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

Percentage Accurate: 95.1% → 97.9%

Time: 16.1s

Alternatives: 24

Speedup: 0.5×

• 36.3% 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: 95.1% 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: 97.9% accurate, 0.1× speedup

Math

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

FPCore

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

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

Julia

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

Wolfram

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

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

      1. +-commutative 100.0%

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

      2. fma-def 100.0%

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

      3. associate--l+ 100.0%

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

      4. sub-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. associate--l+ 100.0%

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

      8. *-commutative 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. fma-neg 100.0%

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

      11. neg-sub0 100.0%

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

      12. sub-neg 100.0%

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

      13. +-commutative 100.0%

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

      14. associate--r+ 100.0%

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

      15. metadata-eval 100.0%

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

      16. metadata-eval 100.0%

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

      17. *-commutative 100.0%

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

      18. distribute-rgt-neg-in 100.0%

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

      19. neg-sub0 100.0%

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

      20. sub-neg 100.0%

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

      21. +-commutative 100.0%

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

      22. associate--r+ 100.0%

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

   3. Simplified 100.0%

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

   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 y around inf 20.0%

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

      1. mul-1-neg 20.0%

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

      2. *-commutative 20.0%

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

      3. distribute-rgt-neg-in 20.0%

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

   4. Simplified 20.0%

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

   5. Taylor expanded in t around 0 20.5%

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

      1. sub-neg 20.5%

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

      2. metadata-eval 20.5%

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

      3. distribute-lft-in 20.5%

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

      4. *-commutative 20.5%

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

      5. associate-+r+ 20.5%

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

      6. +-commutative 20.5%

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

      7. *-commutative 20.5%

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

      8. associate-*r* 20.5%

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

      9. distribute-rgt-in 87.1%

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

      10. mul-1-neg 87.1%

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

      11. unsub-neg 87.1%

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

      12. *-commutative 87.1%

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

   7. Simplified 87.1%

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

4. Final simplification 99.2%

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

Alternative 2: 97.9% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, Infinity], t$95$1, N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(b * -2.0), $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 y around inf 20.0%

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

      1. mul-1-neg 20.0%

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

      2. *-commutative 20.0%

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

      3. distribute-rgt-neg-in 20.0%

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

   4. Simplified 20.0%

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

   5. Taylor expanded in t around 0 20.5%

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

      1. sub-neg 20.5%

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

      2. metadata-eval 20.5%

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

      3. distribute-lft-in 20.5%

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

      4. *-commutative 20.5%

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

      5. associate-+r+ 20.5%

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

      6. +-commutative 20.5%

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

      7. *-commutative 20.5%

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

      8. associate-*r* 20.5%

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

      9. distribute-rgt-in 87.1%

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

      10. mul-1-neg 87.1%

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

      11. unsub-neg 87.1%

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

      12. *-commutative 87.1%

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

   7. Simplified 87.1%

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

4. Final simplification 99.2%

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

Alternative 3: 63.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -7.8 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \left(b - z\right) + b \cdot -2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+124}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ x (* b (+ y -2.0))))) (t_2 (* t (- b a))))
   (if (<= t -7.8e+30)
     t_2
     (if (<= t -1e-137)
       t_1
       (if (<= t -4.4e-253)
         (+ (* y (- b z)) (* b -2.0))
         (if (<= t 3e-8)
           t_1
           (if (<= t 1.55e+124) (- (* (- (+ y t) 2.0) b) (* y z)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (x + (b * (y + -2.0)));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.8e+30) {
		tmp = t_2;
	} else if (t <= -1e-137) {
		tmp = t_1;
	} else if (t <= -4.4e-253) {
		tmp = (y * (b - z)) + (b * -2.0);
	} else if (t <= 3e-8) {
		tmp = t_1;
	} else if (t <= 1.55e+124) {
		tmp = (((y + t) - 2.0) * b) - (y * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (x + (b * (y + (-2.0d0))))
    t_2 = t * (b - a)
    if (t <= (-7.8d+30)) then
        tmp = t_2
    else if (t <= (-1d-137)) then
        tmp = t_1
    else if (t <= (-4.4d-253)) then
        tmp = (y * (b - z)) + (b * (-2.0d0))
    else if (t <= 3d-8) then
        tmp = t_1
    else if (t <= 1.55d+124) then
        tmp = (((y + t) - 2.0d0) * b) - (y * z)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (x + (b * (y + -2.0)));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -7.8e+30) {
		tmp = t_2;
	} else if (t <= -1e-137) {
		tmp = t_1;
	} else if (t <= -4.4e-253) {
		tmp = (y * (b - z)) + (b * -2.0);
	} else if (t <= 3e-8) {
		tmp = t_1;
	} else if (t <= 1.55e+124) {
		tmp = (((y + t) - 2.0) * b) - (y * z);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (x + (b * (y + -2.0)))
	t_2 = t * (b - a)
	tmp = 0
	if t <= -7.8e+30:
		tmp = t_2
	elif t <= -1e-137:
		tmp = t_1
	elif t <= -4.4e-253:
		tmp = (y * (b - z)) + (b * -2.0)
	elif t <= 3e-8:
		tmp = t_1
	elif t <= 1.55e+124:
		tmp = (((y + t) - 2.0) * b) - (y * z)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(x + Float64(b * Float64(y + -2.0))))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -7.8e+30)
		tmp = t_2;
	elseif (t <= -1e-137)
		tmp = t_1;
	elseif (t <= -4.4e-253)
		tmp = Float64(Float64(y * Float64(b - z)) + Float64(b * -2.0));
	elseif (t <= 3e-8)
		tmp = t_1;
	elseif (t <= 1.55e+124)
		tmp = Float64(Float64(Float64(Float64(y + t) - 2.0) * b) - Float64(y * z));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (x + (b * (y + -2.0)));
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -7.8e+30)
		tmp = t_2;
	elseif (t <= -1e-137)
		tmp = t_1;
	elseif (t <= -4.4e-253)
		tmp = (y * (b - z)) + (b * -2.0);
	elseif (t <= 3e-8)
		tmp = t_1;
	elseif (t <= 1.55e+124)
		tmp = (((y + t) - 2.0) * b) - (y * z);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -7.8e+30], t$95$2, If[LessEqual[t, -1e-137], t$95$1, If[LessEqual[t, -4.4e-253], N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(b * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3e-8], t$95$1, If[LessEqual[t, 1.55e+124], N[(N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision] - N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -7.80000000000000021e30 or 1.5500000000000001e124 < t

