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

Percentage Accurate: 95.3% → 97.8%

Time: 18.2s

Alternatives: 29

Speedup: 0.5×

• 36.4% 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: 95.3% 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, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1
         (+ (- (+ x (* z (- 1.0 y))) (* a (+ t -1.0))) (* b (- (+ t y) 2.0)))))
   (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 = ((x + (z * (1.0 - y))) - (a * (t + -1.0))) + (b * ((t + y) - 2.0));
	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 = ((x + (z * (1.0 - y))) - (a * (t + -1.0))) + (b * ((t + y) - 2.0));
	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 = ((x + (z * (1.0 - y))) - (a * (t + -1.0))) + (b * ((t + y) - 2.0))
	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(Float64(x + Float64(z * Float64(1.0 - y))) - Float64(a * Float64(t + -1.0))) + Float64(b * Float64(Float64(t + y) - 2.0)))
	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 = ((x + (z * (1.0 - y))) - (a * (t + -1.0))) + (b * ((t + y) - 2.0));
	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[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(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. Taylor expanded in t around inf 83.4%

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

4. Final simplification 99.6%

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

Alternative 2: 97.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. Taylor expanded in t around 0 97.2%

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

   1. associate--l+ 97.2%

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

   2. fma-def 98.4%

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

   3. associate--l+ 98.4%

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

   4. *-commutative 98.4%

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

   5. fma-def 98.8%

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

   6. sub-neg 98.8%

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

   7. metadata-eval 98.8%

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

   8. sub-neg 98.8%

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

   9. metadata-eval 98.8%

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

   10. associate--r+ 98.8%

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

   11. sub-neg 98.8%

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

4. Simplified 98.8%

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

5. Final simplification 98.8%

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

Alternative 3: 97.3% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 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. +-commutative 97.6%

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

   2. fma-def 98.8%

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

   3. associate--l+ 98.8%

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

   4. sub-neg 98.8%

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

   5. metadata-eval 98.8%

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

   6. sub-neg 98.8%

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

   7. associate-+l- 98.8%

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

   8. fma-neg 98.8%

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

   9. sub-neg 98.8%

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

   10. metadata-eval 98.8%

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

   11. remove-double-neg 98.8%

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

   12. sub-neg 98.8%

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

   13. metadata-eval 98.8%

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

3. Simplified 98.8%

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

4. Final simplification 98.8%

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

Alternative 4: 71.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + b \cdot \left(y - 2\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right) - t \cdot a\\ \mathbf{if}\;b \leq -2500000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-40}:\\ \;\;\;\;x + \left(\left(a + z\right) - y \cdot z\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-83}:\\ \;\;\;\;t_1 + t \cdot b\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + y \cdot z\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+96} \lor \neg \left(b \leq 7.5 \cdot 10^{+142}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* b (- y 2.0)))) (t_2 (- (* b (- (+ t y) 2.0)) (* t a))))
   (if (<= b -2500000.0)
     t_2
     (if (<= b -1.95e-40)
       (+ x (- (+ a z) (* y z)))
       (if (<= b -5.8e-66)
         t_2
         (if (<= b -3e-83)
           (+ t_1 (* t b))
           (if (<= b 1.55e+16)
             (- x (+ (* a (+ t -1.0)) (* y z)))
             (if (or (<= b 6.2e+96) (not (<= b 7.5e+142)))
               t_2
               (+ a t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * (y - 2.0));
	double t_2 = (b * ((t + y) - 2.0)) - (t * a);
	double tmp;
	if (b <= -2500000.0) {
		tmp = t_2;
	} else if (b <= -1.95e-40) {
		tmp = x + ((a + z) - (y * z));
	} else if (b <= -5.8e-66) {
		tmp = t_2;
	} else if (b <= -3e-83) {
		tmp = t_1 + (t * b);
	} else if (b <= 1.55e+16) {
		tmp = x - ((a * (t + -1.0)) + (y * z));
	} else if ((b <= 6.2e+96) || !(b <= 7.5e+142)) {
		tmp = t_2;
	} else {
		tmp = a + 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 = x + (b * (y - 2.0d0))
    t_2 = (b * ((t + y) - 2.0d0)) - (t * a)
    if (b <= (-2500000.0d0)) then
        tmp = t_2
    else if (b <= (-1.95d-40)) then
        tmp = x + ((a + z) - (y * z))
    else if (b <= (-5.8d-66)) then
        tmp = t_2
    else if (b <= (-3d-83)) then
        tmp = t_1 + (t * b)
    else if (b <= 1.55d+16) then
        tmp = x - ((a * (t + (-1.0d0))) + (y * z))
    else if ((b <= 6.2d+96) .or. (.not. (b <= 7.5d+142))) then
        tmp = t_2
    else
        tmp = a + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (b * (y - 2.0));
	double t_2 = (b * ((t + y) - 2.0)) - (t * a);
	double tmp;
	if (b <= -2500000.0) {
		tmp = t_2;
	} else if (b <= -1.95e-40) {
		tmp = x + ((a + z) - (y * z));
	} else if (b <= -5.8e-66) {
		tmp = t_2;
	} else if (b <= -3e-83) {
		tmp = t_1 + (t * b);
	} else if (b <= 1.55e+16) {
		tmp = x - ((a * (t + -1.0)) + (y * z));
	} else if ((b <= 6.2e+96) || !(b <= 7.5e+142)) {
		tmp = t_2;
	} else {
		tmp = a + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (b * (y - 2.0))
	t_2 = (b * ((t + y) - 2.0)) - (t * a)
	tmp = 0
	if b <= -2500000.0:
		tmp = t_2
	elif b <= -1.95e-40:
		tmp = x + ((a + z) - (y * z))
	elif b <= -5.8e-66:
		tmp = t_2
	elif b <= -3e-83:
		tmp = t_1 + (t * b)
	elif b <= 1.55e+16:
		tmp = x - ((a * (t + -1.0)) + (y * z))
	elif (b <= 6.2e+96) or not (b <= 7.5e+142):
		tmp = t_2
	else:
		tmp = a + t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(b * Float64(y - 2.0)))
	t_2 = Float64(Float64(b * Float64(Float64(t + y) - 2.0)) - Float64(t * a))
	tmp = 0.0
	if (b <= -2500000.0)
		tmp = t_2;
	elseif (b <= -1.95e-40)
		tmp = Float64(x + Float64(Float64(a + z) - Float64(y * z)));
	elseif (b <= -5.8e-66)
		tmp = t_2;
	elseif (b <= -3e-83)
		tmp = Float64(t_1 + Float64(t * b));
	elseif (b <= 1.55e+16)
		tmp = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(y * z)));
	elseif ((b <= 6.2e+96) || !(b <= 7.5e+142))
		tmp = t_2;
	else
		tmp = Float64(a + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (b * (y - 2.0));
	t_2 = (b * ((t + y) - 2.0)) - (t * a);
	tmp = 0.0;
	if (b <= -2500000.0)
		tmp = t_2;
	elseif (b <= -1.95e-40)
		tmp = x + ((a + z) - (y * z));
	elseif (b <= -5.8e-66)
		tmp = t_2;
	elseif (b <= -3e-83)
		tmp = t_1 + (t * b);
	elseif (b <= 1.55e+16)
		tmp = x - ((a * (t + -1.0)) + (y * z));
	elseif ((b <= 6.2e+96) || ~((b <= 7.5e+142)))
		tmp = t_2;
	else
		tmp = a + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -2500000.0], t$95$2, If[LessEqual[b, -1.95e-40], N[(x + N[(N[(a + z), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, -5.8e-66], t$95$2, If[LessEqual[b, -3e-83], N[(t$95$1 + N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.55e+16], N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[b, 6.2e+96], N[Not[LessEqual[b, 7.5e+142]], $MachinePrecision]], t$95$2, N[(a + t$95$1), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -2.5e6 or -1.9499999999999999e-40 < b < -5.80000000000000023e-66 or 1.55e16 < b < 6.1999999999999996e96 or 7.5000000000000002e142 < b

   1. Initial program 94.5%

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

   2. Taylor expanded in t around inf 80.7%

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

      1. associate-*r* 80.7%

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

      2. neg-mul-1 80.7%

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

   4. Simplified 80.7%

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

   if -2.5e6 < b < -1.9499999999999999e-40

   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. Taylor expanded in b around 0 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. associate-+l+ 100.0%

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

      5. distribute-lft-out 100.0%

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

      6. mul-1-neg 100.0%

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

      7. remove-double-neg 100.0%

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

      8. mul-1-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. mul-1-neg 100.0%

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

      11. distribute-neg-in 100.0%

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

      12. unsub-neg 100.0%

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

      13. *-commutative 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-in 100.0%

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

      16. mul-1-neg 100.0%

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

      17. remove-double-neg 100.0%

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

      18. mul-1-neg 100.0%

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

      19. remove-double-neg 100.0%

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

   5. Simplified 100.0%

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

   if -5.80000000000000023e-66 < b < -3.0000000000000001e-83

   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. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-def 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--r+ 100.0%

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

      11. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 76.7%

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

   6. Taylor expanded in a around 0 76.0%

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

   if -3.0000000000000001e-83 < b < 1.55e16

   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. Taylor expanded in b around 0 95.4%

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

   3. Taylor expanded in y around inf 84.8%

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

      1. *-commutative 84.8%

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

   5. Simplified 84.8%

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

   if 6.1999999999999996e96 < b < 7.5000000000000002e142

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. fma-def 99.9%

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

      3. associate--l+ 99.9%

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

      4. *-commutative 99.9%

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

      5. fma-def 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--r+ 100.0%

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

      11. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 77.4%

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

   6. Taylor expanded in t around 0 75.7%

      \[\leadsto \color{blue}{a + \left(\left(y - 2\right) \cdot b + x\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2500000:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right) - t \cdot a\\ \mathbf{elif}\;b \leq -1.95 \cdot 10^{-40}:\\ \;\;\;\;x + \left(\left(a + z\right) - y \cdot z\right)\\ \mathbf{elif}\;b \leq -5.8 \cdot 10^{-66}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right) - t \cdot a\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-83}:\\ \;\;\;\;\left(x + b \cdot \left(y - 2\right)\right) + t \cdot b\\ \mathbf{elif}\;b \leq 1.55 \cdot 10^{+16}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + y \cdot z\right)\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{+96} \lor \neg \left(b \leq 7.5 \cdot 10^{+142}\right):\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right) - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \end{array} \]

Alternative 5: 54.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z + x\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+86}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-34}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ z x))) (t_2 (* t (- b a))) (t_3 (* y (- b z))))
   (if (<= y -1.35e+86)
     t_3
     (if (<= y -6.5e+56)
       t_1
       (if (<= y -1.9e+33)
         t_3
         (if (<= y -7.4e-34)
           (* a (- 1.0 t))
           (if (<= y -2.1e-105)
             t_1
             (if (<= y -7.3e-153)
               t_2
               (if (<= y 4.5e-151)
                 t_1
                 (if (<= y 3.3e-72) t_2 (if (<= y 2.1e+18) t_1 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z + x);
	double t_2 = t * (b - a);
	double t_3 = y * (b - z);
	double tmp;
	if (y <= -1.35e+86) {
		tmp = t_3;
	} else if (y <= -6.5e+56) {
		tmp = t_1;
	} else if (y <= -1.9e+33) {
		tmp = t_3;
	} else if (y <= -7.4e-34) {
		tmp = a * (1.0 - t);
	} else if (y <= -2.1e-105) {
		tmp = t_1;
	} else if (y <= -7.3e-153) {
		tmp = t_2;
	} else if (y <= 4.5e-151) {
		tmp = t_1;
	} else if (y <= 3.3e-72) {
		tmp = t_2;
	} else if (y <= 2.1e+18) {
		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 = a + (z + x)
    t_2 = t * (b - a)
    t_3 = y * (b - z)
    if (y <= (-1.35d+86)) then
        tmp = t_3
    else if (y <= (-6.5d+56)) then
        tmp = t_1
    else if (y <= (-1.9d+33)) then
        tmp = t_3
    else if (y <= (-7.4d-34)) then
        tmp = a * (1.0d0 - t)
    else if (y <= (-2.1d-105)) then
        tmp = t_1
    else if (y <= (-7.3d-153)) then
        tmp = t_2
    else if (y <= 4.5d-151) then
        tmp = t_1
    else if (y <= 3.3d-72) then
        tmp = t_2
    else if (y <= 2.1d+18) 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 = a + (z + x);
	double t_2 = t * (b - a);
	double t_3 = y * (b - z);
	double tmp;
	if (y <= -1.35e+86) {
		tmp = t_3;
	} else if (y <= -6.5e+56) {
		tmp = t_1;
	} else if (y <= -1.9e+33) {
		tmp = t_3;
	} else if (y <= -7.4e-34) {
		tmp = a * (1.0 - t);
	} else if (y <= -2.1e-105) {
		tmp = t_1;
	} else if (y <= -7.3e-153) {
		tmp = t_2;
	} else if (y <= 4.5e-151) {
		tmp = t_1;
	} else if (y <= 3.3e-72) {
		tmp = t_2;
	} else if (y <= 2.1e+18) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z + x)
	t_2 = t * (b - a)
	t_3 = y * (b - z)
	tmp = 0
	if y <= -1.35e+86:
		tmp = t_3
	elif y <= -6.5e+56:
		tmp = t_1
	elif y <= -1.9e+33:
		tmp = t_3
	elif y <= -7.4e-34:
		tmp = a * (1.0 - t)
	elif y <= -2.1e-105:
		tmp = t_1
	elif y <= -7.3e-153:
		tmp = t_2
	elif y <= 4.5e-151:
		tmp = t_1
	elif y <= 3.3e-72:
		tmp = t_2
	elif y <= 2.1e+18:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z + x))
	t_2 = Float64(t * Float64(b - a))
	t_3 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.35e+86)
		tmp = t_3;
	elseif (y <= -6.5e+56)
		tmp = t_1;
	elseif (y <= -1.9e+33)
		tmp = t_3;
	elseif (y <= -7.4e-34)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (y <= -2.1e-105)
		tmp = t_1;
	elseif (y <= -7.3e-153)
		tmp = t_2;
	elseif (y <= 4.5e-151)
		tmp = t_1;
	elseif (y <= 3.3e-72)
		tmp = t_2;
	elseif (y <= 2.1e+18)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z + x);
	t_2 = t * (b - a);
	t_3 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.35e+86)
		tmp = t_3;
	elseif (y <= -6.5e+56)
		tmp = t_1;
	elseif (y <= -1.9e+33)
		tmp = t_3;
	elseif (y <= -7.4e-34)
		tmp = a * (1.0 - t);
	elseif (y <= -2.1e-105)
		tmp = t_1;
	elseif (y <= -7.3e-153)
		tmp = t_2;
	elseif (y <= 4.5e-151)
		tmp = t_1;
	elseif (y <= 3.3e-72)
		tmp = t_2;
	elseif (y <= 2.1e+18)
		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[(a + N[(z + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+86], t$95$3, If[LessEqual[y, -6.5e+56], t$95$1, If[LessEqual[y, -1.9e+33], t$95$3, If[LessEqual[y, -7.4e-34], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.1e-105], t$95$1, If[LessEqual[y, -7.3e-153], t$95$2, If[LessEqual[y, 4.5e-151], t$95$1, If[LessEqual[y, 3.3e-72], t$95$2, If[LessEqual[y, 2.1e+18], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.35000000000000009e86 or -6.5000000000000001e56 < y < -1.90000000000000001e33 or 2.1e18 < y

