
		tmp = x - (a * (t + -1.0))
	elif y <= 1.48e-260:
		tmp = t_3
	elif y <= 7.4e-233:
		tmp = t_1
	elif y <= 1.15e+21:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * Float64(b - a)))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(a + Float64(Float64(z + x) + Float64(-2.0 * b)))
	tmp = 0.0
	if (y <= -1.7e+88)
		tmp = t_2;
	elseif (y <= -6.5e-77)
		tmp = t_1;
	elseif (y <= -3.2e-221)
		tmp = t_3;
	elseif (y <= -5.6e-297)
		tmp = Float64(x - Float64(a * Float64(t + -1.0)));
	elseif (y <= 1.48e-260)
		tmp = t_3;
	elseif (y <= 7.4e-233)
		tmp = t_1;
	elseif (y <= 1.15e+21)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * (b - a));
	t_2 = y * (b - z);
	t_3 = a + ((z + x) + (-2.0 * b));
	tmp = 0.0;
	if (y <= -1.7e+88)
		tmp = t_2;
	elseif (y <= -6.5e-77)
		tmp = t_1;
	elseif (y <= -3.2e-221)
		tmp = t_3;
	elseif (y <= -5.6e-297)
		tmp = x - (a * (t + -1.0));
	elseif (y <= 1.48e-260)
		tmp = t_3;
	elseif (y <= 7.4e-233)
		tmp = t_1;
	elseif (y <= 1.15e+21)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(N[(z + x), $MachinePrecision] + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+88], t$95$2, If[LessEqual[y, -6.5e-77], t$95$1, If[LessEqual[y, -3.2e-221], t$95$3, If[LessEqual[y, -5.6e-297], N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.48e-260], t$95$3, If[LessEqual[y, 7.4e-233], t$95$1, If[LessEqual[y, 1.15e+21], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.70000000000000002e88 or 1.15e21 < y

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -1.70000000000000002e88 < y < -6.4999999999999999e-77 or 1.4800000000000001e-260 < y < 7.3999999999999996e-233

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.6%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 97.6%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 97.6%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 97.6%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 97.6%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 97.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 97.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 97.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 97.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 97.6%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 97.6%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 80.6%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in z around 0 69.2%

      \[\leadsto \color{blue}{x - t \cdot \left(a - b\right)} \]

   if -6.4999999999999999e-77 < y < -3.20000000000000015e-221 or -5.59999999999999968e-297 < y < 1.4800000000000001e-260 or 7.3999999999999996e-233 < y < 1.15e21

   1. Initial program 96.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 96.8%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 96.8%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 96.8%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 96.8%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 96.8%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 96.8%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 96.7%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in t around 0 76.7%

      \[\leadsto \color{blue}{a + \left(-2 \cdot b + \left(z + x\right)\right)} \]

   if -3.20000000000000015e-221 < y < -5.59999999999999968e-297

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 91.9%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in b around 0 88.9%

      \[\leadsto \color{blue}{x - \left(t - 1\right) \cdot a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{-77}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-221}:\\ \;\;\;\;a + \left(\left(z + x\right) + -2 \cdot b\right)\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{-297}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{-260}:\\ \;\;\;\;a + \left(\left(z + x\right) + -2 \cdot b\right)\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-233}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+21}:\\ \;\;\;\;a + \left(\left(z + x\right) + -2 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 8: 79.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := x + \left(a + t_1\right)\\ t_3 := \left(x + t_1\right) + t \cdot \left(b - a\right)\\ t_4 := x + b \cdot \left(y - 2\right)\\ \mathbf{if}\;t \leq -0.012:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-182}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-277}:\\ \;\;\;\;a + t_4\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-210}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 29500:\\ \;\;\;\;t_4 + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y)))
        (t_2 (+ x (+ a t_1)))
        (t_3 (+ (+ x t_1) (* t (- b a))))
        (t_4 (+ x (* b (- y 2.0)))))
   (if (<= t -0.012)
     t_3
     (if (<= t -2.2e-182)
       t_2
       (if (<= t 7.5e-277)
         (+ a t_4)
         (if (<= t 6.2e-210)
           t_2
           (if (<= t 29500.0) (+ t_4 (* a (- 1.0 t))) t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (a + t_1);
	double t_3 = (x + t_1) + (t * (b - a));
	double t_4 = x + (b * (y - 2.0));
	double tmp;
	if (t <= -0.012) {
		tmp = t_3;
	} else if (t <= -2.2e-182) {
		tmp = t_2;
	} else if (t <= 7.5e-277) {
		tmp = a + t_4;
	} else if (t <= 6.2e-210) {
		tmp = t_2;
	} else if (t <= 29500.0) {
		tmp = t_4 + (a * (1.0 - t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    t_2 = x + (a + t_1)
    t_3 = (x + t_1) + (t * (b - a))
    t_4 = x + (b * (y - 2.0d0))
    if (t <= (-0.012d0)) then
        tmp = t_3
    else if (t <= (-2.2d-182)) then
        tmp = t_2
    else if (t <= 7.5d-277) then
        tmp = a + t_4
    else if (t <= 6.2d-210) then
        tmp = t_2
    else if (t <= 29500.0d0) then
        tmp = t_4 + (a * (1.0d0 - t))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double t_2 = x + (a + t_1);
	double t_3 = (x + t_1) + (t * (b - a));
	double t_4 = x + (b * (y - 2.0));
	double tmp;
	if (t <= -0.012) {
		tmp = t_3;
	} else if (t <= -2.2e-182) {
		tmp = t_2;
	} else if (t <= 7.5e-277) {
		tmp = a + t_4;
	} else if (t <= 6.2e-210) {
		tmp = t_2;
	} else if (t <= 29500.0) {
		tmp = t_4 + (a * (1.0 - t));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	t_2 = x + (a + t_1)
	t_3 = (x + t_1) + (t * (b - a))
	t_4 = x + (b * (y - 2.0))
	tmp = 0
	if t <= -0.012:
		tmp = t_3
	elif t <= -2.2e-182:
		tmp = t_2
	elif t <= 7.5e-277:
		tmp = a + t_4
	elif t <= 6.2e-210:
		tmp = t_2
	elif t <= 29500.0:
		tmp = t_4 + (a * (1.0 - t))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	t_2 = Float64(x + Float64(a + t_1))
	t_3 = Float64(Float64(x + t_1) + Float64(t * Float64(b - a)))
	t_4 = Float64(x + Float64(b * Float64(y - 2.0)))
	tmp = 0.0
	if (t <= -0.012)
		tmp = t_3;
	elseif (t <= -2.2e-182)
		tmp = t_2;
	elseif (t <= 7.5e-277)
		tmp = Float64(a + t_4);
	elseif (t <= 6.2e-210)
		tmp = t_2;
	elseif (t <= 29500.0)
		tmp = Float64(t_4 + Float64(a * Float64(1.0 - t)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	t_2 = x + (a + t_1);
	t_3 = (x + t_1) + (t * (b - a));
	t_4 = x + (b * (y - 2.0));
	tmp = 0.0;
	if (t <= -0.012)
		tmp = t_3;
	elseif (t <= -2.2e-182)
		tmp = t_2;
	elseif (t <= 7.5e-277)
		tmp = a + t_4;
	elseif (t <= 6.2e-210)
		tmp = t_2;
	elseif (t <= 29500.0)
		tmp = t_4 + (a * (1.0 - t));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(a + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + t$95$1), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.012], t$95$3, If[LessEqual[t, -2.2e-182], t$95$2, If[LessEqual[t, 7.5e-277], N[(a + t$95$4), $MachinePrecision], If[LessEqual[t, 6.2e-210], t$95$2, If[LessEqual[t, 29500.0], N[(t$95$4 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -0.012 or 29500 < t

   1. Initial program 92.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 92.4%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 92.4%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 92.4%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 92.4%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 92.4%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 92.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 92.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 92.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 92.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 92.4%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 92.4%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 92.7%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   if -0.012 < t < -2.2e-182 or 7.49999999999999971e-277 < t < 6.19999999999999973e-210

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 80.8%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   if -2.2e-182 < t < 7.49999999999999971e-277

   1. Initial program 93.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 93.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 93.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 93.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 93.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 93.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 93.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 93.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 93.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 93.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 93.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 75.8%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 75.8%

      \[\leadsto \color{blue}{\left(\left(y - 2\right) \cdot b + x\right) - -1 \cdot a} \]

   if 6.19999999999999973e-210 < t < 29500

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.6%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 97.6%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 97.6%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 97.6%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 97.6%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 97.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 97.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 97.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 97.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 97.6%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 97.6%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 84.0%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 84.0%

      \[\leadsto \left(\color{blue}{\left(y - 2\right) \cdot b} + x\right) - \left(t - 1\right) \cdot a \]
3. Recombined 4 regimes into one program.

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.012:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-182}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-277}:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{-210}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;t \leq 29500:\\ \;\;\;\;\left(x + b \cdot \left(y - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 9: 69.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(z + x\right) + t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := a + \left(\left(z + x\right) + -2 \cdot b\right)\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-186}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-106}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ z x) (* t (- b a))))
        (t_2 (* y (- b z)))
        (t_3 (+ a (+ (+ z x) (* -2.0 b)))))
   (if (<= y -1.05e+96)
     t_2
     (if (<= y -1.4e-79)
       t_1
       (if (<= y -1.8e-186)
         t_3
         (if (<= y 3e-234)
           t_1
           (if (<= y 1.75e-106) t_3 (if (<= y 1.02e+89) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + x) + (t * (b - a));
	double t_2 = y * (b - z);
	double t_3 = a + ((z + x) + (-2.0 * b));
	double tmp;
	if (y <= -1.05e+96) {
		tmp = t_2;
	} else if (y <= -1.4e-79) {
		tmp = t_1;
	} else if (y <= -1.8e-186) {
		tmp = t_3;
	} else if (y <= 3e-234) {
		tmp = t_1;
	} else if (y <= 1.75e-106) {
		tmp = t_3;
	} else if (y <= 1.02e+89) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (z + x) + (t * (b - a))
    t_2 = y * (b - z)
    t_3 = a + ((z + x) + ((-2.0d0) * b))
    if (y <= (-1.05d+96)) then
        tmp = t_2
    else if (y <= (-1.4d-79)) then
        tmp = t_1
    else if (y <= (-1.8d-186)) then
        tmp = t_3
    else if (y <= 3d-234) then
        tmp = t_1
    else if (y <= 1.75d-106) then
        tmp = t_3
    else if (y <= 1.02d+89) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (z + x) + (t * (b - a));
	double t_2 = y * (b - z);
	double t_3 = a + ((z + x) + (-2.0 * b));
	double tmp;
	if (y <= -1.05e+96) {
		tmp = t_2;
	} else if (y <= -1.4e-79) {
		tmp = t_1;
	} else if (y <= -1.8e-186) {
		tmp = t_3;
	} else if (y <= 3e-234) {
		tmp = t_1;
	} else if (y <= 1.75e-106) {
		tmp = t_3;
	} else if (y <= 1.02e+89) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (z + x) + (t * (b - a))
	t_2 = y * (b - z)
	t_3 = a + ((z + x) + (-2.0 * b))
	tmp = 0
	if y <= -1.05e+96:
		tmp = t_2
	elif y <= -1.4e-79:
		tmp = t_1
	elif y <= -1.8e-186:
		tmp = t_3
	elif y <= 3e-234:
		tmp = t_1
	elif y <= 1.75e-106:
		tmp = t_3
	elif y <= 1.02e+89:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(z + x) + Float64(t * Float64(b - a)))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(a + Float64(Float64(z + x) + Float64(-2.0 * b)))
	tmp = 0.0
	if (y <= -1.05e+96)
		tmp = t_2;
	elseif (y <= -1.4e-79)
		tmp = t_1;
	elseif (y <= -1.8e-186)
		tmp = t_3;
	elseif (y <= 3e-234)
		tmp = t_1;
	elseif (y <= 1.75e-106)
		tmp = t_3;
	elseif (y <= 1.02e+89)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (z + x) + (t * (b - a));
	t_2 = y * (b - z);
	t_3 = a + ((z + x) + (-2.0 * b));
	tmp = 0.0;
	if (y <= -1.05e+96)
		tmp = t_2;
	elseif (y <= -1.4e-79)
		tmp = t_1;
	elseif (y <= -1.8e-186)
		tmp = t_3;
	elseif (y <= 3e-234)
		tmp = t_1;
	elseif (y <= 1.75e-106)
		tmp = t_3;
	elseif (y <= 1.02e+89)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(z + x), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(N[(z + x), $MachinePrecision] + N[(-2.0 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+96], t$95$2, If[LessEqual[y, -1.4e-79], t$95$1, If[LessEqual[y, -1.8e-186], t$95$3, If[LessEqual[y, 3e-234], t$95$1, If[LessEqual[y, 1.75e-106], t$95$3, If[LessEqual[y, 1.02e+89], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0500000000000001e96 or 1.0199999999999999e89 < y

   1. Initial program 91.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.4%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.4%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.4%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.4%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.4%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.4%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.4%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 76.2%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -1.0500000000000001e96 < y < -1.40000000000000006e-79 or -1.7999999999999999e-186 < y < 2.99999999999999987e-234 or 1.75e-106 < y < 1.0199999999999999e89

   1. Initial program 95.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.8%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 95.8%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 95.8%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 95.8%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 95.8%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 95.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 95.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 95.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 95.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 95.8%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 95.8%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 79.8%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in y around 0 75.9%

      \[\leadsto \color{blue}{\left(x - -1 \cdot z\right)} - t \cdot \left(a - b\right) \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 75.9%

         \[\leadsto \color{blue}{\left(x + \left(--1\right) \cdot z\right)} - t \cdot \left(a - b\right) \]

      2. metadata-eval 75.9%

         \[\leadsto \left(x + \color{blue}{1} \cdot z\right) - t \cdot \left(a - b\right) \]

      3. *-lft-identity 75.9%

         \[\leadsto \left(x + \color{blue}{z}\right) - t \cdot \left(a - b\right) \]

   7. Simplified 75.9%

      \[\leadsto \color{blue}{\left(x + z\right)} - t \cdot \left(a - b\right) \]

   if -1.40000000000000006e-79 < y < -1.7999999999999999e-186 or 2.99999999999999987e-234 < y < 1.75e-106

