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

Percentage Accurate: 95.4% → 97.8%

Time: 15.4s

Alternatives: 24

Speedup: 0.5×

• 36.8% 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: 95.4% 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: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq 8.5 \cdot 10^{+218}:\\ \;\;\;\;\mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b 8.5e+218)
   (fma (+ t (- y 2.0)) b (- x (fma (+ y -1.0) z (* a (+ t -1.0)))))
   (* b (- (+ t y) 2.0))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= 8.5e+218) {
		tmp = fma((t + (y - 2.0)), b, (x - fma((y + -1.0), z, (a * (t + -1.0)))));
	} else {
		tmp = b * ((t + y) - 2.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= 8.5e+218)
		tmp = fma(Float64(t + Float64(y - 2.0)), b, Float64(x - fma(Float64(y + -1.0), z, Float64(a * Float64(t + -1.0)))));
	else
		tmp = Float64(b * Float64(Float64(t + y) - 2.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, 8.5e+218], 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], N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < 8.50000000000000041e218

   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. +-commutative 95.2%

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

      2. fma-def 97.8%

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

      3. +-commutative 97.8%

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

      4. associate--l+ 97.8%

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

      5. sub-neg 97.8%

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

      6. associate-+l- 97.8%

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

      7. fma-neg 99.1%

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

      8. sub-neg 99.1%

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

      9. metadata-eval 99.1%

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

      10. distribute-lft-neg-in 99.1%

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

      11. distribute-lft-neg-in 99.1%

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

      12. remove-double-neg 99.1%

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

      13. sub-neg 99.1%

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

      14. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   if 8.50000000000000041e218 < b

   1. Initial program 76.0%

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

      1. associate-+l- 76.0%

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

      2. *-commutative 76.0%

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

      3. *-commutative 76.0%

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

      4. sub-neg 76.0%

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

      5. metadata-eval 76.0%

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

      6. remove-double-neg 76.0%

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

      7. remove-double-neg 76.0%

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

      8. sub-neg 76.0%

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

      9. metadata-eval 76.0%

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

      10. associate--l+ 76.0%

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

   3. Simplified 76.0%

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

   4. Taylor expanded in b around inf 93.1%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq 8.5 \cdot 10^{+218}:\\ \;\;\;\;\mathsf{fma}\left(t + \left(y - 2\right), b, x - \mathsf{fma}\left(y + -1, z, a \cdot \left(t + -1\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 2: 98.1% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] + N[(N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(t * N[(b - a), $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 76.7%

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

4. Final simplification 98.4%

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

Alternative 3: 56.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(y + -1\right) \cdot z\\ t_2 := a \cdot \left(1 - t\right)\\ t_3 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -2.95 \cdot 10^{+60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-268}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-211}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+124}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+145}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* (+ y -1.0) z)))
        (t_2 (* a (- 1.0 t)))
        (t_3 (* b (- (+ t y) 2.0))))
   (if (<= b -2.95e+60)
     t_3
     (if (<= b -6.5e-277)
       t_1
       (if (<= b 8e-268)
         (- a (* t a))
         (if (<= b 5.8e-211)
           t_1
           (if (<= b 1.7e-163)
             t_2
             (if (<= b 3.4e-22)
               t_1
               (if (<= b 6.2e+89)
                 (* y (- b z))
                 (if (<= b 2.1e+124)
                   (* b (- t 2.0))
                   (if (<= b 6.6e+145) t_2 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((y + -1.0) * z);
	double t_2 = a * (1.0 - t);
	double t_3 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.95e+60) {
		tmp = t_3;
	} else if (b <= -6.5e-277) {
		tmp = t_1;
	} else if (b <= 8e-268) {
		tmp = a - (t * a);
	} else if (b <= 5.8e-211) {
		tmp = t_1;
	} else if (b <= 1.7e-163) {
		tmp = t_2;
	} else if (b <= 3.4e-22) {
		tmp = t_1;
	} else if (b <= 6.2e+89) {
		tmp = y * (b - z);
	} else if (b <= 2.1e+124) {
		tmp = b * (t - 2.0);
	} else if (b <= 6.6e+145) {
		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 = x - ((y + (-1.0d0)) * z)
    t_2 = a * (1.0d0 - t)
    t_3 = b * ((t + y) - 2.0d0)
    if (b <= (-2.95d+60)) then
        tmp = t_3
    else if (b <= (-6.5d-277)) then
        tmp = t_1
    else if (b <= 8d-268) then
        tmp = a - (t * a)
    else if (b <= 5.8d-211) then
        tmp = t_1
    else if (b <= 1.7d-163) then
        tmp = t_2
    else if (b <= 3.4d-22) then
        tmp = t_1
    else if (b <= 6.2d+89) then
        tmp = y * (b - z)
    else if (b <= 2.1d+124) then
        tmp = b * (t - 2.0d0)
    else if (b <= 6.6d+145) 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 = x - ((y + -1.0) * z);
	double t_2 = a * (1.0 - t);
	double t_3 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -2.95e+60) {
		tmp = t_3;
	} else if (b <= -6.5e-277) {
		tmp = t_1;
	} else if (b <= 8e-268) {
		tmp = a - (t * a);
	} else if (b <= 5.8e-211) {
		tmp = t_1;
	} else if (b <= 1.7e-163) {
		tmp = t_2;
	} else if (b <= 3.4e-22) {
		tmp = t_1;
	} else if (b <= 6.2e+89) {
		tmp = y * (b - z);
	} else if (b <= 2.1e+124) {
		tmp = b * (t - 2.0);
	} else if (b <= 6.6e+145) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((y + -1.0) * z)
	t_2 = a * (1.0 - t)
	t_3 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -2.95e+60:
		tmp = t_3
	elif b <= -6.5e-277:
		tmp = t_1
	elif b <= 8e-268:
		tmp = a - (t * a)
	elif b <= 5.8e-211:
		tmp = t_1
	elif b <= 1.7e-163:
		tmp = t_2
	elif b <= 3.4e-22:
		tmp = t_1
	elif b <= 6.2e+89:
		tmp = y * (b - z)
	elif b <= 2.1e+124:
		tmp = b * (t - 2.0)
	elif b <= 6.6e+145:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(y + -1.0) * z))
	t_2 = Float64(a * Float64(1.0 - t))
	t_3 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -2.95e+60)
		tmp = t_3;
	elseif (b <= -6.5e-277)
		tmp = t_1;
	elseif (b <= 8e-268)
		tmp = Float64(a - Float64(t * a));
	elseif (b <= 5.8e-211)
		tmp = t_1;
	elseif (b <= 1.7e-163)
		tmp = t_2;
	elseif (b <= 3.4e-22)
		tmp = t_1;
	elseif (b <= 6.2e+89)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= 2.1e+124)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (b <= 6.6e+145)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((y + -1.0) * z);
	t_2 = a * (1.0 - t);
	t_3 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -2.95e+60)
		tmp = t_3;
	elseif (b <= -6.5e-277)
		tmp = t_1;
	elseif (b <= 8e-268)
		tmp = a - (t * a);
	elseif (b <= 5.8e-211)
		tmp = t_1;
	elseif (b <= 1.7e-163)
		tmp = t_2;
	elseif (b <= 3.4e-22)
		tmp = t_1;
	elseif (b <= 6.2e+89)
		tmp = y * (b - z);
	elseif (b <= 2.1e+124)
		tmp = b * (t - 2.0);
	elseif (b <= 6.6e+145)
		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[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2.95e+60], t$95$3, If[LessEqual[b, -6.5e-277], t$95$1, If[LessEqual[b, 8e-268], N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.8e-211], t$95$1, If[LessEqual[b, 1.7e-163], t$95$2, If[LessEqual[b, 3.4e-22], t$95$1, If[LessEqual[b, 6.2e+89], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.1e+124], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.6e+145], t$95$2, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -2.9500000000000001e60 or 6.60000000000000054e145 < b

   1. Initial program 87.4%

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

      1. associate-+l- 87.4%

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

      2. *-commutative 87.4%

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

      3. *-commutative 87.4%

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

      4. sub-neg 87.4%

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

      5. metadata-eval 87.4%

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

      6. remove-double-neg 87.4%

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

      7. remove-double-neg 87.4%

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

      8. sub-neg 87.4%

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

      9. metadata-eval 87.4%

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

      10. associate--l+ 87.4%

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

   3. Simplified 87.4%

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

   4. Taylor expanded in b around inf 81.2%

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

   if -2.9500000000000001e60 < b < -6.49999999999999961e-277 or 7.99999999999999966e-268 < b < 5.80000000000000029e-211 or 1.70000000000000007e-163 < b < 3.3999999999999998e-22

   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 a around inf 88.2%

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

      1. sub-neg 88.2%

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

      2. metadata-eval 88.2%

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

      3. *-commutative 88.2%

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

      4. distribute-lft-in 88.2%

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

      5. *-commutative 88.2%

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

      6. mul-1-neg 88.2%

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

      7. unsub-neg 88.2%

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

   6. Simplified 88.2%

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

   7. Taylor expanded in a around 0 64.4%

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

   if -6.49999999999999961e-277 < b < 7.99999999999999966e-268

   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 t around 0 100.0%

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

   5. Taylor expanded in a around inf 68.4%

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

      1. distribute-lft-out-- 68.4%

         \[\leadsto \color{blue}{a \cdot 1 - a \cdot t} \]

      2. *-rgt-identity 68.4%

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

      3. *-commutative 68.4%

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

   7. Simplified 68.4%

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

   if 5.80000000000000029e-211 < b < 1.70000000000000007e-163 or 2.10000000000000011e124 < b < 6.60000000000000054e145

   1. Initial program 81.8%

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

      1. associate-+l- 81.8%

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

      2. *-commutative 81.8%

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

      3. *-commutative 81.8%

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

      4. sub-neg 81.8%

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

      5. metadata-eval 81.8%

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

      6. remove-double-neg 81.8%

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

      7. remove-double-neg 81.8%

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

      8. sub-neg 81.8%

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

      9. metadata-eval 81.8%

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

      10. associate--l+ 81.8%

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

   3. Simplified 81.8%

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

   4. Taylor expanded in a around inf 84.8%

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

   if 3.3999999999999998e-22 < b < 6.2e89

   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 y around inf 61.8%

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

   if 6.2e89 < b < 2.10000000000000011e124

   1. Initial program 87.5%

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

      1. associate-+l- 87.5%

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

      2. *-commutative 87.5%

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

      3. *-commutative 87.5%

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

      4. sub-neg 87.5%

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

      5. metadata-eval 87.5%

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

      6. remove-double-neg 87.5%

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

      7. remove-double-neg 87.5%

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

      8. sub-neg 87.5%

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

      9. metadata-eval 87.5%

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

      10. associate--l+ 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in b around inf 50.7%

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

   5. Taylor expanded in y around 0 50.7%

      \[\leadsto \color{blue}{b \cdot \left(t - 2\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 71.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.95 \cdot 10^{+60}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-277}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-268}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-211}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 3.4 \cdot 10^{-22}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+89}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 2.1 \cdot 10^{+124}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq 6.6 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 4: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := \left(b \cdot y + \left(x + b \cdot \left(t - 2\right)\right)\right) + a \cdot \left(1 - t\right)\\ t_3 := x - \left(y + -1\right) \cdot z\\ \mathbf{if}\;t \leq -4.1 \cdot 10^{+192}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -90000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;t_3 + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+71}:\\ \;\;\;\;b \cdot y + t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a)))
        (t_2 (+ (+ (* b y) (+ x (* b (- t 2.0)))) (* a (- 1.0 t))))
        (t_3 (- x (* (+ y -1.0) z))))
   (if (<= t -4.1e+192)
     t_1
     (if (<= t -90000000000.0)
       t_2
       (if (<= t 2.2e-12)
         (+ t_3 (- a (* b (- 2.0 y))))
         (if (<= t 2.6e+58) t_2 (if (<= t 9.5e+71) (+ (* b y) t_3) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = ((b * y) + (x + (b * (t - 2.0)))) + (a * (1.0 - t));
	double t_3 = x - ((y + -1.0) * z);
	double tmp;
	if (t <= -4.1e+192) {
		tmp = t_1;
	} else if (t <= -90000000000.0) {
		tmp = t_2;
	} else if (t <= 2.2e-12) {
		tmp = t_3 + (a - (b * (2.0 - y)));
	} else if (t <= 2.6e+58) {
		tmp = t_2;
	} else if (t <= 9.5e+71) {
		tmp = (b * y) + t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = ((b * y) + (x + (b * (t - 2.0d0)))) + (a * (1.0d0 - t))
    t_3 = x - ((y + (-1.0d0)) * z)
    if (t <= (-4.1d+192)) then
        tmp = t_1
    else if (t <= (-90000000000.0d0)) then
        tmp = t_2
    else if (t <= 2.2d-12) then
        tmp = t_3 + (a - (b * (2.0d0 - y)))
    else if (t <= 2.6d+58) then
        tmp = t_2
    else if (t <= 9.5d+71) then
        tmp = (b * y) + t_3
    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 t_2 = ((b * y) + (x + (b * (t - 2.0)))) + (a * (1.0 - t));
	double t_3 = x - ((y + -1.0) * z);
	double tmp;
	if (t <= -4.1e+192) {
		tmp = t_1;
	} else if (t <= -90000000000.0) {
		tmp = t_2;
	} else if (t <= 2.2e-12) {
		tmp = t_3 + (a - (b * (2.0 - y)));
	} else if (t <= 2.6e+58) {
		tmp = t_2;
	} else if (t <= 9.5e+71) {
		tmp = (b * y) + t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = ((b * y) + (x + (b * (t - 2.0)))) + (a * (1.0 - t))
	t_3 = x - ((y + -1.0) * z)
	tmp = 0
	if t <= -4.1e+192:
		tmp = t_1
	elif t <= -90000000000.0:
		tmp = t_2
	elif t <= 2.2e-12:
		tmp = t_3 + (a - (b * (2.0 - y)))
	elif t <= 2.6e+58:
		tmp = t_2
	elif t <= 9.5e+71:
		tmp = (b * y) + t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(Float64(Float64(b * y) + Float64(x + Float64(b * Float64(t - 2.0)))) + Float64(a * Float64(1.0 - t)))
	t_3 = Float64(x - Float64(Float64(y + -1.0) * z))
	tmp = 0.0
	if (t <= -4.1e+192)
		tmp = t_1;
	elseif (t <= -90000000000.0)
		tmp = t_2;
	elseif (t <= 2.2e-12)
		tmp = Float64(t_3 + Float64(a - Float64(b * Float64(2.0 - y))));
	elseif (t <= 2.6e+58)
		tmp = t_2;
	elseif (t <= 9.5e+71)
		tmp = Float64(Float64(b * y) + t_3);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = ((b * y) + (x + (b * (t - 2.0)))) + (a * (1.0 - t));
	t_3 = x - ((y + -1.0) * z);
	tmp = 0.0;
	if (t <= -4.1e+192)
		tmp = t_1;
	elseif (t <= -90000000000.0)
		tmp = t_2;
	elseif (t <= 2.2e-12)
		tmp = t_3 + (a - (b * (2.0 - y)));
	elseif (t <= 2.6e+58)
		tmp = t_2;
	elseif (t <= 9.5e+71)
		tmp = (b * y) + t_3;
	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]}, Block[{t$95$2 = N[(N[(N[(b * y), $MachinePrecision] + N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.1e+192], t$95$1, If[LessEqual[t, -90000000000.0], t$95$2, If[LessEqual[t, 2.2e-12], N[(t$95$3 + N[(a - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.6e+58], t$95$2, If[LessEqual[t, 9.5e+71], N[(N[(b * y), $MachinePrecision] + t$95$3), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.10000000000000003e192 or 9.50000000000000015e71 < t