   1. Initial program 91.7%

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

   2. Taylor expanded in t around inf 68.0%

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

   if -7.80000000000000021e30 < t < -9.99999999999999978e-138 or -4.39999999999999992e-253 < t < 2.99999999999999973e-8

   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 t around 0 96.3%

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

   3. Taylor expanded in z around 0 77.8%

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

   4. Taylor expanded in t around 0 76.1%

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

      1. +-commutative 76.1%

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

      2. sub-neg 76.1%

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

      3. metadata-eval 76.1%

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

   6. Simplified 76.1%

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

   if -9.99999999999999978e-138 < t < -4.39999999999999992e-253

   1. Initial program 85.6%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. *-commutative 57.4%

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

      3. distribute-rgt-neg-in 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in t around 0 57.4%

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

      1. sub-neg 57.4%

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

      2. metadata-eval 57.4%

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

      3. distribute-lft-in 57.4%

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

      4. *-commutative 57.4%

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

      5. associate-+r+ 57.4%

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

      6. +-commutative 57.4%

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

      7. *-commutative 57.4%

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

      8. associate-*r* 57.4%

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

      9. distribute-rgt-in 71.6%

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

      10. mul-1-neg 71.6%

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

      11. unsub-neg 71.6%

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

      12. *-commutative 71.6%

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

   7. Simplified 71.6%

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

   if 2.99999999999999973e-8 < t < 1.5500000000000001e124

   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 y around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. *-commutative 61.5%

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

      3. distribute-rgt-neg-in 61.5%

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

   4. Simplified 61.5%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.8 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-137}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \left(b - z\right) + b \cdot -2\\ \mathbf{elif}\;t \leq 3 \cdot 10^{-8}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{+124}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 4: 64.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{+24}:\\ \;\;\;\;t_2 - t \cdot a\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \left(b - z\right) + b \cdot -2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+124}:\\ \;\;\;\;t_2 - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ x (* b (+ y -2.0))))) (t_2 (* (- (+ y t) 2.0) b)))
   (if (<= t -1.9e+24)
     (- t_2 (* t a))
     (if (<= t -1.25e-137)
       t_1
       (if (<= t -4.4e-253)
         (+ (* y (- b z)) (* b -2.0))
         (if (<= t 4.2e-8)
           t_1
           (if (<= t 1.5e+124) (- t_2 (* y z)) (* t (- b a)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (x + (b * (y + -2.0)));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (t <= -1.9e+24) {
		tmp = t_2 - (t * a);
	} else if (t <= -1.25e-137) {
		tmp = t_1;
	} else if (t <= -4.4e-253) {
		tmp = (y * (b - z)) + (b * -2.0);
	} else if (t <= 4.2e-8) {
		tmp = t_1;
	} else if (t <= 1.5e+124) {
		tmp = t_2 - (y * z);
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (x + (b * (y + (-2.0d0))))
    t_2 = ((y + t) - 2.0d0) * b
    if (t <= (-1.9d+24)) then
        tmp = t_2 - (t * a)
    else if (t <= (-1.25d-137)) then
        tmp = t_1
    else if (t <= (-4.4d-253)) then
        tmp = (y * (b - z)) + (b * (-2.0d0))
    else if (t <= 4.2d-8) then
        tmp = t_1
    else if (t <= 1.5d+124) then
        tmp = t_2 - (y * z)
    else
        tmp = t * (b - a)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (x + (b * (y + -2.0)));
	double t_2 = ((y + t) - 2.0) * b;
	double tmp;
	if (t <= -1.9e+24) {
		tmp = t_2 - (t * a);
	} else if (t <= -1.25e-137) {
		tmp = t_1;
	} else if (t <= -4.4e-253) {
		tmp = (y * (b - z)) + (b * -2.0);
	} else if (t <= 4.2e-8) {
		tmp = t_1;
	} else if (t <= 1.5e+124) {
		tmp = t_2 - (y * z);
	} else {
		tmp = t * (b - a);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (x + (b * (y + -2.0)))
	t_2 = ((y + t) - 2.0) * b
	tmp = 0
	if t <= -1.9e+24:
		tmp = t_2 - (t * a)
	elif t <= -1.25e-137:
		tmp = t_1
	elif t <= -4.4e-253:
		tmp = (y * (b - z)) + (b * -2.0)
	elif t <= 4.2e-8:
		tmp = t_1
	elif t <= 1.5e+124:
		tmp = t_2 - (y * z)
	else:
		tmp = t * (b - a)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(x + Float64(b * Float64(y + -2.0))))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (t <= -1.9e+24)
		tmp = Float64(t_2 - Float64(t * a));
	elseif (t <= -1.25e-137)
		tmp = t_1;
	elseif (t <= -4.4e-253)
		tmp = Float64(Float64(y * Float64(b - z)) + Float64(b * -2.0));
	elseif (t <= 4.2e-8)
		tmp = t_1;
	elseif (t <= 1.5e+124)
		tmp = Float64(t_2 - Float64(y * z));
	else
		tmp = Float64(t * Float64(b - a));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (x + (b * (y + -2.0)));
	t_2 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (t <= -1.9e+24)
		tmp = t_2 - (t * a);
	elseif (t <= -1.25e-137)
		tmp = t_1;
	elseif (t <= -4.4e-253)
		tmp = (y * (b - z)) + (b * -2.0);
	elseif (t <= 4.2e-8)
		tmp = t_1;
	elseif (t <= 1.5e+124)
		tmp = t_2 - (y * z);
	else
		tmp = t * (b - a);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[t, -1.9e+24], N[(t$95$2 - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, -1.25e-137], t$95$1, If[LessEqual[t, -4.4e-253], N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(b * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.2e-8], t$95$1, If[LessEqual[t, 1.5e+124], N[(t$95$2 - N[(y * z), $MachinePrecision]), $MachinePrecision], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -1.90000000000000008e24

   1. Initial program 90.3%

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

   2. Taylor expanded in t around inf 62.9%

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

      1. associate-*r* 62.9%

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

      2. neg-mul-1 62.9%

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

   4. Simplified 62.9%

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

   if -1.90000000000000008e24 < t < -1.25e-137 or -4.39999999999999992e-253 < t < 4.19999999999999989e-8