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 100.0%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 100.0%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 100.0%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 100.0%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 100.0%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in t around 0 87.0%

      \[\leadsto \color{blue}{a + \left(-2 \cdot b + \left(z + x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-79}:\\ \;\;\;\;\left(z + x\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -1.8 \cdot 10^{-186}:\\ \;\;\;\;a + \left(\left(z + x\right) + -2 \cdot b\right)\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-234}:\\ \;\;\;\;\left(z + x\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-106}:\\ \;\;\;\;a + \left(\left(z + x\right) + -2 \cdot b\right)\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{+89}:\\ \;\;\;\;\left(z + x\right) + t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 10: 71.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + z \cdot \left(1 - y\right)\right)\\ t_2 := \left(z + x\right) + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -0.012:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-276}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(y - 2\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (* z (- 1.0 y))))) (t_2 (+ (+ z x) (* t (- b a)))))
   (if (<= t -0.012)
     t_2
     (if (<= t -4.2e-268)
       t_1
       (if (<= t -1.9e-276)
         (+ x (* b (- (+ t y) 2.0)))
         (if (<= t 6.8e-131)
           t_1
           (if (<= t 5.5e-35)
             (- (* b (- y 2.0)) (* a (+ t -1.0)))
             (if (<= t 5.6e-16) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = (z + x) + (t * (b - a));
	double tmp;
	if (t <= -0.012) {
		tmp = t_2;
	} else if (t <= -4.2e-268) {
		tmp = t_1;
	} else if (t <= -1.9e-276) {
		tmp = x + (b * ((t + y) - 2.0));
	} else if (t <= 6.8e-131) {
		tmp = t_1;
	} else if (t <= 5.5e-35) {
		tmp = (b * (y - 2.0)) - (a * (t + -1.0));
	} else if (t <= 5.6e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a + (z * (1.0d0 - y)))
    t_2 = (z + x) + (t * (b - a))
    if (t <= (-0.012d0)) then
        tmp = t_2
    else if (t <= (-4.2d-268)) then
        tmp = t_1
    else if (t <= (-1.9d-276)) then
        tmp = x + (b * ((t + y) - 2.0d0))
    else if (t <= 6.8d-131) then
        tmp = t_1
    else if (t <= 5.5d-35) then
        tmp = (b * (y - 2.0d0)) - (a * (t + (-1.0d0)))
    else if (t <= 5.6d-16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = (z + x) + (t * (b - a));
	double tmp;
	if (t <= -0.012) {
		tmp = t_2;
	} else if (t <= -4.2e-268) {
		tmp = t_1;
	} else if (t <= -1.9e-276) {
		tmp = x + (b * ((t + y) - 2.0));
	} else if (t <= 6.8e-131) {
		tmp = t_1;
	} else if (t <= 5.5e-35) {
		tmp = (b * (y - 2.0)) - (a * (t + -1.0));
	} else if (t <= 5.6e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (z * (1.0 - y)))
	t_2 = (z + x) + (t * (b - a))
	tmp = 0
	if t <= -0.012:
		tmp = t_2
	elif t <= -4.2e-268:
		tmp = t_1
	elif t <= -1.9e-276:
		tmp = x + (b * ((t + y) - 2.0))
	elif t <= 6.8e-131:
		tmp = t_1
	elif t <= 5.5e-35:
		tmp = (b * (y - 2.0)) - (a * (t + -1.0))
	elif t <= 5.6e-16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(Float64(z + x) + Float64(t * Float64(b - a)))
	tmp = 0.0
	if (t <= -0.012)
		tmp = t_2;
	elseif (t <= -4.2e-268)
		tmp = t_1;
	elseif (t <= -1.9e-276)
		tmp = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)));
	elseif (t <= 6.8e-131)
		tmp = t_1;
	elseif (t <= 5.5e-35)
		tmp = Float64(Float64(b * Float64(y - 2.0)) - Float64(a * Float64(t + -1.0)));
	elseif (t <= 5.6e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a + (z * (1.0 - y)));
	t_2 = (z + x) + (t * (b - a));
	tmp = 0.0;
	if (t <= -0.012)
		tmp = t_2;
	elseif (t <= -4.2e-268)
		tmp = t_1;
	elseif (t <= -1.9e-276)
		tmp = x + (b * ((t + y) - 2.0));
	elseif (t <= 6.8e-131)
		tmp = t_1;
	elseif (t <= 5.5e-35)
		tmp = (b * (y - 2.0)) - (a * (t + -1.0));
	elseif (t <= 5.6e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + x), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.012], t$95$2, If[LessEqual[t, -4.2e-268], t$95$1, If[LessEqual[t, -1.9e-276], N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-131], t$95$1, If[LessEqual[t, 5.5e-35], N[(N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e-16], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -0.012 or 5.6000000000000003e-16 < t

   1. Initial program 92.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 92.6%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 92.6%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 92.6%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 92.6%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 92.6%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 92.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 92.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 92.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 92.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 92.6%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 91.5%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in y around 0 79.2%

      \[\leadsto \color{blue}{\left(x - -1 \cdot z\right)} - t \cdot \left(a - b\right) \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 79.2%

         \[\leadsto \color{blue}{\left(x + \left(--1\right) \cdot z\right)} - t \cdot \left(a - b\right) \]

      2. metadata-eval 79.2%

         \[\leadsto \left(x + \color{blue}{1} \cdot z\right) - t \cdot \left(a - b\right) \]

      3. *-lft-identity 79.2%

         \[\leadsto \left(x + \color{blue}{z}\right) - t \cdot \left(a - b\right) \]

   7. Simplified 79.2%

      \[\leadsto \color{blue}{\left(x + z\right)} - t \cdot \left(a - b\right) \]

   if -0.012 < t < -4.19999999999999996e-268 or -1.9e-276 < t < 6.7999999999999999e-131 or 5.4999999999999997e-35 < t < 5.6000000000000003e-16

   1. Initial program 99.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 99.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 99.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 99.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 99.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 99.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 99.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 99.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 99.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 99.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 99.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 99.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 75.9%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   if -4.19999999999999996e-268 < t < -1.9e-276

   1. Initial program 79.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 79.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 79.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 79.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 79.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 79.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 79.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 79.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 79.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 79.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 79.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 92.0%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in a around 0 92.0%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + x} \]

   if 6.7999999999999999e-131 < t < 5.4999999999999997e-35

   1. Initial program 94.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 94.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 94.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 94.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 94.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 94.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 94.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 94.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 94.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 94.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 94.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 79.5%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 79.5%

      \[\leadsto \left(\color{blue}{\left(y - 2\right) \cdot b} + x\right) - \left(t - 1\right) \cdot a \]

   6. Taylor expanded in x around 0 79.5%

      \[\leadsto \color{blue}{\left(y - 2\right) \cdot b - \left(t - 1\right) \cdot a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.012:\\ \;\;\;\;\left(z + x\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-268}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-276}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-131}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-35}:\\ \;\;\;\;b \cdot \left(y - 2\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-16}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 11: 84.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -1.02 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{+66}:\\ \;\;\;\;t_1 + t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq -40000000000000:\\ \;\;\;\;\left(x + b \cdot \left(y - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 10^{+34}:\\ \;\;\;\;t_1 + \left(a - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))) (t_2 (+ x (* b (- (+ t y) 2.0)))))
   (if (<= b -1.02e+121)
     t_2
     (if (<= b -2.1e+66)
       (+ t_1 (* t (- b a)))
       (if (<= b -40000000000000.0)
         (+ (+ x (* b (- y 2.0))) (* a (- 1.0 t)))
         (if (<= b 1e+34) (+ t_1 (- a (* a t))) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = x + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -1.02e+121) {
		tmp = t_2;
	} else if (b <= -2.1e+66) {
		tmp = t_1 + (t * (b - a));
	} else if (b <= -40000000000000.0) {
		tmp = (x + (b * (y - 2.0))) + (a * (1.0 - t));
	} else if (b <= 1e+34) {
		tmp = t_1 + (a - (a * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = x + (b * ((t + y) - 2.0d0))
    if (b <= (-1.02d+121)) then
        tmp = t_2
    else if (b <= (-2.1d+66)) then
        tmp = t_1 + (t * (b - a))
    else if (b <= (-40000000000000.0d0)) then
        tmp = (x + (b * (y - 2.0d0))) + (a * (1.0d0 - t))
    else if (b <= 1d+34) then
        tmp = t_1 + (a - (a * t))
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = x + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -1.02e+121) {
		tmp = t_2;
	} else if (b <= -2.1e+66) {
		tmp = t_1 + (t * (b - a));
	} else if (b <= -40000000000000.0) {
		tmp = (x + (b * (y - 2.0))) + (a * (1.0 - t));
	} else if (b <= 1e+34) {
		tmp = t_1 + (a - (a * t));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = x + (b * ((t + y) - 2.0))
	tmp = 0
	if b <= -1.02e+121:
		tmp = t_2
	elif b <= -2.1e+66:
		tmp = t_1 + (t * (b - a))
	elif b <= -40000000000000.0:
		tmp = (x + (b * (y - 2.0))) + (a * (1.0 - t))
	elif b <= 1e+34:
		tmp = t_1 + (a - (a * t))
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)))
	tmp = 0.0
	if (b <= -1.02e+121)
		tmp = t_2;
	elseif (b <= -2.1e+66)
		tmp = Float64(t_1 + Float64(t * Float64(b - a)));
	elseif (b <= -40000000000000.0)
		tmp = Float64(Float64(x + Float64(b * Float64(y - 2.0))) + Float64(a * Float64(1.0 - t)));
	elseif (b <= 1e+34)
		tmp = Float64(t_1 + Float64(a - Float64(a * t)));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = x + (b * ((t + y) - 2.0));
	tmp = 0.0;
	if (b <= -1.02e+121)
		tmp = t_2;
	elseif (b <= -2.1e+66)
		tmp = t_1 + (t * (b - a));
	elseif (b <= -40000000000000.0)
		tmp = (x + (b * (y - 2.0))) + (a * (1.0 - t));
	elseif (b <= 1e+34)
		tmp = t_1 + (a - (a * t));
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.02e+121], t$95$2, If[LessEqual[b, -2.1e+66], N[(t$95$1 + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -40000000000000.0], N[(N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+34], N[(t$95$1 + N[(a - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.02000000000000005e121 or 9.99999999999999946e33 < b

   1. Initial program 86.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 86.8%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 86.8%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 86.8%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 86.8%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 86.8%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 86.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 86.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 86.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 86.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 86.8%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 86.8%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 87.9%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in a around 0 82.6%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + x} \]

   if -1.02000000000000005e121 < b < -2.10000000000000005e66

   1. Initial program 88.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 88.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 88.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 88.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 88.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 88.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 88.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 88.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 88.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 88.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 88.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 88.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 85.9%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   if -2.10000000000000005e66 < b < -4e13

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 92.9%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 78.7%

      \[\leadsto \left(\color{blue}{\left(y - 2\right) \cdot b} + x\right) - \left(t - 1\right) \cdot a \]

   if -4e13 < b < 9.99999999999999946e33

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 91.6%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a} \]
   5. Step-by-step derivation

      1. sub-neg 91.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(t + \left(-1\right)\right)} \cdot a \]

      2. metadata-eval 91.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(t + \color{blue}{-1}\right) \cdot a \]

      3. +-commutative 91.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(-1 + t\right)} \cdot a \]

      4. *-commutative 91.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{a \cdot \left(-1 + t\right)} \]

      5. +-commutative 91.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - a \cdot \color{blue}{\left(t + -1\right)} \]

      6. distribute-rgt-in 91.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(t \cdot a + -1 \cdot a\right)} \]

      7. fma-def 91.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\mathsf{fma}\left(t, a, -1 \cdot a\right)} \]

      8. mul-1-neg 91.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \mathsf{fma}\left(t, a, \color{blue}{-a}\right) \]

      9. fma-neg 91.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(t \cdot a - a\right)} \]

   6. Simplified 91.6%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(t \cdot a - a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.02 \cdot 10^{+121}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.1 \cdot 10^{+66}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq -40000000000000:\\ \;\;\;\;\left(x + b \cdot \left(y - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 10^{+34}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + \left(a - a \cdot t\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 12: 84.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;y \leq -1.6 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-5}:\\ \;\;\;\;t_1 + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 10^{+24}:\\ \;\;\;\;\left(z + \left(x + b \cdot \left(t - 2\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 + y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))))
   (if (<= y -1.6e+93)
     (* y (- b z))
     (if (<= y -7.6e-5)
       (+ t_1 (* t (- b a)))
       (if (<= y 1e+24)
         (+ (+ z (+ x (* b (- t 2.0)))) (* a (- 1.0 t)))
         (+ t_1 (* y b)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double tmp;
	if (y <= -1.6e+93) {
		tmp = y * (b - z);
	} else if (y <= -7.6e-5) {
		tmp = t_1 + (t * (b - a));
	} else if (y <= 1e+24) {
		tmp = (z + (x + (b * (t - 2.0)))) + (a * (1.0 - t));
	} else {
		tmp = t_1 + (y * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    if (y <= (-1.6d+93)) then
        tmp = y * (b - z)
    else if (y <= (-7.6d-5)) then
        tmp = t_1 + (t * (b - a))
    else if (y <= 1d+24) then
        tmp = (z + (x + (b * (t - 2.0d0)))) + (a * (1.0d0 - t))
    else
        tmp = t_1 + (y * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double tmp;
	if (y <= -1.6e+93) {
		tmp = y * (b - z);
	} else if (y <= -7.6e-5) {
		tmp = t_1 + (t * (b - a));
	} else if (y <= 1e+24) {
		tmp = (z + (x + (b * (t - 2.0)))) + (a * (1.0 - t));
	} else {
		tmp = t_1 + (y * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	tmp = 0
	if y <= -1.6e+93:
		tmp = y * (b - z)
	elif y <= -7.6e-5:
		tmp = t_1 + (t * (b - a))
	elif y <= 1e+24:
		tmp = (z + (x + (b * (t - 2.0)))) + (a * (1.0 - t))
	else:
		tmp = t_1 + (y * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (y <= -1.6e+93)
		tmp = Float64(y * Float64(b - z));
	elseif (y <= -7.6e-5)
		tmp = Float64(t_1 + Float64(t * Float64(b - a)));
	elseif (y <= 1e+24)
		tmp = Float64(Float64(z + Float64(x + Float64(b * Float64(t - 2.0)))) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(t_1 + Float64(y * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	tmp = 0.0;
	if (y <= -1.6e+93)
		tmp = y * (b - z);
	elseif (y <= -7.6e-5)
		tmp = t_1 + (t * (b - a));
	elseif (y <= 1e+24)
		tmp = (z + (x + (b * (t - 2.0)))) + (a * (1.0 - t));
	else
		tmp = t_1 + (y * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.6e+93], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.6e-5], N[(t$95$1 + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+24], N[(N[(z + N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(y * b), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6000000000000001e93

   1. Initial program 89.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 89.4%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 89.4%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 89.4%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 89.4%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 89.4%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 89.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 89.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 89.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 89.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 89.4%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 89.4%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 83.6%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -1.6000000000000001e93 < y < -7.6000000000000004e-5

   1. Initial program 94.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 94.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 94.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 94.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 94.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 94.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 94.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 94.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 94.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 94.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 94.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 94.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 91.9%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   if -7.6000000000000004e-5 < y < 9.9999999999999998e23

   1. Initial program 97.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 97.8%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 97.8%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 97.8%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 97.8%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 97.8%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 97.8%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 97.7%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   if 9.9999999999999998e23 < y

   1. Initial program 92.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 92.5%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 92.5%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 92.5%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 92.5%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 92.5%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 92.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 92.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 92.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 92.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 92.5%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 92.5%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 72.3%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{-1 \cdot \left(y \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 72.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(-y \cdot b\right)} \]

      2. distribute-rgt-neg-in 72.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{y \cdot \left(-b\right)} \]

   6. Simplified 72.3%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{y \cdot \left(-b\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{-5}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 10^{+24}:\\ \;\;\;\;\left(z + \left(x + b \cdot \left(t - 2\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + y \cdot b\\ \end{array} \]

Alternative 13: 31.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(-z\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-99}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-255}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-234}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-79}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+202}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- z))) (t_2 (* a (- 1.0 t))))
   (if (<= a -1.7e+124)
     t_2
     (if (<= a -3.8e+24)
       t_1
       (if (<= a -3.5e-99)
         (+ a x)
         (if (<= a 2.7e-255)
           t_1
           (if (<= a 2.5e-234)
             (* y b)
             (if (<= a 7.6e-79) z (if (<= a 6.5e+202) (+ a x) t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -1.7e+124) {
		tmp = t_2;
	} else if (a <= -3.8e+24) {
		tmp = t_1;
	} else if (a <= -3.5e-99) {
		tmp = a + x;
	} else if (a <= 2.7e-255) {
		tmp = t_1;
	} else if (a <= 2.5e-234) {
		tmp = y * b;
	} else if (a <= 7.6e-79) {
		tmp = z;
	} else if (a <= 6.5e+202) {
		tmp = a + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * -z
    t_2 = a * (1.0d0 - t)
    if (a <= (-1.7d+124)) then
        tmp = t_2
    else if (a <= (-3.8d+24)) then
        tmp = t_1
    else if (a <= (-3.5d-99)) then
        tmp = a + x
    else if (a <= 2.7d-255) then
        tmp = t_1
    else if (a <= 2.5d-234) then
        tmp = y * b
    else if (a <= 7.6d-79) then
        tmp = z
    else if (a <= 6.5d+202) then
        tmp = a + x
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * -z;
	double t_2 = a * (1.0 - t);
	double tmp;
	if (a <= -1.7e+124) {
		tmp = t_2;
	} else if (a <= -3.8e+24) {
		tmp = t_1;
	} else if (a <= -3.5e-99) {
		tmp = a + x;
	} else if (a <= 2.7e-255) {
		tmp = t_1;
	} else if (a <= 2.5e-234) {
		tmp = y * b;
	} else if (a <= 7.6e-79) {
		tmp = z;
	} else if (a <= 6.5e+202) {
		tmp = a + x;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * -z
	t_2 = a * (1.0 - t)
	tmp = 0
	if a <= -1.7e+124:
		tmp = t_2
	elif a <= -3.8e+24:
		tmp = t_1
	elif a <= -3.5e-99:
		tmp = a + x
	elif a <= 2.7e-255:
		tmp = t_1
	elif a <= 2.5e-234:
		tmp = y * b
	elif a <= 7.6e-79:
		tmp = z
	elif a <= 6.5e+202:
		tmp = a + x
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(-z))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.7e+124)
		tmp = t_2;
	elseif (a <= -3.8e+24)
		tmp = t_1;
	elseif (a <= -3.5e-99)
		tmp = Float64(a + x);
	elseif (a <= 2.7e-255)
		tmp = t_1;
	elseif (a <= 2.5e-234)
		tmp = Float64(y * b);
	elseif (a <= 7.6e-79)
		tmp = z;
	elseif (a <= 6.5e+202)
		tmp = Float64(a + x);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * -z;
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1.7e+124)
		tmp = t_2;
	elseif (a <= -3.8e+24)
		tmp = t_1;
	elseif (a <= -3.5e-99)
		tmp = a + x;
	elseif (a <= 2.7e-255)
		tmp = t_1;
	elseif (a <= 2.5e-234)
		tmp = y * b;
	elseif (a <= 7.6e-79)
		tmp = z;
	elseif (a <= 6.5e+202)
		tmp = a + x;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * (-z)), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.7e+124], t$95$2, If[LessEqual[a, -3.8e+24], t$95$1, If[LessEqual[a, -3.5e-99], N[(a + x), $MachinePrecision], If[LessEqual[a, 2.7e-255], t$95$1, If[LessEqual[a, 2.5e-234], N[(y * b), $MachinePrecision], If[LessEqual[a, 7.6e-79], z, If[LessEqual[a, 6.5e+202], N[(a + x), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.7e124 or 6.4999999999999996e202 < a