   1. Initial program 80.3%

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

      1. associate-+l- 80.3%

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

      2. *-commutative 80.3%

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

      3. *-commutative 80.3%

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

      4. sub-neg 80.3%

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

      5. metadata-eval 80.3%

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

      6. remove-double-neg 80.3%

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

      7. remove-double-neg 80.3%

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

      8. sub-neg 80.3%

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

      9. metadata-eval 80.3%

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

      10. associate--l+ 80.3%

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

   3. Simplified 80.3%

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

   4. Taylor expanded in t around inf 87.5%

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

   if -4.10000000000000003e192 < t < -9e10 or 2.19999999999999992e-12 < t < 2.59999999999999988e58

   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 98.0%

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

   5. Taylor expanded in z around 0 91.8%

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

   if -9e10 < t < 2.19999999999999992e-12

   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 97.1%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(-1 \cdot a - \left(y - 2\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. sub-neg 97.1%

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

      2. +-commutative 97.1%

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

      3. mul-1-neg 97.1%

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

      4. unsub-neg 97.1%

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

      5. *-commutative 97.1%

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

      6. distribute-rgt-neg-in 97.1%

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

      7. sub-neg 97.1%

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

      8. metadata-eval 97.1%

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

      9. +-commutative 97.1%

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

      10. distribute-neg-in 97.1%

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

      11. metadata-eval 97.1%

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

      12. sub-neg 97.1%

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

   6. Simplified 97.1%

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

   if 2.59999999999999988e58 < t < 9.50000000000000015e71

   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 100.0%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{-1 \cdot \left(y \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 100.0%

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

      2. distribute-rgt-neg-in 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 93.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{+192}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -90000000000:\\ \;\;\;\;\left(b \cdot y + \left(x + b \cdot \left(t - 2\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + \left(a - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{+58}:\\ \;\;\;\;\left(b \cdot y + \left(x + b \cdot \left(t - 2\right)\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{+71}:\\ \;\;\;\;b \cdot y + \left(x - \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 5: 49.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -4.8 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-238}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{-252}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-211}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-22}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))))
   (if (<= b -4.8e+48)
     t_1
     (if (<= b -1.45e-238)
       (+ x z)
       (if (<= b 2.95e-252)
         (- a (* t a))
         (if (<= b 3.6e-211)
           (* z (- 1.0 y))
           (if (<= b 1.6e-163)
             (* a (- 1.0 t))
             (if (<= b 2.3e-22)
               (- x (* y z))
               (if (<= b 1.55e+88)
                 (* y (- b z))
                 (if (<= b 9.5e+128) (* t (- b a)) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -4.8e+48) {
		tmp = t_1;
	} else if (b <= -1.45e-238) {
		tmp = x + z;
	} else if (b <= 2.95e-252) {
		tmp = a - (t * a);
	} else if (b <= 3.6e-211) {
		tmp = z * (1.0 - y);
	} else if (b <= 1.6e-163) {
		tmp = a * (1.0 - t);
	} else if (b <= 2.3e-22) {
		tmp = x - (y * z);
	} else if (b <= 1.55e+88) {
		tmp = y * (b - z);
	} else if (b <= 9.5e+128) {
		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 = b * ((t + y) - 2.0d0)
    if (b <= (-4.8d+48)) then
        tmp = t_1
    else if (b <= (-1.45d-238)) then
        tmp = x + z
    else if (b <= 2.95d-252) then
        tmp = a - (t * a)
    else if (b <= 3.6d-211) then
        tmp = z * (1.0d0 - y)
    else if (b <= 1.6d-163) then
        tmp = a * (1.0d0 - t)
    else if (b <= 2.3d-22) then
        tmp = x - (y * z)
    else if (b <= 1.55d+88) then
        tmp = y * (b - z)
    else if (b <= 9.5d+128) 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 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -4.8e+48) {
		tmp = t_1;
	} else if (b <= -1.45e-238) {
		tmp = x + z;
	} else if (b <= 2.95e-252) {
		tmp = a - (t * a);
	} else if (b <= 3.6e-211) {
		tmp = z * (1.0 - y);
	} else if (b <= 1.6e-163) {
		tmp = a * (1.0 - t);
	} else if (b <= 2.3e-22) {
		tmp = x - (y * z);
	} else if (b <= 1.55e+88) {
		tmp = y * (b - z);
	} else if (b <= 9.5e+128) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -4.8e+48:
		tmp = t_1
	elif b <= -1.45e-238:
		tmp = x + z
	elif b <= 2.95e-252:
		tmp = a - (t * a)
	elif b <= 3.6e-211:
		tmp = z * (1.0 - y)
	elif b <= 1.6e-163:
		tmp = a * (1.0 - t)
	elif b <= 2.3e-22:
		tmp = x - (y * z)
	elif b <= 1.55e+88:
		tmp = y * (b - z)
	elif b <= 9.5e+128:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -4.8e+48)
		tmp = t_1;
	elseif (b <= -1.45e-238)
		tmp = Float64(x + z);
	elseif (b <= 2.95e-252)
		tmp = Float64(a - Float64(t * a));
	elseif (b <= 3.6e-211)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 1.6e-163)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 2.3e-22)
		tmp = Float64(x - Float64(y * z));
	elseif (b <= 1.55e+88)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= 9.5e+128)
		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 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -4.8e+48)
		tmp = t_1;
	elseif (b <= -1.45e-238)
		tmp = x + z;
	elseif (b <= 2.95e-252)
		tmp = a - (t * a);
	elseif (b <= 3.6e-211)
		tmp = z * (1.0 - y);
	elseif (b <= 1.6e-163)
		tmp = a * (1.0 - t);
	elseif (b <= 2.3e-22)
		tmp = x - (y * z);
	elseif (b <= 1.55e+88)
		tmp = y * (b - z);
	elseif (b <= 9.5e+128)
		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[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -4.8e+48], t$95$1, If[LessEqual[b, -1.45e-238], N[(x + z), $MachinePrecision], If[LessEqual[b, 2.95e-252], N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.6e-211], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.6e-163], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e-22], N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e+88], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9.5e+128], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if b < -4.8000000000000002e48 or 9.50000000000000014e128 < b

   1. Initial program 87.5%

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

      1. associate-+l- 87.5%

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

      2. *-commutative 87.5%

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

      3. *-commutative 87.5%

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

      4. sub-neg 87.5%

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

      5. metadata-eval 87.5%

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

      6. remove-double-neg 87.5%

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

      7. remove-double-neg 87.5%

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

      8. sub-neg 87.5%

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

      9. metadata-eval 87.5%

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

      10. associate--l+ 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in b around inf 80.4%

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

   if -4.8000000000000002e48 < b < -1.4499999999999999e-238

   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 a around inf 87.7%

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

      1. sub-neg 87.7%

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

      2. metadata-eval 87.7%

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

      3. *-commutative 87.7%

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

      4. distribute-lft-in 87.7%

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

      5. *-commutative 87.7%

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

      6. mul-1-neg 87.7%

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

      7. unsub-neg 87.7%

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

   6. Simplified 87.7%

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

   7. Taylor expanded in a around 0 59.8%

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

   8. Taylor expanded in y around 0 46.0%

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

      1. cancel-sign-sub-inv 46.0%

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

      2. metadata-eval 46.0%

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity 46.0%

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

   10. Simplified 46.0%

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

   if -1.4499999999999999e-238 < b < 2.9499999999999998e-252

   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 t around 0 100.0%

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

   5. Taylor expanded in a around inf 60.9%

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

      1. distribute-lft-out-- 61.0%

         \[\leadsto \color{blue}{a \cdot 1 - a \cdot t} \]

      2. *-rgt-identity 61.0%

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

      3. *-commutative 61.0%

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

   7. Simplified 61.0%

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

   if 2.9499999999999998e-252 < b < 3.5999999999999999e-211

   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 inf 73.2%

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

   if 3.5999999999999999e-211 < b < 1.59999999999999994e-163

   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 76.1%

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

   if 1.59999999999999994e-163 < b < 2.2999999999999998e-22

   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 79.1%

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

      1. sub-neg 79.1%

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

      2. metadata-eval 79.1%

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

      3. *-commutative 79.1%

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

      4. distribute-lft-in 79.1%

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

      5. *-commutative 79.1%

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

      6. mul-1-neg 79.1%

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

      7. unsub-neg 79.1%

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

   6. Simplified 79.1%

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

   7. Taylor expanded in a around 0 68.1%

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

   8. Taylor expanded in y around inf 68.0%

      \[\leadsto x - \color{blue}{y \cdot z} \]

   if 2.2999999999999998e-22 < b < 1.5500000000000001e88

   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 y around inf 61.8%

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

   if 1.5500000000000001e88 < b < 9.50000000000000014e128

   1. Initial program 72.7%

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

      1. associate-+l- 72.7%

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

      2. *-commutative 72.7%

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

      3. *-commutative 72.7%

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

      4. sub-neg 72.7%

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

      5. metadata-eval 72.7%

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

      6. remove-double-neg 72.7%

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

      7. remove-double-neg 72.7%

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

      8. sub-neg 72.7%

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

      9. metadata-eval 72.7%

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

      10. associate--l+ 72.7%

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

   3. Simplified 72.7%

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

   4. Taylor expanded in t around inf 56.1%

      \[\leadsto \color{blue}{t \cdot \left(b - a\right)} \]
3. Recombined 8 regimes into one program.