   1. Initial program 97.1%

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

   2. Taylor expanded in t around 0 97.1%

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

   3. Taylor expanded in z around 0 77.2%

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

   4. Taylor expanded in t around 0 76.3%

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

      1. +-commutative 76.3%

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

      2. sub-neg 76.3%

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

      3. metadata-eval 76.3%

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

   6. Simplified 76.3%

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

   if -1.25e-137 < t < -4.39999999999999992e-253

   1. Initial program 85.6%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. *-commutative 57.4%

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

      3. distribute-rgt-neg-in 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in t around 0 57.4%

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

      1. sub-neg 57.4%

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

      2. metadata-eval 57.4%

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

      3. distribute-lft-in 57.4%

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

      4. *-commutative 57.4%

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

      5. associate-+r+ 57.4%

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

      6. +-commutative 57.4%

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

      7. *-commutative 57.4%

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

      8. associate-*r* 57.4%

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

      9. distribute-rgt-in 71.6%

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

      10. mul-1-neg 71.6%

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

      11. unsub-neg 71.6%

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

      12. *-commutative 71.6%

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

   7. Simplified 71.6%

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

   if 4.19999999999999989e-8 < t < 1.5e124

   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 y around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. *-commutative 61.5%

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

      3. distribute-rgt-neg-in 61.5%

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

   4. Simplified 61.5%

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

   if 1.5e124 < t

   1. Initial program 91.9%

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

   2. Taylor expanded in t around inf 81.1%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.9 \cdot 10^{+24}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - t \cdot a\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-137}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-253}:\\ \;\;\;\;y \cdot \left(b - z\right) + b \cdot -2\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-8}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{+124}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 5: 83.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b\\ t_3 := x + t_2\\ \mathbf{if}\;b \leq -2.2 \cdot 10^{+97}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+97}:\\ \;\;\;\;t_2 - t \cdot a\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+134}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (+ (* a (- 1.0 t)) (* z (- 1.0 y)))))
        (t_2 (* (- (+ y t) 2.0) b))
        (t_3 (+ x t_2)))
   (if (<= b -2.2e+97)
     t_3
     (if (<= b 1.8e+47)
       t_1
       (if (<= b 2.3e+97) (- t_2 (* t a)) (if (<= b 1.35e+134) t_1 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + t_2;
	double tmp;
	if (b <= -2.2e+97) {
		tmp = t_3;
	} else if (b <= 1.8e+47) {
		tmp = t_1;
	} else if (b <= 2.3e+97) {
		tmp = t_2 - (t * a);
	} else if (b <= 1.35e+134) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x + ((a * (1.0d0 - t)) + (z * (1.0d0 - y)))
    t_2 = ((y + t) - 2.0d0) * b
    t_3 = x + t_2
    if (b <= (-2.2d+97)) then
        tmp = t_3
    else if (b <= 1.8d+47) then
        tmp = t_1
    else if (b <= 2.3d+97) then
        tmp = t_2 - (t * a)
    else if (b <= 1.35d+134) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	double t_2 = ((y + t) - 2.0) * b;
	double t_3 = x + t_2;
	double tmp;
	if (b <= -2.2e+97) {
		tmp = t_3;
	} else if (b <= 1.8e+47) {
		tmp = t_1;
	} else if (b <= 2.3e+97) {
		tmp = t_2 - (t * a);
	} else if (b <= 1.35e+134) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)))
	t_2 = ((y + t) - 2.0) * b
	t_3 = x + t_2
	tmp = 0
	if b <= -2.2e+97:
		tmp = t_3
	elif b <= 1.8e+47:
		tmp = t_1
	elif b <= 2.3e+97:
		tmp = t_2 - (t * a)
	elif b <= 1.35e+134:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(a * Float64(1.0 - t)) + Float64(z * Float64(1.0 - y))))
	t_2 = Float64(Float64(Float64(y + t) - 2.0) * b)
	t_3 = Float64(x + t_2)
	tmp = 0.0
	if (b <= -2.2e+97)
		tmp = t_3;
	elseif (b <= 1.8e+47)
		tmp = t_1;
	elseif (b <= 2.3e+97)
		tmp = Float64(t_2 - Float64(t * a));
	elseif (b <= 1.35e+134)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((a * (1.0 - t)) + (z * (1.0 - y)));
	t_2 = ((y + t) - 2.0) * b;
	t_3 = x + t_2;
	tmp = 0.0;
	if (b <= -2.2e+97)
		tmp = t_3;
	elseif (b <= 1.8e+47)
		tmp = t_1;
	elseif (b <= 2.3e+97)
		tmp = t_2 - (t * a);
	elseif (b <= 1.35e+134)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, Block[{t$95$3 = N[(x + t$95$2), $MachinePrecision]}, If[LessEqual[b, -2.2e+97], t$95$3, If[LessEqual[b, 1.8e+47], t$95$1, If[LessEqual[b, 2.3e+97], N[(t$95$2 - N[(t * a), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.35e+134], t$95$1, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.2000000000000001e97 or 1.35e134 < b

   1. Initial program 86.6%

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

   2. Taylor expanded in a around 0 85.5%

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

   3. Taylor expanded in z around 0 89.0%

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

   if -2.2000000000000001e97 < b < 1.80000000000000004e47 or 2.30000000000000006e97 < b < 1.35e134