   1. Initial program 90.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 90.6%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 90.6%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 90.6%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 90.6%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 90.6%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 90.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 90.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 90.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 90.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 90.6%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 71.4%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -1.7e124 < a < -3.80000000000000015e24 or -3.4999999999999999e-99 < a < 2.70000000000000016e-255

   1. Initial program 95.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.5%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 95.5%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 95.5%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 95.5%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 95.5%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 95.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 95.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 95.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 95.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 95.5%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 95.5%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 49.9%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   5. Taylor expanded in b around 0 35.7%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 35.7%

         \[\leadsto \color{blue}{-y \cdot z} \]

      2. distribute-rgt-neg-in 35.7%

         \[\leadsto \color{blue}{y \cdot \left(-z\right)} \]

   7. Simplified 35.7%

      \[\leadsto \color{blue}{y \cdot \left(-z\right)} \]

   if -3.80000000000000015e24 < a < -3.4999999999999999e-99 or 7.6000000000000002e-79 < a < 6.4999999999999996e202

   1. Initial program 96.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.6%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 96.6%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 96.6%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 96.6%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 96.6%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 96.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 96.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 96.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 96.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 96.6%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 93.3%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 56.0%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   6. Taylor expanded in z around 0 35.6%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   7. Step-by-step derivation

      1. sub-neg 35.6%

         \[\leadsto \color{blue}{x + \left(--1 \cdot a\right)} \]

      2. mul-1-neg 35.6%

         \[\leadsto x + \left(-\color{blue}{\left(-a\right)}\right) \]

      3. remove-double-neg 35.6%

         \[\leadsto x + \color{blue}{a} \]

   8. Simplified 35.6%

      \[\leadsto \color{blue}{x + a} \]

   if 2.70000000000000016e-255 < a < 2.49999999999999989e-234

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 100.0%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 84.6%

      \[\leadsto \left(\color{blue}{\left(y - 2\right) \cdot b} + x\right) - \left(t - 1\right) \cdot a \]

   6. Taylor expanded in y around inf 83.7%

      \[\leadsto \color{blue}{y \cdot b} \]

   if 2.49999999999999989e-234 < a < 7.6000000000000002e-79

   1. Initial program 96.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 96.5%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 96.5%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 96.5%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 96.5%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 96.5%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 96.5%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 96.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 96.5%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 96.5%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 96.5%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 96.5%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 96.5%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 73.3%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in z around inf 30.6%

      \[\leadsto \color{blue}{z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 45.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+124}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -3.8 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-99}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-255}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{-234}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 7.6 \cdot 10^{-79}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+202}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 14: 55.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := a + \left(z + x\right)\\ t_3 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -7 \cdot 10^{+89}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-299}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-263}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+22}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (+ a (+ z x))) (t_3 (* y (- b z))))
   (if (<= y -7e+89)
     t_3
     (if (<= y -3.4e-14)
       t_1
       (if (<= y -6.4e-221)
         t_2
         (if (<= y -1.5e-299)
           (- x (* a t))
           (if (<= y 9e-263)
             (+ a z)
             (if (<= y 1.25e-228) t_1 (if (<= y 6.8e+22) t_2 t_3)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = a + (z + x);
	double t_3 = y * (b - z);
	double tmp;
	if (y <= -7e+89) {
		tmp = t_3;
	} else if (y <= -3.4e-14) {
		tmp = t_1;
	} else if (y <= -6.4e-221) {
		tmp = t_2;
	} else if (y <= -1.5e-299) {
		tmp = x - (a * t);
	} else if (y <= 9e-263) {
		tmp = a + z;
	} else if (y <= 1.25e-228) {
		tmp = t_1;
	} else if (y <= 6.8e+22) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = a + (z + x)
    t_3 = y * (b - z)
    if (y <= (-7d+89)) then
        tmp = t_3
    else if (y <= (-3.4d-14)) then
        tmp = t_1
    else if (y <= (-6.4d-221)) then
        tmp = t_2
    else if (y <= (-1.5d-299)) then
        tmp = x - (a * t)
    else if (y <= 9d-263) then
        tmp = a + z
    else if (y <= 1.25d-228) then
        tmp = t_1
    else if (y <= 6.8d+22) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = a + (z + x);
	double t_3 = y * (b - z);
	double tmp;
	if (y <= -7e+89) {
		tmp = t_3;
	} else if (y <= -3.4e-14) {
		tmp = t_1;
	} else if (y <= -6.4e-221) {
		tmp = t_2;
	} else if (y <= -1.5e-299) {
		tmp = x - (a * t);
	} else if (y <= 9e-263) {
		tmp = a + z;
	} else if (y <= 1.25e-228) {
		tmp = t_1;
	} else if (y <= 6.8e+22) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = a + (z + x)
	t_3 = y * (b - z)
	tmp = 0
	if y <= -7e+89:
		tmp = t_3
	elif y <= -3.4e-14:
		tmp = t_1
	elif y <= -6.4e-221:
		tmp = t_2
	elif y <= -1.5e-299:
		tmp = x - (a * t)
	elif y <= 9e-263:
		tmp = a + z
	elif y <= 1.25e-228:
		tmp = t_1
	elif y <= 6.8e+22:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(a + Float64(z + x))
	t_3 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -7e+89)
		tmp = t_3;
	elseif (y <= -3.4e-14)
		tmp = t_1;
	elseif (y <= -6.4e-221)
		tmp = t_2;
	elseif (y <= -1.5e-299)
		tmp = Float64(x - Float64(a * t));
	elseif (y <= 9e-263)
		tmp = Float64(a + z);
	elseif (y <= 1.25e-228)
		tmp = t_1;
	elseif (y <= 6.8e+22)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = a + (z + x);
	t_3 = y * (b - z);
	tmp = 0.0;
	if (y <= -7e+89)
		tmp = t_3;
	elseif (y <= -3.4e-14)
		tmp = t_1;
	elseif (y <= -6.4e-221)
		tmp = t_2;
	elseif (y <= -1.5e-299)
		tmp = x - (a * t);
	elseif (y <= 9e-263)
		tmp = a + z;
	elseif (y <= 1.25e-228)
		tmp = t_1;
	elseif (y <= 6.8e+22)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a + N[(z + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7e+89], t$95$3, If[LessEqual[y, -3.4e-14], t$95$1, If[LessEqual[y, -6.4e-221], t$95$2, If[LessEqual[y, -1.5e-299], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-263], N[(a + z), $MachinePrecision], If[LessEqual[y, 1.25e-228], t$95$1, If[LessEqual[y, 6.8e+22], t$95$2, t$95$3]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.0000000000000001e89 or 6.8e22 < y

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -7.0000000000000001e89 < y < -3.40000000000000003e-14 or 8.9999999999999994e-263 < y < 1.24999999999999993e-228

   1. Initial program 96.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 96.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 96.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 96.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 96.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 96.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 96.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 96.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 96.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 96.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 58.4%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -3.40000000000000003e-14 < y < -6.40000000000000031e-221 or 1.24999999999999993e-228 < y < 6.8e22

   1. Initial program 98.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 98.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 98.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 98.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 98.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 98.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 98.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 98.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 98.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 98.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 98.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 64.5%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   6. Taylor expanded in y around 0 64.3%

      \[\leadsto \color{blue}{x - \left(-1 \cdot z + -1 \cdot a\right)} \]
   7. Step-by-step derivation

      1. associate--r+ 64.3%

         \[\leadsto \color{blue}{\left(x - -1 \cdot z\right) - -1 \cdot a} \]

      2. sub-neg 64.3%

         \[\leadsto \color{blue}{\left(x - -1 \cdot z\right) + \left(--1 \cdot a\right)} \]

      3. mul-1-neg 64.3%

         \[\leadsto \left(x - \color{blue}{\left(-z\right)}\right) + \left(--1 \cdot a\right) \]

      4. mul-1-neg 64.3%

         \[\leadsto \left(x - \left(-z\right)\right) + \left(-\color{blue}{\left(-a\right)}\right) \]

      5. remove-double-neg 64.3%

         \[\leadsto \left(x - \left(-z\right)\right) + \color{blue}{a} \]

   8. Simplified 64.3%

      \[\leadsto \color{blue}{\left(x - \left(-z\right)\right) + a} \]

   if -6.40000000000000031e-221 < y < -1.49999999999999992e-299

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 83.7%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in z around 0 77.6%

      \[\leadsto \color{blue}{x - t \cdot \left(a - b\right)} \]

   6. Taylor expanded in a around inf 77.8%

      \[\leadsto x - \color{blue}{a \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 77.8%

         \[\leadsto x - \color{blue}{t \cdot a} \]

   8. Simplified 77.8%

      \[\leadsto x - \color{blue}{t \cdot a} \]

   if -1.49999999999999992e-299 < y < 8.9999999999999994e-263

   1. Initial program 86.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 86.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 86.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 86.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 86.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 86.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 86.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in a around inf 80.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]
   6. Step-by-step derivation

      1. associate-*r* 80.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

      2. neg-mul-1 80.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   7. Simplified 80.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   8. Taylor expanded in y around 0 80.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right) - \left(-1 \cdot z + -1 \cdot a\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 80.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(-1 \cdot z + -1 \cdot a\right) \]

      2. mul-1-neg 80.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(-1 \cdot z + -1 \cdot a\right) \]

      3. distribute-lft-out 80.1%

         \[\leadsto \left(-a\right) \cdot t - \color{blue}{-1 \cdot \left(z + a\right)} \]

   10. Simplified 80.1%

       \[\leadsto \color{blue}{\left(-a\right) \cdot t - -1 \cdot \left(z + a\right)} \]

   11. Taylor expanded in t around 0 65.9%

       \[\leadsto \color{blue}{a + z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -3.4 \cdot 10^{-14}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{-221}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-299}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-263}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-228}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+22}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 15: 55.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z + x\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+88}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-18}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-299}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-261}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-229}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ z x))) (t_2 (* y (- b z))))
   (if (<= y -1.55e+88)
     t_2
     (if (<= y -2.55e-18)
       (+ x (* t b))
       (if (<= y -6.2e-221)
         t_1
         (if (<= y -4.8e-299)
           (- x (* a t))
           (if (<= y 7.6e-261)
             (+ a z)
             (if (<= y 2.05e-229)
               (* t (- b a))
               (if (<= y 4e+20) t_1 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z + x);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.55e+88) {
		tmp = t_2;
	} else if (y <= -2.55e-18) {
		tmp = x + (t * b);
	} else if (y <= -6.2e-221) {
		tmp = t_1;
	} else if (y <= -4.8e-299) {
		tmp = x - (a * t);
	} else if (y <= 7.6e-261) {
		tmp = a + z;
	} else if (y <= 2.05e-229) {
		tmp = t * (b - a);
	} else if (y <= 4e+20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (z + x)
    t_2 = y * (b - z)
    if (y <= (-1.55d+88)) then
        tmp = t_2
    else if (y <= (-2.55d-18)) then
        tmp = x + (t * b)
    else if (y <= (-6.2d-221)) then
        tmp = t_1
    else if (y <= (-4.8d-299)) then
        tmp = x - (a * t)
    else if (y <= 7.6d-261) then
        tmp = a + z
    else if (y <= 2.05d-229) then
        tmp = t * (b - a)
    else if (y <= 4d+20) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z + x);
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -1.55e+88) {
		tmp = t_2;
	} else if (y <= -2.55e-18) {
		tmp = x + (t * b);
	} else if (y <= -6.2e-221) {
		tmp = t_1;
	} else if (y <= -4.8e-299) {
		tmp = x - (a * t);
	} else if (y <= 7.6e-261) {
		tmp = a + z;
	} else if (y <= 2.05e-229) {
		tmp = t * (b - a);
	} else if (y <= 4e+20) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z + x)
	t_2 = y * (b - z)
	tmp = 0
	if y <= -1.55e+88:
		tmp = t_2
	elif y <= -2.55e-18:
		tmp = x + (t * b)
	elif y <= -6.2e-221:
		tmp = t_1
	elif y <= -4.8e-299:
		tmp = x - (a * t)
	elif y <= 7.6e-261:
		tmp = a + z
	elif y <= 2.05e-229:
		tmp = t * (b - a)
	elif y <= 4e+20:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z + x))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.55e+88)
		tmp = t_2;
	elseif (y <= -2.55e-18)
		tmp = Float64(x + Float64(t * b));
	elseif (y <= -6.2e-221)
		tmp = t_1;
	elseif (y <= -4.8e-299)
		tmp = Float64(x - Float64(a * t));
	elseif (y <= 7.6e-261)
		tmp = Float64(a + z);
	elseif (y <= 2.05e-229)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 4e+20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z + x);
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.55e+88)
		tmp = t_2;
	elseif (y <= -2.55e-18)
		tmp = x + (t * b);
	elseif (y <= -6.2e-221)
		tmp = t_1;
	elseif (y <= -4.8e-299)
		tmp = x - (a * t);
	elseif (y <= 7.6e-261)
		tmp = a + z;
	elseif (y <= 2.05e-229)
		tmp = t * (b - a);
	elseif (y <= 4e+20)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(z + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+88], t$95$2, If[LessEqual[y, -2.55e-18], N[(x + N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6.2e-221], t$95$1, If[LessEqual[y, -4.8e-299], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.6e-261], N[(a + z), $MachinePrecision], If[LessEqual[y, 2.05e-229], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+20], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -1.5500000000000001e88 or 4e20 < y

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -1.5500000000000001e88 < y < -2.54999999999999991e-18

   1. Initial program 95.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.2%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 95.2%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 95.2%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 95.2%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 95.2%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 95.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 95.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 95.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 95.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 95.2%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 92.7%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in z around 0 72.7%

      \[\leadsto \color{blue}{x - t \cdot \left(a - b\right)} \]

   6. Taylor expanded in a around 0 55.3%

      \[\leadsto x - \color{blue}{-1 \cdot \left(t \cdot b\right)} \]
   7. Step-by-step derivation

      1. associate-*r* 55.3%

         \[\leadsto x - \color{blue}{\left(-1 \cdot t\right) \cdot b} \]

      2. neg-mul-1 55.3%

         \[\leadsto x - \color{blue}{\left(-t\right)} \cdot b \]

   8. Simplified 55.3%

      \[\leadsto x - \color{blue}{\left(-t\right) \cdot b} \]

   if -2.54999999999999991e-18 < y < -6.1999999999999998e-221 or 2.05e-229 < y < 4e20

   1. Initial program 98.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 98.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 98.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 98.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 98.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 98.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 98.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 98.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 98.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 98.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 98.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 64.5%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   6. Taylor expanded in y around 0 64.3%

      \[\leadsto \color{blue}{x - \left(-1 \cdot z + -1 \cdot a\right)} \]
   7. Step-by-step derivation

      1. associate--r+ 64.3%

         \[\leadsto \color{blue}{\left(x - -1 \cdot z\right) - -1 \cdot a} \]

      2. sub-neg 64.3%

         \[\leadsto \color{blue}{\left(x - -1 \cdot z\right) + \left(--1 \cdot a\right)} \]