   1. Initial program 96.5%

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

   2. Taylor expanded in y around inf 70.9%

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

   if -1.35000000000000009e86 < y < -6.5000000000000001e56 or -7.39999999999999976e-34 < y < -2.1e-105 or -7.30000000000000003e-153 < y < 4.5000000000000002e-151 or 3.3e-72 < y < 2.1e18

   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. Taylor expanded in b around 0 80.6%

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

   3. Taylor expanded in t around 0 66.0%

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

      1. sub-neg 66.0%

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

      2. metadata-eval 66.0%

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

      3. distribute-rgt-in 66.1%

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

      4. associate-+l+ 66.1%

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

      5. distribute-lft-out 66.1%

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

      6. mul-1-neg 66.1%

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

      7. remove-double-neg 66.1%

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

      8. mul-1-neg 66.1%

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

      9. remove-double-neg 66.1%

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

      10. mul-1-neg 66.1%

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

      11. distribute-neg-in 66.1%

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

      12. unsub-neg 66.1%

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

      13. *-commutative 66.1%

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

      14. +-commutative 66.1%

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

      15. distribute-neg-in 66.1%

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

      16. mul-1-neg 66.1%

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

      17. remove-double-neg 66.1%

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

      18. mul-1-neg 66.1%

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

      19. remove-double-neg 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in y around 0 63.6%

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

   if -1.90000000000000001e33 < y < -7.39999999999999976e-34

   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. Taylor expanded in a around inf 46.9%

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

   if -2.1e-105 < y < -7.30000000000000003e-153 or 4.5000000000000002e-151 < y < 3.3e-72

   1. Initial program 92.9%

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

   2. Taylor expanded in t around inf 66.1%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+56}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{+33}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-34}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-105}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;y \leq -7.3 \cdot 10^{-153}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-151}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-72}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+18}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 6: 54.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(z + x\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+86}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{+38}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-33}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-150}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ z x))) (t_2 (* t (- b a))) (t_3 (* y (- b z))))
   (if (<= y -1.35e+86)
     t_3
     (if (<= y -1.85e+56)
       t_1
       (if (<= y -1.55e+38)
         t_3
         (if (<= y -6e-33)
           (- a (* t a))
           (if (<= y -7.2e-106)
             t_1
             (if (<= y -4.4e-150)
               t_2
               (if (<= y 6.2e-152)
                 t_1
                 (if (<= y 4.8e-73) t_2 (if (<= y 3.9e+18) t_1 t_3)))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (z + x);
	double t_2 = t * (b - a);
	double t_3 = y * (b - z);
	double tmp;
	if (y <= -1.35e+86) {
		tmp = t_3;
	} else if (y <= -1.85e+56) {
		tmp = t_1;
	} else if (y <= -1.55e+38) {
		tmp = t_3;
	} else if (y <= -6e-33) {
		tmp = a - (t * a);
	} else if (y <= -7.2e-106) {
		tmp = t_1;
	} else if (y <= -4.4e-150) {
		tmp = t_2;
	} else if (y <= 6.2e-152) {
		tmp = t_1;
	} else if (y <= 4.8e-73) {
		tmp = t_2;
	} else if (y <= 3.9e+18) {
		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 = a + (z + x)
    t_2 = t * (b - a)
    t_3 = y * (b - z)
    if (y <= (-1.35d+86)) then
        tmp = t_3
    else if (y <= (-1.85d+56)) then
        tmp = t_1
    else if (y <= (-1.55d+38)) then
        tmp = t_3
    else if (y <= (-6d-33)) then
        tmp = a - (t * a)
    else if (y <= (-7.2d-106)) then
        tmp = t_1
    else if (y <= (-4.4d-150)) then
        tmp = t_2
    else if (y <= 6.2d-152) then
        tmp = t_1
    else if (y <= 4.8d-73) then
        tmp = t_2
    else if (y <= 3.9d+18) 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 = a + (z + x);
	double t_2 = t * (b - a);
	double t_3 = y * (b - z);
	double tmp;
	if (y <= -1.35e+86) {
		tmp = t_3;
	} else if (y <= -1.85e+56) {
		tmp = t_1;
	} else if (y <= -1.55e+38) {
		tmp = t_3;
	} else if (y <= -6e-33) {
		tmp = a - (t * a);
	} else if (y <= -7.2e-106) {
		tmp = t_1;
	} else if (y <= -4.4e-150) {
		tmp = t_2;
	} else if (y <= 6.2e-152) {
		tmp = t_1;
	} else if (y <= 4.8e-73) {
		tmp = t_2;
	} else if (y <= 3.9e+18) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (z + x)
	t_2 = t * (b - a)
	t_3 = y * (b - z)
	tmp = 0
	if y <= -1.35e+86:
		tmp = t_3
	elif y <= -1.85e+56:
		tmp = t_1
	elif y <= -1.55e+38:
		tmp = t_3
	elif y <= -6e-33:
		tmp = a - (t * a)
	elif y <= -7.2e-106:
		tmp = t_1
	elif y <= -4.4e-150:
		tmp = t_2
	elif y <= 6.2e-152:
		tmp = t_1
	elif y <= 4.8e-73:
		tmp = t_2
	elif y <= 3.9e+18:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(z + x))
	t_2 = Float64(t * Float64(b - a))
	t_3 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -1.35e+86)
		tmp = t_3;
	elseif (y <= -1.85e+56)
		tmp = t_1;
	elseif (y <= -1.55e+38)
		tmp = t_3;
	elseif (y <= -6e-33)
		tmp = Float64(a - Float64(t * a));
	elseif (y <= -7.2e-106)
		tmp = t_1;
	elseif (y <= -4.4e-150)
		tmp = t_2;
	elseif (y <= 6.2e-152)
		tmp = t_1;
	elseif (y <= 4.8e-73)
		tmp = t_2;
	elseif (y <= 3.9e+18)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (z + x);
	t_2 = t * (b - a);
	t_3 = y * (b - z);
	tmp = 0.0;
	if (y <= -1.35e+86)
		tmp = t_3;
	elseif (y <= -1.85e+56)
		tmp = t_1;
	elseif (y <= -1.55e+38)
		tmp = t_3;
	elseif (y <= -6e-33)
		tmp = a - (t * a);
	elseif (y <= -7.2e-106)
		tmp = t_1;
	elseif (y <= -4.4e-150)
		tmp = t_2;
	elseif (y <= 6.2e-152)
		tmp = t_1;
	elseif (y <= 4.8e-73)
		tmp = t_2;
	elseif (y <= 3.9e+18)
		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[(a + N[(z + x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.35e+86], t$95$3, If[LessEqual[y, -1.85e+56], t$95$1, If[LessEqual[y, -1.55e+38], t$95$3, If[LessEqual[y, -6e-33], N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.2e-106], t$95$1, If[LessEqual[y, -4.4e-150], t$95$2, If[LessEqual[y, 6.2e-152], t$95$1, If[LessEqual[y, 4.8e-73], t$95$2, If[LessEqual[y, 3.9e+18], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.35000000000000009e86 or -1.84999999999999998e56 < y < -1.55000000000000009e38 or 3.9e18 < y

   1. Initial program 96.5%

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

   2. Taylor expanded in y around inf 70.9%

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

   if -1.35000000000000009e86 < y < -1.84999999999999998e56 or -6.0000000000000003e-33 < y < -7.20000000000000025e-106 or -4.3999999999999999e-150 < y < 6.1999999999999997e-152 or 4.80000000000000011e-73 < y < 3.9e18

   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. Taylor expanded in b around 0 80.6%

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

   3. Taylor expanded in t around 0 66.0%

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

      1. sub-neg 66.0%

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

      2. metadata-eval 66.0%

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

      3. distribute-rgt-in 66.1%

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

      4. associate-+l+ 66.1%

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

      5. distribute-lft-out 66.1%

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

      6. mul-1-neg 66.1%

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

      7. remove-double-neg 66.1%

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

      8. mul-1-neg 66.1%

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

      9. remove-double-neg 66.1%

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

      10. mul-1-neg 66.1%

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

      11. distribute-neg-in 66.1%

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

      12. unsub-neg 66.1%

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

      13. *-commutative 66.1%

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

      14. +-commutative 66.1%

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

      15. distribute-neg-in 66.1%

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

      16. mul-1-neg 66.1%

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

      17. remove-double-neg 66.1%

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

      18. mul-1-neg 66.1%

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

      19. remove-double-neg 66.1%

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

   5. Simplified 66.1%

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

   6. Taylor expanded in y around 0 63.6%

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

   if -1.55000000000000009e38 < y < -6.0000000000000003e-33

   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. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-def 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--r+ 100.0%

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

      11. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in a around inf 46.9%

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

      1. +-commutative 46.9%

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

      2. distribute-lft-in 47.0%

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

      3. *-rgt-identity 47.0%

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

      4. mul-1-neg 47.0%

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

      5. distribute-rgt-neg-in 47.0%

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

      6. unsub-neg 47.0%

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

   7. Simplified 47.0%

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

   if -7.20000000000000025e-106 < y < -4.3999999999999999e-150 or 6.1999999999999997e-152 < y < 4.80000000000000011e-73

   1. Initial program 92.9%

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

   2. Taylor expanded in t around inf 66.1%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.85 \cdot 10^{+56}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{+38}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-33}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-106}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-150}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-152}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+18}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 7: 55.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := y \cdot \left(b - z\right)\\ t_3 := a + \left(z + x\right)\\ \mathbf{if}\;y \leq -8.6 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+50}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-105}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-152}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-73}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+18}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))) (t_2 (* y (- b z))) (t_3 (+ a (+ z x))))
   (if (<= y -8.6e+86)
     t_2
     (if (<= y -6.2e+50)
       (- x (* t a))
       (if (<= y -1.7e+24)
         t_2
         (if (<= y -1.3e-105)
           t_3
           (if (<= y -4.6e-150)
             t_1
             (if (<= y 5.8e-152)
               t_3
               (if (<= y 4.4e-73) t_1 (if (<= y 6.6e+18) t_3 t_2))))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double t_3 = a + (z + x);
	double tmp;
	if (y <= -8.6e+86) {
		tmp = t_2;
	} else if (y <= -6.2e+50) {
		tmp = x - (t * a);
	} else if (y <= -1.7e+24) {
		tmp = t_2;
	} else if (y <= -1.3e-105) {
		tmp = t_3;
	} else if (y <= -4.6e-150) {
		tmp = t_1;
	} else if (y <= 5.8e-152) {
		tmp = t_3;
	} else if (y <= 4.4e-73) {
		tmp = t_1;
	} else if (y <= 6.6e+18) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = t * (b - a)
    t_2 = y * (b - z)
    t_3 = a + (z + x)
    if (y <= (-8.6d+86)) then
        tmp = t_2
    else if (y <= (-6.2d+50)) then
        tmp = x - (t * a)
    else if (y <= (-1.7d+24)) then
        tmp = t_2
    else if (y <= (-1.3d-105)) then
        tmp = t_3
    else if (y <= (-4.6d-150)) then
        tmp = t_1
    else if (y <= 5.8d-152) then
        tmp = t_3
    else if (y <= 4.4d-73) then
        tmp = t_1
    else if (y <= 6.6d+18) then
        tmp = t_3
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double t_2 = y * (b - z);
	double t_3 = a + (z + x);
	double tmp;
	if (y <= -8.6e+86) {
		tmp = t_2;
	} else if (y <= -6.2e+50) {
		tmp = x - (t * a);
	} else if (y <= -1.7e+24) {
		tmp = t_2;
	} else if (y <= -1.3e-105) {
		tmp = t_3;
	} else if (y <= -4.6e-150) {
		tmp = t_1;
	} else if (y <= 5.8e-152) {
		tmp = t_3;
	} else if (y <= 4.4e-73) {
		tmp = t_1;
	} else if (y <= 6.6e+18) {
		tmp = t_3;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	t_2 = y * (b - z)
	t_3 = a + (z + x)
	tmp = 0
	if y <= -8.6e+86:
		tmp = t_2
	elif y <= -6.2e+50:
		tmp = x - (t * a)
	elif y <= -1.7e+24:
		tmp = t_2
	elif y <= -1.3e-105:
		tmp = t_3
	elif y <= -4.6e-150:
		tmp = t_1
	elif y <= 5.8e-152:
		tmp = t_3
	elif y <= 4.4e-73:
		tmp = t_1
	elif y <= 6.6e+18:
		tmp = t_3
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	t_2 = Float64(y * Float64(b - z))
	t_3 = Float64(a + Float64(z + x))
	tmp = 0.0
	if (y <= -8.6e+86)
		tmp = t_2;
	elseif (y <= -6.2e+50)
		tmp = Float64(x - Float64(t * a));
	elseif (y <= -1.7e+24)
		tmp = t_2;
	elseif (y <= -1.3e-105)
		tmp = t_3;
	elseif (y <= -4.6e-150)
		tmp = t_1;
	elseif (y <= 5.8e-152)
		tmp = t_3;
	elseif (y <= 4.4e-73)
		tmp = t_1;
	elseif (y <= 6.6e+18)
		tmp = t_3;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	t_2 = y * (b - z);
	t_3 = a + (z + x);
	tmp = 0.0;
	if (y <= -8.6e+86)
		tmp = t_2;
	elseif (y <= -6.2e+50)
		tmp = x - (t * a);
	elseif (y <= -1.7e+24)
		tmp = t_2;
	elseif (y <= -1.3e-105)
		tmp = t_3;
	elseif (y <= -4.6e-150)
		tmp = t_1;
	elseif (y <= 5.8e-152)
		tmp = t_3;
	elseif (y <= 4.4e-73)
		tmp = t_1;
	elseif (y <= 6.6e+18)
		tmp = t_3;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(a + N[(z + x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.6e+86], t$95$2, If[LessEqual[y, -6.2e+50], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.7e+24], t$95$2, If[LessEqual[y, -1.3e-105], t$95$3, If[LessEqual[y, -4.6e-150], t$95$1, If[LessEqual[y, 5.8e-152], t$95$3, If[LessEqual[y, 4.4e-73], t$95$1, If[LessEqual[y, 6.6e+18], t$95$3, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.6000000000000004e86 or -6.20000000000000006e50 < y < -1.7e24 or 6.6e18 < y