   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 87.7%

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

   if 1.80000000000000004e47 < b < 2.30000000000000006e97

   1. Initial program 88.7%

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

   2. Taylor expanded in t around inf 98.2%

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

      1. associate-*r* 98.2%

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

      2. neg-mul-1 98.2%

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

   4. Simplified 98.2%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.2 \cdot 10^{+97}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+47}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;b \leq 2.3 \cdot 10^{+97}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b - t \cdot a\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{+134}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 6: 45.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2120000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-135}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-241}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-124}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 10^{-54}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+70}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* t (- b a))))
   (if (<= t -2120000000.0)
     t_1
     (if (<= t -2.5e-135)
       (+ x z)
       (if (<= t -3.4e-241)
         (* y (- z))
         (if (<= t 2.6e-124)
           (* b (- y 2.0))
           (if (<= t 1e-54)
             (+ x z)
             (if (<= t 5.4e-15)
               (* a (- 1.0 t))
               (if (<= t 5.3e+70) (+ x z) t_1)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2120000000.0) {
		tmp = t_1;
	} else if (t <= -2.5e-135) {
		tmp = x + z;
	} else if (t <= -3.4e-241) {
		tmp = y * -z;
	} else if (t <= 2.6e-124) {
		tmp = b * (y - 2.0);
	} else if (t <= 1e-54) {
		tmp = x + z;
	} else if (t <= 5.4e-15) {
		tmp = a * (1.0 - t);
	} else if (t <= 5.3e+70) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t * (b - a)
    if (t <= (-2120000000.0d0)) then
        tmp = t_1
    else if (t <= (-2.5d-135)) then
        tmp = x + z
    else if (t <= (-3.4d-241)) then
        tmp = y * -z
    else if (t <= 2.6d-124) then
        tmp = b * (y - 2.0d0)
    else if (t <= 1d-54) then
        tmp = x + z
    else if (t <= 5.4d-15) then
        tmp = a * (1.0d0 - t)
    else if (t <= 5.3d+70) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t * (b - a);
	double tmp;
	if (t <= -2120000000.0) {
		tmp = t_1;
	} else if (t <= -2.5e-135) {
		tmp = x + z;
	} else if (t <= -3.4e-241) {
		tmp = y * -z;
	} else if (t <= 2.6e-124) {
		tmp = b * (y - 2.0);
	} else if (t <= 1e-54) {
		tmp = x + z;
	} else if (t <= 5.4e-15) {
		tmp = a * (1.0 - t);
	} else if (t <= 5.3e+70) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t * (b - a)
	tmp = 0
	if t <= -2120000000.0:
		tmp = t_1
	elif t <= -2.5e-135:
		tmp = x + z
	elif t <= -3.4e-241:
		tmp = y * -z
	elif t <= 2.6e-124:
		tmp = b * (y - 2.0)
	elif t <= 1e-54:
		tmp = x + z
	elif t <= 5.4e-15:
		tmp = a * (1.0 - t)
	elif t <= 5.3e+70:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -2120000000.0)
		tmp = t_1;
	elseif (t <= -2.5e-135)
		tmp = Float64(x + z);
	elseif (t <= -3.4e-241)
		tmp = Float64(y * Float64(-z));
	elseif (t <= 2.6e-124)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (t <= 1e-54)
		tmp = Float64(x + z);
	elseif (t <= 5.4e-15)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (t <= 5.3e+70)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = t * (b - a);
	tmp = 0.0;
	if (t <= -2120000000.0)
		tmp = t_1;
	elseif (t <= -2.5e-135)
		tmp = x + z;
	elseif (t <= -3.4e-241)
		tmp = y * -z;
	elseif (t <= 2.6e-124)
		tmp = b * (y - 2.0);
	elseif (t <= 1e-54)
		tmp = x + z;
	elseif (t <= 5.4e-15)
		tmp = a * (1.0 - t);
	elseif (t <= 5.3e+70)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2120000000.0], t$95$1, If[LessEqual[t, -2.5e-135], N[(x + z), $MachinePrecision], If[LessEqual[t, -3.4e-241], N[(y * (-z)), $MachinePrecision], If[LessEqual[t, 2.6e-124], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-54], N[(x + z), $MachinePrecision], If[LessEqual[t, 5.4e-15], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 5.3e+70], N[(x + z), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if t < -2.12e9 or 5.3e70 < t

   1. Initial program 92.0%

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

   2. Taylor expanded in t around inf 62.5%

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

   if -2.12e9 < t < -2.5000000000000001e-135 or 2.6e-124 < t < 1e-54 or 5.40000000000000018e-15 < t < 5.3e70

   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 0 81.5%

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

   3. Taylor expanded in y around 0 42.6%

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

      1. associate--l+ 42.6%

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

      2. sub-neg 42.6%

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

      3. metadata-eval 42.6%

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

      4. neg-mul-1 42.6%

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

   5. Simplified 42.6%

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

   6. Taylor expanded in b around 0 38.8%

      \[\leadsto \color{blue}{x + z} \]
   7. Step-by-step derivation

      1. +-commutative 38.8%

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

   8. Simplified 38.8%

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

   if -2.5000000000000001e-135 < t < -3.3999999999999999e-241

   1. Initial program 87.4%

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

   2. Taylor expanded in y around inf 50.5%

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

      1. mul-1-neg 50.5%

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

      2. *-commutative 50.5%

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

      3. distribute-rgt-neg-in 50.5%

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

   4. Simplified 50.5%

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

   5. Taylor expanded in z around inf 46.2%

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

      1. mul-1-neg 46.2%

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

      2. distribute-rgt-neg-in 46.2%

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

   7. Simplified 46.2%

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

   if -3.3999999999999999e-241 < t < 2.6e-124

   1. Initial program 92.7%

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

   2. Taylor expanded in t around inf 54.5%

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

      1. associate-*r* 54.5%

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

      2. neg-mul-1 54.5%

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

   4. Simplified 54.5%

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

   5. Taylor expanded in t around 0 54.6%

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

   if 1e-54 < t < 5.40000000000000018e-15

   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 75.4%

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

4. Final simplification 54.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2120000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-135}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-241}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-124}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 10^{-54}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 5.4 \cdot 10^{-15}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+70}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 7: 86.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -2.7 \cdot 10^{-18} \lor \neg \left(b \leq 2 \cdot 10^{-12}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(t_1 + z \cdot \left(1 - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (or (<= b -2.7e-18) (not (<= b 2e-12)))
     (+ (+ x (* (- (+ y t) 2.0) b)) t_1)
     (+ x (+ t_1 (* z (- 1.0 y)))))))

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 <= -2.7e-18) || !(b <= 2e-12)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + (t_1 + (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) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if ((b <= (-2.7d-18)) .or. (.not. (b <= 2d-12))) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + t_1
    else
        tmp = x + (t_1 + (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 t_1 = a * (1.0 - t);
	double tmp;
	if ((b <= -2.7e-18) || !(b <= 2e-12)) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else {
		tmp = x + (t_1 + (z * (1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if (b <= -2.7e-18) or not (b <= 2e-12):
		tmp = (x + (((y + t) - 2.0) * b)) + t_1
	else:
		tmp = x + (t_1 + (z * (1.0 - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if ((b <= -2.7e-18) || !(b <= 2e-12))
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + t_1);
	else
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	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 <= -2.7e-18) || ~((b <= 2e-12)))
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	else
		tmp = x + (t_1 + (z * (1.0 - y)));
	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[Or[LessEqual[b, -2.7e-18], N[Not[LessEqual[b, 2e-12]], $MachinePrecision]], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if b < -2.69999999999999989e-18 or 1.99999999999999996e-12 < b