      3. mul-1-neg 64.3%

         \[\leadsto \left(x - \color{blue}{\left(-z\right)}\right) + \left(--1 \cdot a\right) \]

      4. mul-1-neg 64.3%

         \[\leadsto \left(x - \left(-z\right)\right) + \left(-\color{blue}{\left(-a\right)}\right) \]

      5. remove-double-neg 64.3%

         \[\leadsto \left(x - \left(-z\right)\right) + \color{blue}{a} \]

   8. Simplified 64.3%

      \[\leadsto \color{blue}{\left(x - \left(-z\right)\right) + a} \]

   if -6.1999999999999998e-221 < y < -4.80000000000000039e-299

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 83.7%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in z around 0 77.6%

      \[\leadsto \color{blue}{x - t \cdot \left(a - b\right)} \]

   6. Taylor expanded in a around inf 77.8%

      \[\leadsto x - \color{blue}{a \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 77.8%

         \[\leadsto x - \color{blue}{t \cdot a} \]

   8. Simplified 77.8%

      \[\leadsto x - \color{blue}{t \cdot a} \]

   if -4.80000000000000039e-299 < y < 7.5999999999999999e-261

   1. Initial program 86.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 86.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 86.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 86.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 86.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 86.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 86.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in a around inf 80.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]
   6. Step-by-step derivation

      1. associate-*r* 80.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

      2. neg-mul-1 80.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   7. Simplified 80.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   8. Taylor expanded in y around 0 80.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right) - \left(-1 \cdot z + -1 \cdot a\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 80.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(-1 \cdot z + -1 \cdot a\right) \]

      2. mul-1-neg 80.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(-1 \cdot z + -1 \cdot a\right) \]

      3. distribute-lft-out 80.1%

         \[\leadsto \left(-a\right) \cdot t - \color{blue}{-1 \cdot \left(z + a\right)} \]

   10. Simplified 80.1%

       \[\leadsto \color{blue}{\left(-a\right) \cdot t - -1 \cdot \left(z + a\right)} \]

   11. Taylor expanded in t around 0 65.9%

       \[\leadsto \color{blue}{a + z} \]

   if 7.5999999999999999e-261 < y < 2.05e-229

   1. Initial program 99.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 99.8%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 99.8%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 99.8%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 99.8%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 99.8%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 99.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 99.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 99.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 99.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 99.8%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 65.9%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-18}:\\ \;\;\;\;x + t \cdot b\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-221}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-299}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-261}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-229}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+20}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 16: 57.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := a + \left(z + x\right)\\ \mathbf{if}\;y \leq -5.4 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-221}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-299}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-263}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-229}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+21}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t (- b a)))) (t_2 (* y (- b z))) (t_3 (+ a (+ z x))))
   (if (<= y -5.4e+91)
     t_2
     (if (<= y -1.05e-79)
       t_1
       (if (<= y -2.8e-221)
         t_3
         (if (<= y -2.05e-299)
           (- x (* a t))
           (if (<= y 9e-263)
             (+ a z)
             (if (<= y 4.4e-229) t_1 (if (<= y 4.1e+21) t_3 t_2)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double t_2 = y * (b - z);
	double t_3 = a + (z + x);
	double tmp;
	if (y <= -5.4e+91) {
		tmp = t_2;
	} else if (y <= -1.05e-79) {
		tmp = t_1;
	} else if (y <= -2.8e-221) {
		tmp = t_3;
	} else if (y <= -2.05e-299) {
		tmp = x - (a * t);
	} else if (y <= 9e-263) {
		tmp = a + z;
	} else if (y <= 4.4e-229) {
		tmp = t_1;
	} else if (y <= 4.1e+21) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (t * (b - a))
    t_2 = y * (b - z)
    t_3 = a + (z + x)
    if (y <= (-5.4d+91)) then
        tmp = t_2
    else if (y <= (-1.05d-79)) then
        tmp = t_1
    else if (y <= (-2.8d-221)) then
        tmp = t_3
    else if (y <= (-2.05d-299)) then
        tmp = x - (a * t)
    else if (y <= 9d-263) then
        tmp = a + z
    else if (y <= 4.4d-229) then
        tmp = t_1
    else if (y <= 4.1d+21) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double t_2 = y * (b - z);
	double t_3 = a + (z + x);
	double tmp;
	if (y <= -5.4e+91) {
		tmp = t_2;
	} else if (y <= -1.05e-79) {
		tmp = t_1;
	} else if (y <= -2.8e-221) {
		tmp = t_3;
	} else if (y <= -2.05e-299) {
		tmp = x - (a * t);
	} else if (y <= 9e-263) {
		tmp = a + z;
	} else if (y <= 4.4e-229) {
		tmp = t_1;
	} else if (y <= 4.1e+21) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * (b - a))
	t_2 = y * (b - z)
	t_3 = a + (z + x)
	tmp = 0
	if y <= -5.4e+91:
		tmp = t_2
	elif y <= -1.05e-79:
		tmp = t_1
	elif y <= -2.8e-221:
		tmp = t_3
	elif y <= -2.05e-299:
		tmp = x - (a * t)
	elif y <= 9e-263:
		tmp = a + z
	elif y <= 4.4e-229:
		tmp = t_1
	elif y <= 4.1e+21:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * Float64(b - a)))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(a + Float64(z + x))
	tmp = 0.0
	if (y <= -5.4e+91)
		tmp = t_2;
	elseif (y <= -1.05e-79)
		tmp = t_1;
	elseif (y <= -2.8e-221)
		tmp = t_3;
	elseif (y <= -2.05e-299)
		tmp = Float64(x - Float64(a * t));
	elseif (y <= 9e-263)
		tmp = Float64(a + z);
	elseif (y <= 4.4e-229)
		tmp = t_1;
	elseif (y <= 4.1e+21)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * (b - a));
	t_2 = y * (b - z);
	t_3 = a + (z + x);
	tmp = 0.0;
	if (y <= -5.4e+91)
		tmp = t_2;
	elseif (y <= -1.05e-79)
		tmp = t_1;
	elseif (y <= -2.8e-221)
		tmp = t_3;
	elseif (y <= -2.05e-299)
		tmp = x - (a * t);
	elseif (y <= 9e-263)
		tmp = a + z;
	elseif (y <= 4.4e-229)
		tmp = t_1;
	elseif (y <= 4.1e+21)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(z + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.4e+91], t$95$2, If[LessEqual[y, -1.05e-79], t$95$1, If[LessEqual[y, -2.8e-221], t$95$3, If[LessEqual[y, -2.05e-299], N[(x - N[(a * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e-263], N[(a + z), $MachinePrecision], If[LessEqual[y, 4.4e-229], t$95$1, If[LessEqual[y, 4.1e+21], t$95$3, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.4e91 or 4.1e21 < y

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -5.4e91 < y < -1.05e-79 or 8.9999999999999994e-263 < y < 4.3999999999999998e-229

   1. Initial program 97.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.6%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 97.6%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 97.6%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 97.6%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 97.6%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 97.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 97.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 97.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 97.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 97.6%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 97.6%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 78.8%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in z around 0 67.7%

      \[\leadsto \color{blue}{x - t \cdot \left(a - b\right)} \]

   if -1.05e-79 < y < -2.80000000000000019e-221 or 4.3999999999999998e-229 < y < 4.1e21

   1. Initial program 98.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 98.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 98.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 98.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 98.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 98.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 98.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 98.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 98.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 98.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 98.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 67.7%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   6. Taylor expanded in y around 0 67.5%

      \[\leadsto \color{blue}{x - \left(-1 \cdot z + -1 \cdot a\right)} \]
   7. Step-by-step derivation

      1. associate--r+ 67.5%

         \[\leadsto \color{blue}{\left(x - -1 \cdot z\right) - -1 \cdot a} \]

      2. sub-neg 67.5%

         \[\leadsto \color{blue}{\left(x - -1 \cdot z\right) + \left(--1 \cdot a\right)} \]

      3. mul-1-neg 67.5%

         \[\leadsto \left(x - \color{blue}{\left(-z\right)}\right) + \left(--1 \cdot a\right) \]

      4. mul-1-neg 67.5%

         \[\leadsto \left(x - \left(-z\right)\right) + \left(-\color{blue}{\left(-a\right)}\right) \]

      5. remove-double-neg 67.5%

         \[\leadsto \left(x - \left(-z\right)\right) + \color{blue}{a} \]

   8. Simplified 67.5%

      \[\leadsto \color{blue}{\left(x - \left(-z\right)\right) + a} \]

   if -2.80000000000000019e-221 < y < -2.05e-299

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 83.7%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in z around 0 77.6%

      \[\leadsto \color{blue}{x - t \cdot \left(a - b\right)} \]

   6. Taylor expanded in a around inf 77.8%

      \[\leadsto x - \color{blue}{a \cdot t} \]
   7. Step-by-step derivation

      1. *-commutative 77.8%

         \[\leadsto x - \color{blue}{t \cdot a} \]

   8. Simplified 77.8%

      \[\leadsto x - \color{blue}{t \cdot a} \]

   if -2.05e-299 < y < 8.9999999999999994e-263

   1. Initial program 86.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 86.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 86.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 86.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 86.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 86.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 86.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in a around inf 80.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]
   6. Step-by-step derivation

      1. associate-*r* 80.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

      2. neg-mul-1 80.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   7. Simplified 80.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   8. Taylor expanded in y around 0 80.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right) - \left(-1 \cdot z + -1 \cdot a\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 80.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(-1 \cdot z + -1 \cdot a\right) \]

      2. mul-1-neg 80.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(-1 \cdot z + -1 \cdot a\right) \]

      3. distribute-lft-out 80.1%

         \[\leadsto \left(-a\right) \cdot t - \color{blue}{-1 \cdot \left(z + a\right)} \]

   10. Simplified 80.1%

       \[\leadsto \color{blue}{\left(-a\right) \cdot t - -1 \cdot \left(z + a\right)} \]

   11. Taylor expanded in t around 0 65.9%

       \[\leadsto \color{blue}{a + z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-79}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-221}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-299}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-263}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-229}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+21}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 17: 73.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + z \cdot \left(1 - y\right)\right)\\ t_2 := \left(z + x\right) + t \cdot \left(b - a\right)\\ t_3 := a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{if}\;t \leq -0.012:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-277}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-218}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 0.027:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (* z (- 1.0 y)))))
        (t_2 (+ (+ z x) (* t (- b a))))
        (t_3 (+ a (+ x (* b (- y 2.0))))))
   (if (<= t -0.012)
     t_2
     (if (<= t -1.35e-182)
       t_1
       (if (<= t 4e-277)
         t_3
         (if (<= t 1.95e-218) t_1 (if (<= t 0.027) t_3 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = (z + x) + (t * (b - a));
	double t_3 = a + (x + (b * (y - 2.0)));
	double tmp;
	if (t <= -0.012) {
		tmp = t_2;
	} else if (t <= -1.35e-182) {
		tmp = t_1;
	} else if (t <= 4e-277) {
		tmp = t_3;
	} else if (t <= 1.95e-218) {
		tmp = t_1;
	} else if (t <= 0.027) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + (a + (z * (1.0d0 - y)))
    t_2 = (z + x) + (t * (b - a))
    t_3 = a + (x + (b * (y - 2.0d0)))
    if (t <= (-0.012d0)) then
        tmp = t_2
    else if (t <= (-1.35d-182)) then
        tmp = t_1
    else if (t <= 4d-277) then
        tmp = t_3
    else if (t <= 1.95d-218) then
        tmp = t_1
    else if (t <= 0.027d0) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = (z + x) + (t * (b - a));
	double t_3 = a + (x + (b * (y - 2.0)));
	double tmp;
	if (t <= -0.012) {
		tmp = t_2;
	} else if (t <= -1.35e-182) {
		tmp = t_1;
	} else if (t <= 4e-277) {
		tmp = t_3;
	} else if (t <= 1.95e-218) {
		tmp = t_1;
	} else if (t <= 0.027) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (z * (1.0 - y)))
	t_2 = (z + x) + (t * (b - a))
	t_3 = a + (x + (b * (y - 2.0)))
	tmp = 0
	if t <= -0.012:
		tmp = t_2
	elif t <= -1.35e-182:
		tmp = t_1
	elif t <= 4e-277:
		tmp = t_3
	elif t <= 1.95e-218:
		tmp = t_1
	elif t <= 0.027:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(Float64(z + x) + Float64(t * Float64(b - a)))
	t_3 = Float64(a + Float64(x + Float64(b * Float64(y - 2.0))))
	tmp = 0.0
	if (t <= -0.012)
		tmp = t_2;
	elseif (t <= -1.35e-182)
		tmp = t_1;
	elseif (t <= 4e-277)
		tmp = t_3;
	elseif (t <= 1.95e-218)
		tmp = t_1;
	elseif (t <= 0.027)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a + (z * (1.0 - y)));
	t_2 = (z + x) + (t * (b - a));
	t_3 = a + (x + (b * (y - 2.0)));
	tmp = 0.0;
	if (t <= -0.012)
		tmp = t_2;
	elseif (t <= -1.35e-182)
		tmp = t_1;
	elseif (t <= 4e-277)
		tmp = t_3;
	elseif (t <= 1.95e-218)
		tmp = t_1;
	elseif (t <= 0.027)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + x), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.012], t$95$2, If[LessEqual[t, -1.35e-182], t$95$1, If[LessEqual[t, 4e-277], t$95$3, If[LessEqual[t, 1.95e-218], t$95$1, If[LessEqual[t, 0.027], t$95$3, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.012 or 0.0269999999999999997 < t

   1. Initial program 92.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 92.5%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 92.5%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 92.5%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 92.5%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 92.5%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 92.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 92.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 92.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 92.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 92.5%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 92.5%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 92.1%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in y around 0 79.7%

      \[\leadsto \color{blue}{\left(x - -1 \cdot z\right)} - t \cdot \left(a - b\right) \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 79.7%

         \[\leadsto \color{blue}{\left(x + \left(--1\right) \cdot z\right)} - t \cdot \left(a - b\right) \]

      2. metadata-eval 79.7%

         \[\leadsto \left(x + \color{blue}{1} \cdot z\right) - t \cdot \left(a - b\right) \]

      3. *-lft-identity 79.7%

         \[\leadsto \left(x + \color{blue}{z}\right) - t \cdot \left(a - b\right) \]

   7. Simplified 79.7%

      \[\leadsto \color{blue}{\left(x + z\right)} - t \cdot \left(a - b\right) \]

   if -0.012 < t < -1.35e-182 or 3.99999999999999988e-277 < t < 1.95e-218

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 80.8%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   if -1.35e-182 < t < 3.99999999999999988e-277 or 1.95e-218 < t < 0.0269999999999999997

   1. Initial program 95.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 95.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 95.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 95.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 95.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 95.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 95.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 95.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 95.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 95.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 80.1%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 80.1%

      \[\leadsto \color{blue}{\left(\left(y - 2\right) \cdot b + x\right) - -1 \cdot a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.012:\\ \;\;\;\;\left(z + x\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-182}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-277}:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-218}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;t \leq 0.027:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 18: 76.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z \cdot \left(1 - y\right)\right) - a \cdot t\\ t_2 := x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -40000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(y - 2\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ x (* z (- 1.0 y))) (* a t)))
        (t_2 (+ x (* b (- (+ t y) 2.0)))))
   (if (<= b -40000000000000.0)
     t_2
     (if (<= b -4.1e-24)
       t_1
       (if (<= b -2.9e-41)
         (- (* b (- y 2.0)) (* a (+ t -1.0)))
         (if (<= b 2.15e+23) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (1.0 - y))) - (a * t);
	double t_2 = x + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -40000000000000.0) {
		tmp = t_2;
	} else if (b <= -4.1e-24) {
		tmp = t_1;
	} else if (b <= -2.9e-41) {
		tmp = (b * (y - 2.0)) - (a * (t + -1.0));
	} else if (b <= 2.15e+23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + (z * (1.0d0 - y))) - (a * t)
    t_2 = x + (b * ((t + y) - 2.0d0))
    if (b <= (-40000000000000.0d0)) then
        tmp = t_2
    else if (b <= (-4.1d-24)) then
        tmp = t_1
    else if (b <= (-2.9d-41)) then
        tmp = (b * (y - 2.0d0)) - (a * (t + (-1.0d0)))
    else if (b <= 2.15d+23) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (z * (1.0 - y))) - (a * t);
	double t_2 = x + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -40000000000000.0) {
		tmp = t_2;
	} else if (b <= -4.1e-24) {
		tmp = t_1;
	} else if (b <= -2.9e-41) {
		tmp = (b * (y - 2.0)) - (a * (t + -1.0));
	} else if (b <= 2.15e+23) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + (z * (1.0 - y))) - (a * t)
	t_2 = x + (b * ((t + y) - 2.0))
	tmp = 0
	if b <= -40000000000000.0:
		tmp = t_2
	elif b <= -4.1e-24:
		tmp = t_1
	elif b <= -2.9e-41:
		tmp = (b * (y - 2.0)) - (a * (t + -1.0))
	elif b <= 2.15e+23:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(z * Float64(1.0 - y))) - Float64(a * t))
	t_2 = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)))
	tmp = 0.0
	if (b <= -40000000000000.0)
		tmp = t_2;
	elseif (b <= -4.1e-24)
		tmp = t_1;
	elseif (b <= -2.9e-41)
		tmp = Float64(Float64(b * Float64(y - 2.0)) - Float64(a * Float64(t + -1.0)));
	elseif (b <= 2.15e+23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (z * (1.0 - y))) - (a * t);
	t_2 = x + (b * ((t + y) - 2.0));
	tmp = 0.0;
	if (b <= -40000000000000.0)
		tmp = t_2;
	elseif (b <= -4.1e-24)
		tmp = t_1;
	elseif (b <= -2.9e-41)
		tmp = (b * (y - 2.0)) - (a * (t + -1.0));
	elseif (b <= 2.15e+23)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -40000000000000.0], t$95$2, If[LessEqual[b, -4.1e-24], t$95$1, If[LessEqual[b, -2.9e-41], N[(N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e+23], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4e13 or 2.1499999999999999e23 < b