   1. Initial program 96.5%

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

   2. Taylor expanded in y around inf 70.8%

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

   if -8.6000000000000004e86 < y < -6.20000000000000006e50

   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. Taylor expanded in b around 0 93.6%

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

   3. Taylor expanded in t around inf 64.7%

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

   if -1.7e24 < y < -1.2999999999999999e-105 or -4.60000000000000006e-150 < y < 5.8000000000000003e-152 or 4.4e-73 < y < 6.6e18

   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. Taylor expanded in b around 0 79.6%

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

   3. Taylor expanded in t around 0 63.4%

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

      1. sub-neg 63.4%

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

      2. metadata-eval 63.4%

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

      3. distribute-rgt-in 63.4%

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

      4. associate-+l+ 63.4%

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

      5. distribute-lft-out 63.4%

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

      6. mul-1-neg 63.4%

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

      7. remove-double-neg 63.4%

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

      8. mul-1-neg 63.4%

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

      9. remove-double-neg 63.4%

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

      10. mul-1-neg 63.4%

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

      11. distribute-neg-in 63.4%

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

      12. unsub-neg 63.4%

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

      13. *-commutative 63.4%

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

      14. +-commutative 63.4%

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

      15. distribute-neg-in 63.4%

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

      16. mul-1-neg 63.4%

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

      17. remove-double-neg 63.4%

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

      18. mul-1-neg 63.4%

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

      19. remove-double-neg 63.4%

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

   5. Simplified 63.4%

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

   6. Taylor expanded in y around 0 60.9%

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

   if -1.2999999999999999e-105 < y < -4.60000000000000006e-150 or 5.8000000000000003e-152 < y < 4.4e-73

   1. Initial program 92.9%

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

   2. Taylor expanded in t around inf 66.1%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+86}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{+50}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+24}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-105}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-150}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-152}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-73}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+18}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 8: 40.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -520000000000:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-29}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-204}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-109}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+107}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1e+63)
     t_1
     (if (<= a -520000000000.0)
       (* y (- z))
       (if (<= a -3.2e-29)
         (+ z x)
         (if (<= a -1.65e-55)
           (* b (- t 2.0))
           (if (<= a 5.4e-204)
             (+ z x)
             (if (<= a 8e-109) (* b y) (if (<= a 8e+107) (+ z x) 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 <= -1e+63) {
		tmp = t_1;
	} else if (a <= -520000000000.0) {
		tmp = y * -z;
	} else if (a <= -3.2e-29) {
		tmp = z + x;
	} else if (a <= -1.65e-55) {
		tmp = b * (t - 2.0);
	} else if (a <= 5.4e-204) {
		tmp = z + x;
	} else if (a <= 8e-109) {
		tmp = b * y;
	} else if (a <= 8e+107) {
		tmp = z + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-1d+63)) then
        tmp = t_1
    else if (a <= (-520000000000.0d0)) then
        tmp = y * -z
    else if (a <= (-3.2d-29)) then
        tmp = z + x
    else if (a <= (-1.65d-55)) then
        tmp = b * (t - 2.0d0)
    else if (a <= 5.4d-204) then
        tmp = z + x
    else if (a <= 8d-109) then
        tmp = b * y
    else if (a <= 8d+107) then
        tmp = z + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1e+63) {
		tmp = t_1;
	} else if (a <= -520000000000.0) {
		tmp = y * -z;
	} else if (a <= -3.2e-29) {
		tmp = z + x;
	} else if (a <= -1.65e-55) {
		tmp = b * (t - 2.0);
	} else if (a <= 5.4e-204) {
		tmp = z + x;
	} else if (a <= 8e-109) {
		tmp = b * y;
	} else if (a <= 8e+107) {
		tmp = z + x;
	} 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 <= -1e+63:
		tmp = t_1
	elif a <= -520000000000.0:
		tmp = y * -z
	elif a <= -3.2e-29:
		tmp = z + x
	elif a <= -1.65e-55:
		tmp = b * (t - 2.0)
	elif a <= 5.4e-204:
		tmp = z + x
	elif a <= 8e-109:
		tmp = b * y
	elif a <= 8e+107:
		tmp = z + x
	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 <= -1e+63)
		tmp = t_1;
	elseif (a <= -520000000000.0)
		tmp = Float64(y * Float64(-z));
	elseif (a <= -3.2e-29)
		tmp = Float64(z + x);
	elseif (a <= -1.65e-55)
		tmp = Float64(b * Float64(t - 2.0));
	elseif (a <= 5.4e-204)
		tmp = Float64(z + x);
	elseif (a <= 8e-109)
		tmp = Float64(b * y);
	elseif (a <= 8e+107)
		tmp = Float64(z + x);
	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 <= -1e+63)
		tmp = t_1;
	elseif (a <= -520000000000.0)
		tmp = y * -z;
	elseif (a <= -3.2e-29)
		tmp = z + x;
	elseif (a <= -1.65e-55)
		tmp = b * (t - 2.0);
	elseif (a <= 5.4e-204)
		tmp = z + x;
	elseif (a <= 8e-109)
		tmp = b * y;
	elseif (a <= 8e+107)
		tmp = z + x;
	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, -1e+63], t$95$1, If[LessEqual[a, -520000000000.0], N[(y * (-z)), $MachinePrecision], If[LessEqual[a, -3.2e-29], N[(z + x), $MachinePrecision], If[LessEqual[a, -1.65e-55], N[(b * N[(t - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 5.4e-204], N[(z + x), $MachinePrecision], If[LessEqual[a, 8e-109], N[(b * y), $MachinePrecision], If[LessEqual[a, 8e+107], N[(z + x), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if a < -1.00000000000000006e63 or 7.9999999999999998e107 < a

   1. Initial program 96.1%

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

   2. Taylor expanded in a around inf 62.7%

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

   if -1.00000000000000006e63 < a < -5.2e11

   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. Taylor expanded in z around inf 83.9%

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

   3. Taylor expanded in y around inf 68.9%

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

      1. mul-1-neg 68.9%

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

      2. distribute-rgt-neg-in 68.9%

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

   5. Simplified 68.9%

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

   if -5.2e11 < a < -3.2e-29 or -1.65e-55 < a < 5.39999999999999983e-204 or 7.9999999999999999e-109 < a < 7.9999999999999998e107

   1. Initial program 99.2%

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

   2. Taylor expanded in b around 0 69.2%

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

   3. Taylor expanded in a around 0 59.9%

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

   4. Taylor expanded in y around 0 39.2%

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

      1. sub-neg 39.2%

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

      2. neg-mul-1 39.2%

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

      3. remove-double-neg 39.2%

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

      4. +-commutative 39.2%

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

   6. Simplified 39.2%

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

   if -3.2e-29 < a < -1.65e-55

   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. Taylor expanded in b around inf 60.8%

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

   3. Taylor expanded in y around 0 60.8%

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

   if 5.39999999999999983e-204 < a < 7.9999999999999999e-109

   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. Taylor expanded in y around inf 54.7%

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

   3. Taylor expanded in b around inf 48.0%

      \[\leadsto \color{blue}{y \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1 \cdot 10^{+63}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -520000000000:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-29}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq -1.65 \cdot 10^{-55}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-204}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 8 \cdot 10^{-109}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;a \leq 8 \cdot 10^{+107}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 9: 50.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-204}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-55}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 10500:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -1.7e+62)
     t_2
     (if (<= t -8.6e+38)
       (* z (- 1.0 y))
       (if (<= t -5.6e-15)
         t_1
         (if (<= t -2.3e-204)
           (+ a x)
           (if (<= t 4.3e-186)
             t_1
             (if (<= t 8e-55) (+ z x) (if (<= t 10500.0) 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 <= -1.7e+62) {
		tmp = t_2;
	} else if (t <= -8.6e+38) {
		tmp = z * (1.0 - y);
	} else if (t <= -5.6e-15) {
		tmp = t_1;
	} else if (t <= -2.3e-204) {
		tmp = a + x;
	} else if (t <= 4.3e-186) {
		tmp = t_1;
	} else if (t <= 8e-55) {
		tmp = z + x;
	} else if (t <= 10500.0) {
		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 <= (-1.7d+62)) then
        tmp = t_2
    else if (t <= (-8.6d+38)) then
        tmp = z * (1.0d0 - y)
    else if (t <= (-5.6d-15)) then
        tmp = t_1
    else if (t <= (-2.3d-204)) then
        tmp = a + x
    else if (t <= 4.3d-186) then
        tmp = t_1
    else if (t <= 8d-55) then
        tmp = z + x
    else if (t <= 10500.0d0) 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 <= -1.7e+62) {
		tmp = t_2;
	} else if (t <= -8.6e+38) {
		tmp = z * (1.0 - y);
	} else if (t <= -5.6e-15) {
		tmp = t_1;
	} else if (t <= -2.3e-204) {
		tmp = a + x;
	} else if (t <= 4.3e-186) {
		tmp = t_1;
	} else if (t <= 8e-55) {
		tmp = z + x;
	} else if (t <= 10500.0) {
		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 <= -1.7e+62:
		tmp = t_2
	elif t <= -8.6e+38:
		tmp = z * (1.0 - y)
	elif t <= -5.6e-15:
		tmp = t_1
	elif t <= -2.3e-204:
		tmp = a + x
	elif t <= 4.3e-186:
		tmp = t_1
	elif t <= 8e-55:
		tmp = z + x
	elif t <= 10500.0:
		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 <= -1.7e+62)
		tmp = t_2;
	elseif (t <= -8.6e+38)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= -5.6e-15)
		tmp = t_1;
	elseif (t <= -2.3e-204)
		tmp = Float64(a + x);
	elseif (t <= 4.3e-186)
		tmp = t_1;
	elseif (t <= 8e-55)
		tmp = Float64(z + x);
	elseif (t <= 10500.0)
		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 <= -1.7e+62)
		tmp = t_2;
	elseif (t <= -8.6e+38)
		tmp = z * (1.0 - y);
	elseif (t <= -5.6e-15)
		tmp = t_1;
	elseif (t <= -2.3e-204)
		tmp = a + x;
	elseif (t <= 4.3e-186)
		tmp = t_1;
	elseif (t <= 8e-55)
		tmp = z + x;
	elseif (t <= 10500.0)
		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, -1.7e+62], t$95$2, If[LessEqual[t, -8.6e+38], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -5.6e-15], t$95$1, If[LessEqual[t, -2.3e-204], N[(a + x), $MachinePrecision], If[LessEqual[t, 4.3e-186], t$95$1, If[LessEqual[t, 8e-55], N[(z + x), $MachinePrecision], If[LessEqual[t, 10500.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.70000000000000007e62 or 10500 < t

   1. Initial program 95.4%

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

   2. Taylor expanded in t around inf 66.2%

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

   if -1.70000000000000007e62 < t < -8.5999999999999994e38

   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. Taylor expanded in z around inf 80.8%

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

   if -8.5999999999999994e38 < t < -5.60000000000000028e-15 or -2.2999999999999999e-204 < t < 4.2999999999999999e-186 or 7.99999999999999996e-55 < t < 10500

   1. Initial program 98.6%

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

   2. Taylor expanded in y around inf 54.6%

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

   if -5.60000000000000028e-15 < t < -2.2999999999999999e-204

   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. Taylor expanded in b around 0 74.1%

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

   3. Taylor expanded in t around 0 74.0%

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

      1. sub-neg 74.0%

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

      2. metadata-eval 74.0%

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

      3. distribute-rgt-in 74.0%

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

      4. associate-+l+ 74.0%

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

      5. distribute-lft-out 74.0%

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

      6. mul-1-neg 74.0%

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

      7. remove-double-neg 74.0%

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

      8. mul-1-neg 74.0%

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

      9. remove-double-neg 74.0%

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

      10. mul-1-neg 74.0%

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

      11. distribute-neg-in 74.0%

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

      12. unsub-neg 74.0%

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

      13. *-commutative 74.0%

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

      14. +-commutative 74.0%

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

      15. distribute-neg-in 74.0%

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

      16. mul-1-neg 74.0%

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

      17. remove-double-neg 74.0%

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

      18. mul-1-neg 74.0%

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

      19. remove-double-neg 74.0%

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

   5. Simplified 74.0%

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

   6. Taylor expanded in z around 0 55.5%

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

   if 4.2999999999999999e-186 < t < 7.99999999999999996e-55

   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. Taylor expanded in b around 0 80.8%