   1. Initial program 89.6%

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

   2. Taylor expanded in z around 0 87.8%

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

   if -2.69999999999999989e-18 < b < 1.99999999999999996e-12

   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 93.9%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.7 \cdot 10^{-18} \lor \neg \left(b \leq 2 \cdot 10^{-12}\right):\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \end{array} \]

Alternative 8: 86.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -4.4 \cdot 10^{-18}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + t_1\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-12}:\\ \;\;\;\;x + \left(t_1 + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= b -4.4e-18)
     (+ (+ x (* (- (+ y t) 2.0) b)) t_1)
     (if (<= b 1.15e-12)
       (+ x (+ t_1 (* z (- 1.0 y))))
       (+ a (+ x (+ (* b (- y 2.0)) (* t (- b a)))))))))

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 <= -4.4e-18) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else if (b <= 1.15e-12) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = a + (x + ((b * (y - 2.0)) + (t * (b - a))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (b <= (-4.4d-18)) then
        tmp = (x + (((y + t) - 2.0d0) * b)) + t_1
    else if (b <= 1.15d-12) then
        tmp = x + (t_1 + (z * (1.0d0 - y)))
    else
        tmp = a + (x + ((b * (y - 2.0d0)) + (t * (b - a))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (b <= -4.4e-18) {
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	} else if (b <= 1.15e-12) {
		tmp = x + (t_1 + (z * (1.0 - y)));
	} else {
		tmp = a + (x + ((b * (y - 2.0)) + (t * (b - a))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if b <= -4.4e-18:
		tmp = (x + (((y + t) - 2.0) * b)) + t_1
	elif b <= 1.15e-12:
		tmp = x + (t_1 + (z * (1.0 - y)))
	else:
		tmp = a + (x + ((b * (y - 2.0)) + (t * (b - a))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (b <= -4.4e-18)
		tmp = Float64(Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b)) + t_1);
	elseif (b <= 1.15e-12)
		tmp = Float64(x + Float64(t_1 + Float64(z * Float64(1.0 - y))));
	else
		tmp = Float64(a + Float64(x + Float64(Float64(b * Float64(y - 2.0)) + Float64(t * Float64(b - a)))));
	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 <= -4.4e-18)
		tmp = (x + (((y + t) - 2.0) * b)) + t_1;
	elseif (b <= 1.15e-12)
		tmp = x + (t_1 + (z * (1.0 - y)));
	else
		tmp = a + (x + ((b * (y - 2.0)) + (t * (b - a))));
	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, -4.4e-18], N[(N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[b, 1.15e-12], N[(x + N[(t$95$1 + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a + N[(x + N[(N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if b < -4.3999999999999997e-18

   1. Initial program 90.6%

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

   2. Taylor expanded in z around 0 88.4%

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

   if -4.3999999999999997e-18 < b < 1.14999999999999995e-12

   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 93.9%

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

   if 1.14999999999999995e-12 < b

   1. Initial program 88.7%

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

   2. Taylor expanded in t around 0 90.3%

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

   3. Taylor expanded in z around 0 88.7%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -4.4 \cdot 10^{-18}:\\ \;\;\;\;\left(x + \left(\left(y + t\right) - 2\right) \cdot b\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 1.15 \cdot 10^{-12}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) + z \cdot \left(1 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(x + \left(b \cdot \left(y - 2\right) + t \cdot \left(b - a\right)\right)\right)\\ \end{array} \]

Alternative 9: 49.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -6.8 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-132}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-69}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* (- (+ y t) 2.0) b)))
   (if (<= b -6.8e-18)
     t_1
     (if (<= b 7.8e-197)
       (* z (- 1.0 y))
       (if (<= b 5.3e-132)
         (* a (- 1.0 t))
         (if (<= b 9e-69) (+ x z) (if (<= b 2.75e+73) (* t (- b a)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -6.8e-18) {
		tmp = t_1;
	} else if (b <= 7.8e-197) {
		tmp = z * (1.0 - y);
	} else if (b <= 5.3e-132) {
		tmp = a * (1.0 - t);
	} else if (b <= 9e-69) {
		tmp = x + z;
	} else if (b <= 2.75e+73) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((y + t) - 2.0d0) * b
    if (b <= (-6.8d-18)) then
        tmp = t_1
    else if (b <= 7.8d-197) then
        tmp = z * (1.0d0 - y)
    else if (b <= 5.3d-132) then
        tmp = a * (1.0d0 - t)
    else if (b <= 9d-69) then
        tmp = x + z
    else if (b <= 2.75d+73) then
        tmp = t * (b - a)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = ((y + t) - 2.0) * b;
	double tmp;
	if (b <= -6.8e-18) {
		tmp = t_1;
	} else if (b <= 7.8e-197) {
		tmp = z * (1.0 - y);
	} else if (b <= 5.3e-132) {
		tmp = a * (1.0 - t);
	} else if (b <= 9e-69) {
		tmp = x + z;
	} else if (b <= 2.75e+73) {
		tmp = t * (b - a);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = ((y + t) - 2.0) * b
	tmp = 0
	if b <= -6.8e-18:
		tmp = t_1
	elif b <= 7.8e-197:
		tmp = z * (1.0 - y)
	elif b <= 5.3e-132:
		tmp = a * (1.0 - t)
	elif b <= 9e-69:
		tmp = x + z
	elif b <= 2.75e+73:
		tmp = t * (b - a)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(Float64(y + t) - 2.0) * b)
	tmp = 0.0
	if (b <= -6.8e-18)
		tmp = t_1;
	elseif (b <= 7.8e-197)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 5.3e-132)
		tmp = Float64(a * Float64(1.0 - t));
	elseif (b <= 9e-69)
		tmp = Float64(x + z);
	elseif (b <= 2.75e+73)
		tmp = Float64(t * Float64(b - a));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = ((y + t) - 2.0) * b;
	tmp = 0.0;
	if (b <= -6.8e-18)
		tmp = t_1;
	elseif (b <= 7.8e-197)
		tmp = z * (1.0 - y);
	elseif (b <= 5.3e-132)
		tmp = a * (1.0 - t);
	elseif (b <= 9e-69)
		tmp = x + z;
	elseif (b <= 2.75e+73)
		tmp = t * (b - a);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]}, If[LessEqual[b, -6.8e-18], t$95$1, If[LessEqual[b, 7.8e-197], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 5.3e-132], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 9e-69], N[(x + z), $MachinePrecision], If[LessEqual[b, 2.75e+73], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if b < -6.80000000000000002e-18 or 2.7500000000000001e73 < b