   1. Initial program 88.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 88.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 88.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 88.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 88.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 88.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 88.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 88.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 88.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 88.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 88.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 88.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 85.3%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in a around 0 77.0%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + x} \]

   if -4e13 < b < -4.10000000000000015e-24 or -2.89999999999999977e-41 < b < 2.1499999999999999e23

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 85.7%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in a around inf 82.7%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{a \cdot t} \]
   6. Step-by-step derivation

      1. *-commutative 40.3%

         \[\leadsto x - \color{blue}{t \cdot a} \]

   7. Simplified 82.7%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot a} \]

   if -4.10000000000000015e-24 < b < -2.89999999999999977e-41

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 87.6%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 87.6%

      \[\leadsto \left(\color{blue}{\left(y - 2\right) \cdot b} + x\right) - \left(t - 1\right) \cdot a \]

   6. Taylor expanded in x around 0 88.0%

      \[\leadsto \color{blue}{\left(y - 2\right) \cdot b - \left(t - 1\right) \cdot a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -40000000000000:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -4.1 \cdot 10^{-24}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) - a \cdot t\\ \mathbf{elif}\;b \leq -2.9 \cdot 10^{-41}:\\ \;\;\;\;b \cdot \left(y - 2\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+23}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) - a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 19: 76.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -1.6 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-20}:\\ \;\;\;\;t_1 + y \cdot b\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(y - 2\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+26}:\\ \;\;\;\;t_1 - a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))) (t_2 (+ x (* b (- (+ t y) 2.0)))))
   (if (<= b -1.6e+70)
     t_2
     (if (<= b -2.6e-20)
       (+ t_1 (* y b))
       (if (<= b -4e-51)
         (- (* b (- y 2.0)) (* a (+ t -1.0)))
         (if (<= b 2.4e+26) (- t_1 (* a t)) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = x + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -1.6e+70) {
		tmp = t_2;
	} else if (b <= -2.6e-20) {
		tmp = t_1 + (y * b);
	} else if (b <= -4e-51) {
		tmp = (b * (y - 2.0)) - (a * (t + -1.0));
	} else if (b <= 2.4e+26) {
		tmp = t_1 - (a * t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = x + (b * ((t + y) - 2.0d0))
    if (b <= (-1.6d+70)) then
        tmp = t_2
    else if (b <= (-2.6d-20)) then
        tmp = t_1 + (y * b)
    else if (b <= (-4d-51)) then
        tmp = (b * (y - 2.0d0)) - (a * (t + (-1.0d0)))
    else if (b <= 2.4d+26) then
        tmp = t_1 - (a * t)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = x + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -1.6e+70) {
		tmp = t_2;
	} else if (b <= -2.6e-20) {
		tmp = t_1 + (y * b);
	} else if (b <= -4e-51) {
		tmp = (b * (y - 2.0)) - (a * (t + -1.0));
	} else if (b <= 2.4e+26) {
		tmp = t_1 - (a * t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = x + (b * ((t + y) - 2.0))
	tmp = 0
	if b <= -1.6e+70:
		tmp = t_2
	elif b <= -2.6e-20:
		tmp = t_1 + (y * b)
	elif b <= -4e-51:
		tmp = (b * (y - 2.0)) - (a * (t + -1.0))
	elif b <= 2.4e+26:
		tmp = t_1 - (a * t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)))
	tmp = 0.0
	if (b <= -1.6e+70)
		tmp = t_2;
	elseif (b <= -2.6e-20)
		tmp = Float64(t_1 + Float64(y * b));
	elseif (b <= -4e-51)
		tmp = Float64(Float64(b * Float64(y - 2.0)) - Float64(a * Float64(t + -1.0)));
	elseif (b <= 2.4e+26)
		tmp = Float64(t_1 - Float64(a * t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = x + (b * ((t + y) - 2.0));
	tmp = 0.0;
	if (b <= -1.6e+70)
		tmp = t_2;
	elseif (b <= -2.6e-20)
		tmp = t_1 + (y * b);
	elseif (b <= -4e-51)
		tmp = (b * (y - 2.0)) - (a * (t + -1.0));
	elseif (b <= 2.4e+26)
		tmp = t_1 - (a * t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.6e+70], t$95$2, If[LessEqual[b, -2.6e-20], N[(t$95$1 + N[(y * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -4e-51], N[(N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.4e+26], N[(t$95$1 - N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.6000000000000001e70 or 2.40000000000000005e26 < b

   1. Initial program 86.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 86.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 86.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 86.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 86.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 86.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 86.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 86.8%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in a around 0 80.0%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + x} \]

   if -1.6000000000000001e70 < b < -2.59999999999999995e-20

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 76.1%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{-1 \cdot \left(y \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 76.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(-y \cdot b\right)} \]

      2. distribute-rgt-neg-in 76.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{y \cdot \left(-b\right)} \]

   6. Simplified 76.1%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{y \cdot \left(-b\right)} \]

   if -2.59999999999999995e-20 < b < -4e-51

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 91.7%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 91.7%

      \[\leadsto \left(\color{blue}{\left(y - 2\right) \cdot b} + x\right) - \left(t - 1\right) \cdot a \]

   6. Taylor expanded in x around 0 92.0%

      \[\leadsto \color{blue}{\left(y - 2\right) \cdot b - \left(t - 1\right) \cdot a} \]

   if -4e-51 < b < 2.40000000000000005e26

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 85.3%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in a around inf 82.1%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{a \cdot t} \]
   6. Step-by-step derivation

      1. *-commutative 39.8%

         \[\leadsto x - \color{blue}{t \cdot a} \]

   7. Simplified 82.1%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.6 \cdot 10^{+70}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.6 \cdot 10^{-20}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + y \cdot b\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-51}:\\ \;\;\;\;b \cdot \left(y - 2\right) - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+26}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) - a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 20: 86.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1200000000000 \lor \neg \left(b \leq 1.1 \cdot 10^{+18}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + \left(a - a \cdot t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1200000000000.0) (not (<= b 1.1e+18)))
   (+ (+ x (* b (- (+ t y) 2.0))) (* a (- 1.0 t)))
   (+ (+ x (* z (- 1.0 y))) (- a (* a t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1200000000000.0) || !(b <= 1.1e+18)) {
		tmp = (x + (b * ((t + y) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = (x + (z * (1.0 - y))) + (a - (a * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((b <= (-1200000000000.0d0)) .or. (.not. (b <= 1.1d+18))) then
        tmp = (x + (b * ((t + y) - 2.0d0))) + (a * (1.0d0 - t))
    else
        tmp = (x + (z * (1.0d0 - y))) + (a - (a * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1200000000000.0) || !(b <= 1.1e+18)) {
		tmp = (x + (b * ((t + y) - 2.0))) + (a * (1.0 - t));
	} else {
		tmp = (x + (z * (1.0 - y))) + (a - (a * t));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1200000000000.0) or not (b <= 1.1e+18):
		tmp = (x + (b * ((t + y) - 2.0))) + (a * (1.0 - t))
	else:
		tmp = (x + (z * (1.0 - y))) + (a - (a * t))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1200000000000.0) || !(b <= 1.1e+18))
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(t + y) - 2.0))) + Float64(a * Float64(1.0 - t)));
	else
		tmp = Float64(Float64(x + Float64(z * Float64(1.0 - y))) + Float64(a - Float64(a * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1200000000000.0) || ~((b <= 1.1e+18)))
		tmp = (x + (b * ((t + y) - 2.0))) + (a * (1.0 - t));
	else
		tmp = (x + (z * (1.0 - y))) + (a - (a * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1200000000000.0], N[Not[LessEqual[b, 1.1e+18]], $MachinePrecision]], N[(N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a - N[(a * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.2e12 or 1.1e18 < b

   1. Initial program 88.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 88.8%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 88.8%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 88.8%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 88.8%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 88.8%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 88.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 88.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 88.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 88.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 88.8%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 88.8%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 84.8%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   if -1.2e12 < b < 1.1e18

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 92.2%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(t - 1\right) \cdot a} \]
   5. Step-by-step derivation

      1. sub-neg 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(t + \left(-1\right)\right)} \cdot a \]

      2. metadata-eval 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(t + \color{blue}{-1}\right) \cdot a \]

      3. +-commutative 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(-1 + t\right)} \cdot a \]

      4. *-commutative 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{a \cdot \left(-1 + t\right)} \]

      5. +-commutative 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - a \cdot \color{blue}{\left(t + -1\right)} \]

      6. distribute-rgt-in 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(t \cdot a + -1 \cdot a\right)} \]

      7. fma-def 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\mathsf{fma}\left(t, a, -1 \cdot a\right)} \]

      8. mul-1-neg 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \mathsf{fma}\left(t, a, \color{blue}{-a}\right) \]

      9. fma-neg 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(t \cdot a - a\right)} \]

   6. Simplified 92.2%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(t \cdot a - a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1200000000000 \lor \neg \left(b \leq 1.1 \cdot 10^{+18}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + \left(a - a \cdot t\right)\\ \end{array} \]

Alternative 21: 46.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -19000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9.4 \cdot 10^{-101}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-182}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-132}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-29}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1100000000:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -19000000000.0)
     t_1
     (if (<= t -9.4e-101)
       (+ a x)
       (if (<= t -2.3e-182)
         (* y (- z))
         (if (<= t 7.5e-132)
           (+ a x)
           (if (<= t 6.8e-29)
             (* y b)
             (if (<= t 1100000000.0) (+ a x) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -19000000000.0) {
		tmp = t_1;
	} else if (t <= -9.4e-101) {
		tmp = a + x;
	} else if (t <= -2.3e-182) {
		tmp = y * -z;
	} else if (t <= 7.5e-132) {
		tmp = a + x;
	} else if (t <= 6.8e-29) {
		tmp = y * b;
	} else if (t <= 1100000000.0) {
		tmp = a + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-19000000000.0d0)) then
        tmp = t_1
    else if (t <= (-9.4d-101)) then
        tmp = a + x
    else if (t <= (-2.3d-182)) then
        tmp = y * -z
    else if (t <= 7.5d-132) then
        tmp = a + x
    else if (t <= 6.8d-29) then
        tmp = y * b
    else if (t <= 1100000000.0d0) then
        tmp = a + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -19000000000.0) {
		tmp = t_1;
	} else if (t <= -9.4e-101) {
		tmp = a + x;
	} else if (t <= -2.3e-182) {
		tmp = y * -z;
	} else if (t <= 7.5e-132) {
		tmp = a + x;
	} else if (t <= 6.8e-29) {
		tmp = y * b;
	} else if (t <= 1100000000.0) {
		tmp = a + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -19000000000.0:
		tmp = t_1
	elif t <= -9.4e-101:
		tmp = a + x
	elif t <= -2.3e-182:
		tmp = y * -z
	elif t <= 7.5e-132:
		tmp = a + x
	elif t <= 6.8e-29:
		tmp = y * b
	elif t <= 1100000000.0:
		tmp = a + x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -19000000000.0)
		tmp = t_1;
	elseif (t <= -9.4e-101)
		tmp = Float64(a + x);
	elseif (t <= -2.3e-182)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 7.5e-132)
		tmp = Float64(a + x);
	elseif (t <= 6.8e-29)
		tmp = Float64(y * b);
	elseif (t <= 1100000000.0)
		tmp = Float64(a + x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -19000000000.0)
		tmp = t_1;
	elseif (t <= -9.4e-101)
		tmp = a + x;
	elseif (t <= -2.3e-182)
		tmp = y * -z;
	elseif (t <= 7.5e-132)
		tmp = a + x;
	elseif (t <= 6.8e-29)
		tmp = y * b;
	elseif (t <= 1100000000.0)
		tmp = a + x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -19000000000.0], t$95$1, If[LessEqual[t, -9.4e-101], N[(a + x), $MachinePrecision], If[LessEqual[t, -2.3e-182], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 7.5e-132], N[(a + x), $MachinePrecision], If[LessEqual[t, 6.8e-29], N[(y * b), $MachinePrecision], If[LessEqual[t, 1100000000.0], N[(a + x), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.9e10 or 1.1e9 < t

   1. Initial program 92.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 92.2%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 92.2%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 92.2%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 92.2%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 92.2%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 92.2%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 60.2%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]

   if -1.9e10 < t < -9.3999999999999999e-101 or -2.2999999999999999e-182 < t < 7.49999999999999989e-132 or 6.79999999999999945e-29 < t < 1.1e9

   1. Initial program 97.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 97.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 97.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 97.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 97.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 97.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 97.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 97.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 97.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 97.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 97.7%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 69.0%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   6. Taylor expanded in z around 0 43.9%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   7. Step-by-step derivation

      1. sub-neg 43.9%

         \[\leadsto \color{blue}{x + \left(--1 \cdot a\right)} \]

      2. mul-1-neg 43.9%

         \[\leadsto x + \left(-\color{blue}{\left(-a\right)}\right) \]

      3. remove-double-neg 43.9%

         \[\leadsto x + \color{blue}{a} \]

   8. Simplified 43.9%

      \[\leadsto \color{blue}{x + a} \]

   if -9.3999999999999999e-101 < t < -2.2999999999999999e-182

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 56.9%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   5. Taylor expanded in b around 0 45.9%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 45.9%

         \[\leadsto \color{blue}{-y \cdot z} \]

      2. distribute-rgt-neg-in 45.9%

         \[\leadsto \color{blue}{y \cdot \left(-z\right)} \]

   7. Simplified 45.9%

      \[\leadsto \color{blue}{y \cdot \left(-z\right)} \]

   if 7.49999999999999989e-132 < t < 6.79999999999999945e-29

   1. Initial program 95.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.2%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 95.2%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 95.2%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 95.2%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 95.2%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 95.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 95.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 95.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 95.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 95.2%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 81.5%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 81.5%

      \[\leadsto \left(\color{blue}{\left(y - 2\right) \cdot b} + x\right) - \left(t - 1\right) \cdot a \]