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

   3. Taylor expanded in a around 0 67.2%

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

   4. Taylor expanded in y around 0 52.7%

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

      1. sub-neg 52.7%

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

      2. neg-mul-1 52.7%

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

      3. remove-double-neg 52.7%

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

      4. +-commutative 52.7%

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

   6. Simplified 52.7%

      \[\leadsto \color{blue}{z + x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -5.6 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-204}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 4.3 \cdot 10^{-186}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 8 \cdot 10^{-55}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 10500:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 10: 50.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-183}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-161}:\\ \;\;\;\;a + b \cdot y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-56}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 10500:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))) (t_2 (* t (- b a))))
   (if (<= t -1.85e+62)
     t_2
     (if (<= t -3.8e+38)
       (* z (- 1.0 y))
       (if (<= t -2.75e-14)
         t_1
         (if (<= t -3.3e-183)
           (+ a x)
           (if (<= t 4e-161)
             (+ a (* b y))
             (if (<= t 6.8e-56) (+ z x) (if (<= t 10500.0) 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 <= -1.85e+62) {
		tmp = t_2;
	} else if (t <= -3.8e+38) {
		tmp = z * (1.0 - y);
	} else if (t <= -2.75e-14) {
		tmp = t_1;
	} else if (t <= -3.3e-183) {
		tmp = a + x;
	} else if (t <= 4e-161) {
		tmp = a + (b * y);
	} else if (t <= 6.8e-56) {
		tmp = z + x;
	} else if (t <= 10500.0) {
		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 <= (-1.85d+62)) then
        tmp = t_2
    else if (t <= (-3.8d+38)) then
        tmp = z * (1.0d0 - y)
    else if (t <= (-2.75d-14)) then
        tmp = t_1
    else if (t <= (-3.3d-183)) then
        tmp = a + x
    else if (t <= 4d-161) then
        tmp = a + (b * y)
    else if (t <= 6.8d-56) then
        tmp = z + x
    else if (t <= 10500.0d0) 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 <= -1.85e+62) {
		tmp = t_2;
	} else if (t <= -3.8e+38) {
		tmp = z * (1.0 - y);
	} else if (t <= -2.75e-14) {
		tmp = t_1;
	} else if (t <= -3.3e-183) {
		tmp = a + x;
	} else if (t <= 4e-161) {
		tmp = a + (b * y);
	} else if (t <= 6.8e-56) {
		tmp = z + x;
	} else if (t <= 10500.0) {
		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 <= -1.85e+62:
		tmp = t_2
	elif t <= -3.8e+38:
		tmp = z * (1.0 - y)
	elif t <= -2.75e-14:
		tmp = t_1
	elif t <= -3.3e-183:
		tmp = a + x
	elif t <= 4e-161:
		tmp = a + (b * y)
	elif t <= 6.8e-56:
		tmp = z + x
	elif t <= 10500.0:
		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 <= -1.85e+62)
		tmp = t_2;
	elseif (t <= -3.8e+38)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (t <= -2.75e-14)
		tmp = t_1;
	elseif (t <= -3.3e-183)
		tmp = Float64(a + x);
	elseif (t <= 4e-161)
		tmp = Float64(a + Float64(b * y));
	elseif (t <= 6.8e-56)
		tmp = Float64(z + x);
	elseif (t <= 10500.0)
		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 <= -1.85e+62)
		tmp = t_2;
	elseif (t <= -3.8e+38)
		tmp = z * (1.0 - y);
	elseif (t <= -2.75e-14)
		tmp = t_1;
	elseif (t <= -3.3e-183)
		tmp = a + x;
	elseif (t <= 4e-161)
		tmp = a + (b * y);
	elseif (t <= 6.8e-56)
		tmp = z + x;
	elseif (t <= 10500.0)
		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, -1.85e+62], t$95$2, If[LessEqual[t, -3.8e+38], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -2.75e-14], t$95$1, If[LessEqual[t, -3.3e-183], N[(a + x), $MachinePrecision], If[LessEqual[t, 4e-161], N[(a + N[(b * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e-56], N[(z + x), $MachinePrecision], If[LessEqual[t, 10500.0], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if t < -1.85000000000000007e62 or 10500 < t

   1. Initial program 95.4%

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

   2. Taylor expanded in t around inf 66.2%

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

   if -1.85000000000000007e62 < t < -3.7999999999999998e38

   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. Taylor expanded in z around inf 80.8%

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

   if -3.7999999999999998e38 < t < -2.74999999999999996e-14 or 6.79999999999999964e-56 < t < 10500

   1. Initial program 95.7%

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

   2. Taylor expanded in y around inf 54.9%

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

   if -2.74999999999999996e-14 < t < -3.3e-183

   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. Taylor expanded in b around 0 77.8%

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

   3. Taylor expanded in t around 0 77.7%

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

      1. sub-neg 77.7%

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

      2. metadata-eval 77.7%

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

      3. distribute-rgt-in 77.7%

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

      4. associate-+l+ 77.7%

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

      5. distribute-lft-out 77.7%

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

      6. mul-1-neg 77.7%

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

      7. remove-double-neg 77.7%

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

      8. mul-1-neg 77.7%

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

      9. remove-double-neg 77.7%

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

      10. mul-1-neg 77.7%

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

      11. distribute-neg-in 77.7%

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

      12. unsub-neg 77.7%

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

      13. *-commutative 77.7%

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

      14. +-commutative 77.7%

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

      15. distribute-neg-in 77.7%

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

      16. mul-1-neg 77.7%

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

      17. remove-double-neg 77.7%

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

      18. mul-1-neg 77.7%

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

      19. remove-double-neg 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in z around 0 54.8%

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

   if -3.3e-183 < t < 4.00000000000000011e-161

   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. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-def 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--r+ 100.0%

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

      11. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 72.5%

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

   6. Taylor expanded in x around 0 60.3%

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

      1. fma-def 60.3%

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

      2. sub-neg 60.3%

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

      3. metadata-eval 60.3%

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

      4. *-commutative 60.3%

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

   8. Simplified 60.3%

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

   9. Taylor expanded in y around inf 54.4%

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

   if 4.00000000000000011e-161 < t < 6.79999999999999964e-56

   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. Taylor expanded in b around 0 81.3%

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

   3. Taylor expanded in a around 0 71.9%

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

   4. Taylor expanded in y around 0 60.4%

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

      1. sub-neg 60.4%

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

      2. neg-mul-1 60.4%

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

      3. remove-double-neg 60.4%

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

      4. +-commutative 60.4%

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

   6. Simplified 60.4%

      \[\leadsto \color{blue}{z + x} \]
3. Recombined 6 regimes into one program.

4. Final simplification 60.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+62}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -3.8 \cdot 10^{+38}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -2.75 \cdot 10^{-14}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -3.3 \cdot 10^{-183}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-161}:\\ \;\;\;\;a + b \cdot y\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{-56}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 10500:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 11: 59.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -1.16 \cdot 10^{+110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-170}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-77}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 10^{+16}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (* z (- 1.0 y)))) (t_2 (* b (- (+ t y) 2.0))))
   (if (<= b -1.16e+110)
     t_2
     (if (<= b 3.7e-225)
       t_1
       (if (<= b 5.8e-170)
         (- a (* t a))
         (if (<= b 1.05e-129)
           t_1
           (if (<= b 6e-77) (- x (* t a)) (if (<= b 1e+16) t_1 t_2))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -1.16e+110) {
		tmp = t_2;
	} else if (b <= 3.7e-225) {
		tmp = t_1;
	} else if (b <= 5.8e-170) {
		tmp = a - (t * a);
	} else if (b <= 1.05e-129) {
		tmp = t_1;
	} else if (b <= 6e-77) {
		tmp = x - (t * a);
	} else if (b <= 1e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (1.0d0 - y))
    t_2 = b * ((t + y) - 2.0d0)
    if (b <= (-1.16d+110)) then
        tmp = t_2
    else if (b <= 3.7d-225) then
        tmp = t_1
    else if (b <= 5.8d-170) then
        tmp = a - (t * a)
    else if (b <= 1.05d-129) then
        tmp = t_1
    else if (b <= 6d-77) then
        tmp = x - (t * a)
    else if (b <= 1d+16) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + (z * (1.0 - y));
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -1.16e+110) {
		tmp = t_2;
	} else if (b <= 3.7e-225) {
		tmp = t_1;
	} else if (b <= 5.8e-170) {
		tmp = a - (t * a);
	} else if (b <= 1.05e-129) {
		tmp = t_1;
	} else if (b <= 6e-77) {
		tmp = x - (t * a);
	} else if (b <= 1e+16) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + (z * (1.0 - y))
	t_2 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -1.16e+110:
		tmp = t_2
	elif b <= 3.7e-225:
		tmp = t_1
	elif b <= 5.8e-170:
		tmp = a - (t * a)
	elif b <= 1.05e-129:
		tmp = t_1
	elif b <= 6e-77:
		tmp = x - (t * a)
	elif b <= 1e+16:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -1.16e+110)
		tmp = t_2;
	elseif (b <= 3.7e-225)
		tmp = t_1;
	elseif (b <= 5.8e-170)
		tmp = Float64(a - Float64(t * a));
	elseif (b <= 1.05e-129)
		tmp = t_1;
	elseif (b <= 6e-77)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 1e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + (z * (1.0 - y));
	t_2 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -1.16e+110)
		tmp = t_2;
	elseif (b <= 3.7e-225)
		tmp = t_1;
	elseif (b <= 5.8e-170)
		tmp = a - (t * a);
	elseif (b <= 1.05e-129)
		tmp = t_1;
	elseif (b <= 6e-77)
		tmp = x - (t * a);
	elseif (b <= 1e+16)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.16e+110], t$95$2, If[LessEqual[b, 3.7e-225], t$95$1, If[LessEqual[b, 5.8e-170], N[(a - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.05e-129], t$95$1, If[LessEqual[b, 6e-77], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1e+16], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -1.16e110 or 1e16 < b

   1. Initial program 93.8%

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

   2. Taylor expanded in b around inf 72.8%

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

   if -1.16e110 < b < 3.69999999999999988e-225 or 5.8000000000000001e-170 < b < 1.05e-129 or 6.00000000000000033e-77 < b < 1e16

   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. Taylor expanded in b around 0 90.8%

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

   3. Taylor expanded in a around 0 63.6%

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

   if 3.69999999999999988e-225 < b < 5.8000000000000001e-170

   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. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-def 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--r+ 100.0%

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

      11. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in a around inf 67.9%

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

      1. +-commutative 67.9%

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

      2. distribute-lft-in 68.1%

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

      3. *-rgt-identity 68.1%

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

      4. mul-1-neg 68.1%

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

      5. distribute-rgt-neg-in 68.1%

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

      6. unsub-neg 68.1%

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

   7. Simplified 68.1%

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

   if 1.05e-129 < b < 6.00000000000000033e-77

   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. Taylor expanded in b around 0 93.3%

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

   3. Taylor expanded in t around inf 79.4%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.16 \cdot 10^{+110}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-225}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-170}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;b \leq 1.05 \cdot 10^{-129}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-77}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 10^{+16}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 12: 74.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \left(a \cdot \left(t + -1\right) + y \cdot z\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -1.15 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+115}:\\ \;\;\;\;\left(x + b \cdot \left(y - 2\right)\right) + t \cdot b\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (- x (+ (* a (+ t -1.0)) (* y z)))) (t_2 (* b (- (+ t y) 2.0))))
   (if (<= b -1.15e+89)
     t_2
     (if (<= b 2.4e+24)
       t_1
       (if (<= b 4e+115)
         (+ (+ x (* b (- y 2.0))) (* t b))
         (if (<= b 1.35e+133) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((a * (t + -1.0)) + (y * z));
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -1.15e+89) {
		tmp = t_2;
	} else if (b <= 2.4e+24) {
		tmp = t_1;
	} else if (b <= 4e+115) {
		tmp = (x + (b * (y - 2.0))) + (t * b);
	} else if (b <= 1.35e+133) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x - ((a * (t + (-1.0d0))) + (y * z))
    t_2 = b * ((t + y) - 2.0d0)
    if (b <= (-1.15d+89)) then
        tmp = t_2
    else if (b <= 2.4d+24) then
        tmp = t_1
    else if (b <= 4d+115) then
        tmp = (x + (b * (y - 2.0d0))) + (t * b)
    else if (b <= 1.35d+133) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x - ((a * (t + -1.0)) + (y * z));
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -1.15e+89) {
		tmp = t_2;
	} else if (b <= 2.4e+24) {
		tmp = t_1;
	} else if (b <= 4e+115) {
		tmp = (x + (b * (y - 2.0))) + (t * b);
	} else if (b <= 1.35e+133) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x - ((a * (t + -1.0)) + (y * z))
	t_2 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -1.15e+89:
		tmp = t_2
	elif b <= 2.4e+24:
		tmp = t_1
	elif b <= 4e+115:
		tmp = (x + (b * (y - 2.0))) + (t * b)
	elif b <= 1.35e+133:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x - Float64(Float64(a * Float64(t + -1.0)) + Float64(y * z)))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -1.15e+89)
		tmp = t_2;
	elseif (b <= 2.4e+24)
		tmp = t_1;
	elseif (b <= 4e+115)
		tmp = Float64(Float64(x + Float64(b * Float64(y - 2.0))) + Float64(t * b));
	elseif (b <= 1.35e+133)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x - ((a * (t + -1.0)) + (y * z));
	t_2 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -1.15e+89)
		tmp = t_2;
	elseif (b <= 2.4e+24)
		tmp = t_1;
	elseif (b <= 4e+115)
		tmp = (x + (b * (y - 2.0))) + (t * b);
	elseif (b <= 1.35e+133)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x - N[(N[(a * N[(t + -1.0), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -1.15e+89], t$95$2, If[LessEqual[b, 2.4e+24], t$95$1, If[LessEqual[b, 4e+115], N[(N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * b), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+133], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -1.1499999999999999e89 or 1.3500000000000001e133 < b