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.8 \cdot 10^{+48}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq -1.45 \cdot 10^{-238}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 2.95 \cdot 10^{-252}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-211}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{-163}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{-22}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+88}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 9.5 \cdot 10^{+128}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 6: 59.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + a\right) - t \cdot a\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ t_3 := x - \left(y + -1\right) \cdot z\\ \mathbf{if}\;b \leq -7000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-211}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 7.9 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+123}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- (+ x a) (* t a)))
        (t_2 (* b (- (+ t y) 2.0)))
        (t_3 (- x (* (+ y -1.0) z))))
   (if (<= b -7000.0)
     t_2
     (if (<= b 2.6e-247)
       t_1
       (if (<= b 3e-211)
         t_3
         (if (<= b 7.9e-150)
           t_1
           (if (<= b 9e-23)
             t_3
             (if (<= b 6.2e+91)
               (* y (- b z))
               (if (<= b 8e+123)
                 (* b (- t 2.0))
                 (if (<= b 6.2e+145) (* a (- 1.0 t)) t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + a) - (t * a);
	double t_2 = b * ((t + y) - 2.0);
	double t_3 = x - ((y + -1.0) * z);
	double tmp;
	if (b <= -7000.0) {
		tmp = t_2;
	} else if (b <= 2.6e-247) {
		tmp = t_1;
	} else if (b <= 3e-211) {
		tmp = t_3;
	} else if (b <= 7.9e-150) {
		tmp = t_1;
	} else if (b <= 9e-23) {
		tmp = t_3;
	} else if (b <= 6.2e+91) {
		tmp = y * (b - z);
	} else if (b <= 8e+123) {
		tmp = b * (t - 2.0);
	} else if (b <= 6.2e+145) {
		tmp = a * (1.0 - 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) :: t_3
    real(8) :: tmp
    t_1 = (x + a) - (t * a)
    t_2 = b * ((t + y) - 2.0d0)
    t_3 = x - ((y + (-1.0d0)) * z)
    if (b <= (-7000.0d0)) then
        tmp = t_2
    else if (b <= 2.6d-247) then
        tmp = t_1
    else if (b <= 3d-211) then
        tmp = t_3
    else if (b <= 7.9d-150) then
        tmp = t_1
    else if (b <= 9d-23) then
        tmp = t_3
    else if (b <= 6.2d+91) then
        tmp = y * (b - z)
    else if (b <= 8d+123) then
        tmp = b * (t - 2.0d0)
    else if (b <= 6.2d+145) then
        tmp = a * (1.0d0 - 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 + a) - (t * a);
	double t_2 = b * ((t + y) - 2.0);
	double t_3 = x - ((y + -1.0) * z);
	double tmp;
	if (b <= -7000.0) {
		tmp = t_2;
	} else if (b <= 2.6e-247) {
		tmp = t_1;
	} else if (b <= 3e-211) {
		tmp = t_3;
	} else if (b <= 7.9e-150) {
		tmp = t_1;
	} else if (b <= 9e-23) {
		tmp = t_3;
	} else if (b <= 6.2e+91) {
		tmp = y * (b - z);
	} else if (b <= 8e+123) {
		tmp = b * (t - 2.0);
	} else if (b <= 6.2e+145) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + a) - (t * a)
	t_2 = b * ((t + y) - 2.0)
	t_3 = x - ((y + -1.0) * z)
	tmp = 0
	if b <= -7000.0:
		tmp = t_2
	elif b <= 2.6e-247:
		tmp = t_1
	elif b <= 3e-211:
		tmp = t_3
	elif b <= 7.9e-150:
		tmp = t_1
	elif b <= 9e-23:
		tmp = t_3
	elif b <= 6.2e+91:
		tmp = y * (b - z)
	elif b <= 8e+123:
		tmp = b * (t - 2.0)
	elif b <= 6.2e+145:
		tmp = a * (1.0 - t)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + a) - Float64(t * a))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	t_3 = Float64(x - Float64(Float64(y + -1.0) * z))
	tmp = 0.0
	if (b <= -7000.0)
		tmp = t_2;
	elseif (b <= 2.6e-247)
		tmp = t_1;
	elseif (b <= 3e-211)
		tmp = t_3;
	elseif (b <= 7.9e-150)
		tmp = t_1;
	elseif (b <= 9e-23)
		tmp = t_3;
	elseif (b <= 6.2e+91)
		tmp = Float64(y * Float64(b - z));
	elseif (b <= 8e+123)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (b <= 6.2e+145)
		tmp = Float64(a * Float64(1.0 - t));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + a) - (t * a);
	t_2 = b * ((t + y) - 2.0);
	t_3 = x - ((y + -1.0) * z);
	tmp = 0.0;
	if (b <= -7000.0)
		tmp = t_2;
	elseif (b <= 2.6e-247)
		tmp = t_1;
	elseif (b <= 3e-211)
		tmp = t_3;
	elseif (b <= 7.9e-150)
		tmp = t_1;
	elseif (b <= 9e-23)
		tmp = t_3;
	elseif (b <= 6.2e+91)
		tmp = y * (b - z);
	elseif (b <= 8e+123)
		tmp = b * (t - 2.0);
	elseif (b <= 6.2e+145)
		tmp = a * (1.0 - t);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + a), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7000.0], t$95$2, If[LessEqual[b, 2.6e-247], t$95$1, If[LessEqual[b, 3e-211], t$95$3, If[LessEqual[b, 7.9e-150], t$95$1, If[LessEqual[b, 9e-23], t$95$3, If[LessEqual[b, 6.2e+91], N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 8e+123], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 6.2e+145], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if b < -7e3 or 6.19999999999999977e145 < b

   1. Initial program 88.3%

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

      1. associate-+l- 88.3%

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

      2. *-commutative 88.3%

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

      3. *-commutative 88.3%

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

      4. sub-neg 88.3%

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

      5. metadata-eval 88.3%

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

      6. remove-double-neg 88.3%

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

      7. remove-double-neg 88.3%

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

      8. sub-neg 88.3%

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

      9. metadata-eval 88.3%

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

      10. associate--l+ 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in b around inf 77.1%

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

   if -7e3 < b < 2.6e-247 or 3.00000000000000005e-211 < b < 7.9e-150

   1. Initial program 98.8%

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

      1. associate-+l- 98.8%

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

      2. *-commutative 98.8%

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

      3. *-commutative 98.8%

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

      4. sub-neg 98.8%

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

      5. metadata-eval 98.8%

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

      6. remove-double-neg 98.8%

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

      7. remove-double-neg 98.8%

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

      8. sub-neg 98.8%

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

      9. metadata-eval 98.8%

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

      10. associate--l+ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in a around inf 93.3%

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

      1. sub-neg 93.3%

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

      2. metadata-eval 93.3%

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

      3. *-commutative 93.3%

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

      4. distribute-lft-in 93.3%

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

      5. *-commutative 93.3%

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

      6. mul-1-neg 93.3%

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

      7. unsub-neg 93.3%

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

   6. Simplified 93.3%

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

   7. Taylor expanded in z around 0 73.9%

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

      1. *-commutative 73.9%

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

   9. Simplified 73.9%

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

   if 2.6e-247 < b < 3.00000000000000005e-211 or 7.9e-150 < b < 8.9999999999999995e-23

   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 86.1%

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

      1. sub-neg 86.1%

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

      2. metadata-eval 86.1%

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

      3. *-commutative 86.1%

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

      4. distribute-lft-in 86.1%

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

      5. *-commutative 86.1%

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

      6. mul-1-neg 86.1%

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

      7. unsub-neg 86.1%

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

   6. Simplified 86.1%

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

   7. Taylor expanded in a around 0 77.3%

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

   if 8.9999999999999995e-23 < b < 6.19999999999999995e91

   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 y around inf 61.8%

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

   if 6.19999999999999995e91 < b < 7.99999999999999982e123

   1. Initial program 87.5%

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

      1. associate-+l- 87.5%

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

      2. *-commutative 87.5%

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

      3. *-commutative 87.5%

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

      4. sub-neg 87.5%

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

      5. metadata-eval 87.5%

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

      6. remove-double-neg 87.5%

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

      7. remove-double-neg 87.5%

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

      8. sub-neg 87.5%

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

      9. metadata-eval 87.5%

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

      10. associate--l+ 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in b around inf 50.7%

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

   5. Taylor expanded in y around 0 50.7%

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

   if 7.99999999999999982e123 < b < 6.19999999999999977e145

   1. Initial program 50.0%

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

      1. associate-+l- 50.0%

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

      2. *-commutative 50.0%

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

      3. *-commutative 50.0%

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

      4. sub-neg 50.0%

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

      5. metadata-eval 50.0%

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

      6. remove-double-neg 50.0%

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

      7. remove-double-neg 50.0%

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

      8. sub-neg 50.0%

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

      9. metadata-eval 50.0%

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

      10. associate--l+ 50.0%

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

   3. Simplified 50.0%

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

   4. Taylor expanded in a around inf 100.0%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]
3. Recombined 6 regimes into one program.

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7000:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-247}:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \mathbf{elif}\;b \leq 3 \cdot 10^{-211}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 7.9 \cdot 10^{-150}:\\ \;\;\;\;\left(x + a\right) - t \cdot a\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-23}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+91}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{+123}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+145}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 7: 35.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(t - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -8.6 \cdot 10^{+257}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+220}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-239}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{-265}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-223}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-148}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- t 2.0))) (t_2 (* a (- 1.0 t))))
   (if (<= b -8.6e+257)
     t_1
     (if (<= b -5.5e+220)
       (* b y)
       (if (<= b -1.9e+68)
         t_1
         (if (<= b -9.2e-239)
           (+ x z)
           (if (<= b 1.08e-265)
             t_2
             (if (<= b 6e-223)
               (+ x z)
               (if (<= b 3.3e-148)
                 t_2
                 (if (<= b 8.2e+87) (* y (- z)) t_1))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (b <= -8.6e+257) {
		tmp = t_1;
	} else if (b <= -5.5e+220) {
		tmp = b * y;
	} else if (b <= -1.9e+68) {
		tmp = t_1;
	} else if (b <= -9.2e-239) {
		tmp = x + z;
	} else if (b <= 1.08e-265) {
		tmp = t_2;
	} else if (b <= 6e-223) {
		tmp = x + z;
	} else if (b <= 3.3e-148) {
		tmp = t_2;
	} else if (b <= 8.2e+87) {
		tmp = y * -z;
	} 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) :: t_2
    real(8) :: tmp
    t_1 = b * (t - 2.0d0)
    t_2 = a * (1.0d0 - t)
    if (b <= (-8.6d+257)) then
        tmp = t_1
    else if (b <= (-5.5d+220)) then
        tmp = b * y
    else if (b <= (-1.9d+68)) then
        tmp = t_1
    else if (b <= (-9.2d-239)) then
        tmp = x + z
    else if (b <= 1.08d-265) then
        tmp = t_2
    else if (b <= 6d-223) then
        tmp = x + z
    else if (b <= 3.3d-148) then
        tmp = t_2
    else if (b <= 8.2d+87) then
        tmp = y * -z
    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 = b * (t - 2.0);
	double t_2 = a * (1.0 - t);
	double tmp;
	if (b <= -8.6e+257) {
		tmp = t_1;
	} else if (b <= -5.5e+220) {
		tmp = b * y;
	} else if (b <= -1.9e+68) {
		tmp = t_1;
	} else if (b <= -9.2e-239) {
		tmp = x + z;
	} else if (b <= 1.08e-265) {
		tmp = t_2;
	} else if (b <= 6e-223) {
		tmp = x + z;
	} else if (b <= 3.3e-148) {
		tmp = t_2;
	} else if (b <= 8.2e+87) {
		tmp = y * -z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * (t - 2.0)
	t_2 = a * (1.0 - t)
	tmp = 0
	if b <= -8.6e+257:
		tmp = t_1
	elif b <= -5.5e+220:
		tmp = b * y
	elif b <= -1.9e+68:
		tmp = t_1
	elif b <= -9.2e-239:
		tmp = x + z
	elif b <= 1.08e-265:
		tmp = t_2
	elif b <= 6e-223:
		tmp = x + z
	elif b <= 3.3e-148:
		tmp = t_2
	elif b <= 8.2e+87:
		tmp = y * -z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(t - 2.0))
	t_2 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -8.6e+257)
		tmp = t_1;
	elseif (b <= -5.5e+220)
		tmp = Float64(b * y);
	elseif (b <= -1.9e+68)
		tmp = t_1;
	elseif (b <= -9.2e-239)
		tmp = Float64(x + z);
	elseif (b <= 1.08e-265)
		tmp = t_2;
	elseif (b <= 6e-223)
		tmp = Float64(x + z);
	elseif (b <= 3.3e-148)
		tmp = t_2;
	elseif (b <= 8.2e+87)
		tmp = Float64(y * Float64(-z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * (t - 2.0);
	t_2 = a * (1.0 - t);
	tmp = 0.0;
	if (b <= -8.6e+257)
		tmp = t_1;
	elseif (b <= -5.5e+220)
		tmp = b * y;
	elseif (b <= -1.9e+68)
		tmp = t_1;
	elseif (b <= -9.2e-239)
		tmp = x + z;
	elseif (b <= 1.08e-265)
		tmp = t_2;
	elseif (b <= 6e-223)
		tmp = x + z;
	elseif (b <= 3.3e-148)
		tmp = t_2;
	elseif (b <= 8.2e+87)
		tmp = y * -z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -8.6e+257], t$95$1, If[LessEqual[b, -5.5e+220], N[(b * y), $MachinePrecision], If[LessEqual[b, -1.9e+68], t$95$1, If[LessEqual[b, -9.2e-239], N[(x + z), $MachinePrecision], If[LessEqual[b, 1.08e-265], t$95$2, If[LessEqual[b, 6e-223], N[(x + z), $MachinePrecision], If[LessEqual[b, 3.3e-148], t$95$2, If[LessEqual[b, 8.2e+87], N[(y * (-z)), $MachinePrecision], t$95$1]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -8.5999999999999996e257 or -5.4999999999999999e220 < b < -1.9e68 or 8.1999999999999998e87 < b

   1. Initial program 85.7%

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

      1. associate-+l- 85.7%

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

      2. *-commutative 85.7%

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

      3. *-commutative 85.7%

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

      4. sub-neg 85.7%

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

      5. metadata-eval 85.7%

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

      6. remove-double-neg 85.7%

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

      7. remove-double-neg 85.7%

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

      8. sub-neg 85.7%

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

      9. metadata-eval 85.7%

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

      10. associate--l+ 85.7%

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

   3. Simplified 85.7%

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

   4. Taylor expanded in b around inf 75.8%

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

   5. Taylor expanded in y around 0 61.7%

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

   if -8.5999999999999996e257 < b < -5.4999999999999999e220

   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 100.0%

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

   5. Taylor expanded in z around 0 100.0%

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

   6. Taylor expanded in y around inf 85.8%

      \[\leadsto \color{blue}{y \cdot b} \]

   if -1.9e68 < b < -9.1999999999999995e-239 or 1.07999999999999998e-265 < b < 5.99999999999999983e-223

   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 a around inf 88.4%

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

      1. sub-neg 88.4%

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

      2. metadata-eval 88.4%

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

      3. *-commutative 88.4%

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

      4. distribute-lft-in 88.4%

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

      5. *-commutative 88.4%

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

      6. mul-1-neg 88.4%

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

      7. unsub-neg 88.4%

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

   6. Simplified 88.4%

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

   7. Taylor expanded in a around 0 62.2%

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

   8. Taylor expanded in y around 0 47.6%

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

      1. cancel-sign-sub-inv 47.6%

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

      2. metadata-eval 47.6%

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity 47.6%

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

   10. Simplified 47.6%

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

   if -9.1999999999999995e-239 < b < 1.07999999999999998e-265 or 5.99999999999999983e-223 < b < 3.29999999999999974e-148

   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 56.3%

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

   if 3.29999999999999974e-148 < b < 8.1999999999999998e87

   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 a around inf 71.8%

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

      1. sub-neg 71.8%

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

      2. metadata-eval 71.8%

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

      3. *-commutative 71.8%

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

      4. distribute-lft-in 71.8%

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

      5. *-commutative 71.8%

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

      6. mul-1-neg 71.8%

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

      7. unsub-neg 71.8%

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

   6. Simplified 71.8%

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

   7. Taylor expanded in a around 0 56.0%

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

   8. Taylor expanded in y around inf 38.1%

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

      1. associate-*r* 38.1%

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

      2. mul-1-neg 38.1%

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

   10. Simplified 38.1%

       \[\leadsto \color{blue}{\left(-y\right) \cdot z} \]
3. Recombined 5 regimes into one program.