   6. Taylor expanded in y around inf 49.1%

      \[\leadsto \color{blue}{y \cdot b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -19000000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -9.4 \cdot 10^{-101}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-182}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-132}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-29}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1100000000:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 22: 57.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{+96}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-13}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-301}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-263}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-228}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+21}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* t (- b a)))) (t_2 (* y (- b z))))
   (if (<= y -6.4e+96)
     t_2
     (if (<= y -1.3e-13)
       t_1
       (if (<= y -4.2e-301)
         (- x (* a (+ t -1.0)))
         (if (<= y 3.9e-263)
           (+ a z)
           (if (<= y 1.9e-228) t_1 (if (<= y 3.4e+21) (+ a (+ z x)) t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -6.4e+96) {
		tmp = t_2;
	} else if (y <= -1.3e-13) {
		tmp = t_1;
	} else if (y <= -4.2e-301) {
		tmp = x - (a * (t + -1.0));
	} else if (y <= 3.9e-263) {
		tmp = a + z;
	} else if (y <= 1.9e-228) {
		tmp = t_1;
	} else if (y <= 3.4e+21) {
		tmp = a + (z + x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (t * (b - a))
    t_2 = y * (b - z)
    if (y <= (-6.4d+96)) then
        tmp = t_2
    else if (y <= (-1.3d-13)) then
        tmp = t_1
    else if (y <= (-4.2d-301)) then
        tmp = x - (a * (t + (-1.0d0)))
    else if (y <= 3.9d-263) then
        tmp = a + z
    else if (y <= 1.9d-228) then
        tmp = t_1
    else if (y <= 3.4d+21) then
        tmp = a + (z + x)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (t * (b - a));
	double t_2 = y * (b - z);
	double tmp;
	if (y <= -6.4e+96) {
		tmp = t_2;
	} else if (y <= -1.3e-13) {
		tmp = t_1;
	} else if (y <= -4.2e-301) {
		tmp = x - (a * (t + -1.0));
	} else if (y <= 3.9e-263) {
		tmp = a + z;
	} else if (y <= 1.9e-228) {
		tmp = t_1;
	} else if (y <= 3.4e+21) {
		tmp = a + (z + x);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (t * (b - a))
	t_2 = y * (b - z)
	tmp = 0
	if y <= -6.4e+96:
		tmp = t_2
	elif y <= -1.3e-13:
		tmp = t_1
	elif y <= -4.2e-301:
		tmp = x - (a * (t + -1.0))
	elif y <= 3.9e-263:
		tmp = a + z
	elif y <= 1.9e-228:
		tmp = t_1
	elif y <= 3.4e+21:
		tmp = a + (z + x)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(t * Float64(b - a)))
	t_2 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -6.4e+96)
		tmp = t_2;
	elseif (y <= -1.3e-13)
		tmp = t_1;
	elseif (y <= -4.2e-301)
		tmp = Float64(x - Float64(a * Float64(t + -1.0)));
	elseif (y <= 3.9e-263)
		tmp = Float64(a + z);
	elseif (y <= 1.9e-228)
		tmp = t_1;
	elseif (y <= 3.4e+21)
		tmp = Float64(a + Float64(z + x));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (t * (b - a));
	t_2 = y * (b - z);
	tmp = 0.0;
	if (y <= -6.4e+96)
		tmp = t_2;
	elseif (y <= -1.3e-13)
		tmp = t_1;
	elseif (y <= -4.2e-301)
		tmp = x - (a * (t + -1.0));
	elseif (y <= 3.9e-263)
		tmp = a + z;
	elseif (y <= 1.9e-228)
		tmp = t_1;
	elseif (y <= 3.4e+21)
		tmp = a + (z + x);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.4e+96], t$95$2, If[LessEqual[y, -1.3e-13], t$95$1, If[LessEqual[y, -4.2e-301], N[(x - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e-263], N[(a + z), $MachinePrecision], If[LessEqual[y, 1.9e-228], t$95$1, If[LessEqual[y, 3.4e+21], N[(a + N[(z + x), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -6.40000000000000013e96 or 3.4e21 < y

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 73.4%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   if -6.40000000000000013e96 < y < -1.3e-13 or 3.8999999999999997e-263 < y < 1.8999999999999999e-228

   1. Initial program 96.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.6%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 96.6%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 96.6%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 96.6%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 96.6%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 96.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 96.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 96.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 96.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 96.6%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 85.4%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in z around 0 69.7%

      \[\leadsto \color{blue}{x - t \cdot \left(a - b\right)} \]

   if -1.3e-13 < y < -4.1999999999999997e-301

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 85.7%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in b around 0 69.5%

      \[\leadsto \color{blue}{x - \left(t - 1\right) \cdot a} \]

   if -4.1999999999999997e-301 < y < 3.8999999999999997e-263

   1. Initial program 86.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 86.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 86.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 86.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 86.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 86.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 86.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 86.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 86.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in a around inf 80.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]
   6. Step-by-step derivation

      1. associate-*r* 80.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

      2. neg-mul-1 80.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   7. Simplified 80.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   8. Taylor expanded in y around 0 80.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right) - \left(-1 \cdot z + -1 \cdot a\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 80.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(-1 \cdot z + -1 \cdot a\right) \]

      2. mul-1-neg 80.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(-1 \cdot z + -1 \cdot a\right) \]

      3. distribute-lft-out 80.1%

         \[\leadsto \left(-a\right) \cdot t - \color{blue}{-1 \cdot \left(z + a\right)} \]

   10. Simplified 80.1%

       \[\leadsto \color{blue}{\left(-a\right) \cdot t - -1 \cdot \left(z + a\right)} \]

   11. Taylor expanded in t around 0 65.9%

       \[\leadsto \color{blue}{a + z} \]

   if 1.8999999999999999e-228 < y < 3.4e21

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 98.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 98.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 98.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 98.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 98.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 98.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 98.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 98.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 98.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 98.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 67.8%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   6. Taylor expanded in y around 0 67.5%

      \[\leadsto \color{blue}{x - \left(-1 \cdot z + -1 \cdot a\right)} \]
   7. Step-by-step derivation

      1. associate--r+ 67.5%

         \[\leadsto \color{blue}{\left(x - -1 \cdot z\right) - -1 \cdot a} \]

      2. sub-neg 67.5%

         \[\leadsto \color{blue}{\left(x - -1 \cdot z\right) + \left(--1 \cdot a\right)} \]

      3. mul-1-neg 67.5%

         \[\leadsto \left(x - \color{blue}{\left(-z\right)}\right) + \left(--1 \cdot a\right) \]

      4. mul-1-neg 67.5%

         \[\leadsto \left(x - \left(-z\right)\right) + \left(-\color{blue}{\left(-a\right)}\right) \]

      5. remove-double-neg 67.5%

         \[\leadsto \left(x - \left(-z\right)\right) + \color{blue}{a} \]

   8. Simplified 67.5%

      \[\leadsto \color{blue}{\left(x - \left(-z\right)\right) + a} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{+96}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-13}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-301}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-263}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-228}:\\ \;\;\;\;x + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+21}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 23: 73.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a + z \cdot \left(1 - y\right)\right)\\ t_2 := \left(z + x\right) + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -0.012:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-268}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-276}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ a (* z (- 1.0 y))))) (t_2 (+ (+ z x) (* t (- b a)))))
   (if (<= t -0.012)
     t_2
     (if (<= t -5e-268)
       t_1
       (if (<= t -3.8e-276)
         (+ x (* b (- (+ t y) 2.0)))
         (if (<= t 5.6e-16) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = (z + x) + (t * (b - a));
	double tmp;
	if (t <= -0.012) {
		tmp = t_2;
	} else if (t <= -5e-268) {
		tmp = t_1;
	} else if (t <= -3.8e-276) {
		tmp = x + (b * ((t + y) - 2.0));
	} else if (t <= 5.6e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (a + (z * (1.0d0 - y)))
    t_2 = (z + x) + (t * (b - a))
    if (t <= (-0.012d0)) then
        tmp = t_2
    else if (t <= (-5d-268)) then
        tmp = t_1
    else if (t <= (-3.8d-276)) then
        tmp = x + (b * ((t + y) - 2.0d0))
    else if (t <= 5.6d-16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (a + (z * (1.0 - y)));
	double t_2 = (z + x) + (t * (b - a));
	double tmp;
	if (t <= -0.012) {
		tmp = t_2;
	} else if (t <= -5e-268) {
		tmp = t_1;
	} else if (t <= -3.8e-276) {
		tmp = x + (b * ((t + y) - 2.0));
	} else if (t <= 5.6e-16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (a + (z * (1.0 - y)))
	t_2 = (z + x) + (t * (b - a))
	tmp = 0
	if t <= -0.012:
		tmp = t_2
	elif t <= -5e-268:
		tmp = t_1
	elif t <= -3.8e-276:
		tmp = x + (b * ((t + y) - 2.0))
	elif t <= 5.6e-16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(a + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(Float64(z + x) + Float64(t * Float64(b - a)))
	tmp = 0.0
	if (t <= -0.012)
		tmp = t_2;
	elseif (t <= -5e-268)
		tmp = t_1;
	elseif (t <= -3.8e-276)
		tmp = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)));
	elseif (t <= 5.6e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (a + (z * (1.0 - y)));
	t_2 = (z + x) + (t * (b - a));
	tmp = 0.0;
	if (t <= -0.012)
		tmp = t_2;
	elseif (t <= -5e-268)
		tmp = t_1;
	elseif (t <= -3.8e-276)
		tmp = x + (b * ((t + y) - 2.0));
	elseif (t <= 5.6e-16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(a + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z + x), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -0.012], t$95$2, If[LessEqual[t, -5e-268], t$95$1, If[LessEqual[t, -3.8e-276], N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.6e-16], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -0.012 or 5.6000000000000003e-16 < t

   1. Initial program 92.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 92.6%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 92.6%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 92.6%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 92.6%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 92.6%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 92.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 92.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 92.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 92.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 92.6%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 91.5%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in y around 0 79.2%

      \[\leadsto \color{blue}{\left(x - -1 \cdot z\right)} - t \cdot \left(a - b\right) \]
   6. Step-by-step derivation

      1. cancel-sign-sub-inv 79.2%

         \[\leadsto \color{blue}{\left(x + \left(--1\right) \cdot z\right)} - t \cdot \left(a - b\right) \]

      2. metadata-eval 79.2%

         \[\leadsto \left(x + \color{blue}{1} \cdot z\right) - t \cdot \left(a - b\right) \]

      3. *-lft-identity 79.2%

         \[\leadsto \left(x + \color{blue}{z}\right) - t \cdot \left(a - b\right) \]

   7. Simplified 79.2%

      \[\leadsto \color{blue}{\left(x + z\right)} - t \cdot \left(a - b\right) \]

   if -0.012 < t < -4.9999999999999999e-268 or -3.8e-276 < t < 5.6000000000000003e-16

   1. Initial program 98.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.2%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 98.2%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 98.2%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 98.2%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 98.2%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 98.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 98.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 98.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 98.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 98.2%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 98.2%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 98.2%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 71.4%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   if -4.9999999999999999e-268 < t < -3.8e-276

   1. Initial program 79.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 79.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 79.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 79.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 79.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 79.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 79.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 79.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 79.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 79.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 79.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 79.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 92.0%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in a around 0 92.0%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.012:\\ \;\;\;\;\left(z + x\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-268}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{-276}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-16}:\\ \;\;\;\;x + \left(a + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 24: 76.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -1.55 \cdot 10^{+138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-54}:\\ \;\;\;\;\left(x + b \cdot \left(y - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+33}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) - a \cdot t\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- (+ t y) 2.0)))))
   (if (<= b -1.55e+138)
     t_1
     (if (<= b -2.8e-54)
       (+ (+ x (* b (- y 2.0))) (* a (- 1.0 t)))
       (if (<= b 1.35e+33) (- (+ x (* z (- 1.0 y))) (* a t)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -1.55e+138) {
		tmp = t_1;
	} else if (b <= -2.8e-54) {
		tmp = (x + (b * (y - 2.0))) + (a * (1.0 - t));
	} else if (b <= 1.35e+33) {
		tmp = (x + (z * (1.0 - y))) - (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (b * ((t + y) - 2.0d0))
    if (b <= (-1.55d+138)) then
        tmp = t_1
    else if (b <= (-2.8d-54)) then
        tmp = (x + (b * (y - 2.0d0))) + (a * (1.0d0 - t))
    else if (b <= 1.35d+33) then
        tmp = (x + (z * (1.0d0 - y))) - (a * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * ((t + y) - 2.0));
	double tmp;
	if (b <= -1.55e+138) {
		tmp = t_1;
	} else if (b <= -2.8e-54) {
		tmp = (x + (b * (y - 2.0))) + (a * (1.0 - t));
	} else if (b <= 1.35e+33) {
		tmp = (x + (z * (1.0 - y))) - (a * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * ((t + y) - 2.0))
	tmp = 0
	if b <= -1.55e+138:
		tmp = t_1
	elif b <= -2.8e-54:
		tmp = (x + (b * (y - 2.0))) + (a * (1.0 - t))
	elif b <= 1.35e+33:
		tmp = (x + (z * (1.0 - y))) - (a * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(Float64(t + y) - 2.0)))
	tmp = 0.0
	if (b <= -1.55e+138)
		tmp = t_1;
	elseif (b <= -2.8e-54)
		tmp = Float64(Float64(x + Float64(b * Float64(y - 2.0))) + Float64(a * Float64(1.0 - t)));
	elseif (b <= 1.35e+33)
		tmp = Float64(Float64(x + Float64(z * Float64(1.0 - y))) - Float64(a * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * ((t + y) - 2.0));
	tmp = 0.0;
	if (b <= -1.55e+138)
		tmp = t_1;
	elseif (b <= -2.8e-54)
		tmp = (x + (b * (y - 2.0))) + (a * (1.0 - t));
	elseif (b <= 1.35e+33)
		tmp = (x + (z * (1.0 - y))) - (a * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.55e+138], t$95$1, If[LessEqual[b, -2.8e-54], N[(N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+33], N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.5499999999999999e138 or 1.34999999999999996e33 < b

   1. Initial program 85.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 85.8%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 85.8%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 85.8%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 85.8%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 85.8%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 85.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 85.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 85.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 85.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 85.8%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 85.8%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 87.1%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in a around 0 81.4%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + x} \]

   if -1.5499999999999999e138 < b < -2.8000000000000002e-54

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 97.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 97.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 97.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 97.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 97.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 97.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 97.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 97.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 97.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 97.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 77.3%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 72.6%

      \[\leadsto \left(\color{blue}{\left(y - 2\right) \cdot b} + x\right) - \left(t - 1\right) \cdot a \]

   if -2.8000000000000002e-54 < b < 1.34999999999999996e33

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 85.3%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot \left(a - b\right)} \]

   5. Taylor expanded in a around inf 82.1%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{a \cdot t} \]
   6. Step-by-step derivation

      1. *-commutative 39.8%

         \[\leadsto x - \color{blue}{t \cdot a} \]

   7. Simplified 82.1%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{t \cdot a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+138}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -2.8 \cdot 10^{-54}:\\ \;\;\;\;\left(x + b \cdot \left(y - 2\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+33}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) - a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 25: 32.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+41}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-100}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-131}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-28}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+58}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.2e+41)
   (* t b)
   (if (<= t -5.4e-100)
     (+ a x)
     (if (<= t -1.35e-158)
       (* y (- z))
       (if (<= t 1.95e-131)
         (+ a x)
         (if (<= t 1.42e-28)
           (* y b)
           (if (<= t 9.8e+58) (+ a x) (* a (- t)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.2e+41) {
		tmp = t * b;
	} else if (t <= -5.4e-100) {
		tmp = a + x;
	} else if (t <= -1.35e-158) {
		tmp = y * -z;
	} else if (t <= 1.95e-131) {
		tmp = a + x;
	} else if (t <= 1.42e-28) {
		tmp = y * b;
	} else if (t <= 9.8e+58) {
		tmp = a + x;
	} else {
		tmp = a * -t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.2d+41)) then
        tmp = t * b
    else if (t <= (-5.4d-100)) then
        tmp = a + x
    else if (t <= (-1.35d-158)) then
        tmp = y * -z
    else if (t <= 1.95d-131) then
        tmp = a + x
    else if (t <= 1.42d-28) then
        tmp = y * b
    else if (t <= 9.8d+58) then
        tmp = a + x
    else
        tmp = a * -t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.2e+41) {
		tmp = t * b;
	} else if (t <= -5.4e-100) {
		tmp = a + x;
	} else if (t <= -1.35e-158) {
		tmp = y * -z;
	} else if (t <= 1.95e-131) {
		tmp = a + x;
	} else if (t <= 1.42e-28) {
		tmp = y * b;
	} else if (t <= 9.8e+58) {
		tmp = a + x;
	} else {
		tmp = a * -t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.2e+41:
		tmp = t * b
	elif t <= -5.4e-100:
		tmp = a + x
	elif t <= -1.35e-158:
		tmp = y * -z
	elif t <= 1.95e-131:
		tmp = a + x
	elif t <= 1.42e-28:
		tmp = y * b
	elif t <= 9.8e+58:
		tmp = a + x
	else:
		tmp = a * -t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.2e+41)
		tmp = Float64(t * b);
	elseif (t <= -5.4e-100)
		tmp = Float64(a + x);
	elseif (t <= -1.35e-158)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 1.95e-131)
		tmp = Float64(a + x);
	elseif (t <= 1.42e-28)
		tmp = Float64(y * b);
	elseif (t <= 9.8e+58)
		tmp = Float64(a + x);
	else
		tmp = Float64(a * Float64(-t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.2e+41)
		tmp = t * b;
	elseif (t <= -5.4e-100)
		tmp = a + x;
	elseif (t <= -1.35e-158)
		tmp = y * -z;
	elseif (t <= 1.95e-131)
		tmp = a + x;
	elseif (t <= 1.42e-28)
		tmp = y * b;
	elseif (t <= 9.8e+58)
		tmp = a + x;
	else
		tmp = a * -t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.2e+41], N[(t * b), $MachinePrecision], If[LessEqual[t, -5.4e-100], N[(a + x), $MachinePrecision], If[LessEqual[t, -1.35e-158], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 1.95e-131], N[(a + x), $MachinePrecision], If[LessEqual[t, 1.42e-28], N[(y * b), $MachinePrecision], If[LessEqual[t, 9.8e+58], N[(a + x), $MachinePrecision], N[(a * (-t)), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.1999999999999999e41