   1. Initial program 92.3%

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

   2. Taylor expanded in b around inf 80.2%

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

   if -1.1499999999999999e89 < b < 2.4000000000000001e24 or 4.0000000000000001e115 < b < 1.3500000000000001e133

   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. Taylor expanded in b around 0 91.7%

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

   3. Taylor expanded in y around inf 80.5%

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

      1. *-commutative 80.5%

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

   5. Simplified 80.5%

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

   if 2.4000000000000001e24 < b < 4.0000000000000001e115

   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. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. *-commutative 100.0%

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

      5. fma-def 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--r+ 100.0%

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

      11. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 77.0%

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

   6. Taylor expanded in a around 0 66.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.15 \cdot 10^{+89}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 2.4 \cdot 10^{+24}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + y \cdot z\right)\\ \mathbf{elif}\;b \leq 4 \cdot 10^{+115}:\\ \;\;\;\;\left(x + b \cdot \left(y - 2\right)\right) + t \cdot b\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+133}:\\ \;\;\;\;x - \left(a \cdot \left(t + -1\right) + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 13: 86.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+30} \lor \neg \left(b \leq 3.5 \cdot 10^{+15}\right):\\ \;\;\;\;t \cdot \left(b - a\right) + \left(a + \left(x + b \cdot \left(y - 2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -4.5e+30) (not (<= b 3.5e+15)))
   (+ (* t (- b a)) (+ a (+ x (* b (- y 2.0)))))
   (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -4.5e+30) || !(b <= 3.5e+15)) {
		tmp = (t * (b - a)) + (a + (x + (b * (y - 2.0))));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - 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 ((b <= (-4.5d+30)) .or. (.not. (b <= 3.5d+15))) then
        tmp = (t * (b - a)) + (a + (x + (b * (y - 2.0d0))))
    else
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - 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 ((b <= -4.5e+30) || !(b <= 3.5e+15)) {
		tmp = (t * (b - a)) + (a + (x + (b * (y - 2.0))));
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -4.5e+30) or not (b <= 3.5e+15):
		tmp = (t * (b - a)) + (a + (x + (b * (y - 2.0))))
	else:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -4.5e+30) || !(b <= 3.5e+15))
		tmp = Float64(Float64(t * Float64(b - a)) + Float64(a + Float64(x + Float64(b * Float64(y - 2.0)))));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -4.5e+30) || ~((b <= 3.5e+15)))
		tmp = (t * (b - a)) + (a + (x + (b * (y - 2.0))));
	else
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -4.5e+30], N[Not[LessEqual[b, 3.5e+15]], $MachinePrecision]], N[(N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision] + N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -4.49999999999999995e30 or 3.5e15 < b

   1. Initial program 94.6%

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

   2. Taylor expanded in t around 0 93.7%

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

      1. associate--l+ 93.7%

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

      2. fma-def 96.4%

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

      3. associate--l+ 96.4%

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

      4. *-commutative 96.4%

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

      5. fma-def 97.3%

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

      6. sub-neg 97.3%

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

      7. metadata-eval 97.3%

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

      8. sub-neg 97.3%

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

      9. metadata-eval 97.3%

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

      10. associate--r+ 97.3%

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

      11. sub-neg 97.3%

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

   4. Simplified 97.3%

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

   5. Taylor expanded in z around 0 85.1%

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

   if -4.49999999999999995e30 < b < 3.5e15

   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. Taylor expanded in b around 0 93.5%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.5 \cdot 10^{+30} \lor \neg \left(b \leq 3.5 \cdot 10^{+15}\right):\\ \;\;\;\;t \cdot \left(b - a\right) + \left(a + \left(x + b \cdot \left(y - 2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 14: 86.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -4.7 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(b - a\right) + \left(a + \left(x + b \cdot \left(y - 2\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+15}:\\ \;\;\;\;x + \left(t_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -4.7e+30)
     (+ (* t (- b a)) (+ a (+ x (* b (- y 2.0)))))
     (if (<= b 1.8e+15)
       (+ x (+ t_1 (* z (- 1.0 y))))
       (+ (+ x (* b (- (+ t y) 2.0))) 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 (b <= -4.7e+30) {
		tmp = (t * (b - a)) + (a + (x + (b * (y - 2.0))));
	} else if (b <= 1.8e+15) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (x + (b * ((t + y) - 2.0))) + 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 (b <= (-4.7d+30)) then
        tmp = (t * (b - a)) + (a + (x + (b * (y - 2.0d0))))
    else if (b <= 1.8d+15) then
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    else
        tmp = (x + (b * ((t + y) - 2.0d0))) + 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 (b <= -4.7e+30) {
		tmp = (t * (b - a)) + (a + (x + (b * (y - 2.0))));
	} else if (b <= 1.8e+15) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = (x + (b * ((t + y) - 2.0))) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -4.7e+30:
		tmp = (t * (b - a)) + (a + (x + (b * (y - 2.0))))
	elif b <= 1.8e+15:
		tmp = x + (t_1 + (z * (1.0 - y)))
	else:
		tmp = (x + (b * ((t + y) - 2.0))) + 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 (b <= -4.7e+30)
		tmp = Float64(Float64(t * Float64(b - a)) + Float64(a + Float64(x + Float64(b * Float64(y - 2.0)))));
	elseif (b <= 1.8e+15)
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(Float64(x + Float64(b * Float64(Float64(t + y) - 2.0))) + 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 (b <= -4.7e+30)
		tmp = (t * (b - a)) + (a + (x + (b * (y - 2.0))));
	elseif (b <= 1.8e+15)
		tmp = x + (t_1 + (z * (1.0 - y)));
	else
		tmp = (x + (b * ((t + y) - 2.0))) + 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[b, -4.7e+30], N[(N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision] + N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.8e+15], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.6999999999999999e30

   1. Initial program 92.9%

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

   2. Taylor expanded in t around 0 94.7%

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

      1. associate--l+ 94.7%

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

      2. fma-def 96.5%

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

      3. associate--l+ 96.5%

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

      4. *-commutative 96.5%

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

      5. fma-def 96.5%

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

      6. sub-neg 96.5%

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

      7. metadata-eval 96.5%

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

      8. sub-neg 96.5%

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

      9. metadata-eval 96.5%

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

      10. associate--r+ 96.5%

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

      11. sub-neg 96.5%

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

   4. Simplified 96.5%

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

   5. Taylor expanded in z around 0 86.4%

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

   if -4.6999999999999999e30 < b < 1.8e15

   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. Taylor expanded in b around 0 93.5%

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

   if 1.8e15 < b

   1. Initial program 96.3%

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

   2. Taylor expanded in z around 0 87.4%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.7 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(b - a\right) + \left(a + \left(x + b \cdot \left(y - 2\right)\right)\right)\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+15}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 15: 42.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-291}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-8}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+30}:\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- 1.0 y))))
   (if (<= z -2.4e+81)
     t_1
     (if (<= z -4.4e-84)
       (* a (- 1.0 t))
       (if (<= z 2.5e-291)
         (+ a x)
         (if (<= z 1.85e-103)
           (* t (- b a))
           (if (<= z 4.5e-8) (+ a x) (if (<= z 3.2e+30) (* b y) t_1))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -2.4e+81) {
		tmp = t_1;
	} else if (z <= -4.4e-84) {
		tmp = a * (1.0 - t);
	} else if (z <= 2.5e-291) {
		tmp = a + x;
	} else if (z <= 1.85e-103) {
		tmp = t * (b - a);
	} else if (z <= 4.5e-8) {
		tmp = a + x;
	} else if (z <= 3.2e+30) {
		tmp = b * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = z * (1.0d0 - y)
    if (z <= (-2.4d+81)) then
        tmp = t_1
    else if (z <= (-4.4d-84)) then
        tmp = a * (1.0d0 - t)
    else if (z <= 2.5d-291) then
        tmp = a + x
    else if (z <= 1.85d-103) then
        tmp = t * (b - a)
    else if (z <= 4.5d-8) then
        tmp = a + x
    else if (z <= 3.2d+30) then
        tmp = b * y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (1.0 - y);
	double tmp;
	if (z <= -2.4e+81) {
		tmp = t_1;
	} else if (z <= -4.4e-84) {
		tmp = a * (1.0 - t);
	} else if (z <= 2.5e-291) {
		tmp = a + x;
	} else if (z <= 1.85e-103) {
		tmp = t * (b - a);
	} else if (z <= 4.5e-8) {
		tmp = a + x;
	} else if (z <= 3.2e+30) {
		tmp = b * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (1.0 - y)
	tmp = 0
	if z <= -2.4e+81:
		tmp = t_1
	elif z <= -4.4e-84:
		tmp = a * (1.0 - t)
	elif z <= 2.5e-291:
		tmp = a + x
	elif z <= 1.85e-103:
		tmp = t * (b - a)
	elif z <= 4.5e-8:
		tmp = a + x
	elif z <= 3.2e+30:
		tmp = b * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(1.0 - y))
	tmp = 0.0
	if (z <= -2.4e+81)
		tmp = t_1;
	elseif (z <= -4.4e-84)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (z <= 2.5e-291)
		tmp = Float64(a + x);
	elseif (z <= 1.85e-103)
		tmp = Float64(t * Float64(b - a));
	elseif (z <= 4.5e-8)
		tmp = Float64(a + x);
	elseif (z <= 3.2e+30)
		tmp = Float64(b * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (1.0 - y);
	tmp = 0.0;
	if (z <= -2.4e+81)
		tmp = t_1;
	elseif (z <= -4.4e-84)
		tmp = a * (1.0 - t);
	elseif (z <= 2.5e-291)
		tmp = a + x;
	elseif (z <= 1.85e-103)
		tmp = t * (b - a);
	elseif (z <= 4.5e-8)
		tmp = a + x;
	elseif (z <= 3.2e+30)
		tmp = b * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.4e+81], t$95$1, If[LessEqual[z, -4.4e-84], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.5e-291], N[(a + x), $MachinePrecision], If[LessEqual[z, 1.85e-103], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.5e-8], N[(a + x), $MachinePrecision], If[LessEqual[z, 3.2e+30], N[(b * y), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.3999999999999999e81 or 3.19999999999999973e30 < z

   1. Initial program 96.8%

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

   2. Taylor expanded in z around inf 62.1%

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

   if -2.3999999999999999e81 < z < -4.3999999999999998e-84

   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. Taylor expanded in a around inf 54.7%

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

   if -4.3999999999999998e-84 < z < 2.5000000000000002e-291 or 1.85e-103 < z < 4.49999999999999993e-8

   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. Taylor expanded in b around 0 69.5%

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

   3. Taylor expanded in t around 0 57.5%

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

      1. sub-neg 57.5%

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

      2. metadata-eval 57.5%

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

      3. distribute-rgt-in 57.5%

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

      4. associate-+l+ 57.5%

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

      5. distribute-lft-out 57.5%

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

      6. mul-1-neg 57.5%

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

      7. remove-double-neg 57.5%

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

      8. mul-1-neg 57.5%

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

      9. remove-double-neg 57.5%

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

      10. mul-1-neg 57.5%

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

      11. distribute-neg-in 57.5%

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

      12. unsub-neg 57.5%

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

      13. *-commutative 57.5%

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

      14. +-commutative 57.5%

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

      15. distribute-neg-in 57.5%

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

      16. mul-1-neg 57.5%

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

      17. remove-double-neg 57.5%

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

      18. mul-1-neg 57.5%

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

      19. remove-double-neg 57.5%

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

   5. Simplified 57.5%

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

   6. Taylor expanded in z around 0 53.7%

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

   if 2.5000000000000002e-291 < z < 1.85e-103

   1. Initial program 92.6%

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

   2. Taylor expanded in t around inf 45.5%

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

   if 4.49999999999999993e-8 < z < 3.19999999999999973e30

   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. Taylor expanded in y around inf 58.6%

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

   3. Taylor expanded in b around inf 51.4%

      \[\leadsto \color{blue}{y \cdot b} \]
3. Recombined 5 regimes into one program.