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -8.6 \cdot 10^{+257}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -5.5 \cdot 10^{+220}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-239}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.08 \cdot 10^{-265}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-223}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 3.3 \cdot 10^{-148}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+87}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \end{array} \]

Alternative 8: 50.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-189}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-292}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-191}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 650000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+57}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -2.3e+85)
     t_2
     (if (<= t -2.9e-77)
       t_1
       (if (<= t -1.35e-189)
         (+ x z)
         (if (<= t -1.85e-292)
           t_1
           (if (<= t 8.2e-191)
             (+ x z)
             (if (<= t 650000.0)
               t_1
               (if (<= t 1.55e+57) (+ x z) (if (<= t 7.8e+72) t_1 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.3e+85) {
		tmp = t_2;
	} else if (t <= -2.9e-77) {
		tmp = t_1;
	} else if (t <= -1.35e-189) {
		tmp = x + z;
	} else if (t <= -1.85e-292) {
		tmp = t_1;
	} else if (t <= 8.2e-191) {
		tmp = x + z;
	} else if (t <= 650000.0) {
		tmp = t_1;
	} else if (t <= 1.55e+57) {
		tmp = x + z;
	} else if (t <= 7.8e+72) {
		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 = y * (b - z)
    t_2 = t * (b - a)
    if (t <= (-2.3d+85)) then
        tmp = t_2
    else if (t <= (-2.9d-77)) then
        tmp = t_1
    else if (t <= (-1.35d-189)) then
        tmp = x + z
    else if (t <= (-1.85d-292)) then
        tmp = t_1
    else if (t <= 8.2d-191) then
        tmp = x + z
    else if (t <= 650000.0d0) then
        tmp = t_1
    else if (t <= 1.55d+57) then
        tmp = x + z
    else if (t <= 7.8d+72) 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 = y * (b - z);
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -2.3e+85) {
		tmp = t_2;
	} else if (t <= -2.9e-77) {
		tmp = t_1;
	} else if (t <= -1.35e-189) {
		tmp = x + z;
	} else if (t <= -1.85e-292) {
		tmp = t_1;
	} else if (t <= 8.2e-191) {
		tmp = x + z;
	} else if (t <= 650000.0) {
		tmp = t_1;
	} else if (t <= 1.55e+57) {
		tmp = x + z;
	} else if (t <= 7.8e+72) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	t_2 = t * (b - a)
	tmp = 0
	if t <= -2.3e+85:
		tmp = t_2
	elif t <= -2.9e-77:
		tmp = t_1
	elif t <= -1.35e-189:
		tmp = x + z
	elif t <= -1.85e-292:
		tmp = t_1
	elif t <= 8.2e-191:
		tmp = x + z
	elif t <= 650000.0:
		tmp = t_1
	elif t <= 1.55e+57:
		tmp = x + z
	elif t <= 7.8e+72:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2.3e+85)
		tmp = t_2;
	elseif (t <= -2.9e-77)
		tmp = t_1;
	elseif (t <= -1.35e-189)
		tmp = Float64(x + z);
	elseif (t <= -1.85e-292)
		tmp = t_1;
	elseif (t <= 8.2e-191)
		tmp = Float64(x + z);
	elseif (t <= 650000.0)
		tmp = t_1;
	elseif (t <= 1.55e+57)
		tmp = Float64(x + z);
	elseif (t <= 7.8e+72)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -2.3e+85)
		tmp = t_2;
	elseif (t <= -2.9e-77)
		tmp = t_1;
	elseif (t <= -1.35e-189)
		tmp = x + z;
	elseif (t <= -1.85e-292)
		tmp = t_1;
	elseif (t <= 8.2e-191)
		tmp = x + z;
	elseif (t <= 650000.0)
		tmp = t_1;
	elseif (t <= 1.55e+57)
		tmp = x + z;
	elseif (t <= 7.8e+72)
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.3e+85], t$95$2, If[LessEqual[t, -2.9e-77], t$95$1, If[LessEqual[t, -1.35e-189], N[(x + z), $MachinePrecision], If[LessEqual[t, -1.85e-292], t$95$1, If[LessEqual[t, 8.2e-191], N[(x + z), $MachinePrecision], If[LessEqual[t, 650000.0], t$95$1, If[LessEqual[t, 1.55e+57], N[(x + z), $MachinePrecision], If[LessEqual[t, 7.8e+72], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.2999999999999999e85 or 7.79999999999999984e72 < t

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. *-commutative 85.3%

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

      3. *-commutative 85.3%

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

      4. sub-neg 85.3%

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

      5. metadata-eval 85.3%

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

      6. remove-double-neg 85.3%

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

      7. remove-double-neg 85.3%

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

      8. sub-neg 85.3%

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

      9. metadata-eval 85.3%

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

      10. associate--l+ 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in t around inf 85.5%

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

   if -2.2999999999999999e85 < t < -2.8999999999999999e-77 or -1.35e-189 < t < -1.84999999999999998e-292 or 8.2000000000000004e-191 < t < 6.5e5 or 1.55000000000000007e57 < t < 7.79999999999999984e72

   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 y around inf 50.5%

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

   if -2.8999999999999999e-77 < t < -1.35e-189 or -1.84999999999999998e-292 < t < 8.2000000000000004e-191 or 6.5e5 < t < 1.55000000000000007e57

   1. Initial program 97.0%

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

      1. associate-+l- 97.0%

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

      2. *-commutative 97.0%

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

      3. *-commutative 97.0%

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

      4. sub-neg 97.0%

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

      5. metadata-eval 97.0%

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

      6. remove-double-neg 97.0%

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

      7. remove-double-neg 97.0%

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

      8. sub-neg 97.0%

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

      9. metadata-eval 97.0%

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

      10. associate--l+ 97.0%

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

   3. Simplified 97.0%

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

   4. Taylor expanded in a around inf 80.1%

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

      1. sub-neg 80.1%

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

      2. metadata-eval 80.1%

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

      3. *-commutative 80.1%

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

      4. distribute-lft-in 80.1%

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

      5. *-commutative 80.1%

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

      6. mul-1-neg 80.1%

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

      7. unsub-neg 80.1%

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

   6. Simplified 80.1%

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

   7. Taylor expanded in a around 0 56.3%

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

   8. Taylor expanded in y around 0 45.9%

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

      1. cancel-sign-sub-inv 45.9%

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

      2. metadata-eval 45.9%

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity 45.9%

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

   10. Simplified 45.9%

       \[\leadsto \color{blue}{x + z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.3 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-77}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-189}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-292}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-191}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 650000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+57}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{+72}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 9: 65.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x + z\right) + \left(a - t \cdot a\right)\\ \mathbf{if}\;b \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-58}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+18} \lor \neg \left(b \leq 2 \cdot 10^{+149}\right):\\ \;\;\;\;b \cdot y + \left(x + b \cdot \left(t - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x z) (- a (* t a)))))
   (if (<= b -1.9e+68)
     (* b (- (+ t y) 2.0))
     (if (<= b 5.5e-150)
       t_1
       (if (<= b 2e-58)
         (- x (* (+ y -1.0) z))
         (if (or (<= b 4.4e+18) (not (<= b 2e+149)))
           (+ (* b y) (+ x (* b (- t 2.0))))
           t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + z) + (a - (t * a));
	double tmp;
	if (b <= -1.9e+68) {
		tmp = b * ((t + y) - 2.0);
	} else if (b <= 5.5e-150) {
		tmp = t_1;
	} else if (b <= 2e-58) {
		tmp = x - ((y + -1.0) * z);
	} else if ((b <= 4.4e+18) || !(b <= 2e+149)) {
		tmp = (b * y) + (x + (b * (t - 2.0)));
	} 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 + z) + (a - (t * a))
    if (b <= (-1.9d+68)) then
        tmp = b * ((t + y) - 2.0d0)
    else if (b <= 5.5d-150) then
        tmp = t_1
    else if (b <= 2d-58) then
        tmp = x - ((y + (-1.0d0)) * z)
    else if ((b <= 4.4d+18) .or. (.not. (b <= 2d+149))) then
        tmp = (b * y) + (x + (b * (t - 2.0d0)))
    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 + z) + (a - (t * a));
	double tmp;
	if (b <= -1.9e+68) {
		tmp = b * ((t + y) - 2.0);
	} else if (b <= 5.5e-150) {
		tmp = t_1;
	} else if (b <= 2e-58) {
		tmp = x - ((y + -1.0) * z);
	} else if ((b <= 4.4e+18) || !(b <= 2e+149)) {
		tmp = (b * y) + (x + (b * (t - 2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (x + z) + (a - (t * a))
	tmp = 0
	if b <= -1.9e+68:
		tmp = b * ((t + y) - 2.0)
	elif b <= 5.5e-150:
		tmp = t_1
	elif b <= 2e-58:
		tmp = x - ((y + -1.0) * z)
	elif (b <= 4.4e+18) or not (b <= 2e+149):
		tmp = (b * y) + (x + (b * (t - 2.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + z) + Float64(a - Float64(t * a)))
	tmp = 0.0
	if (b <= -1.9e+68)
		tmp = Float64(b * Float64(Float64(t + y) - 2.0));
	elseif (b <= 5.5e-150)
		tmp = t_1;
	elseif (b <= 2e-58)
		tmp = Float64(x - Float64(Float64(y + -1.0) * z));
	elseif ((b <= 4.4e+18) || !(b <= 2e+149))
		tmp = Float64(Float64(b * y) + Float64(x + Float64(b * Float64(t - 2.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + z) + (a - (t * a));
	tmp = 0.0;
	if (b <= -1.9e+68)
		tmp = b * ((t + y) - 2.0);
	elseif (b <= 5.5e-150)
		tmp = t_1;
	elseif (b <= 2e-58)
		tmp = x - ((y + -1.0) * z);
	elseif ((b <= 4.4e+18) || ~((b <= 2e+149)))
		tmp = (b * y) + (x + (b * (t - 2.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + z), $MachinePrecision] + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.9e+68], N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.5e-150], t$95$1, If[LessEqual[b, 2e-58], N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 4.4e+18], N[Not[LessEqual[b, 2e+149]], $MachinePrecision]], N[(N[(b * y), $MachinePrecision] + N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.9e68

   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 b around inf 82.4%

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

   if -1.9e68 < b < 5.4999999999999996e-150 or 4.4e18 < b < 2.0000000000000001e149

   1. Initial program 95.6%

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

      1. associate-+l- 95.6%

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

      2. *-commutative 95.6%

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

      3. *-commutative 95.6%

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

      4. sub-neg 95.6%

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

      5. metadata-eval 95.6%

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

      6. remove-double-neg 95.6%

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

      7. remove-double-neg 95.6%

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

      8. sub-neg 95.6%

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

      9. metadata-eval 95.6%

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

      10. associate--l+ 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in a around inf 86.2%

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

      1. sub-neg 86.2%

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

      2. metadata-eval 86.2%

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

      3. *-commutative 86.2%

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

      4. distribute-lft-in 86.2%

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

      5. *-commutative 86.2%

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

      6. mul-1-neg 86.2%

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

      7. unsub-neg 86.2%

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

   6. Simplified 86.2%

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

   7. Taylor expanded in y around 0 74.7%

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

      1. cancel-sign-sub-inv 74.7%

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

      2. metadata-eval 74.7%

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

      3. *-lft-identity 74.7%

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

      4. +-commutative 74.7%

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

   9. Simplified 74.7%

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

   if 5.4999999999999996e-150 < b < 2.0000000000000001e-58

   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 93.9%

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

      1. sub-neg 93.9%

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

      2. metadata-eval 93.9%

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

      3. *-commutative 93.9%

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

      4. distribute-lft-in 93.9%

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

      5. *-commutative 93.9%

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

      6. mul-1-neg 93.9%

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

      7. unsub-neg 93.9%

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

   6. Simplified 93.9%

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

   7. Taylor expanded in a around 0 87.4%

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

   if 2.0000000000000001e-58 < b < 4.4e18 or 2.0000000000000001e149 < b

   1. Initial program 80.4%

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

      1. associate-+l- 80.4%

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

      2. *-commutative 80.4%

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

      3. *-commutative 80.4%

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

      4. sub-neg 80.4%

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

      5. metadata-eval 80.4%

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

      6. remove-double-neg 80.4%

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

      7. remove-double-neg 80.4%

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

      8. sub-neg 80.4%

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

      9. metadata-eval 80.4%

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

      10. associate--l+ 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in y around inf 78.4%