   1. Initial program 86.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 86.7%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 86.7%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 86.7%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 86.7%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 86.7%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 86.7%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 93.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 93.3%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 93.3%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 93.3%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 93.3%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 93.3%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 96.7%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 96.7%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 96.7%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 96.7%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 96.7%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 96.7%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 67.4%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in b around inf 39.3%

      \[\leadsto \color{blue}{\left(t - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf 39.3%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -2.1999999999999999e41 < t < -5.40000000000000031e-100 or -1.3499999999999999e-158 < t < 1.9500000000000001e-131 or 1.42000000000000001e-28 < t < 9.80000000000000037e58

   1. Initial program 98.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 98.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 98.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 98.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 98.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 98.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 98.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 98.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 98.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 98.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 98.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 98.1%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 66.9%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   6. Taylor expanded in z around 0 40.9%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   7. Step-by-step derivation

      1. sub-neg 40.9%

         \[\leadsto \color{blue}{x + \left(--1 \cdot a\right)} \]

      2. mul-1-neg 40.9%

         \[\leadsto x + \left(-\color{blue}{\left(-a\right)}\right) \]

      3. remove-double-neg 40.9%

         \[\leadsto x + \color{blue}{a} \]

   8. Simplified 40.9%

      \[\leadsto \color{blue}{x + a} \]

   if -5.40000000000000031e-100 < t < -1.3499999999999999e-158

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 62.4%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   5. Taylor expanded in b around 0 47.8%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 47.8%

         \[\leadsto \color{blue}{-y \cdot z} \]

      2. distribute-rgt-neg-in 47.8%

         \[\leadsto \color{blue}{y \cdot \left(-z\right)} \]

   7. Simplified 47.8%

      \[\leadsto \color{blue}{y \cdot \left(-z\right)} \]

   if 1.9500000000000001e-131 < t < 1.42000000000000001e-28

   1. Initial program 95.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.2%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 95.2%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 95.2%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 95.2%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 95.2%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 95.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 95.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 95.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 95.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 95.2%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 81.5%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 81.5%

      \[\leadsto \left(\color{blue}{\left(y - 2\right) \cdot b} + x\right) - \left(t - 1\right) \cdot a \]

   6. Taylor expanded in y around inf 49.1%

      \[\leadsto \color{blue}{y \cdot b} \]

   if 9.80000000000000037e58 < t

   1. Initial program 96.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.3%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 96.3%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 96.3%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 96.3%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 96.3%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 96.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 96.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 96.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 96.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 96.3%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 88.9%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in a around inf 74.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]
   6. Step-by-step derivation

      1. associate-*r* 74.7%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

      2. neg-mul-1 74.7%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   7. Simplified 74.7%

      \[\leadsto \color{blue}{\left(-a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   8. Taylor expanded in t around inf 48.7%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 48.7%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} \]

      2. mul-1-neg 48.7%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t \]

   10. Simplified 48.7%

       \[\leadsto \color{blue}{\left(-a\right) \cdot t} \]
3. Recombined 5 regimes into one program.

4. Final simplification 43.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+41}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-100}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-131}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 1.42 \cdot 10^{-28}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 9.8 \cdot 10^{+58}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \end{array} \]

Alternative 26: 26.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+88}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-27}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-190}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-112}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-77}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.3e+88)
   (* y b)
   (if (<= y -1.9e-27)
     (* t b)
     (if (<= y -2.6e-190)
       a
       (if (<= y 3.2e-112)
         z
         (if (<= y 8.2e-77) (* t b) (if (<= y 1.15e+20) x (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.3e+88) {
		tmp = y * b;
	} else if (y <= -1.9e-27) {
		tmp = t * b;
	} else if (y <= -2.6e-190) {
		tmp = a;
	} else if (y <= 3.2e-112) {
		tmp = z;
	} else if (y <= 8.2e-77) {
		tmp = t * b;
	} else if (y <= 1.15e+20) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.3d+88)) then
        tmp = y * b
    else if (y <= (-1.9d-27)) then
        tmp = t * b
    else if (y <= (-2.6d-190)) then
        tmp = a
    else if (y <= 3.2d-112) then
        tmp = z
    else if (y <= 8.2d-77) then
        tmp = t * b
    else if (y <= 1.15d+20) then
        tmp = x
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.3e+88) {
		tmp = y * b;
	} else if (y <= -1.9e-27) {
		tmp = t * b;
	} else if (y <= -2.6e-190) {
		tmp = a;
	} else if (y <= 3.2e-112) {
		tmp = z;
	} else if (y <= 8.2e-77) {
		tmp = t * b;
	} else if (y <= 1.15e+20) {
		tmp = x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.3e+88:
		tmp = y * b
	elif y <= -1.9e-27:
		tmp = t * b
	elif y <= -2.6e-190:
		tmp = a
	elif y <= 3.2e-112:
		tmp = z
	elif y <= 8.2e-77:
		tmp = t * b
	elif y <= 1.15e+20:
		tmp = x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.3e+88)
		tmp = Float64(y * b);
	elseif (y <= -1.9e-27)
		tmp = Float64(t * b);
	elseif (y <= -2.6e-190)
		tmp = a;
	elseif (y <= 3.2e-112)
		tmp = z;
	elseif (y <= 8.2e-77)
		tmp = Float64(t * b);
	elseif (y <= 1.15e+20)
		tmp = x;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.3e+88)
		tmp = y * b;
	elseif (y <= -1.9e-27)
		tmp = t * b;
	elseif (y <= -2.6e-190)
		tmp = a;
	elseif (y <= 3.2e-112)
		tmp = z;
	elseif (y <= 8.2e-77)
		tmp = t * b;
	elseif (y <= 1.15e+20)
		tmp = x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.3e+88], N[(y * b), $MachinePrecision], If[LessEqual[y, -1.9e-27], N[(t * b), $MachinePrecision], If[LessEqual[y, -2.6e-190], a, If[LessEqual[y, 3.2e-112], z, If[LessEqual[y, 8.2e-77], N[(t * b), $MachinePrecision], If[LessEqual[y, 1.15e+20], x, N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.3e88 or 1.15e20 < y

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 63.8%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 57.0%

      \[\leadsto \left(\color{blue}{\left(y - 2\right) \cdot b} + x\right) - \left(t - 1\right) \cdot a \]

   6. Taylor expanded in y around inf 38.9%

      \[\leadsto \color{blue}{y \cdot b} \]

   if -1.3e88 < y < -1.9e-27 or 3.19999999999999993e-112 < y < 8.19999999999999925e-77

   1. Initial program 96.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 96.4%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 96.4%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 96.4%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 96.4%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 96.4%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 96.4%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 78.9%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in b around inf 50.2%

      \[\leadsto \color{blue}{\left(t - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf 46.3%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -1.9e-27 < y < -2.5999999999999998e-190

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 46.9%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   5. Taylor expanded in t around 0 28.8%

      \[\leadsto \color{blue}{a} \]

   if -2.5999999999999998e-190 < y < 3.19999999999999993e-112

   1. Initial program 96.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 96.9%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 96.9%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 96.9%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 96.9%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 96.9%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 96.9%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 96.9%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in z around inf 29.8%

      \[\leadsto \color{blue}{z} \]

   if 8.19999999999999925e-77 < y < 1.15e20

   1. Initial program 96.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.3%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 96.3%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 96.3%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 96.3%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 96.3%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 96.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 96.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 96.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 96.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 96.3%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in x around inf 24.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+88}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-27}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq -2.6 \cdot 10^{-190}:\\ \;\;\;\;a\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-112}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-77}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 27: 33.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+88}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-18}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-198}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-72}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-42}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+23}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.45e+88)
   (* y b)
   (if (<= y -4.1e-18)
     (* t b)
     (if (<= y 1.52e-198)
       (+ a z)
       (if (<= y 1.1e-72)
         (+ a x)
         (if (<= y 2.55e-42) (+ a z) (if (<= y 2e+23) (+ a x) (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.45e+88) {
		tmp = y * b;
	} else if (y <= -4.1e-18) {
		tmp = t * b;
	} else if (y <= 1.52e-198) {
		tmp = a + z;
	} else if (y <= 1.1e-72) {
		tmp = a + x;
	} else if (y <= 2.55e-42) {
		tmp = a + z;
	} else if (y <= 2e+23) {
		tmp = a + x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.45d+88)) then
        tmp = y * b
    else if (y <= (-4.1d-18)) then
        tmp = t * b
    else if (y <= 1.52d-198) then
        tmp = a + z
    else if (y <= 1.1d-72) then
        tmp = a + x
    else if (y <= 2.55d-42) then
        tmp = a + z
    else if (y <= 2d+23) then
        tmp = a + x
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.45e+88) {
		tmp = y * b;
	} else if (y <= -4.1e-18) {
		tmp = t * b;
	} else if (y <= 1.52e-198) {
		tmp = a + z;
	} else if (y <= 1.1e-72) {
		tmp = a + x;
	} else if (y <= 2.55e-42) {
		tmp = a + z;
	} else if (y <= 2e+23) {
		tmp = a + x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.45e+88:
		tmp = y * b
	elif y <= -4.1e-18:
		tmp = t * b
	elif y <= 1.52e-198:
		tmp = a + z
	elif y <= 1.1e-72:
		tmp = a + x
	elif y <= 2.55e-42:
		tmp = a + z
	elif y <= 2e+23:
		tmp = a + x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.45e+88)
		tmp = Float64(y * b);
	elseif (y <= -4.1e-18)
		tmp = Float64(t * b);
	elseif (y <= 1.52e-198)
		tmp = Float64(a + z);
	elseif (y <= 1.1e-72)
		tmp = Float64(a + x);
	elseif (y <= 2.55e-42)
		tmp = Float64(a + z);
	elseif (y <= 2e+23)
		tmp = Float64(a + x);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.45e+88)
		tmp = y * b;
	elseif (y <= -4.1e-18)
		tmp = t * b;
	elseif (y <= 1.52e-198)
		tmp = a + z;
	elseif (y <= 1.1e-72)
		tmp = a + x;
	elseif (y <= 2.55e-42)
		tmp = a + z;
	elseif (y <= 2e+23)
		tmp = a + x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.45e+88], N[(y * b), $MachinePrecision], If[LessEqual[y, -4.1e-18], N[(t * b), $MachinePrecision], If[LessEqual[y, 1.52e-198], N[(a + z), $MachinePrecision], If[LessEqual[y, 1.1e-72], N[(a + x), $MachinePrecision], If[LessEqual[y, 2.55e-42], N[(a + z), $MachinePrecision], If[LessEqual[y, 2e+23], N[(a + x), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.45e88 or 1.9999999999999998e23 < y

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 63.8%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 57.0%

      \[\leadsto \left(\color{blue}{\left(y - 2\right) \cdot b} + x\right) - \left(t - 1\right) \cdot a \]

   6. Taylor expanded in y around inf 38.9%

      \[\leadsto \color{blue}{y \cdot b} \]

   if -1.45e88 < y < -4.0999999999999998e-18

   1. Initial program 95.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 95.2%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 95.2%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 95.2%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 95.2%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 95.2%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 95.2%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 71.8%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in b around inf 38.3%

      \[\leadsto \color{blue}{\left(t - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf 37.6%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -4.0999999999999998e-18 < y < 1.5199999999999999e-198 or 1.10000000000000001e-72 < y < 2.55e-42

   1. Initial program 97.9%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.9%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 97.9%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 97.9%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 97.9%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 97.9%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 97.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 97.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 97.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 97.9%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 97.9%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 97.9%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in a around inf 67.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]
   6. Step-by-step derivation

      1. associate-*r* 67.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

      2. neg-mul-1 67.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   7. Simplified 67.1%

      \[\leadsto \color{blue}{\left(-a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   8. Taylor expanded in y around 0 67.1%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right) - \left(-1 \cdot z + -1 \cdot a\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 67.1%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(-1 \cdot z + -1 \cdot a\right) \]

      2. mul-1-neg 67.1%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(-1 \cdot z + -1 \cdot a\right) \]

      3. distribute-lft-out 67.1%

         \[\leadsto \left(-a\right) \cdot t - \color{blue}{-1 \cdot \left(z + a\right)} \]

   10. Simplified 67.1%

       \[\leadsto \color{blue}{\left(-a\right) \cdot t - -1 \cdot \left(z + a\right)} \]

   11. Taylor expanded in t around 0 43.2%

       \[\leadsto \color{blue}{a + z} \]

   if 1.5199999999999999e-198 < y < 1.10000000000000001e-72 or 2.55e-42 < y < 1.9999999999999998e23

   1. Initial program 97.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 97.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 97.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 97.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 97.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 97.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 97.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 97.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 97.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 97.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 97.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 64.1%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   6. Taylor expanded in z around 0 52.3%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   7. Step-by-step derivation

      1. sub-neg 52.3%

         \[\leadsto \color{blue}{x + \left(--1 \cdot a\right)} \]

      2. mul-1-neg 52.3%

         \[\leadsto x + \left(-\color{blue}{\left(-a\right)}\right) \]

      3. remove-double-neg 52.3%

         \[\leadsto x + \color{blue}{a} \]

   8. Simplified 52.3%

      \[\leadsto \color{blue}{x + a} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+88}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-18}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{-198}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-72}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 2.55 \cdot 10^{-42}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+23}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 28: 34.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -3.71 \cdot 10^{-96}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-198}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-72}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-43}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+23}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.45e+45)
   (* y (- z))
   (if (<= y -3.71e-96)
     (+ a x)
     (if (<= y 2e-198)
       (+ a z)
       (if (<= y 2.05e-72)
         (+ a x)
         (if (<= y 6e-43) (+ a z) (if (<= y 4.1e+23) (+ a x) (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.45e+45) {
		tmp = y * -z;
	} else if (y <= -3.71e-96) {
		tmp = a + x;
	} else if (y <= 2e-198) {
		tmp = a + z;
	} else if (y <= 2.05e-72) {
		tmp = a + x;
	} else if (y <= 6e-43) {
		tmp = a + z;
	} else if (y <= 4.1e+23) {
		tmp = a + x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.45d+45)) then
        tmp = y * -z
    else if (y <= (-3.71d-96)) then
        tmp = a + x
    else if (y <= 2d-198) then
        tmp = a + z
    else if (y <= 2.05d-72) then
        tmp = a + x
    else if (y <= 6d-43) then
        tmp = a + z
    else if (y <= 4.1d+23) then
        tmp = a + x
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.45e+45) {
		tmp = y * -z;
	} else if (y <= -3.71e-96) {
		tmp = a + x;
	} else if (y <= 2e-198) {
		tmp = a + z;
	} else if (y <= 2.05e-72) {
		tmp = a + x;
	} else if (y <= 6e-43) {
		tmp = a + z;
	} else if (y <= 4.1e+23) {
		tmp = a + x;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.45e+45:
		tmp = y * -z
	elif y <= -3.71e-96:
		tmp = a + x
	elif y <= 2e-198:
		tmp = a + z
	elif y <= 2.05e-72:
		tmp = a + x
	elif y <= 6e-43:
		tmp = a + z
	elif y <= 4.1e+23:
		tmp = a + x
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.45e+45)
		tmp = Float64(y * Float64(-z));
	elseif (y <= -3.71e-96)
		tmp = Float64(a + x);
	elseif (y <= 2e-198)
		tmp = Float64(a + z);
	elseif (y <= 2.05e-72)
		tmp = Float64(a + x);
	elseif (y <= 6e-43)
		tmp = Float64(a + z);
	elseif (y <= 4.1e+23)
		tmp = Float64(a + x);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.45e+45)
		tmp = y * -z;
	elseif (y <= -3.71e-96)
		tmp = a + x;
	elseif (y <= 2e-198)
		tmp = a + z;
	elseif (y <= 2.05e-72)
		tmp = a + x;
	elseif (y <= 6e-43)
		tmp = a + z;
	elseif (y <= 4.1e+23)
		tmp = a + x;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.45e+45], N[(y * (-z)), $MachinePrecision], If[LessEqual[y, -3.71e-96], N[(a + x), $MachinePrecision], If[LessEqual[y, 2e-198], N[(a + z), $MachinePrecision], If[LessEqual[y, 2.05e-72], N[(a + x), $MachinePrecision], If[LessEqual[y, 6e-43], N[(a + z), $MachinePrecision], If[LessEqual[y, 4.1e+23], N[(a + x), $MachinePrecision], N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.4500000000000001e45