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+81}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-84}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-291}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-103}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-8}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+30}:\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 16: 60.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -1600000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-135}:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-76}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-52}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;b \leq 52000000000000:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* b (- (+ t y) 2.0))))
   (if (<= b -1600000.0)
     t_1
     (if (<= b 5.8e-135)
       (+ x (- a (* y z)))
       (if (<= b 7.5e-76)
         (- x (* t a))
         (if (<= b 7.2e-52)
           (+ a (+ z x))
           (if (<= b 52000000000000.0) (+ x (* z (- 1.0 y))) 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 <= -1600000.0) {
		tmp = t_1;
	} else if (b <= 5.8e-135) {
		tmp = x + (a - (y * z));
	} else if (b <= 7.5e-76) {
		tmp = x - (t * a);
	} else if (b <= 7.2e-52) {
		tmp = a + (z + x);
	} else if (b <= 52000000000000.0) {
		tmp = x + (z * (1.0 - y));
	} 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 <= (-1600000.0d0)) then
        tmp = t_1
    else if (b <= 5.8d-135) then
        tmp = x + (a - (y * z))
    else if (b <= 7.5d-76) then
        tmp = x - (t * a)
    else if (b <= 7.2d-52) then
        tmp = a + (z + x)
    else if (b <= 52000000000000.0d0) then
        tmp = x + (z * (1.0d0 - y))
    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 <= -1600000.0) {
		tmp = t_1;
	} else if (b <= 5.8e-135) {
		tmp = x + (a - (y * z));
	} else if (b <= 7.5e-76) {
		tmp = x - (t * a);
	} else if (b <= 7.2e-52) {
		tmp = a + (z + x);
	} else if (b <= 52000000000000.0) {
		tmp = x + (z * (1.0 - y));
	} 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 <= -1600000.0:
		tmp = t_1
	elif b <= 5.8e-135:
		tmp = x + (a - (y * z))
	elif b <= 7.5e-76:
		tmp = x - (t * a)
	elif b <= 7.2e-52:
		tmp = a + (z + x)
	elif b <= 52000000000000.0:
		tmp = x + (z * (1.0 - y))
	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 <= -1600000.0)
		tmp = t_1;
	elseif (b <= 5.8e-135)
		tmp = Float64(x + Float64(a - Float64(y * z)));
	elseif (b <= 7.5e-76)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 7.2e-52)
		tmp = Float64(a + Float64(z + x));
	elseif (b <= 52000000000000.0)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	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 <= -1600000.0)
		tmp = t_1;
	elseif (b <= 5.8e-135)
		tmp = x + (a - (y * z));
	elseif (b <= 7.5e-76)
		tmp = x - (t * a);
	elseif (b <= 7.2e-52)
		tmp = a + (z + x);
	elseif (b <= 52000000000000.0)
		tmp = x + (z * (1.0 - y));
	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, -1600000.0], t$95$1, If[LessEqual[b, 5.8e-135], N[(x + N[(a - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.5e-76], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 7.2e-52], N[(a + N[(z + x), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 52000000000000.0], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -1.6e6 or 5.2e13 < b

   1. Initial program 94.8%

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

   2. Taylor expanded in b around inf 67.0%

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

   if -1.6e6 < b < 5.8000000000000004e-135

   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. Taylor expanded in b around 0 94.4%

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

   3. Taylor expanded in y around inf 85.3%

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

      1. *-commutative 85.3%

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

   5. Simplified 85.3%

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

   6. Taylor expanded in t around 0 66.7%

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

      1. neg-mul-1 66.7%

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

   8. Simplified 66.7%

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

   if 5.8000000000000004e-135 < b < 7.4999999999999997e-76

   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. Taylor expanded in b around 0 94.5%

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

   3. Taylor expanded in t around inf 77.2%

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

   if 7.4999999999999997e-76 < b < 7.19999999999999976e-52

   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. Taylor expanded in b around 0 100.0%

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

   3. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. metadata-eval 100.0%

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

      3. distribute-rgt-in 100.0%

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

      4. associate-+l+ 100.0%

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

      5. distribute-lft-out 100.0%

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

      6. mul-1-neg 100.0%

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

      7. remove-double-neg 100.0%

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

      8. mul-1-neg 100.0%

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

      9. remove-double-neg 100.0%

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

      10. mul-1-neg 100.0%

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

      11. distribute-neg-in 100.0%

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

      12. unsub-neg 100.0%

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

      13. *-commutative 100.0%

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

      14. +-commutative 100.0%

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

      15. distribute-neg-in 100.0%

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

      16. mul-1-neg 100.0%

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

      17. remove-double-neg 100.0%

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

      18. mul-1-neg 100.0%

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

      19. remove-double-neg 100.0%

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

   5. Simplified 100.0%

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

   6. Taylor expanded in y around 0 87.2%

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

   if 7.19999999999999976e-52 < b < 5.2e13

   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. Taylor expanded in b around 0 85.5%

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

   3. Taylor expanded in a around 0 69.6%

      \[\leadsto \color{blue}{x - z \cdot \left(y - 1\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1600000:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{-135}:\\ \;\;\;\;x + \left(a - y \cdot z\right)\\ \mathbf{elif}\;b \leq 7.5 \cdot 10^{-76}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-52}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;b \leq 52000000000000:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 17: 67.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(\left(a + z\right) - y \cdot z\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -7.2 \cdot 10^{+109}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-76}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+133}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (- (+ a z) (* y z)))) (t_2 (* b (- (+ t y) 2.0))))
   (if (<= b -7.2e+109)
     t_2
     (if (<= b 2e-126)
       t_1
       (if (<= b 1.25e-76) (- x (* t a)) (if (<= b 1.35e+133) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a + z) - (y * z));
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -7.2e+109) {
		tmp = t_2;
	} else if (b <= 2e-126) {
		tmp = t_1;
	} else if (b <= 1.25e-76) {
		tmp = x - (t * a);
	} else if (b <= 1.35e+133) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((a + z) - (y * z))
    t_2 = b * ((t + y) - 2.0d0)
    if (b <= (-7.2d+109)) then
        tmp = t_2
    else if (b <= 2d-126) then
        tmp = t_1
    else if (b <= 1.25d-76) then
        tmp = x - (t * a)
    else if (b <= 1.35d+133) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a + z) - (y * z));
	double t_2 = b * ((t + y) - 2.0);
	double tmp;
	if (b <= -7.2e+109) {
		tmp = t_2;
	} else if (b <= 2e-126) {
		tmp = t_1;
	} else if (b <= 1.25e-76) {
		tmp = x - (t * a);
	} else if (b <= 1.35e+133) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((a + z) - (y * z))
	t_2 = b * ((t + y) - 2.0)
	tmp = 0
	if b <= -7.2e+109:
		tmp = t_2
	elif b <= 2e-126:
		tmp = t_1
	elif b <= 1.25e-76:
		tmp = x - (t * a)
	elif b <= 1.35e+133:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(a + z) - Float64(y * z)))
	t_2 = Float64(b * Float64(Float64(t + y) - 2.0))
	tmp = 0.0
	if (b <= -7.2e+109)
		tmp = t_2;
	elseif (b <= 2e-126)
		tmp = t_1;
	elseif (b <= 1.25e-76)
		tmp = Float64(x - Float64(t * a));
	elseif (b <= 1.35e+133)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((a + z) - (y * z));
	t_2 = b * ((t + y) - 2.0);
	tmp = 0.0;
	if (b <= -7.2e+109)
		tmp = t_2;
	elseif (b <= 2e-126)
		tmp = t_1;
	elseif (b <= 1.25e-76)
		tmp = x - (t * a);
	elseif (b <= 1.35e+133)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(a + z), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -7.2e+109], t$95$2, If[LessEqual[b, 2e-126], t$95$1, If[LessEqual[b, 1.25e-76], N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+133], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -7.2e109 or 1.3500000000000001e133 < b

   1. Initial program 91.8%

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

   2. Taylor expanded in b around inf 81.5%

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

   if -7.2e109 < b < 1.9999999999999999e-126 or 1.2499999999999999e-76 < b < 1.3500000000000001e133

   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. Taylor expanded in b around 0 86.8%

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

   3. Taylor expanded in t around 0 69.7%

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

      1. sub-neg 69.7%

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

      2. metadata-eval 69.7%

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

      3. distribute-rgt-in 69.7%

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

      4. associate-+l+ 69.7%

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

      5. distribute-lft-out 69.7%

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

      6. mul-1-neg 69.7%

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

      7. remove-double-neg 69.7%

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

      8. mul-1-neg 69.7%

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

      9. remove-double-neg 69.7%

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

      10. mul-1-neg 69.7%

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

      11. distribute-neg-in 69.7%

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

      12. unsub-neg 69.7%

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

      13. *-commutative 69.7%

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

      14. +-commutative 69.7%

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

      15. distribute-neg-in 69.7%

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

      16. mul-1-neg 69.7%

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

      17. remove-double-neg 69.7%

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

      18. mul-1-neg 69.7%

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

      19. remove-double-neg 69.7%

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

   5. Simplified 69.7%

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

   if 1.9999999999999999e-126 < b < 1.2499999999999999e-76

   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. Taylor expanded in b around 0 93.3%

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

   3. Taylor expanded in t around inf 79.4%

      \[\leadsto x - \color{blue}{a \cdot t} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -7.2 \cdot 10^{+109}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-126}:\\ \;\;\;\;x + \left(\left(a + z\right) - y \cdot z\right)\\ \mathbf{elif}\;b \leq 1.25 \cdot 10^{-76}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+133}:\\ \;\;\;\;x + \left(\left(a + z\right) - y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \end{array} \]

Alternative 18: 81.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+110} \lor \neg \left(b \leq 1.6 \cdot 10^{+133}\right):\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right) - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -1.55e+110) (not (<= b 1.6e+133)))
   (- (* b (- (+ t y) 2.0)) (* t a))
   (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -1.55e+110) || !(b <= 1.6e+133)) {
		tmp = (b * ((t + y) - 2.0)) - (t * a);
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - 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 ((b <= (-1.55d+110)) .or. (.not. (b <= 1.6d+133))) then
        tmp = (b * ((t + y) - 2.0d0)) - (t * a)
    else
        tmp = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - 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 ((b <= -1.55e+110) || !(b <= 1.6e+133)) {
		tmp = (b * ((t + y) - 2.0)) - (t * a);
	} else {
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -1.55e+110) or not (b <= 1.6e+133):
		tmp = (b * ((t + y) - 2.0)) - (t * a)
	else:
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -1.55e+110) || !(b <= 1.6e+133))
		tmp = Float64(Float64(b * Float64(Float64(t + y) - 2.0)) - Float64(t * a));
	else
		tmp = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -1.55e+110) || ~((b <= 1.6e+133)))
		tmp = (b * ((t + y) - 2.0)) - (t * a);
	else
		tmp = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -1.55e+110], N[Not[LessEqual[b, 1.6e+133]], $MachinePrecision]], N[(N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision] - N[(t * a), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -1.55000000000000009e110 or 1.59999999999999999e133 < b

   1. Initial program 91.8%

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

   2. Taylor expanded in t around inf 84.1%

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

      1. associate-*r* 84.1%

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

      2. neg-mul-1 84.1%

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

   4. Simplified 84.1%

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

   if -1.55000000000000009e110 < b < 1.59999999999999999e133

   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. Taylor expanded in b around 0 87.3%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -1.55 \cdot 10^{+110} \lor \neg \left(b \leq 1.6 \cdot 10^{+133}\right):\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right) - t \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 19: 66.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+102}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+25}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 10500:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -1.05e+102)
     t_1
     (if (<= t -5e+25)
       (+ x (* z (- 1.0 y)))
       (if (<= t 10500.0) (+ a (+ x (* b (- y 2.0)))) 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 <= -1.05e+102) {
		tmp = t_1;
	} else if (t <= -5e+25) {
		tmp = x + (z * (1.0 - y));
	} else if (t <= 10500.0) {
		tmp = a + (x + (b * (y - 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 = t * (b - a)
    if (t <= (-1.05d+102)) then
        tmp = t_1
    else if (t <= (-5d+25)) then
        tmp = x + (z * (1.0d0 - y))
    else if (t <= 10500.0d0) then
        tmp = a + (x + (b * (y - 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 = t * (b - a);
	double tmp;
	if (t <= -1.05e+102) {
		tmp = t_1;
	} else if (t <= -5e+25) {
		tmp = x + (z * (1.0 - y));
	} else if (t <= 10500.0) {
		tmp = a + (x + (b * (y - 2.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -1.05e+102:
		tmp = t_1
	elif t <= -5e+25:
		tmp = x + (z * (1.0 - y))
	elif t <= 10500.0:
		tmp = a + (x + (b * (y - 2.0)))
	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 <= -1.05e+102)
		tmp = t_1;
	elseif (t <= -5e+25)
		tmp = Float64(x + Float64(z * Float64(1.0 - y)));
	elseif (t <= 10500.0)
		tmp = Float64(a + Float64(x + Float64(b * Float64(y - 2.0))));
	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 <= -1.05e+102)
		tmp = t_1;
	elseif (t <= -5e+25)
		tmp = x + (z * (1.0 - y));
	elseif (t <= 10500.0)
		tmp = a + (x + (b * (y - 2.0)));
	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, -1.05e+102], t$95$1, If[LessEqual[t, -5e+25], N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 10500.0], N[(a + N[(x + N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05000000000000001e102 or 10500 < t

   1. Initial program 94.9%

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

   2. Taylor expanded in t around inf 68.2%

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

   if -1.05000000000000001e102 < t < -5.00000000000000024e25

   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. Taylor expanded in b around 0 86.2%

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

   3. Taylor expanded in a around 0 62.9%

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

   if -5.00000000000000024e25 < t < 10500

   1. Initial program 99.2%

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

   2. Taylor expanded in t around 0 99.2%

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

      1. associate--l+ 99.2%

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

      2. fma-def 99.2%

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

      3. associate--l+ 99.2%

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

      4. *-commutative 99.2%

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

      5. fma-def 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. associate--r+ 100.0%

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

      11. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around 0 71.5%

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

   6. Taylor expanded in t around 0 69.2%

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

4. Final simplification 68.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+102}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -5 \cdot 10^{+25}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 10500:\\ \;\;\;\;a + \left(x + b \cdot \left(y - 2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 20: 41.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.3 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-204}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-108}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+107}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -1.3e+64)
     t_1
     (if (<= a 8.2e-204)
       (+ z x)
       (if (<= a 5.3e-108) (* b y) (if (<= a 5.6e+107) (+ z x) 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 <= -1.3e+64) {
		tmp = t_1;
	} else if (a <= 8.2e-204) {
		tmp = z + x;
	} else if (a <= 5.3e-108) {
		tmp = b * y;
	} else if (a <= 5.6e+107) {
		tmp = z + x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-1.3d+64)) then
        tmp = t_1
    else if (a <= 8.2d-204) then
        tmp = z + x
    else if (a <= 5.3d-108) then
        tmp = b * y
    else if (a <= 5.6d+107) then
        tmp = z + x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -1.3e+64) {
		tmp = t_1;
	} else if (a <= 8.2e-204) {
		tmp = z + x;
	} else if (a <= 5.3e-108) {
		tmp = b * y;
	} else if (a <= 5.6e+107) {
		tmp = z + x;
	} 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 <= -1.3e+64:
		tmp = t_1
	elif a <= 8.2e-204:
		tmp = z + x
	elif a <= 5.3e-108:
		tmp = b * y
	elif a <= 5.6e+107:
		tmp = z + x
	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 <= -1.3e+64)
		tmp = t_1;
	elseif (a <= 8.2e-204)
		tmp = Float64(z + x);
	elseif (a <= 5.3e-108)
		tmp = Float64(b * y);
	elseif (a <= 5.6e+107)
		tmp = Float64(z + x);
	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 <= -1.3e+64)
		tmp = t_1;
	elseif (a <= 8.2e-204)
		tmp = z + x;
	elseif (a <= 5.3e-108)
		tmp = b * y;
	elseif (a <= 5.6e+107)
		tmp = z + x;
	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, -1.3e+64], t$95$1, If[LessEqual[a, 8.2e-204], N[(z + x), $MachinePrecision], If[LessEqual[a, 5.3e-108], N[(b * y), $MachinePrecision], If[LessEqual[a, 5.6e+107], N[(z + x), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.29999999999999998e64 or 5.59999999999999969e107 < a