   1. Initial program 87.9%

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

   2. Taylor expanded in b around inf 71.4%

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

   if -6.80000000000000002e-18 < b < 7.7999999999999998e-197

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 49.1%

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

   if 7.7999999999999998e-197 < b < 5.3000000000000003e-132

   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 70.0%

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

   if 5.3000000000000003e-132 < b < 9.00000000000000019e-69

   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 0 80.2%

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

   3. Taylor expanded in y around 0 64.0%

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

      1. associate--l+ 64.0%

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

      2. sub-neg 64.0%

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

      3. metadata-eval 64.0%

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

      4. neg-mul-1 64.0%

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

   5. Simplified 64.0%

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

   6. Taylor expanded in b around 0 63.7%

      \[\leadsto \color{blue}{x + z} \]
   7. Step-by-step derivation

      1. +-commutative 63.7%

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

   8. Simplified 63.7%

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

   if 9.00000000000000019e-69 < b < 2.7500000000000001e73

   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 t around inf 54.5%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.8 \cdot 10^{-18}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 7.8 \cdot 10^{-197}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-132}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;b \leq 9 \cdot 10^{-69}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 2.75 \cdot 10^{+73}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 10: 62.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(x - t \cdot a\right)\\ t_2 := x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{if}\;b \leq -9.1 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-305}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-221}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (- x (* t a)))) (t_2 (+ x (* (- (+ y t) 2.0) b))))
   (if (<= b -9.1e+42)
     t_2
     (if (<= b 1.95e-305)
       t_1
       (if (<= b 3.6e-221) (* z (- 1.0 y)) (if (<= b 1.32e+74) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (x - (t * a));
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -9.1e+42) {
		tmp = t_2;
	} else if (b <= 1.95e-305) {
		tmp = t_1;
	} else if (b <= 3.6e-221) {
		tmp = z * (1.0 - y);
	} else if (b <= 1.32e+74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (x - (t * a))
    t_2 = x + (((y + t) - 2.0d0) * b)
    if (b <= (-9.1d+42)) then
        tmp = t_2
    else if (b <= 1.95d-305) then
        tmp = t_1
    else if (b <= 3.6d-221) then
        tmp = z * (1.0d0 - y)
    else if (b <= 1.32d+74) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (x - (t * a));
	double t_2 = x + (((y + t) - 2.0) * b);
	double tmp;
	if (b <= -9.1e+42) {
		tmp = t_2;
	} else if (b <= 1.95e-305) {
		tmp = t_1;
	} else if (b <= 3.6e-221) {
		tmp = z * (1.0 - y);
	} else if (b <= 1.32e+74) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (x - (t * a))
	t_2 = x + (((y + t) - 2.0) * b)
	tmp = 0
	if b <= -9.1e+42:
		tmp = t_2
	elif b <= 1.95e-305:
		tmp = t_1
	elif b <= 3.6e-221:
		tmp = z * (1.0 - y)
	elif b <= 1.32e+74:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(x - Float64(t * a)))
	t_2 = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b))
	tmp = 0.0
	if (b <= -9.1e+42)
		tmp = t_2;
	elseif (b <= 1.95e-305)
		tmp = t_1;
	elseif (b <= 3.6e-221)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (b <= 1.32e+74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (x - (t * a));
	t_2 = x + (((y + t) - 2.0) * b);
	tmp = 0.0;
	if (b <= -9.1e+42)
		tmp = t_2;
	elseif (b <= 1.95e-305)
		tmp = t_1;
	elseif (b <= 3.6e-221)
		tmp = z * (1.0 - y);
	elseif (b <= 1.32e+74)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(x - N[(t * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[b, -9.1e+42], t$95$2, If[LessEqual[b, 1.95e-305], t$95$1, If[LessEqual[b, 3.6e-221], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[b, 1.32e+74], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -9.0999999999999995e42 or 1.32000000000000012e74 < b

   1. Initial program 87.0%

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

   2. Taylor expanded in a around 0 81.2%

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

   3. Taylor expanded in z around 0 80.7%

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

   if -9.0999999999999995e42 < b < 1.95000000000000013e-305 or 3.60000000000000011e-221 < b < 1.32000000000000012e74

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0 98.6%

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

   3. Taylor expanded in z around 0 69.7%

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

   4. Taylor expanded in b around 0 59.7%

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

      1. mul-1-neg 59.7%

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

      2. *-commutative 59.7%

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

      3. unsub-neg 59.7%

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

   6. Simplified 59.7%

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

   if 1.95000000000000013e-305 < b < 3.60000000000000011e-221

   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 74.2%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -9.1 \cdot 10^{+42}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;b \leq 1.95 \cdot 10^{-305}:\\ \;\;\;\;a + \left(x - t \cdot a\right)\\ \mathbf{elif}\;b \leq 3.6 \cdot 10^{-221}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;b \leq 1.32 \cdot 10^{+74}:\\ \;\;\;\;a + \left(x - t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 11: 63.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \left(b - z\right) + b \cdot -2\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ a (+ x (* b (+ y -2.0))))) (t_2 (* t (- b a))))
   (if (<= t -5.5e+30)
     t_2
     (if (<= t -2e-137)
       t_1
       (if (<= t -1.6e-252)
         (+ (* y (- b z)) (* b -2.0))
         (if (<= t 1.1e+69) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (x + (b * (y + -2.0)));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -5.5e+30) {
		tmp = t_2;
	} else if (t <= -2e-137) {
		tmp = t_1;
	} else if (t <= -1.6e-252) {
		tmp = (y * (b - z)) + (b * -2.0);
	} else if (t <= 1.1e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = a + (x + (b * (y + (-2.0d0))))
    t_2 = t * (b - a)
    if (t <= (-5.5d+30)) then
        tmp = t_2
    else if (t <= (-2d-137)) then
        tmp = t_1
    else if (t <= (-1.6d-252)) then
        tmp = (y * (b - z)) + (b * (-2.0d0))
    else if (t <= 1.1d+69) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a + (x + (b * (y + -2.0)));
	double t_2 = t * (b - a);
	double tmp;
	if (t <= -5.5e+30) {
		tmp = t_2;
	} else if (t <= -2e-137) {
		tmp = t_1;
	} else if (t <= -1.6e-252) {
		tmp = (y * (b - z)) + (b * -2.0);
	} else if (t <= 1.1e+69) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a + (x + (b * (y + -2.0)))
	t_2 = t * (b - a)
	tmp = 0
	if t <= -5.5e+30:
		tmp = t_2
	elif t <= -2e-137:
		tmp = t_1
	elif t <= -1.6e-252:
		tmp = (y * (b - z)) + (b * -2.0)
	elif t <= 1.1e+69:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a + Float64(x + Float64(b * Float64(y + -2.0))))
	t_2 = Float64(t * Float64(b - a))
	tmp = 0.0
	if (t <= -5.5e+30)
		tmp = t_2;
	elseif (t <= -2e-137)
		tmp = t_1;
	elseif (t <= -1.6e-252)
		tmp = Float64(Float64(y * Float64(b - z)) + Float64(b * -2.0));
	elseif (t <= 1.1e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a + (x + (b * (y + -2.0)));
	t_2 = t * (b - a);
	tmp = 0.0;
	if (t <= -5.5e+30)
		tmp = t_2;
	elseif (t <= -2e-137)
		tmp = t_1;
	elseif (t <= -1.6e-252)
		tmp = (y * (b - z)) + (b * -2.0);
	elseif (t <= 1.1e+69)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a + N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e+30], t$95$2, If[LessEqual[t, -2e-137], t$95$1, If[LessEqual[t, -1.6e-252], N[(N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision] + N[(b * -2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e+69], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.50000000000000025e30 or 1.1000000000000001e69 < t