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

   5. Taylor expanded in z around 0 80.5%

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

   6. Taylor expanded in a around 0 82.4%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 5.5 \cdot 10^{-150}:\\ \;\;\;\;\left(x + z\right) + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-58}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{elif}\;b \leq 4.4 \cdot 10^{+18} \lor \neg \left(b \leq 2 \cdot 10^{+149}\right):\\ \;\;\;\;b \cdot y + \left(x + b \cdot \left(t - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + \left(a - t \cdot a\right)\\ \end{array} \]

Alternative 10: 83.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+85} \lor \neg \left(t \leq 2.4 \cdot 10^{+72}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + \left(a - b \cdot \left(2 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= t -5.2e+85) (not (<= t 2.4e+72)))
   (* t (- b a))
   (+ (- x (* (+ y -1.0) z)) (- a (* b (- 2.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((t <= -5.2e+85) || !(t <= 2.4e+72)) {
		tmp = t * (b - a);
	} else {
		tmp = (x - ((y + -1.0) * z)) + (a - (b * (2.0 - y)));
	}
	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 <= (-5.2d+85)) .or. (.not. (t <= 2.4d+72))) then
        tmp = t * (b - a)
    else
        tmp = (x - ((y + (-1.0d0)) * z)) + (a - (b * (2.0d0 - y)))
    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 <= -5.2e+85) || !(t <= 2.4e+72)) {
		tmp = t * (b - a);
	} else {
		tmp = (x - ((y + -1.0) * z)) + (a - (b * (2.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (t <= -5.2e+85) or not (t <= 2.4e+72):
		tmp = t * (b - a)
	else:
		tmp = (x - ((y + -1.0) * z)) + (a - (b * (2.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((t <= -5.2e+85) || !(t <= 2.4e+72))
		tmp = Float64(t * Float64(b - a));
	else
		tmp = Float64(Float64(x - Float64(Float64(y + -1.0) * z)) + Float64(a - Float64(b * Float64(2.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((t <= -5.2e+85) || ~((t <= 2.4e+72)))
		tmp = t * (b - a);
	else
		tmp = (x - ((y + -1.0) * z)) + (a - (b * (2.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[t, -5.2e+85], N[Not[LessEqual[t, 2.4e+72]], $MachinePrecision]], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(a - N[(b * N[(2.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -5.20000000000000021e85 or 2.4000000000000001e72 < t

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. *-commutative 85.3%

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

      3. *-commutative 85.3%

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

      4. sub-neg 85.3%

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

      5. metadata-eval 85.3%

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

      6. remove-double-neg 85.3%

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

      7. remove-double-neg 85.3%

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

      8. sub-neg 85.3%

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

      9. metadata-eval 85.3%

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

      10. associate--l+ 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in t around inf 85.5%

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

   if -5.20000000000000021e85 < t < 2.4000000000000001e72

   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 91.9%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{\left(-1 \cdot a - \left(y - 2\right) \cdot b\right)} \]
   5. Step-by-step derivation

      1. sub-neg 91.9%

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

      2. +-commutative 91.9%

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

      3. mul-1-neg 91.9%

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

      4. unsub-neg 91.9%

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

      5. *-commutative 91.9%

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

      6. distribute-rgt-neg-in 91.9%

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

      7. sub-neg 91.9%

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

      8. metadata-eval 91.9%

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

      9. +-commutative 91.9%

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

      10. distribute-neg-in 91.9%

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

      11. metadata-eval 91.9%

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

      12. sub-neg 91.9%

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

   6. Simplified 91.9%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.2 \cdot 10^{+85} \lor \neg \left(t \leq 2.4 \cdot 10^{+72}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + \left(a - b \cdot \left(2 - y\right)\right)\\ \end{array} \]

Alternative 11: 47.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-107}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-70}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 470000:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 10^{+70}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -2.7e-12)
     t_1
     (if (<= t 9e-107)
       (+ x z)
       (if (<= t 5.6e-70)
         (* b y)
         (if (<= t 1.02e-14)
           (* z (- 1.0 y))
           (if (<= t 470000.0) (* b y) (if (<= t 1e+70) (+ x z) 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 <= -2.7e-12) {
		tmp = t_1;
	} else if (t <= 9e-107) {
		tmp = x + z;
	} else if (t <= 5.6e-70) {
		tmp = b * y;
	} else if (t <= 1.02e-14) {
		tmp = z * (1.0 - y);
	} else if (t <= 470000.0) {
		tmp = b * y;
	} else if (t <= 1e+70) {
		tmp = x + z;
	} 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 <= (-2.7d-12)) then
        tmp = t_1
    else if (t <= 9d-107) then
        tmp = x + z
    else if (t <= 5.6d-70) then
        tmp = b * y
    else if (t <= 1.02d-14) then
        tmp = z * (1.0d0 - y)
    else if (t <= 470000.0d0) then
        tmp = b * y
    else if (t <= 1d+70) then
        tmp = x + z
    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 <= -2.7e-12) {
		tmp = t_1;
	} else if (t <= 9e-107) {
		tmp = x + z;
	} else if (t <= 5.6e-70) {
		tmp = b * y;
	} else if (t <= 1.02e-14) {
		tmp = z * (1.0 - y);
	} else if (t <= 470000.0) {
		tmp = b * y;
	} else if (t <= 1e+70) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -2.7e-12:
		tmp = t_1
	elif t <= 9e-107:
		tmp = x + z
	elif t <= 5.6e-70:
		tmp = b * y
	elif t <= 1.02e-14:
		tmp = z * (1.0 - y)
	elif t <= 470000.0:
		tmp = b * y
	elif t <= 1e+70:
		tmp = x + z
	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 <= -2.7e-12)
		tmp = t_1;
	elseif (t <= 9e-107)
		tmp = Float64(x + z);
	elseif (t <= 5.6e-70)
		tmp = Float64(b * y);
	elseif (t <= 1.02e-14)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= 470000.0)
		tmp = Float64(b * y);
	elseif (t <= 1e+70)
		tmp = Float64(x + z);
	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 <= -2.7e-12)
		tmp = t_1;
	elseif (t <= 9e-107)
		tmp = x + z;
	elseif (t <= 5.6e-70)
		tmp = b * y;
	elseif (t <= 1.02e-14)
		tmp = z * (1.0 - y);
	elseif (t <= 470000.0)
		tmp = b * y;
	elseif (t <= 1e+70)
		tmp = x + z;
	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, -2.7e-12], t$95$1, If[LessEqual[t, 9e-107], N[(x + z), $MachinePrecision], If[LessEqual[t, 5.6e-70], N[(b * y), $MachinePrecision], If[LessEqual[t, 1.02e-14], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 470000.0], N[(b * y), $MachinePrecision], If[LessEqual[t, 1e+70], N[(x + z), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.6999999999999998e-12 or 1.00000000000000007e70 < t

   1. Initial program 87.6%

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

      1. associate-+l- 87.6%

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

      2. *-commutative 87.6%

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

      3. *-commutative 87.6%

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

      4. sub-neg 87.6%

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

      5. metadata-eval 87.6%

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

      6. remove-double-neg 87.6%

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

      7. remove-double-neg 87.6%

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

      8. sub-neg 87.6%

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

      9. metadata-eval 87.6%

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

      10. associate--l+ 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in t around inf 75.4%

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

   if -2.6999999999999998e-12 < t < 9.00000000000000032e-107 or 4.7e5 < t < 1.00000000000000007e70

   1. Initial program 97.4%

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

      1. associate-+l- 97.4%

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

      2. *-commutative 97.4%

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

      3. *-commutative 97.4%

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

      4. sub-neg 97.4%

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

      5. metadata-eval 97.4%

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

      6. remove-double-neg 97.4%

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

      7. remove-double-neg 97.4%

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

      8. sub-neg 97.4%

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

      9. metadata-eval 97.4%

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

      10. associate--l+ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in a around inf 74.7%

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

      1. sub-neg 74.7%

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

      2. metadata-eval 74.7%

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

      3. *-commutative 74.7%

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

      4. distribute-lft-in 74.7%

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

      5. *-commutative 74.7%

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

      6. mul-1-neg 74.7%

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

      7. unsub-neg 74.7%

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

   6. Simplified 74.7%

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

   7. Taylor expanded in a around 0 54.9%

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

   8. Taylor expanded in y around 0 37.5%

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

      1. cancel-sign-sub-inv 37.5%

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

      2. metadata-eval 37.5%

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity 37.5%

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

   10. Simplified 37.5%

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

   if 9.00000000000000032e-107 < t < 5.5999999999999998e-70 or 1.02e-14 < t < 4.7e5

   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 y around inf 100.0%

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

   5. Taylor expanded in z around 0 94.3%

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

   6. Taylor expanded in y around inf 57.1%

      \[\leadsto \color{blue}{y \cdot b} \]

   if 5.5999999999999998e-70 < t < 1.02e-14

   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 inf 59.7%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 9 \cdot 10^{-107}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 5.6 \cdot 10^{-70}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-14}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 470000:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 10^{+70}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 12: 51.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - y \cdot z\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.7 \cdot 10^{+85}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-241}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 660000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (* y z))) (t_2 (* y (- b z))) (t_3 (* t (- b a))))
   (if (<= t -3.7e+85)
     t_3
     (if (<= t -1.25e-187)
       t_1
       (if (<= t -3.4e-241)
         t_2
         (if (<= t 2e-106)
           t_1
           (if (<= t 660000.0) t_2 (if (<= t 1.3e+72) t_1 t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - (y * z);
	double t_2 = y * (b - z);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -3.7e+85) {
		tmp = t_3;
	} else if (t <= -1.25e-187) {
		tmp = t_1;
	} else if (t <= -3.4e-241) {
		tmp = t_2;
	} else if (t <= 2e-106) {
		tmp = t_1;
	} else if (t <= 660000.0) {
		tmp = t_2;
	} else if (t <= 1.3e+72) {
		tmp = t_1;
	} 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 = x - (y * z)
    t_2 = y * (b - z)
    t_3 = t * (b - a)
    if (t <= (-3.7d+85)) then
        tmp = t_3
    else if (t <= (-1.25d-187)) then
        tmp = t_1
    else if (t <= (-3.4d-241)) then
        tmp = t_2
    else if (t <= 2d-106) then
        tmp = t_1
    else if (t <= 660000.0d0) then
        tmp = t_2
    else if (t <= 1.3d+72) then
        tmp = t_1
    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 = x - (y * z);
	double t_2 = y * (b - z);
	double t_3 = t * (b - a);
	double tmp;
	if (t <= -3.7e+85) {
		tmp = t_3;
	} else if (t <= -1.25e-187) {
		tmp = t_1;
	} else if (t <= -3.4e-241) {
		tmp = t_2;
	} else if (t <= 2e-106) {
		tmp = t_1;
	} else if (t <= 660000.0) {
		tmp = t_2;
	} else if (t <= 1.3e+72) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - (y * z)
	t_2 = y * (b - z)
	t_3 = t * (b - a)
	tmp = 0
	if t <= -3.7e+85:
		tmp = t_3
	elif t <= -1.25e-187:
		tmp = t_1
	elif t <= -3.4e-241:
		tmp = t_2
	elif t <= 2e-106:
		tmp = t_1
	elif t <= 660000.0:
		tmp = t_2
	elif t <= 1.3e+72:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(y * z))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -3.7e+85)
		tmp = t_3;
	elseif (t <= -1.25e-187)
		tmp = t_1;
	elseif (t <= -3.4e-241)
		tmp = t_2;
	elseif (t <= 2e-106)
		tmp = t_1;
	elseif (t <= 660000.0)
		tmp = t_2;
	elseif (t <= 1.3e+72)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - (y * z);
	t_2 = y * (b - z);
	t_3 = t * (b - a);
	tmp = 0.0;
	if (t <= -3.7e+85)
		tmp = t_3;
	elseif (t <= -1.25e-187)
		tmp = t_1;
	elseif (t <= -3.4e-241)
		tmp = t_2;
	elseif (t <= 2e-106)
		tmp = t_1;
	elseif (t <= 660000.0)
		tmp = t_2;
	elseif (t <= 1.3e+72)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -3.7e+85], t$95$3, If[LessEqual[t, -1.25e-187], t$95$1, If[LessEqual[t, -3.4e-241], t$95$2, If[LessEqual[t, 2e-106], t$95$1, If[LessEqual[t, 660000.0], t$95$2, If[LessEqual[t, 1.3e+72], t$95$1, t$95$3]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.7000000000000002e85 or 1.29999999999999991e72 < t

   1. Initial program 85.3%

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

      1. associate-+l- 85.3%

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

      2. *-commutative 85.3%

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

      3. *-commutative 85.3%

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

      4. sub-neg 85.3%

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

      5. metadata-eval 85.3%

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

      6. remove-double-neg 85.3%

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

      7. remove-double-neg 85.3%

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

      8. sub-neg 85.3%

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

      9. metadata-eval 85.3%

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

      10. associate--l+ 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in t around inf 85.5%

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

   if -3.7000000000000002e85 < t < -1.2499999999999999e-187 or -3.3999999999999999e-241 < t < 1.99999999999999988e-106 or 6.6e5 < t < 1.29999999999999991e72

   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 a around inf 74.4%

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

      1. sub-neg 74.4%

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

      2. metadata-eval 74.4%

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

      3. *-commutative 74.4%

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

      4. distribute-lft-in 74.5%

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

      5. *-commutative 74.5%

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

      6. mul-1-neg 74.5%

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

      7. unsub-neg 74.5%

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

   6. Simplified 74.5%

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

   7. Taylor expanded in a around 0 54.9%

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

   8. Taylor expanded in y around inf 43.2%

      \[\leadsto x - \color{blue}{y \cdot z} \]

   if -1.2499999999999999e-187 < t < -3.3999999999999999e-241 or 1.99999999999999988e-106 < t < 6.6e5