   1. Initial program 96.1%

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

   2. Taylor expanded in a around inf 62.7%

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

   if -1.29999999999999998e64 < a < 8.2000000000000002e-204 or 5.29999999999999989e-108 < a < 5.59999999999999969e107

   1. Initial program 99.2%

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

   2. Taylor expanded in b around 0 68.8%

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

   3. Taylor expanded in a around 0 60.3%

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

   4. Taylor expanded in y around 0 37.7%

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

      1. sub-neg 37.7%

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

      2. neg-mul-1 37.7%

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

      3. remove-double-neg 37.7%

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

      4. +-commutative 37.7%

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

   6. Simplified 37.7%

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

   if 8.2000000000000002e-204 < a < 5.29999999999999989e-108

   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. Taylor expanded in y around inf 54.7%

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

   3. Taylor expanded in b around inf 48.0%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.3 \cdot 10^{+64}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{-204}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 5.3 \cdot 10^{-108}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{+107}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 21: 47.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -0.00045:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-172}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-54}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -0.00045)
     t_1
     (if (<= t 7e-172)
       (+ a x)
       (if (<= t 7.6e-54) (+ z x) (if (<= t 4.5e+49) (* a (- 1.0 t)) 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 <= -0.00045) {
		tmp = t_1;
	} else if (t <= 7e-172) {
		tmp = a + x;
	} else if (t <= 7.6e-54) {
		tmp = z + x;
	} else if (t <= 4.5e+49) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-0.00045d0)) then
        tmp = t_1
    else if (t <= 7d-172) then
        tmp = a + x
    else if (t <= 7.6d-54) then
        tmp = z + x
    else if (t <= 4.5d+49) then
        tmp = a * (1.0d0 - t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -0.00045) {
		tmp = t_1;
	} else if (t <= 7e-172) {
		tmp = a + x;
	} else if (t <= 7.6e-54) {
		tmp = z + x;
	} else if (t <= 4.5e+49) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -0.00045:
		tmp = t_1
	elif t <= 7e-172:
		tmp = a + x
	elif t <= 7.6e-54:
		tmp = z + x
	elif t <= 4.5e+49:
		tmp = a * (1.0 - t)
	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 <= -0.00045)
		tmp = t_1;
	elseif (t <= 7e-172)
		tmp = Float64(a + x);
	elseif (t <= 7.6e-54)
		tmp = Float64(z + x);
	elseif (t <= 4.5e+49)
		tmp = Float64(a * Float64(1.0 - t));
	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 <= -0.00045)
		tmp = t_1;
	elseif (t <= 7e-172)
		tmp = a + x;
	elseif (t <= 7.6e-54)
		tmp = z + x;
	elseif (t <= 4.5e+49)
		tmp = a * (1.0 - t);
	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, -0.00045], t$95$1, If[LessEqual[t, 7e-172], N[(a + x), $MachinePrecision], If[LessEqual[t, 7.6e-54], N[(z + x), $MachinePrecision], If[LessEqual[t, 4.5e+49], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -4.4999999999999999e-4 or 4.49999999999999982e49 < t

   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. Taylor expanded in t around inf 62.7%

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

   if -4.4999999999999999e-4 < t < 7.00000000000000057e-172

   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. Taylor expanded in b around 0 72.6%

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

   3. Taylor expanded in t around 0 72.5%

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

      1. sub-neg 72.5%

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

      2. metadata-eval 72.5%

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

      3. distribute-rgt-in 72.5%

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

      4. associate-+l+ 72.5%

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

      5. distribute-lft-out 72.5%

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

      6. mul-1-neg 72.5%

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

      7. remove-double-neg 72.5%

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

      8. mul-1-neg 72.5%

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

      9. remove-double-neg 72.5%

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

      10. mul-1-neg 72.5%

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

      11. distribute-neg-in 72.5%

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

      12. unsub-neg 72.5%

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

      13. *-commutative 72.5%

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

      14. +-commutative 72.5%

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

      15. distribute-neg-in 72.5%

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

      16. mul-1-neg 72.5%

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

      17. remove-double-neg 72.5%

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

      18. mul-1-neg 72.5%

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

      19. remove-double-neg 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in z around 0 43.3%

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

   if 7.00000000000000057e-172 < t < 7.6000000000000005e-54

   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. Taylor expanded in b around 0 78.6%

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

   3. Taylor expanded in a around 0 71.0%

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

   4. Taylor expanded in y around 0 54.8%

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

      1. sub-neg 54.8%

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

      2. neg-mul-1 54.8%

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

      3. remove-double-neg 54.8%

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

      4. +-commutative 54.8%

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

   6. Simplified 54.8%

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

   if 7.6000000000000005e-54 < t < 4.49999999999999982e49

   1. Initial program 94.4%

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

   2. Taylor expanded in a around inf 37.3%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.00045:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{-172}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-54}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+49}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 22: 35.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -215000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-172}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-56}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-10}:\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- a))))
   (if (<= t -215000000000.0)
     t_1
     (if (<= t 8.2e-172)
       (+ a x)
       (if (<= t 2.8e-56) (+ z x) (if (<= t 1.35e-10) (* b y) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * -a;
	double tmp;
	if (t <= -215000000000.0) {
		tmp = t_1;
	} else if (t <= 8.2e-172) {
		tmp = a + x;
	} else if (t <= 2.8e-56) {
		tmp = z + x;
	} else if (t <= 1.35e-10) {
		tmp = b * y;
	} 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 * -a
    if (t <= (-215000000000.0d0)) then
        tmp = t_1
    else if (t <= 8.2d-172) then
        tmp = a + x
    else if (t <= 2.8d-56) then
        tmp = z + x
    else if (t <= 1.35d-10) then
        tmp = b * y
    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 * -a;
	double tmp;
	if (t <= -215000000000.0) {
		tmp = t_1;
	} else if (t <= 8.2e-172) {
		tmp = a + x;
	} else if (t <= 2.8e-56) {
		tmp = z + x;
	} else if (t <= 1.35e-10) {
		tmp = b * y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * -a
	tmp = 0
	if t <= -215000000000.0:
		tmp = t_1
	elif t <= 8.2e-172:
		tmp = a + x
	elif t <= 2.8e-56:
		tmp = z + x
	elif t <= 1.35e-10:
		tmp = b * y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(-a))
	tmp = 0.0
	if (t <= -215000000000.0)
		tmp = t_1;
	elseif (t <= 8.2e-172)
		tmp = Float64(a + x);
	elseif (t <= 2.8e-56)
		tmp = Float64(z + x);
	elseif (t <= 1.35e-10)
		tmp = Float64(b * y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * -a;
	tmp = 0.0;
	if (t <= -215000000000.0)
		tmp = t_1;
	elseif (t <= 8.2e-172)
		tmp = a + x;
	elseif (t <= 2.8e-56)
		tmp = z + x;
	elseif (t <= 1.35e-10)
		tmp = b * y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * (-a)), $MachinePrecision]}, If[LessEqual[t, -215000000000.0], t$95$1, If[LessEqual[t, 8.2e-172], N[(a + x), $MachinePrecision], If[LessEqual[t, 2.8e-56], N[(z + x), $MachinePrecision], If[LessEqual[t, 1.35e-10], N[(b * y), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -2.15e11 or 1.35e-10 < t

   1. Initial program 96.0%

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

   2. Taylor expanded in a around inf 41.2%

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

   3. Taylor expanded in t around inf 39.9%

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

      1. mul-1-neg 39.9%

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

      2. distribute-rgt-neg-in 39.9%

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

   5. Simplified 39.9%

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

   if -2.15e11 < t < 8.2e-172

   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. Taylor expanded in b around 0 71.8%

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

   3. Taylor expanded in t around 0 71.8%

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

      1. sub-neg 71.8%

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

      2. metadata-eval 71.8%

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

      3. distribute-rgt-in 71.8%

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

      4. associate-+l+ 71.8%

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

      5. distribute-lft-out 71.8%

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

      6. mul-1-neg 71.8%

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

      7. remove-double-neg 71.8%

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

      8. mul-1-neg 71.8%

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

      9. remove-double-neg 71.8%

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

      10. mul-1-neg 71.8%

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

      11. distribute-neg-in 71.8%

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

      12. unsub-neg 71.8%

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

      13. *-commutative 71.8%

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

      14. +-commutative 71.8%

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

      15. distribute-neg-in 71.8%

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

      16. mul-1-neg 71.8%

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

      17. remove-double-neg 71.8%

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

      18. mul-1-neg 71.8%

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

      19. remove-double-neg 71.8%

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

   5. Simplified 71.8%

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

   6. Taylor expanded in z around 0 42.9%

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

   if 8.2e-172 < t < 2.79999999999999993e-56

   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. Taylor expanded in b around 0 78.6%

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

   3. Taylor expanded in a around 0 71.0%

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

   4. Taylor expanded in y around 0 54.8%

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

      1. sub-neg 54.8%

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

      2. neg-mul-1 54.8%

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

      3. remove-double-neg 54.8%

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

      4. +-commutative 54.8%

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

   6. Simplified 54.8%

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

   if 2.79999999999999993e-56 < t < 1.35e-10

   1. Initial program 90.9%

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

   2. Taylor expanded in y around inf 64.3%

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

   3. Taylor expanded in b around inf 38.1%

      \[\leadsto \color{blue}{y \cdot b} \]
3. Recombined 4 regimes into one program.

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -215000000000:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{-172}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-56}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-10}:\\ \;\;\;\;b \cdot y\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \end{array} \]

Alternative 23: 36.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+94}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-93}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-92}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+21}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -4.2e+94)
   (* b y)
   (if (<= y -3e-93)
     (+ a x)
     (if (<= y 2.7e-92) (+ z x) (if (<= y 2.4e+21) (+ a x) (* y (- z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.2e+94) {
		tmp = b * y;
	} else if (y <= -3e-93) {
		tmp = a + x;
	} else if (y <= 2.7e-92) {
		tmp = z + x;
	} else if (y <= 2.4e+21) {
		tmp = a + x;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-4.2d+94)) then
        tmp = b * y
    else if (y <= (-3d-93)) then
        tmp = a + x
    else if (y <= 2.7d-92) then
        tmp = z + x
    else if (y <= 2.4d+21) then
        tmp = a + x
    else
        tmp = y * -z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -4.2e+94) {
		tmp = b * y;
	} else if (y <= -3e-93) {
		tmp = a + x;
	} else if (y <= 2.7e-92) {
		tmp = z + x;
	} else if (y <= 2.4e+21) {
		tmp = a + x;
	} else {
		tmp = y * -z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -4.2e+94:
		tmp = b * y
	elif y <= -3e-93:
		tmp = a + x
	elif y <= 2.7e-92:
		tmp = z + x
	elif y <= 2.4e+21:
		tmp = a + x
	else:
		tmp = y * -z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -4.2e+94)
		tmp = Float64(b * y);
	elseif (y <= -3e-93)
		tmp = Float64(a + x);
	elseif (y <= 2.7e-92)
		tmp = Float64(z + x);
	elseif (y <= 2.4e+21)
		tmp = Float64(a + x);
	else
		tmp = Float64(y * Float64(-z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -4.2e+94)
		tmp = b * y;
	elseif (y <= -3e-93)
		tmp = a + x;
	elseif (y <= 2.7e-92)
		tmp = z + x;
	elseif (y <= 2.4e+21)
		tmp = a + x;
	else
		tmp = y * -z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -4.2e+94], N[(b * y), $MachinePrecision], If[LessEqual[y, -3e-93], N[(a + x), $MachinePrecision], If[LessEqual[y, 2.7e-92], N[(z + x), $MachinePrecision], If[LessEqual[y, 2.4e+21], N[(a + x), $MachinePrecision], N[(y * (-z)), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.19999999999999979e94

   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. Taylor expanded in y around inf 73.7%

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

   3. Taylor expanded in b around inf 50.2%

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

   if -4.19999999999999979e94 < y < -3.0000000000000001e-93 or 2.69999999999999995e-92 < y < 2.4e21

   1. Initial program 98.4%

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

   2. Taylor expanded in b around 0 76.4%

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

   3. Taylor expanded in t around 0 58.4%

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

      1. sub-neg 58.4%

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

      2. metadata-eval 58.4%

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

      3. distribute-rgt-in 58.4%

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

      4. associate-+l+ 58.4%

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

      5. distribute-lft-out 58.4%

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

      6. mul-1-neg 58.4%

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

      7. remove-double-neg 58.4%

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

      8. mul-1-neg 58.4%

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

      9. remove-double-neg 58.4%

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

      10. mul-1-neg 58.4%

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

      11. distribute-neg-in 58.4%

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

      12. unsub-neg 58.4%

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

      13. *-commutative 58.4%

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

      14. +-commutative 58.4%

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

      15. distribute-neg-in 58.4%

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

      16. mul-1-neg 58.4%

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

      17. remove-double-neg 58.4%

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

      18. mul-1-neg 58.4%

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

      19. remove-double-neg 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in z around 0 44.0%

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

   if -3.0000000000000001e-93 < y < 2.69999999999999995e-92

   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. Taylor expanded in b around 0 77.9%

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

   3. Taylor expanded in a around 0 43.4%

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

   4. Taylor expanded in y around 0 43.4%

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

      1. sub-neg 43.4%

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

      2. neg-mul-1 43.4%

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

      3. remove-double-neg 43.4%

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

      4. +-commutative 43.4%

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

   6. Simplified 43.4%

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

   if 2.4e21 < y

   1. Initial program 96.7%

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

   2. Taylor expanded in z around inf 41.8%

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

   3. Taylor expanded in y around inf 41.8%

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

      1. mul-1-neg 41.8%

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

      2. distribute-rgt-neg-in 41.8%

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

   5. Simplified 41.8%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+94}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-93}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-92}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+21}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \end{array} \]