   1. Initial program 92.4%

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

   2. Taylor expanded in t around inf 65.3%

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

   if -5.50000000000000025e30 < t < -1.99999999999999996e-137 or -1.6000000000000001e-252 < t < 1.1000000000000001e69

   1. Initial program 96.9%

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

   2. Taylor expanded in t around 0 96.9%

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

   3. Taylor expanded in z around 0 76.5%

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

   4. Taylor expanded in t around 0 71.9%

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

      1. +-commutative 71.9%

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

      2. sub-neg 71.9%

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

      3. metadata-eval 71.9%

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

   6. Simplified 71.9%

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

   if -1.99999999999999996e-137 < t < -1.6000000000000001e-252

   1. Initial program 85.6%

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

   2. Taylor expanded in y around inf 57.4%

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

      1. mul-1-neg 57.4%

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

      2. *-commutative 57.4%

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

      3. distribute-rgt-neg-in 57.4%

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

   4. Simplified 57.4%

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

   5. Taylor expanded in t around 0 57.4%

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

      1. sub-neg 57.4%

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

      2. metadata-eval 57.4%

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

      3. distribute-lft-in 57.4%

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

      4. *-commutative 57.4%

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

      5. associate-+r+ 57.4%

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

      6. +-commutative 57.4%

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

      7. *-commutative 57.4%

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

      8. associate-*r* 57.4%

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

      9. distribute-rgt-in 71.6%

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

      10. mul-1-neg 71.6%

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

      11. unsub-neg 71.6%

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

      12. *-commutative 71.6%

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

   7. Simplified 71.6%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{+30}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-137}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-252}:\\ \;\;\;\;y \cdot \left(b - z\right) + b \cdot -2\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+69}:\\ \;\;\;\;a + \left(x + b \cdot \left(y + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \end{array} \]

Alternative 12: 31.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(-t\right)\\ \mathbf{if}\;b \leq -2.5 \cdot 10^{+39}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-297}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{-211}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-68}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- t))))
   (if (<= b -2.5e+39)
     (* y b)
     (if (<= b 4.7e-297)
       (+ x z)
       (if (<= b 1.28e-211)
         (* y (- z))
         (if (<= b 4.5e-135)
           t_1
           (if (<= b 5e-68) (+ x z) (if (<= b 1.6e+73) t_1 (* y b)))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * -t;
	double tmp;
	if (b <= -2.5e+39) {
		tmp = y * b;
	} else if (b <= 4.7e-297) {
		tmp = x + z;
	} else if (b <= 1.28e-211) {
		tmp = y * -z;
	} else if (b <= 4.5e-135) {
		tmp = t_1;
	} else if (b <= 5e-68) {
		tmp = x + z;
	} else if (b <= 1.6e+73) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * -t
    if (b <= (-2.5d+39)) then
        tmp = y * b
    else if (b <= 4.7d-297) then
        tmp = x + z
    else if (b <= 1.28d-211) then
        tmp = y * -z
    else if (b <= 4.5d-135) then
        tmp = t_1
    else if (b <= 5d-68) then
        tmp = x + z
    else if (b <= 1.6d+73) then
        tmp = t_1
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * -t;
	double tmp;
	if (b <= -2.5e+39) {
		tmp = y * b;
	} else if (b <= 4.7e-297) {
		tmp = x + z;
	} else if (b <= 1.28e-211) {
		tmp = y * -z;
	} else if (b <= 4.5e-135) {
		tmp = t_1;
	} else if (b <= 5e-68) {
		tmp = x + z;
	} else if (b <= 1.6e+73) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * -t
	tmp = 0
	if b <= -2.5e+39:
		tmp = y * b
	elif b <= 4.7e-297:
		tmp = x + z
	elif b <= 1.28e-211:
		tmp = y * -z
	elif b <= 4.5e-135:
		tmp = t_1
	elif b <= 5e-68:
		tmp = x + z
	elif b <= 1.6e+73:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(-t))
	tmp = 0.0
	if (b <= -2.5e+39)
		tmp = Float64(y * b);
	elseif (b <= 4.7e-297)
		tmp = Float64(x + z);
	elseif (b <= 1.28e-211)
		tmp = Float64(y * Float64(-z));
	elseif (b <= 4.5e-135)
		tmp = t_1;
	elseif (b <= 5e-68)
		tmp = Float64(x + z);
	elseif (b <= 1.6e+73)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * -t;
	tmp = 0.0;
	if (b <= -2.5e+39)
		tmp = y * b;
	elseif (b <= 4.7e-297)
		tmp = x + z;
	elseif (b <= 1.28e-211)
		tmp = y * -z;
	elseif (b <= 4.5e-135)
		tmp = t_1;
	elseif (b <= 5e-68)
		tmp = x + z;
	elseif (b <= 1.6e+73)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * (-t)), $MachinePrecision]}, If[LessEqual[b, -2.5e+39], N[(y * b), $MachinePrecision], If[LessEqual[b, 4.7e-297], N[(x + z), $MachinePrecision], If[LessEqual[b, 1.28e-211], N[(y * (-z)), $MachinePrecision], If[LessEqual[b, 4.5e-135], t$95$1, If[LessEqual[b, 5e-68], N[(x + z), $MachinePrecision], If[LessEqual[b, 1.6e+73], t$95$1, N[(y * b), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if b < -2.50000000000000008e39 or 1.59999999999999991e73 < b