   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 56.3%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+85}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-187}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-241}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-106}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 660000:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{+72}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 13: 68.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-163}:\\ \;\;\;\;\left(x + z\right) + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+87}:\\ \;\;\;\;b \cdot y + \left(x - \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot y + \left(x + b \cdot \left(t - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.9e+68)
   (* b (- (+ t y) 2.0))
   (if (<= b 1.7e-163)
     (+ (+ x z) (- a (* t a)))
     (if (<= b 3.7e+87)
       (+ (* b y) (- x (* (+ y -1.0) z)))
       (+ (* b y) (+ x (* b (- t 2.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.9e+68) {
		tmp = b * ((t + y) - 2.0);
	} else if (b <= 1.7e-163) {
		tmp = (x + z) + (a - (t * a));
	} else if (b <= 3.7e+87) {
		tmp = (b * y) + (x - ((y + -1.0) * z));
	} else {
		tmp = (b * y) + (x + (b * (t - 2.0)));
	}
	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 <= (-1.9d+68)) then
        tmp = b * ((t + y) - 2.0d0)
    else if (b <= 1.7d-163) then
        tmp = (x + z) + (a - (t * a))
    else if (b <= 3.7d+87) then
        tmp = (b * y) + (x - ((y + (-1.0d0)) * z))
    else
        tmp = (b * y) + (x + (b * (t - 2.0d0)))
    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 <= -1.9e+68) {
		tmp = b * ((t + y) - 2.0);
	} else if (b <= 1.7e-163) {
		tmp = (x + z) + (a - (t * a));
	} else if (b <= 3.7e+87) {
		tmp = (b * y) + (x - ((y + -1.0) * z));
	} else {
		tmp = (b * y) + (x + (b * (t - 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.9e+68:
		tmp = b * ((t + y) - 2.0)
	elif b <= 1.7e-163:
		tmp = (x + z) + (a - (t * a))
	elif b <= 3.7e+87:
		tmp = (b * y) + (x - ((y + -1.0) * z))
	else:
		tmp = (b * y) + (x + (b * (t - 2.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.9e+68)
		tmp = Float64(b * Float64(Float64(t + y) - 2.0));
	elseif (b <= 1.7e-163)
		tmp = Float64(Float64(x + z) + Float64(a - Float64(t * a)));
	elseif (b <= 3.7e+87)
		tmp = Float64(Float64(b * y) + Float64(x - Float64(Float64(y + -1.0) * z)));
	else
		tmp = Float64(Float64(b * y) + Float64(x + Float64(b * Float64(t - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.9e+68)
		tmp = b * ((t + y) - 2.0);
	elseif (b <= 1.7e-163)
		tmp = (x + z) + (a - (t * a));
	elseif (b <= 3.7e+87)
		tmp = (b * y) + (x - ((y + -1.0) * z));
	else
		tmp = (b * y) + (x + (b * (t - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.9e+68], N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.7e-163], N[(N[(x + z), $MachinePrecision] + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 3.7e+87], N[(N[(b * y), $MachinePrecision] + N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * y), $MachinePrecision] + N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.9e68

   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 b around inf 82.4%

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

   if -1.9e68 < b < 1.70000000000000007e-163

   1. Initial program 98.0%

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

      1. associate-+l- 98.0%

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

      2. *-commutative 98.0%

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

      3. *-commutative 98.0%

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

      4. sub-neg 98.0%

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

      5. metadata-eval 98.0%

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

      6. remove-double-neg 98.0%

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

      7. remove-double-neg 98.0%

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

      8. sub-neg 98.0%

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

      9. metadata-eval 98.0%

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

      10. associate--l+ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in a around inf 92.5%

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

      1. sub-neg 92.5%

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

      2. metadata-eval 92.5%

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

      3. *-commutative 92.5%

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

      4. distribute-lft-in 92.6%

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

      5. *-commutative 92.6%

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

      6. mul-1-neg 92.6%

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

      7. unsub-neg 92.6%

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

   6. Simplified 92.6%

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

   7. Taylor expanded in y around 0 79.5%

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

      1. cancel-sign-sub-inv 79.5%

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

      2. metadata-eval 79.5%

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

      3. *-lft-identity 79.5%

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

      4. +-commutative 79.5%

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

   9. Simplified 79.5%

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

   if 1.70000000000000007e-163 < b < 3.70000000000000003e87

   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 y around inf 73.0%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \color{blue}{-1 \cdot \left(y \cdot b\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 73.0%

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

      2. distribute-rgt-neg-in 73.0%

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

   6. Simplified 73.0%

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

   if 3.70000000000000003e87 < b

   1. Initial program 75.0%

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

      1. associate-+l- 75.0%

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

      2. *-commutative 75.0%

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

      3. *-commutative 75.0%

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

      4. sub-neg 75.0%

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

      5. metadata-eval 75.0%

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

      6. remove-double-neg 75.0%

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

      7. remove-double-neg 75.0%

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

      8. sub-neg 75.0%

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

      9. metadata-eval 75.0%

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

      10. associate--l+ 75.0%

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

   3. Simplified 75.0%

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

   4. Taylor expanded in y around inf 73.1%

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

   5. Taylor expanded in z around 0 75.1%

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

   6. Taylor expanded in a around 0 73.8%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.9 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 1.7 \cdot 10^{-163}:\\ \;\;\;\;\left(x + z\right) + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+87}:\\ \;\;\;\;b \cdot y + \left(x - \left(y + -1\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot y + \left(x + b \cdot \left(t - 2\right)\right)\\ \end{array} \]

Alternative 14: 80.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+69}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+156}:\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + \left(a - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot y + \left(x + b \cdot \left(t - 2\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -1.35e+69)
   (* b (- (+ t y) 2.0))
   (if (<= b 2.3e+156)
     (+ (- x (* (+ y -1.0) z)) (- a (* t a)))
     (+ (* b y) (+ x (* b (- t 2.0)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -1.35e+69) {
		tmp = b * ((t + y) - 2.0);
	} else if (b <= 2.3e+156) {
		tmp = (x - ((y + -1.0) * z)) + (a - (t * a));
	} else {
		tmp = (b * y) + (x + (b * (t - 2.0)));
	}
	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 <= (-1.35d+69)) then
        tmp = b * ((t + y) - 2.0d0)
    else if (b <= 2.3d+156) then
        tmp = (x - ((y + (-1.0d0)) * z)) + (a - (t * a))
    else
        tmp = (b * y) + (x + (b * (t - 2.0d0)))
    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 <= -1.35e+69) {
		tmp = b * ((t + y) - 2.0);
	} else if (b <= 2.3e+156) {
		tmp = (x - ((y + -1.0) * z)) + (a - (t * a));
	} else {
		tmp = (b * y) + (x + (b * (t - 2.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -1.35e+69:
		tmp = b * ((t + y) - 2.0)
	elif b <= 2.3e+156:
		tmp = (x - ((y + -1.0) * z)) + (a - (t * a))
	else:
		tmp = (b * y) + (x + (b * (t - 2.0)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -1.35e+69)
		tmp = Float64(b * Float64(Float64(t + y) - 2.0));
	elseif (b <= 2.3e+156)
		tmp = Float64(Float64(x - Float64(Float64(y + -1.0) * z)) + Float64(a - Float64(t * a)));
	else
		tmp = Float64(Float64(b * y) + Float64(x + Float64(b * Float64(t - 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -1.35e+69)
		tmp = b * ((t + y) - 2.0);
	elseif (b <= 2.3e+156)
		tmp = (x - ((y + -1.0) * z)) + (a - (t * a));
	else
		tmp = (b * y) + (x + (b * (t - 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -1.35e+69], N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.3e+156], N[(N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b * y), $MachinePrecision] + N[(x + N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.3499999999999999e69

   1. Initial program 98.0%

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

      1. associate-+l- 98.0%

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

      2. *-commutative 98.0%

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

      3. *-commutative 98.0%

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

      4. sub-neg 98.0%

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

      5. metadata-eval 98.0%

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

      6. remove-double-neg 98.0%

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

      7. remove-double-neg 98.0%

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

      8. sub-neg 98.0%

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

      9. metadata-eval 98.0%

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

      10. associate--l+ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in b around inf 82.0%

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

   if -1.3499999999999999e69 < b < 2.2999999999999999e156

   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 a around inf 83.5%

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

      1. sub-neg 83.5%

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

      2. metadata-eval 83.5%

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

      3. *-commutative 83.5%

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

      4. distribute-lft-in 83.5%

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

      5. *-commutative 83.5%

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

      6. mul-1-neg 83.5%

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

      7. unsub-neg 83.5%

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

   6. Simplified 83.5%

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

   if 2.2999999999999999e156 < b

   1. Initial program 75.7%

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

      1. associate-+l- 75.7%

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

      2. *-commutative 75.7%

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

      3. *-commutative 75.7%

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

      4. sub-neg 75.7%

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

      5. metadata-eval 75.7%

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

      6. remove-double-neg 75.7%

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

      7. remove-double-neg 75.7%

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

      8. sub-neg 75.7%

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

      9. metadata-eval 75.7%

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

      10. associate--l+ 75.7%

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

   3. Simplified 75.7%

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

   4. Taylor expanded in y around inf 73.0%

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

   5. Taylor expanded in z around 0 81.1%

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

   6. Taylor expanded in a around 0 86.8%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.35 \cdot 10^{+69}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+156}:\\ \;\;\;\;\left(x - \left(y + -1\right) \cdot z\right) + \left(a - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot y + \left(x + b \cdot \left(t - 2\right)\right)\\ \end{array} \]

Alternative 15: 47.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.7 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-106}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-71}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 10^{+70}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -2.7e-12)
     t_1
     (if (<= t 1.8e-106)
       (+ x z)
       (if (<= t 3.5e-71) (* b y) (if (<= t 1e+70) (+ x z) 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 <= -2.7e-12) {
		tmp = t_1;
	} else if (t <= 1.8e-106) {
		tmp = x + z;
	} else if (t <= 3.5e-71) {
		tmp = b * y;
	} else if (t <= 1e+70) {
		tmp = x + z;
	} 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 <= (-2.7d-12)) then
        tmp = t_1
    else if (t <= 1.8d-106) then
        tmp = x + z
    else if (t <= 3.5d-71) then
        tmp = b * y
    else if (t <= 1d+70) then
        tmp = x + z
    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 <= -2.7e-12) {
		tmp = t_1;
	} else if (t <= 1.8e-106) {
		tmp = x + z;
	} else if (t <= 3.5e-71) {
		tmp = b * y;
	} else if (t <= 1e+70) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -2.7e-12:
		tmp = t_1
	elif t <= 1.8e-106:
		tmp = x + z
	elif t <= 3.5e-71:
		tmp = b * y
	elif t <= 1e+70:
		tmp = x + z
	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 <= -2.7e-12)
		tmp = t_1;
	elseif (t <= 1.8e-106)
		tmp = Float64(x + z);
	elseif (t <= 3.5e-71)
		tmp = Float64(b * y);
	elseif (t <= 1e+70)
		tmp = Float64(x + z);
	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 <= -2.7e-12)
		tmp = t_1;
	elseif (t <= 1.8e-106)
		tmp = x + z;
	elseif (t <= 3.5e-71)
		tmp = b * y;
	elseif (t <= 1e+70)
		tmp = x + z;
	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, -2.7e-12], t$95$1, If[LessEqual[t, 1.8e-106], N[(x + z), $MachinePrecision], If[LessEqual[t, 3.5e-71], N[(b * y), $MachinePrecision], If[LessEqual[t, 1e+70], N[(x + z), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.6999999999999998e-12 or 1.00000000000000007e70 < t

   1. Initial program 87.6%

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

      1. associate-+l- 87.6%

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

      2. *-commutative 87.6%

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

      3. *-commutative 87.6%

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

      4. sub-neg 87.6%

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

      5. metadata-eval 87.6%

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

      6. remove-double-neg 87.6%

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

      7. remove-double-neg 87.6%

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

      8. sub-neg 87.6%

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

      9. metadata-eval 87.6%

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

      10. associate--l+ 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in t around inf 75.4%

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

   if -2.6999999999999998e-12 < t < 1.80000000000000006e-106 or 3.4999999999999999e-71 < t < 1.00000000000000007e70