   1. Initial program 91.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.2%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.2%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.2%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.2%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.2%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.2%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.2%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in y around inf 74.7%

      \[\leadsto \color{blue}{\left(b - z\right) \cdot y} \]

   5. Taylor expanded in b around 0 49.6%

      \[\leadsto \color{blue}{-1 \cdot \left(y \cdot z\right)} \]
   6. Step-by-step derivation

      1. mul-1-neg 49.6%

         \[\leadsto \color{blue}{-y \cdot z} \]

      2. distribute-rgt-neg-in 49.6%

         \[\leadsto \color{blue}{y \cdot \left(-z\right)} \]

   7. Simplified 49.6%

      \[\leadsto \color{blue}{y \cdot \left(-z\right)} \]

   if -2.4500000000000001e45 < y < -3.70999999999999984e-96 or 1.9999999999999998e-198 < y < 2.05000000000000002e-72 or 6.00000000000000007e-43 < y < 4.09999999999999996e23

   1. Initial program 96.8%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.8%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 96.8%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 96.8%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 96.8%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 96.8%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 96.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 96.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 96.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 96.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 96.8%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 56.6%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   6. Taylor expanded in z around 0 46.6%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   7. Step-by-step derivation

      1. sub-neg 46.6%

         \[\leadsto \color{blue}{x + \left(--1 \cdot a\right)} \]

      2. mul-1-neg 46.6%

         \[\leadsto x + \left(-\color{blue}{\left(-a\right)}\right) \]

      3. remove-double-neg 46.6%

         \[\leadsto x + \color{blue}{a} \]

   8. Simplified 46.6%

      \[\leadsto \color{blue}{x + a} \]

   if -3.70999999999999984e-96 < y < 1.9999999999999998e-198 or 2.05000000000000002e-72 < y < 6.00000000000000007e-43

   1. Initial program 97.5%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 97.5%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 97.5%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 97.5%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 97.5%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 97.5%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 97.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 97.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 97.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 97.5%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 97.5%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 97.5%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in a around inf 70.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]
   6. Step-by-step derivation

      1. associate-*r* 70.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

      2. neg-mul-1 70.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   7. Simplified 70.0%

      \[\leadsto \color{blue}{\left(-a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   8. Taylor expanded in y around 0 70.0%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right) - \left(-1 \cdot z + -1 \cdot a\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 70.0%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(-1 \cdot z + -1 \cdot a\right) \]

      2. mul-1-neg 70.0%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(-1 \cdot z + -1 \cdot a\right) \]

      3. distribute-lft-out 70.0%

         \[\leadsto \left(-a\right) \cdot t - \color{blue}{-1 \cdot \left(z + a\right)} \]

   10. Simplified 70.0%

       \[\leadsto \color{blue}{\left(-a\right) \cdot t - -1 \cdot \left(z + a\right)} \]

   11. Taylor expanded in t around 0 46.4%

       \[\leadsto \color{blue}{a + z} \]

   if 4.09999999999999996e23 < y

   1. Initial program 92.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 92.6%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 92.6%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 92.6%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 92.6%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 92.6%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 92.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 92.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 92.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 92.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 92.6%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 92.6%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 66.3%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 60.2%

      \[\leadsto \left(\color{blue}{\left(y - 2\right) \cdot b} + x\right) - \left(t - 1\right) \cdot a \]

   6. Taylor expanded in y around inf 36.1%

      \[\leadsto \color{blue}{y \cdot b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.45 \cdot 10^{+45}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;y \leq -3.71 \cdot 10^{-96}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-198}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-72}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-43}:\\ \;\;\;\;a + z\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+23}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 29: 43.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-194}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+134}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= z -1.15e+90)
     t_1
     (if (<= z -7.2e-122)
       (* a (- 1.0 t))
       (if (<= z -2.5e-194) (+ a x) (if (<= z 1.4e+134) (* t (- b a)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -1.15e+90) {
		tmp = t_1;
	} else if (z <= -7.2e-122) {
		tmp = a * (1.0 - t);
	} else if (z <= -2.5e-194) {
		tmp = a + x;
	} else if (z <= 1.4e+134) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if (z <= (-1.15d+90)) then
        tmp = t_1
    else if (z <= (-7.2d-122)) then
        tmp = a * (1.0d0 - t)
    else if (z <= (-2.5d-194)) then
        tmp = a + x
    else if (z <= 1.4d+134) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -1.15e+90) {
		tmp = t_1;
	} else if (z <= -7.2e-122) {
		tmp = a * (1.0 - t);
	} else if (z <= -2.5e-194) {
		tmp = a + x;
	} else if (z <= 1.4e+134) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if z <= -1.15e+90:
		tmp = t_1
	elif z <= -7.2e-122:
		tmp = a * (1.0 - t)
	elif z <= -2.5e-194:
		tmp = a + x
	elif z <= 1.4e+134:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -1.15e+90)
		tmp = t_1;
	elseif (z <= -7.2e-122)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (z <= -2.5e-194)
		tmp = Float64(a + x);
	elseif (z <= 1.4e+134)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (z <= -1.15e+90)
		tmp = t_1;
	elseif (z <= -7.2e-122)
		tmp = a * (1.0 - t);
	elseif (z <= -2.5e-194)
		tmp = a + x;
	elseif (z <= 1.4e+134)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+90], t$95$1, If[LessEqual[z, -7.2e-122], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-194], N[(a + x), $MachinePrecision], If[LessEqual[z, 1.4e+134], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.15e90 or 1.3999999999999999e134 < z

   1. Initial program 93.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 93.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 93.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 93.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 93.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 93.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 93.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 93.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 93.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 93.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 93.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 93.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around inf 74.3%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   if -1.15e90 < z < -7.19999999999999989e-122

   1. Initial program 92.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 92.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 92.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 92.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 92.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 92.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 92.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 92.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 92.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 92.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 92.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 92.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 39.0%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   if -7.19999999999999989e-122 < z < -2.5000000000000001e-194

   1. Initial program 100.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 100.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 100.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 100.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 100.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in x around inf 55.2%

      \[\leadsto \color{blue}{x} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   6. Taylor expanded in z around 0 41.2%

      \[\leadsto \color{blue}{x - -1 \cdot a} \]
   7. Step-by-step derivation

      1. sub-neg 41.2%

         \[\leadsto \color{blue}{x + \left(--1 \cdot a\right)} \]

      2. mul-1-neg 41.2%

         \[\leadsto x + \left(-\color{blue}{\left(-a\right)}\right) \]

      3. remove-double-neg 41.2%

         \[\leadsto x + \color{blue}{a} \]

   8. Simplified 41.2%

      \[\leadsto \color{blue}{x + a} \]

   if -2.5000000000000001e-194 < z < 1.3999999999999999e134

   1. Initial program 96.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.4%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 96.4%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 96.4%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 96.4%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 96.4%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 96.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 96.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 96.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 96.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 96.4%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 96.4%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around inf 40.0%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 49.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-122}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-194}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+134}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 30: 33.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+88}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-15}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+14}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -2.2e+88)
   (* y b)
   (if (<= y -8.2e-15) (* t b) (if (<= y 2.1e+14) (+ a z) (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.2e+88) {
		tmp = y * b;
	} else if (y <= -8.2e-15) {
		tmp = t * b;
	} else if (y <= 2.1e+14) {
		tmp = a + z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-2.2d+88)) then
        tmp = y * b
    else if (y <= (-8.2d-15)) then
        tmp = t * b
    else if (y <= 2.1d+14) then
        tmp = a + z
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -2.2e+88) {
		tmp = y * b;
	} else if (y <= -8.2e-15) {
		tmp = t * b;
	} else if (y <= 2.1e+14) {
		tmp = a + z;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -2.2e+88:
		tmp = y * b
	elif y <= -8.2e-15:
		tmp = t * b
	elif y <= 2.1e+14:
		tmp = a + z
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -2.2e+88)
		tmp = Float64(y * b);
	elseif (y <= -8.2e-15)
		tmp = Float64(t * b);
	elseif (y <= 2.1e+14)
		tmp = Float64(a + z);
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -2.2e+88)
		tmp = y * b;
	elseif (y <= -8.2e-15)
		tmp = t * b;
	elseif (y <= 2.1e+14)
		tmp = a + z;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -2.2e+88], N[(y * b), $MachinePrecision], If[LessEqual[y, -8.2e-15], N[(t * b), $MachinePrecision], If[LessEqual[y, 2.1e+14], N[(a + z), $MachinePrecision], N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.20000000000000009e88 or 2.1e14 < y

   1. Initial program 90.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 90.4%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 90.4%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 90.4%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 90.4%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 90.4%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 90.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 90.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 90.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 90.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 90.4%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 90.4%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in z around 0 63.9%

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - \left(t - 1\right) \cdot a} \]

   5. Taylor expanded in t around 0 57.3%

      \[\leadsto \left(\color{blue}{\left(y - 2\right) \cdot b} + x\right) - \left(t - 1\right) \cdot a \]

   6. Taylor expanded in y around inf 37.9%

      \[\leadsto \color{blue}{y \cdot b} \]

   if -2.20000000000000009e88 < y < -8.20000000000000072e-15

   1. Initial program 95.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 95.2%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 95.2%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 95.2%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 95.2%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 95.2%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 95.2%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 100.0%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 100.0%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 71.8%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in b around inf 38.3%

      \[\leadsto \color{blue}{\left(t - 2\right) \cdot b} \]

   6. Taylor expanded in t around inf 37.6%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -8.20000000000000072e-15 < y < 2.1e14

   1. Initial program 98.4%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 98.4%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 98.4%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 98.4%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 98.4%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 98.4%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 98.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 98.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 98.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 98.4%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 98.4%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 98.4%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{\left(t \cdot \left(b - a\right) + \left(\left(y - 2\right) \cdot b + x\right)\right) - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right)} \]

   5. Taylor expanded in a around inf 61.3%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right)} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]
   6. Step-by-step derivation

      1. associate-*r* 61.3%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

      2. neg-mul-1 61.3%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   7. Simplified 61.3%

      \[\leadsto \color{blue}{\left(-a\right) \cdot t} - \left(z \cdot \left(y - 1\right) + -1 \cdot a\right) \]

   8. Taylor expanded in y around 0 61.2%

      \[\leadsto \color{blue}{-1 \cdot \left(a \cdot t\right) - \left(-1 \cdot z + -1 \cdot a\right)} \]
   9. Step-by-step derivation

      1. associate-*r* 61.2%

         \[\leadsto \color{blue}{\left(-1 \cdot a\right) \cdot t} - \left(-1 \cdot z + -1 \cdot a\right) \]

      2. mul-1-neg 61.2%

         \[\leadsto \color{blue}{\left(-a\right)} \cdot t - \left(-1 \cdot z + -1 \cdot a\right) \]

      3. distribute-lft-out 61.2%

         \[\leadsto \left(-a\right) \cdot t - \color{blue}{-1 \cdot \left(z + a\right)} \]

   10. Simplified 61.2%

       \[\leadsto \color{blue}{\left(-a\right) \cdot t - -1 \cdot \left(z + a\right)} \]

   11. Taylor expanded in t around 0 39.7%

       \[\leadsto \color{blue}{a + z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{+88}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-15}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+14}:\\ \;\;\;\;a + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 31: 20.3% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+148}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+144}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.2e+148) x (if (<= x 1.12e+144) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.2e+148) {
		tmp = x;
	} else if (x <= 1.12e+144) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6.2d+148)) then
        tmp = x
    else if (x <= 1.12d+144) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.2e+148) {
		tmp = x;
	} else if (x <= 1.12e+144) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.2e+148:
		tmp = x
	elif x <= 1.12e+144:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.2e+148)
		tmp = x;
	elseif (x <= 1.12e+144)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.2e+148)
		tmp = x;
	elseif (x <= 1.12e+144)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.2e+148], x, If[LessEqual[x, 1.12e+144], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.19999999999999951e148 or 1.11999999999999999e144 < x

   1. Initial program 91.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in x around inf 45.0%

      \[\leadsto \color{blue}{x} \]

   if -6.19999999999999951e148 < x < 1.11999999999999999e144

   1. Initial program 96.3%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 96.3%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 96.3%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 96.3%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 96.3%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 96.3%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 96.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 96.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 96.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 96.3%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 96.3%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 34.1%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   5. Taylor expanded in t around 0 14.2%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{+148}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+144}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 32: 21.7% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+145}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+63}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.6e+145) x (if (<= x 2.85e+63) z x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.6e+145) {
		tmp = x;
	} else if (x <= 2.85e+63) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6.6d+145)) then
        tmp = x
    else if (x <= 2.85d+63) then
        tmp = z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.6e+145) {
		tmp = x;
	} else if (x <= 2.85e+63) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.6e+145:
		tmp = x
	elif x <= 2.85e+63:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.6e+145)
		tmp = x;
	elseif (x <= 2.85e+63)
		tmp = z;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.6e+145)
		tmp = x;
	elseif (x <= 2.85e+63)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.6e+145], x, If[LessEqual[x, 2.85e+63], z, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.60000000000000054e145 or 2.8500000000000001e63 < x

   1. Initial program 92.2%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 92.2%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 92.2%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 92.2%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 92.2%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 92.2%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 92.2%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 92.2%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 92.2%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in x around inf 39.7%

      \[\leadsto \color{blue}{x} \]

   if -6.60000000000000054e145 < x < 2.8500000000000001e63

   1. Initial program 96.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. sub-neg 96.0%

         \[\leadsto \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      2. +-commutative 96.0%

         \[\leadsto \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

      3. associate-+l+ 96.0%

         \[\leadsto \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      4. *-commutative 96.0%

         \[\leadsto \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. distribute-rgt-neg-in 96.0%

         \[\leadsto \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. +-commutative 96.0%

         \[\leadsto a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      7. fma-def 97.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]

      8. neg-sub0 97.2%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      9. associate--r- 97.2%

         \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      10. neg-sub0 97.2%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      11. +-commutative 97.2%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      12. sub-neg 97.2%

          \[\leadsto \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]

      13. fma-def 97.7%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]

      14. sub-neg 97.7%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      15. associate-+l+ 97.7%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]

      16. metadata-eval 97.7%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]

      17. sub-neg 97.7%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]

      18. +-commutative 97.7%

          \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Simplified 97.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(z, 1 - y, x\right)\right)\right)} \]

   4. Taylor expanded in y around 0 67.1%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right) + \left(z + \left(\left(t - 2\right) \cdot b + x\right)\right)} \]

   5. Taylor expanded in z around inf 17.7%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 24.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+145}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{+63}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 33: 10.7% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 94.9%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Step-by-step derivation

   1. associate-+l- 94.9%

      \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

   2. *-commutative 94.9%

      \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   3. *-commutative 94.9%

      \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   4. sub-neg 94.9%

      \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   5. metadata-eval 94.9%

      \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   6. remove-double-neg 94.9%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   7. remove-double-neg 94.9%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   8. sub-neg 94.9%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   9. metadata-eval 94.9%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   10. associate--l+ 94.9%

       \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

3. Simplified 94.9%

   \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

4. Taylor expanded in a around inf 28.9%

   \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

5. Taylor expanded in t around 0 11.6%

   \[\leadsto \color{blue}{a} \]

6. Final simplification 11.6%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023181 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))