Alternative 24: 36.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+94}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-93}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-92}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 8.1 \cdot 10^{+108}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8e+94)
   (* b y)
   (if (<= y -7.2e-93)
     (+ a x)
     (if (<= y 2.65e-92) (+ z x) (if (<= y 8.1e+108) (+ a x) (* b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8e+94) {
		tmp = b * y;
	} else if (y <= -7.2e-93) {
		tmp = a + x;
	} else if (y <= 2.65e-92) {
		tmp = z + x;
	} else if (y <= 8.1e+108) {
		tmp = a + x;
	} else {
		tmp = b * 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 (y <= (-8d+94)) then
        tmp = b * y
    else if (y <= (-7.2d-93)) then
        tmp = a + x
    else if (y <= 2.65d-92) then
        tmp = z + x
    else if (y <= 8.1d+108) then
        tmp = a + x
    else
        tmp = b * 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 (y <= -8e+94) {
		tmp = b * y;
	} else if (y <= -7.2e-93) {
		tmp = a + x;
	} else if (y <= 2.65e-92) {
		tmp = z + x;
	} else if (y <= 8.1e+108) {
		tmp = a + x;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8e+94:
		tmp = b * y
	elif y <= -7.2e-93:
		tmp = a + x
	elif y <= 2.65e-92:
		tmp = z + x
	elif y <= 8.1e+108:
		tmp = a + x
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8e+94)
		tmp = Float64(b * y);
	elseif (y <= -7.2e-93)
		tmp = Float64(a + x);
	elseif (y <= 2.65e-92)
		tmp = Float64(z + x);
	elseif (y <= 8.1e+108)
		tmp = Float64(a + x);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8e+94)
		tmp = b * y;
	elseif (y <= -7.2e-93)
		tmp = a + x;
	elseif (y <= 2.65e-92)
		tmp = z + x;
	elseif (y <= 8.1e+108)
		tmp = a + x;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8e+94], N[(b * y), $MachinePrecision], If[LessEqual[y, -7.2e-93], N[(a + x), $MachinePrecision], If[LessEqual[y, 2.65e-92], N[(z + x), $MachinePrecision], If[LessEqual[y, 8.1e+108], N[(a + x), $MachinePrecision], N[(b * y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.0000000000000002e94 or 8.1e108 < y

   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. Taylor expanded in y around inf 74.9%

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

   3. Taylor expanded in b around inf 43.4%

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

   if -8.0000000000000002e94 < y < -7.2000000000000003e-93 or 2.65000000000000015e-92 < y < 8.1e108

   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. Taylor expanded in b around 0 75.7%

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

   3. Taylor expanded in t around 0 58.4%

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

      1. sub-neg 58.4%

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

      2. metadata-eval 58.4%

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

      3. distribute-rgt-in 58.4%

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

      4. associate-+l+ 58.4%

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

      5. distribute-lft-out 58.4%

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

      6. mul-1-neg 58.4%

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

      7. remove-double-neg 58.4%

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

      8. mul-1-neg 58.4%

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

      9. remove-double-neg 58.4%

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

      10. mul-1-neg 58.4%

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

      11. distribute-neg-in 58.4%

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

      12. unsub-neg 58.4%

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

      13. *-commutative 58.4%

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

      14. +-commutative 58.4%

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

      15. distribute-neg-in 58.4%

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

      16. mul-1-neg 58.4%

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

      17. remove-double-neg 58.4%

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

      18. mul-1-neg 58.4%

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

      19. remove-double-neg 58.4%

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

   5. Simplified 58.4%

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

   6. Taylor expanded in z around 0 40.5%

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

   if -7.2000000000000003e-93 < y < 2.65000000000000015e-92

   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. Taylor expanded in b around 0 77.9%

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

   3. Taylor expanded in a around 0 43.4%

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

   4. Taylor expanded in y around 0 43.4%

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

      1. sub-neg 43.4%

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

      2. neg-mul-1 43.4%

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

      3. remove-double-neg 43.4%

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

      4. +-commutative 43.4%

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

   6. Simplified 43.4%

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

4. Final simplification 42.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+94}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-93}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-92}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;y \leq 8.1 \cdot 10^{+108}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]

Alternative 25: 20.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-212}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -4.5e+85) x (if (<= x -3.9e-212) z (if (<= x 5.2e-25) a x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -4.5e+85) {
		tmp = x;
	} else if (x <= -3.9e-212) {
		tmp = z;
	} else if (x <= 5.2e-25) {
		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 <= (-4.5d+85)) then
        tmp = x
    else if (x <= (-3.9d-212)) then
        tmp = z
    else if (x <= 5.2d-25) 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 <= -4.5e+85) {
		tmp = x;
	} else if (x <= -3.9e-212) {
		tmp = z;
	} else if (x <= 5.2e-25) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -4.5e+85:
		tmp = x
	elif x <= -3.9e-212:
		tmp = z
	elif x <= 5.2e-25:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -4.5e+85)
		tmp = x;
	elseif (x <= -3.9e-212)
		tmp = z;
	elseif (x <= 5.2e-25)
		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 <= -4.5e+85)
		tmp = x;
	elseif (x <= -3.9e-212)
		tmp = z;
	elseif (x <= 5.2e-25)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -4.5e+85], x, If[LessEqual[x, -3.9e-212], z, If[LessEqual[x, 5.2e-25], a, x]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.50000000000000007e85 or 5.2e-25 < x

   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. Taylor expanded in x around inf 33.5%

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

   if -4.50000000000000007e85 < x < -3.9e-212

   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. Taylor expanded in z around inf 39.8%

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

   3. Taylor expanded in y around 0 18.2%

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

   if -3.9e-212 < x < 5.2e-25

   1. Initial program 96.2%

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

   2. Taylor expanded in b around 0 68.5%

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

   3. Taylor expanded in t around 0 48.2%

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

      1. sub-neg 48.2%

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

      2. metadata-eval 48.2%

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

      3. distribute-rgt-in 48.2%

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

      4. associate-+l+ 48.2%

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

      5. distribute-lft-out 48.2%

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

      6. mul-1-neg 48.2%

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

      7. remove-double-neg 48.2%

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

      8. mul-1-neg 48.2%

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

      9. remove-double-neg 48.2%

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

      10. mul-1-neg 48.2%

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

      11. distribute-neg-in 48.2%

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

      12. unsub-neg 48.2%

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

      13. *-commutative 48.2%

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

      14. +-commutative 48.2%

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

      15. distribute-neg-in 48.2%

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

      16. mul-1-neg 48.2%

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

      17. remove-double-neg 48.2%

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

      18. mul-1-neg 48.2%

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

      19. remove-double-neg 48.2%

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

   5. Simplified 48.2%

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

   6. Taylor expanded in a around inf 18.9%

      \[\leadsto \color{blue}{a} \]
3. Recombined 3 regimes into one program.

4. Final simplification 25.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+85}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-212}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 26: 25.6% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{-65}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= b -9.8e-65) (* b y) (if (<= b 9e+20) x (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (b <= -9.8e-65) {
		tmp = b * y;
	} else if (b <= 9e+20) {
		tmp = x;
	} else {
		tmp = b * 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 (b <= (-9.8d-65)) then
        tmp = b * y
    else if (b <= 9d+20) then
        tmp = x
    else
        tmp = b * 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 (b <= -9.8e-65) {
		tmp = b * y;
	} else if (b <= 9e+20) {
		tmp = x;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if b <= -9.8e-65:
		tmp = b * y
	elif b <= 9e+20:
		tmp = x
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (b <= -9.8e-65)
		tmp = Float64(b * y);
	elseif (b <= 9e+20)
		tmp = x;
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (b <= -9.8e-65)
		tmp = b * y;
	elseif (b <= 9e+20)
		tmp = x;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[b, -9.8e-65], N[(b * y), $MachinePrecision], If[LessEqual[b, 9e+20], x, N[(b * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -9.79999999999999929e-65 or 9e20 < b

   1. Initial program 95.3%

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

   2. Taylor expanded in y around inf 40.4%

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

   3. Taylor expanded in b around inf 33.4%

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

   if -9.79999999999999929e-65 < b < 9e20

   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. Taylor expanded in x around inf 27.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.8 \cdot 10^{-65}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]

Alternative 27: 34.0% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{+96}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+109}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.46e+96) (* b y) (if (<= y 4.7e+109) (+ a x) (* b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.46e+96) {
		tmp = b * y;
	} else if (y <= 4.7e+109) {
		tmp = a + x;
	} else {
		tmp = b * 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 (y <= (-1.46d+96)) then
        tmp = b * y
    else if (y <= 4.7d+109) then
        tmp = a + x
    else
        tmp = b * 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 (y <= -1.46e+96) {
		tmp = b * y;
	} else if (y <= 4.7e+109) {
		tmp = a + x;
	} else {
		tmp = b * y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.46e+96:
		tmp = b * y
	elif y <= 4.7e+109:
		tmp = a + x
	else:
		tmp = b * y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.46e+96)
		tmp = Float64(b * y);
	elseif (y <= 4.7e+109)
		tmp = Float64(a + x);
	else
		tmp = Float64(b * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.46e+96)
		tmp = b * y;
	elseif (y <= 4.7e+109)
		tmp = a + x;
	else
		tmp = b * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.46e+96], N[(b * y), $MachinePrecision], If[LessEqual[y, 4.7e+109], N[(a + x), $MachinePrecision], N[(b * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4600000000000001e96 or 4.69999999999999998e109 < y

   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. Taylor expanded in y around inf 74.9%

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

   3. Taylor expanded in b around inf 43.4%

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

   if -1.4600000000000001e96 < y < 4.69999999999999998e109

   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. Taylor expanded in b around 0 76.8%

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

   3. Taylor expanded in t around 0 55.5%

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

      1. sub-neg 55.5%

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

      2. metadata-eval 55.5%

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

      3. distribute-rgt-in 55.5%

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

      4. associate-+l+ 55.5%

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

      5. distribute-lft-out 55.5%

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

      6. mul-1-neg 55.5%

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

      7. remove-double-neg 55.5%

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

      8. mul-1-neg 55.5%

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

      9. remove-double-neg 55.5%

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

      10. mul-1-neg 55.5%

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

      11. distribute-neg-in 55.5%

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

      12. unsub-neg 55.5%

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

      13. *-commutative 55.5%

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

      14. +-commutative 55.5%

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

      15. distribute-neg-in 55.5%

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

      16. mul-1-neg 55.5%

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

      17. remove-double-neg 55.5%

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

      18. mul-1-neg 55.5%

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

      19. remove-double-neg 55.5%

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

   5. Simplified 55.5%

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

   6. Taylor expanded in z around 0 35.1%

      \[\leadsto \color{blue}{a + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.46 \cdot 10^{+96}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+109}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]

Alternative 28: 20.8% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -1.35e+136) x (if (<= x 7e-25) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -1.35e+136) {
		tmp = x;
	} else if (x <= 7e-25) {
		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 <= (-1.35d+136)) then
        tmp = x
    else if (x <= 7d-25) 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 <= -1.35e+136) {
		tmp = x;
	} else if (x <= 7e-25) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -1.35e+136:
		tmp = x
	elif x <= 7e-25:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -1.35e+136)
		tmp = x;
	elseif (x <= 7e-25)
		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 <= -1.35e+136)
		tmp = x;
	elseif (x <= 7e-25)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -1.35e+136], x, If[LessEqual[x, 7e-25], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3500000000000001e136 or 7.0000000000000004e-25 < x

   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. Taylor expanded in x around inf 35.4%

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

   if -1.3500000000000001e136 < x < 7.0000000000000004e-25

   1. Initial program 96.7%

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

   2. Taylor expanded in b around 0 67.7%

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

   3. Taylor expanded in t around 0 48.5%

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

      1. sub-neg 48.5%

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

      2. metadata-eval 48.5%

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

      3. distribute-rgt-in 48.5%

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

      4. associate-+l+ 48.5%

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

      5. distribute-lft-out 48.5%

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

      6. mul-1-neg 48.5%

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

      7. remove-double-neg 48.5%

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

      8. mul-1-neg 48.5%

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

      9. remove-double-neg 48.5%

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

      10. mul-1-neg 48.5%

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

      11. distribute-neg-in 48.5%

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

      12. unsub-neg 48.5%

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

      13. *-commutative 48.5%

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

      14. +-commutative 48.5%

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

      15. distribute-neg-in 48.5%

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

      16. mul-1-neg 48.5%

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

      17. remove-double-neg 48.5%

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

      18. mul-1-neg 48.5%

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

      19. remove-double-neg 48.5%

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

   5. Simplified 48.5%

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

   6. Taylor expanded in a around inf 15.9%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-25}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 29: 11.3% 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 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. Taylor expanded in b around 0 71.9%

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

3. Taylor expanded in t around 0 53.2%

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

   1. sub-neg 53.2%

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

   2. metadata-eval 53.2%

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

   3. distribute-rgt-in 53.2%

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

   4. associate-+l+ 53.2%

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

   5. distribute-lft-out 53.2%

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

   6. mul-1-neg 53.2%

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

   7. remove-double-neg 53.2%

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

   8. mul-1-neg 53.2%

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

   9. remove-double-neg 53.2%

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

   10. mul-1-neg 53.2%

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

   11. distribute-neg-in 53.2%

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

   12. unsub-neg 53.2%

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

   13. *-commutative 53.2%

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

   14. +-commutative 53.2%

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

   15. distribute-neg-in 53.2%

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

   16. mul-1-neg 53.2%

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

   17. remove-double-neg 53.2%

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

   18. mul-1-neg 53.2%

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

   19. remove-double-neg 53.2%

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

5. Simplified 53.2%

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

6. Taylor expanded in a around inf 12.7%

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

7. Final simplification 12.7%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023268 
(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)))