   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 a around inf 73.0%

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

      1. sub-neg 73.0%

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

      2. metadata-eval 73.0%

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

      3. *-commutative 73.0%

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

      4. distribute-lft-in 73.0%

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

      5. *-commutative 73.0%

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

      6. mul-1-neg 73.0%

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

      7. unsub-neg 73.0%

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

   6. Simplified 73.0%

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

   7. Taylor expanded in a around 0 54.6%

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

   8. Taylor expanded in y around 0 36.5%

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

      1. cancel-sign-sub-inv 36.5%

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

      2. metadata-eval 36.5%

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity 36.5%

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

   10. Simplified 36.5%

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

   if 1.80000000000000006e-106 < t < 3.4999999999999999e-71

   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 y around inf 100.0%

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

   5. Taylor expanded in z around 0 91.1%

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

   6. Taylor expanded in y around inf 60.4%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{-12}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{-106}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-71}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 10^{+70}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 16: 66.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -1.7 \cdot 10^{+68}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 10^{-149}:\\ \;\;\;\;\left(x + z\right) + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+61}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))))
   (if (<= b -1.7e+68)
     t_1
     (if (<= b 1e-149)
       (+ (+ x z) (- a (* t a)))
       (if (<= b 2.15e+61) (- x (* (+ y -1.0) z)) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -1.7e+68) {
		tmp = t_1;
	} else if (b <= 1e-149) {
		tmp = (x + z) + (a - (t * a));
	} else if (b <= 2.15e+61) {
		tmp = x - ((y + -1.0) * z);
	} 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 = b * ((t + y) - 2.0d0)
    if (b <= (-1.7d+68)) then
        tmp = t_1
    else if (b <= 1d-149) then
        tmp = (x + z) + (a - (t * a))
    else if (b <= 2.15d+61) then
        tmp = x - ((y + (-1.0d0)) * z)
    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 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -1.7e+68) {
		tmp = t_1;
	} else if (b <= 1e-149) {
		tmp = (x + z) + (a - (t * a));
	} else if (b <= 2.15e+61) {
		tmp = x - ((y + -1.0) * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -1.7e+68:
		tmp = t_1
	elif b <= 1e-149:
		tmp = (x + z) + (a - (t * a))
	elif b <= 2.15e+61:
		tmp = x - ((y + -1.0) * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -1.7e+68)
		tmp = t_1;
	elseif (b <= 1e-149)
		tmp = Float64(Float64(x + z) + Float64(a - Float64(t * a)));
	elseif (b <= 2.15e+61)
		tmp = Float64(x - Float64(Float64(y + -1.0) * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -1.7e+68)
		tmp = t_1;
	elseif (b <= 1e-149)
		tmp = (x + z) + (a - (t * a));
	elseif (b <= 2.15e+61)
		tmp = x - ((y + -1.0) * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.7e+68], t$95$1, If[LessEqual[b, 1e-149], N[(N[(x + z), $MachinePrecision] + N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 2.15e+61], N[(x - N[(N[(y + -1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.70000000000000008e68 or 2.1500000000000001e61 < b

   1. Initial program 87.5%

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

      1. associate-+l- 87.5%

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

      2. *-commutative 87.5%

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

      3. *-commutative 87.5%

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

      4. sub-neg 87.5%

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

      5. metadata-eval 87.5%

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

      6. remove-double-neg 87.5%

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

      7. remove-double-neg 87.5%

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

      8. sub-neg 87.5%

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

      9. metadata-eval 87.5%

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

      10. associate--l+ 87.5%

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

   3. Simplified 87.5%

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

   4. Taylor expanded in b around inf 76.3%

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

   if -1.70000000000000008e68 < b < 9.99999999999999979e-150

   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 a around inf 92.0%

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

      1. sub-neg 92.0%

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

      2. metadata-eval 92.0%

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

      3. *-commutative 92.0%

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

      4. distribute-lft-in 92.0%

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

      5. *-commutative 92.0%

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

      6. mul-1-neg 92.0%

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

      7. unsub-neg 92.0%

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

   6. Simplified 92.0%

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

   7. Taylor expanded in y around 0 79.3%

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

      1. cancel-sign-sub-inv 79.3%

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

      2. metadata-eval 79.3%

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

      3. *-lft-identity 79.3%

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

      4. +-commutative 79.3%

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

   9. Simplified 79.3%

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

   if 9.99999999999999979e-150 < b < 2.1500000000000001e61

   1. Initial program 97.3%

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

      1. associate-+l- 97.3%

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

      2. *-commutative 97.3%

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

      3. *-commutative 97.3%

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

      4. sub-neg 97.3%

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

      5. metadata-eval 97.3%

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

      6. remove-double-neg 97.3%

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

      7. remove-double-neg 97.3%

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

      8. sub-neg 97.3%

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

      9. metadata-eval 97.3%

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

      10. associate--l+ 97.3%

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

   3. Simplified 97.3%

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

   4. Taylor expanded in a around inf 76.4%

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

      1. sub-neg 76.4%

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

      2. metadata-eval 76.4%

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

      3. *-commutative 76.4%

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

      4. distribute-lft-in 76.4%

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

      5. *-commutative 76.4%

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

      6. mul-1-neg 76.4%

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

      7. unsub-neg 76.4%

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

   6. Simplified 76.4%

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

   7. Taylor expanded in a around 0 60.6%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.7 \cdot 10^{+68}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 10^{-149}:\\ \;\;\;\;\left(x + z\right) + \left(a - t \cdot a\right)\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+61}:\\ \;\;\;\;x - \left(y + -1\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 17: 34.3% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+82}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-106}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-71}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+71}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.45e+82)
   (* b t)
   (if (<= t 1.55e-106)
     (+ x z)
     (if (<= t 2.9e-71) (* b y) (if (<= t 3.5e+71) (+ x z) (* t (- a)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.45e+82) {
		tmp = b * t;
	} else if (t <= 1.55e-106) {
		tmp = x + z;
	} else if (t <= 2.9e-71) {
		tmp = b * y;
	} else if (t <= 3.5e+71) {
		tmp = x + z;
	} else {
		tmp = t * -a;
	}
	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 <= (-1.45d+82)) then
        tmp = b * t
    else if (t <= 1.55d-106) then
        tmp = x + z
    else if (t <= 2.9d-71) then
        tmp = b * y
    else if (t <= 3.5d+71) then
        tmp = x + z
    else
        tmp = t * -a
    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 <= -1.45e+82) {
		tmp = b * t;
	} else if (t <= 1.55e-106) {
		tmp = x + z;
	} else if (t <= 2.9e-71) {
		tmp = b * y;
	} else if (t <= 3.5e+71) {
		tmp = x + z;
	} else {
		tmp = t * -a;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.45e+82:
		tmp = b * t
	elif t <= 1.55e-106:
		tmp = x + z
	elif t <= 2.9e-71:
		tmp = b * y
	elif t <= 3.5e+71:
		tmp = x + z
	else:
		tmp = t * -a
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.45e+82)
		tmp = Float64(b * t);
	elseif (t <= 1.55e-106)
		tmp = Float64(x + z);
	elseif (t <= 2.9e-71)
		tmp = Float64(b * y);
	elseif (t <= 3.5e+71)
		tmp = Float64(x + z);
	else
		tmp = Float64(t * Float64(-a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.45e+82)
		tmp = b * t;
	elseif (t <= 1.55e-106)
		tmp = x + z;
	elseif (t <= 2.9e-71)
		tmp = b * y;
	elseif (t <= 3.5e+71)
		tmp = x + z;
	else
		tmp = t * -a;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.45e+82], N[(b * t), $MachinePrecision], If[LessEqual[t, 1.55e-106], N[(x + z), $MachinePrecision], If[LessEqual[t, 2.9e-71], N[(b * y), $MachinePrecision], If[LessEqual[t, 3.5e+71], N[(x + z), $MachinePrecision], N[(t * (-a)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.4500000000000001e82

   1. Initial program 89.6%

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

      1. associate-+l- 89.6%

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

      2. *-commutative 89.6%

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

      3. *-commutative 89.6%

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

      4. sub-neg 89.6%

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

      5. metadata-eval 89.6%

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

      6. remove-double-neg 89.6%

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

      7. remove-double-neg 89.6%

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

      8. sub-neg 89.6%

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

      9. metadata-eval 89.6%

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

      10. associate--l+ 89.6%

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

   3. Simplified 89.6%

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

   4. Taylor expanded in b around inf 53.4%

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

   5. Taylor expanded in t around inf 51.5%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -1.4500000000000001e82 < t < 1.54999999999999993e-106 or 2.8999999999999999e-71 < t < 3.4999999999999999e71

   1. Initial program 98.0%

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

      1. associate-+l- 98.0%

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

      2. *-commutative 98.0%

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

      3. *-commutative 98.0%

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

      4. sub-neg 98.0%

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

      5. metadata-eval 98.0%

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

      6. remove-double-neg 98.0%

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

      7. remove-double-neg 98.0%

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

      8. sub-neg 98.0%

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

      9. metadata-eval 98.0%

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

      10. associate--l+ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in a around inf 70.6%

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

      1. sub-neg 70.6%

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

      2. metadata-eval 70.6%

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

      3. *-commutative 70.6%

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

      4. distribute-lft-in 70.6%

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

      5. *-commutative 70.6%

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

      6. mul-1-neg 70.6%

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

      7. unsub-neg 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in a around 0 52.3%

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

   8. Taylor expanded in y around 0 34.9%

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

      1. cancel-sign-sub-inv 34.9%

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

      2. metadata-eval 34.9%

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity 34.9%

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

   10. Simplified 34.9%

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

   if 1.54999999999999993e-106 < t < 2.8999999999999999e-71

   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 y around inf 100.0%

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

   5. Taylor expanded in z around 0 91.1%

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

   6. Taylor expanded in y around inf 60.4%

      \[\leadsto \color{blue}{y \cdot b} \]

   if 3.4999999999999999e71 < t

   1. Initial program 81.6%

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

      1. associate-+l- 81.6%

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

      2. *-commutative 81.6%

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

      3. *-commutative 81.6%

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

      4. sub-neg 81.6%

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

      5. metadata-eval 81.6%

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

      6. remove-double-neg 81.6%

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

      7. remove-double-neg 81.6%

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

      8. sub-neg 81.6%

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

      9. metadata-eval 81.6%

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

      10. associate--l+ 81.6%

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

   3. Simplified 81.6%

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

   4. Taylor expanded in a around inf 48.5%

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

   5. Taylor expanded in t around inf 48.5%

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

      1. associate-*r* 48.5%

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

      2. neg-mul-1 48.5%

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

   7. Simplified 48.5%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.45 \cdot 10^{+82}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-106}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{-71}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{+71}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]

Alternative 18: 33.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+84}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-106}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-70}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+88}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.2e+84)
   (* b t)
   (if (<= t 2.1e-106)
     (+ x z)
     (if (<= t 3.2e-70) (* b y) (if (<= t 2.2e+88) (+ x z) (* b t))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.2e+84) {
		tmp = b * t;
	} else if (t <= 2.1e-106) {
		tmp = x + z;
	} else if (t <= 3.2e-70) {
		tmp = b * y;
	} else if (t <= 2.2e+88) {
		tmp = x + z;
	} else {
		tmp = b * 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+84)) then
        tmp = b * t
    else if (t <= 2.1d-106) then
        tmp = x + z
    else if (t <= 3.2d-70) then
        tmp = b * y
    else if (t <= 2.2d+88) then
        tmp = x + z
    else
        tmp = b * 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+84) {
		tmp = b * t;
	} else if (t <= 2.1e-106) {
		tmp = x + z;
	} else if (t <= 3.2e-70) {
		tmp = b * y;
	} else if (t <= 2.2e+88) {
		tmp = x + z;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.2e+84:
		tmp = b * t
	elif t <= 2.1e-106:
		tmp = x + z
	elif t <= 3.2e-70:
		tmp = b * y
	elif t <= 2.2e+88:
		tmp = x + z
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.2e+84)
		tmp = Float64(b * t);
	elseif (t <= 2.1e-106)
		tmp = Float64(x + z);
	elseif (t <= 3.2e-70)
		tmp = Float64(b * y);
	elseif (t <= 2.2e+88)
		tmp = Float64(x + z);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.2e+84)
		tmp = b * t;
	elseif (t <= 2.1e-106)
		tmp = x + z;
	elseif (t <= 3.2e-70)
		tmp = b * y;
	elseif (t <= 2.2e+88)
		tmp = x + z;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.2e+84], N[(b * t), $MachinePrecision], If[LessEqual[t, 2.1e-106], N[(x + z), $MachinePrecision], If[LessEqual[t, 3.2e-70], N[(b * y), $MachinePrecision], If[LessEqual[t, 2.2e+88], N[(x + z), $MachinePrecision], N[(b * t), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.1999999999999998e84 or 2.20000000000000009e88 < t

   1. Initial program 84.6%

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

      1. associate-+l- 84.6%

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

      2. *-commutative 84.6%

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

      3. *-commutative 84.6%

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

      4. sub-neg 84.6%

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

      5. metadata-eval 84.6%

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

      6. remove-double-neg 84.6%

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

      7. remove-double-neg 84.6%

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

      8. sub-neg 84.6%

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

      9. metadata-eval 84.6%

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

      10. associate--l+ 84.6%

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

   3. Simplified 84.6%

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

   4. Taylor expanded in b around inf 51.7%

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

   5. Taylor expanded in t around inf 50.9%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -2.1999999999999998e84 < t < 2.10000000000000003e-106 or 3.1999999999999997e-70 < t < 2.20000000000000009e88

   1. Initial program 98.0%

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

      1. associate-+l- 98.0%

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

      2. *-commutative 98.0%

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

      3. *-commutative 98.0%

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

      4. sub-neg 98.0%

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

      5. metadata-eval 98.0%

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

      6. remove-double-neg 98.0%

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

      7. remove-double-neg 98.0%

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

      8. sub-neg 98.0%

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

      9. metadata-eval 98.0%

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

      10. associate--l+ 98.0%

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

   3. Simplified 98.0%

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

   4. Taylor expanded in a around inf 70.6%

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

      1. sub-neg 70.6%

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

      2. metadata-eval 70.6%

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

      3. *-commutative 70.6%

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

      4. distribute-lft-in 70.6%

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

      5. *-commutative 70.6%

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

      6. mul-1-neg 70.6%

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

      7. unsub-neg 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in a around 0 51.8%

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

   8. Taylor expanded in y around 0 34.4%

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

      1. cancel-sign-sub-inv 34.4%

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

      2. metadata-eval 34.4%

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity 34.4%

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

   10. Simplified 34.4%

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

   if 2.10000000000000003e-106 < t < 3.1999999999999997e-70

   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 y around inf 100.0%

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

   5. Taylor expanded in z around 0 91.1%

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

   6. Taylor expanded in y around inf 60.4%

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

4. Final simplification 41.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{+84}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 2.1 \cdot 10^{-106}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-70}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+88}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]

Alternative 19: 39.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.45 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-258}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+51}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1.45e-52)
     t_1
     (if (<= a -2.8e-258) (* b t) (if (<= a 3.8e+51) (+ x z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.45e-52) {
		tmp = t_1;
	} else if (a <= -2.8e-258) {
		tmp = b * t;
	} else if (a <= 3.8e+51) {
		tmp = x + z;
	} 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 = a * (1.0d0 - t)
    if (a <= (-1.45d-52)) then
        tmp = t_1
    else if (a <= (-2.8d-258)) then
        tmp = b * t
    else if (a <= 3.8d+51) then
        tmp = x + z
    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 = a * (1.0 - t);
	double tmp;
	if (a <= -1.45e-52) {
		tmp = t_1;
	} else if (a <= -2.8e-258) {
		tmp = b * t;
	} else if (a <= 3.8e+51) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -1.45e-52:
		tmp = t_1
	elif a <= -2.8e-258:
		tmp = b * t
	elif a <= 3.8e+51:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -1.45e-52)
		tmp = t_1;
	elseif (a <= -2.8e-258)
		tmp = Float64(b * t);
	elseif (a <= 3.8e+51)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -1.45e-52)
		tmp = t_1;
	elseif (a <= -2.8e-258)
		tmp = b * t;
	elseif (a <= 3.8e+51)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.45e-52], t$95$1, If[LessEqual[a, -2.8e-258], N[(b * t), $MachinePrecision], If[LessEqual[a, 3.8e+51], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.4500000000000001e-52 or 3.7999999999999997e51 < a

   1. Initial program 89.0%

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

      1. associate-+l- 89.0%

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

      2. *-commutative 89.0%

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

      3. *-commutative 89.0%

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

      4. sub-neg 89.0%

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

      5. metadata-eval 89.0%

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

      6. remove-double-neg 89.0%

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

      7. remove-double-neg 89.0%

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

      8. sub-neg 89.0%

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

      9. metadata-eval 89.0%

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

      10. associate--l+ 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in a around inf 52.5%

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

   if -1.4500000000000001e-52 < a < -2.8000000000000002e-258

   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 b around inf 51.4%

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

   5. Taylor expanded in t around inf 37.5%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -2.8000000000000002e-258 < a < 3.7999999999999997e51

   1. Initial program 97.4%

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

      1. associate-+l- 97.4%

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

      2. *-commutative 97.4%

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

      3. *-commutative 97.4%

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

      4. sub-neg 97.4%

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

      5. metadata-eval 97.4%

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

      6. remove-double-neg 97.4%

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

      7. remove-double-neg 97.4%

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

      8. sub-neg 97.4%

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

      9. metadata-eval 97.4%

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

      10. associate--l+ 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in a around inf 55.7%

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

      1. sub-neg 55.7%

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

      2. metadata-eval 55.7%

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

      3. *-commutative 55.7%

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

      4. distribute-lft-in 55.7%

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

      5. *-commutative 55.7%

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

      6. mul-1-neg 55.7%

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

      7. unsub-neg 55.7%

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

   6. Simplified 55.7%

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

   7. Taylor expanded in a around 0 53.2%

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

   8. Taylor expanded in y around 0 37.3%

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

      1. cancel-sign-sub-inv 37.3%

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

      2. metadata-eval 37.3%

         \[\leadsto x + \color{blue}{1} \cdot z \]

      3. *-lft-identity 37.3%

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

   10. Simplified 37.3%

       \[\leadsto \color{blue}{x + z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.45 \cdot 10^{-52}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-258}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;a \leq 3.8 \cdot 10^{+51}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 20: 27.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-194}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 10200000:\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.4e-9)
   (* b t)
   (if (<= t 5.4e-194) a (if (<= t 10200000.0) (* b y) (* b t)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.4e-9) {
		tmp = b * t;
	} else if (t <= 5.4e-194) {
		tmp = a;
	} else if (t <= 10200000.0) {
		tmp = b * y;
	} else {
		tmp = b * 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 <= (-2.4d-9)) then
        tmp = b * t
    else if (t <= 5.4d-194) then
        tmp = a
    else if (t <= 10200000.0d0) then
        tmp = b * y
    else
        tmp = b * 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 <= -2.4e-9) {
		tmp = b * t;
	} else if (t <= 5.4e-194) {
		tmp = a;
	} else if (t <= 10200000.0) {
		tmp = b * y;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.4e-9:
		tmp = b * t
	elif t <= 5.4e-194:
		tmp = a
	elif t <= 10200000.0:
		tmp = b * y
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.4e-9)
		tmp = Float64(b * t);
	elseif (t <= 5.4e-194)
		tmp = a;
	elseif (t <= 10200000.0)
		tmp = Float64(b * y);
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.4e-9)
		tmp = b * t;
	elseif (t <= 5.4e-194)
		tmp = a;
	elseif (t <= 10200000.0)
		tmp = b * y;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.4e-9], N[(b * t), $MachinePrecision], If[LessEqual[t, 5.4e-194], a, If[LessEqual[t, 10200000.0], N[(b * y), $MachinePrecision], N[(b * t), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4e-9 or 1.02e7 < t

   1. Initial program 88.6%

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

      1. associate-+l- 88.6%

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

      2. *-commutative 88.6%

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

      3. *-commutative 88.6%

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

      4. sub-neg 88.6%

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

      5. metadata-eval 88.6%

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

      6. remove-double-neg 88.6%

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

      7. remove-double-neg 88.6%

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

      8. sub-neg 88.6%

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

      9. metadata-eval 88.6%

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

      10. associate--l+ 88.6%

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

   3. Simplified 88.6%

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

   4. Taylor expanded in b around inf 49.2%

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

   5. Taylor expanded in t around inf 42.9%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -2.4e-9 < t < 5.4e-194

   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. associate-+l- 97.8%

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

      2. *-commutative 97.8%

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

      3. *-commutative 97.8%

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

      4. sub-neg 97.8%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 97.8%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 97.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 97.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 97.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 97.8%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 97.8%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 97.8%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 26.8%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   5. Taylor expanded in t around 0 26.6%

      \[\leadsto \color{blue}{a} \]

   if 5.4e-194 < t < 1.02e7

   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 y around inf 97.7%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y \cdot b + \left(t - 2\right) \cdot b\right)}\right) \]

   5. Taylor expanded in z around 0 71.0%

      \[\leadsto \color{blue}{\left(y \cdot b + \left(\left(t - 2\right) \cdot b + x\right)\right) - \left(t - 1\right) \cdot a} \]

   6. Taylor expanded in y around inf 35.6%

      \[\leadsto \color{blue}{y \cdot b} \]
3. Recombined 3 regimes into one program.

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-9}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-194}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 10200000:\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]

Alternative 21: 20.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-206}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-55}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3e+34) x (if (<= x -7.6e-206) a (if (<= x 4e-55) z x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3e+34) {
		tmp = x;
	} else if (x <= -7.6e-206) {
		tmp = a;
	} else if (x <= 4e-55) {
		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 <= (-3d+34)) then
        tmp = x
    else if (x <= (-7.6d-206)) then
        tmp = a
    else if (x <= 4d-55) 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 <= -3e+34) {
		tmp = x;
	} else if (x <= -7.6e-206) {
		tmp = a;
	} else if (x <= 4e-55) {
		tmp = z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3e+34:
		tmp = x
	elif x <= -7.6e-206:
		tmp = a
	elif x <= 4e-55:
		tmp = z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3e+34)
		tmp = x;
	elseif (x <= -7.6e-206)
		tmp = a;
	elseif (x <= 4e-55)
		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 <= -3e+34)
		tmp = x;
	elseif (x <= -7.6e-206)
		tmp = a;
	elseif (x <= 4e-55)
		tmp = z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3e+34], x, If[LessEqual[x, -7.6e-206], a, If[LessEqual[x, 4e-55], z, x]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.00000000000000018e34 or 3.99999999999999998e-55 < x

   1. Initial program 91.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in x around inf 27.3%

      \[\leadsto \color{blue}{x} \]

   if -3.00000000000000018e34 < x < -7.60000000000000005e-206

   1. Initial program 94.0%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 94.0%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 94.0%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 94.0%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 94.0%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 94.0%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 94.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 94.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 94.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 94.0%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 94.0%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 94.0%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 37.9%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   5. Taylor expanded in t around 0 18.4%

      \[\leadsto \color{blue}{a} \]

   if -7.60000000000000005e-206 < x < 3.99999999999999998e-55

   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 z around inf 35.9%

      \[\leadsto \color{blue}{z \cdot \left(1 - y\right)} \]

   5. Taylor expanded in y around 0 21.9%

      \[\leadsto \color{blue}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 24.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-206}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-55}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22: 26.7% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+83}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -1.7e+83) (* b t) (if (<= t 1.8e+70) x (* b t))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -1.7e+83) {
		tmp = b * t;
	} else if (t <= 1.8e+70) {
		tmp = x;
	} else {
		tmp = b * 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 <= (-1.7d+83)) then
        tmp = b * t
    else if (t <= 1.8d+70) then
        tmp = x
    else
        tmp = b * 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 <= -1.7e+83) {
		tmp = b * t;
	} else if (t <= 1.8e+70) {
		tmp = x;
	} else {
		tmp = b * t;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -1.7e+83:
		tmp = b * t
	elif t <= 1.8e+70:
		tmp = x
	else:
		tmp = b * t
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -1.7e+83)
		tmp = Float64(b * t);
	elseif (t <= 1.8e+70)
		tmp = x;
	else
		tmp = Float64(b * t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -1.7e+83)
		tmp = b * t;
	elseif (t <= 1.8e+70)
		tmp = x;
	else
		tmp = b * t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -1.7e+83], N[(b * t), $MachinePrecision], If[LessEqual[t, 1.8e+70], x, N[(b * t), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6999999999999999e83 or 1.8e70 < t

   1. Initial program 85.6%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 85.6%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 85.6%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 85.6%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 85.6%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 85.6%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 85.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 85.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 85.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 85.6%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 85.6%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 85.6%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in b around inf 50.6%

      \[\leadsto \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b} \]

   5. Taylor expanded in t around inf 48.9%

      \[\leadsto \color{blue}{t \cdot b} \]

   if -1.6999999999999999e83 < t < 1.8e70

   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 x around inf 21.8%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+83}:\\ \;\;\;\;b \cdot t\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot t\\ \end{array} \]

Alternative 23: 21.0% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{-55}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -3.7e+34) x (if (<= x 5.9e-55) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -3.7e+34) {
		tmp = x;
	} else if (x <= 5.9e-55) {
		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 <= (-3.7d+34)) then
        tmp = x
    else if (x <= 5.9d-55) 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 <= -3.7e+34) {
		tmp = x;
	} else if (x <= 5.9e-55) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -3.7e+34:
		tmp = x
	elif x <= 5.9e-55:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -3.7e+34)
		tmp = x;
	elseif (x <= 5.9e-55)
		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 <= -3.7e+34)
		tmp = x;
	elseif (x <= 5.9e-55)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -3.7e+34], x, If[LessEqual[x, 5.9e-55], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.70000000000000009e34 or 5.8999999999999998e-55 < x

   1. Initial program 91.7%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 91.7%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 91.7%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 91.7%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 91.7%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 91.7%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 91.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 91.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 91.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 91.7%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 91.7%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 91.7%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in x around inf 27.3%

      \[\leadsto \color{blue}{x} \]

   if -3.70000000000000009e34 < x < 5.8999999999999998e-55

   1. Initial program 95.1%

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   2. Step-by-step derivation

      1. associate-+l- 95.1%

         \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

      2. *-commutative 95.1%

         \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      3. *-commutative 95.1%

         \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      4. sub-neg 95.1%

         \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      5. metadata-eval 95.1%

         \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      6. remove-double-neg 95.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      7. remove-double-neg 95.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      8. sub-neg 95.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      9. metadata-eval 95.1%

         \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

      10. associate--l+ 95.1%

          \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

   4. Taylor expanded in a around inf 35.5%

      \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

   5. Taylor expanded in t around 0 16.7%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.9 \cdot 10^{-55}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 11.1% 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 93.3%

   \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
2. Step-by-step derivation

   1. associate-+l- 93.3%

      \[\leadsto \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right)} \]

   2. *-commutative 93.3%

      \[\leadsto \left(x - \color{blue}{z \cdot \left(y - 1\right)}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   3. *-commutative 93.3%

      \[\leadsto \left(x - \color{blue}{\left(y - 1\right) \cdot z}\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   4. sub-neg 93.3%

      \[\leadsto \left(x - \color{blue}{\left(y + \left(-1\right)\right)} \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   5. metadata-eval 93.3%

      \[\leadsto \left(x - \left(y + \color{blue}{-1}\right) \cdot z\right) - \left(\left(t - 1\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   6. remove-double-neg 93.3%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   7. remove-double-neg 93.3%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t - 1\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   8. sub-neg 93.3%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\color{blue}{\left(t + \left(-1\right)\right)} \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   9. metadata-eval 93.3%

      \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + \color{blue}{-1}\right) \cdot a - \left(\left(y + t\right) - 2\right) \cdot b\right) \]

   10. associate--l+ 93.3%

       \[\leadsto \left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) \]

3. Simplified 93.3%

   \[\leadsto \color{blue}{\left(x - \left(y + -1\right) \cdot z\right) - \left(\left(t + -1\right) \cdot a - \left(y + \left(t - 2\right)\right) \cdot b\right)} \]

4. Taylor expanded in a around inf 29.1%

   \[\leadsto \color{blue}{a \cdot \left(1 - t\right)} \]

5. Taylor expanded in t around 0 12.1%

   \[\leadsto \color{blue}{a} \]

6. Final simplification 12.1%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023257 
(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)))