   1. Initial program 87.1%

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

   2. Taylor expanded in y around inf 48.9%

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

   3. Taylor expanded in b around inf 39.2%

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

   if -2.50000000000000008e39 < b < 4.69999999999999986e-297 or 4.49999999999999987e-135 < b < 4.99999999999999971e-68

   1. Initial program 98.8%

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

   2. Taylor expanded in a around 0 66.3%

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

   3. Taylor expanded in y around 0 46.2%

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

      1. associate--l+ 46.2%

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

      2. sub-neg 46.2%

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

      3. metadata-eval 46.2%

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

      4. neg-mul-1 46.2%

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

   5. Simplified 46.2%

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

   6. Taylor expanded in b around 0 45.1%

      \[\leadsto \color{blue}{x + z} \]
   7. Step-by-step derivation

      1. +-commutative 45.1%

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

   8. Simplified 45.1%

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

   if 4.69999999999999986e-297 < b < 1.2799999999999999e-211

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 54.2%

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

      1. mul-1-neg 54.2%

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

      2. *-commutative 54.2%

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

      3. distribute-rgt-neg-in 54.2%

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

   4. Simplified 54.2%

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

   5. Taylor expanded in z around inf 54.1%

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

      1. mul-1-neg 54.1%

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

      2. distribute-rgt-neg-in 54.1%

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

   7. Simplified 54.1%

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

   if 1.2799999999999999e-211 < b < 4.49999999999999987e-135 or 4.99999999999999971e-68 < b < 1.59999999999999991e73

   1. Initial program 98.0%

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

   2. Taylor expanded in t around inf 55.8%

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

      1. associate-*r* 55.8%

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

      2. neg-mul-1 55.8%

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

   4. Simplified 55.8%

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

   5. Taylor expanded in a around inf 40.3%

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

      1. associate-*r* 40.3%

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

      2. neg-mul-1 40.3%

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

      3. *-commutative 40.3%

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

   7. Simplified 40.3%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.5 \cdot 10^{+39}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{-297}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.28 \cdot 10^{-211}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;b \leq 4.5 \cdot 10^{-135}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{elif}\;b \leq 5 \cdot 10^{-68}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+73}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 13: 48.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -0.00047:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-123}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+16} \lor \neg \left(y \leq 4.1 \cdot 10^{+69}\right) \land y \leq 8.6 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -0.00047)
     t_1
     (if (<= y -3e-123)
       (+ x z)
       (if (or (<= y 2.65e+16) (and (not (<= y 4.1e+69)) (<= y 8.6e+88)))
         (* a (- 1.0 t))
         t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -0.00047) {
		tmp = t_1;
	} else if (y <= -3e-123) {
		tmp = x + z;
	} else if ((y <= 2.65e+16) || (!(y <= 4.1e+69) && (y <= 8.6e+88))) {
		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 = y * (b - z)
    if (y <= (-0.00047d0)) then
        tmp = t_1
    else if (y <= (-3d-123)) then
        tmp = x + z
    else if ((y <= 2.65d+16) .or. (.not. (y <= 4.1d+69)) .and. (y <= 8.6d+88)) 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 = y * (b - z);
	double tmp;
	if (y <= -0.00047) {
		tmp = t_1;
	} else if (y <= -3e-123) {
		tmp = x + z;
	} else if ((y <= 2.65e+16) || (!(y <= 4.1e+69) && (y <= 8.6e+88))) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -0.00047:
		tmp = t_1
	elif y <= -3e-123:
		tmp = x + z
	elif (y <= 2.65e+16) or (not (y <= 4.1e+69) and (y <= 8.6e+88)):
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -0.00047)
		tmp = t_1;
	elseif (y <= -3e-123)
		tmp = Float64(x + z);
	elseif ((y <= 2.65e+16) || (!(y <= 4.1e+69) && (y <= 8.6e+88)))
		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 = y * (b - z);
	tmp = 0.0;
	if (y <= -0.00047)
		tmp = t_1;
	elseif (y <= -3e-123)
		tmp = x + z;
	elseif ((y <= 2.65e+16) || (~((y <= 4.1e+69)) && (y <= 8.6e+88)))
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.00047], t$95$1, If[LessEqual[y, -3e-123], N[(x + z), $MachinePrecision], If[Or[LessEqual[y, 2.65e+16], And[N[Not[LessEqual[y, 4.1e+69]], $MachinePrecision], LessEqual[y, 8.6e+88]]], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.69999999999999986e-4 or 2.65e16 < y < 4.0999999999999999e69 or 8.59999999999999947e88 < y

   1. Initial program 87.8%

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

   2. Taylor expanded in y around inf 74.9%

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

   if -4.69999999999999986e-4 < y < -2.99999999999999984e-123

   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 0 68.0%

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

   3. Taylor expanded in y around 0 68.0%

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

      1. associate--l+ 68.0%

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

      2. sub-neg 68.0%

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

      3. metadata-eval 68.0%

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

      4. neg-mul-1 68.0%

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

   5. Simplified 68.0%

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

   6. Taylor expanded in b around 0 49.7%

      \[\leadsto \color{blue}{x + z} \]
   7. Step-by-step derivation

      1. +-commutative 49.7%

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

   8. Simplified 49.7%

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

   if -2.99999999999999984e-123 < y < 2.65e16 or 4.0999999999999999e69 < y < 8.59999999999999947e88

   1. Initial program 99.1%

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

   2. Taylor expanded in a around inf 44.6%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00047:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-123}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+16} \lor \neg \left(y \leq 4.1 \cdot 10^{+69}\right) \land y \leq 8.6 \cdot 10^{+88}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 14: 41.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -750000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-72}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-216}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 3.55 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+65}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -750000.0)
     t_1
     (if (<= a -1.3e-72)
       (* y b)
       (if (<= a 3.2e-216)
         (+ x z)
         (if (<= a 3.55e-106)
           (* b (- y 2.0))
           (if (<= a 1.02e+65) (+ x z) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -750000.0) {
		tmp = t_1;
	} else if (a <= -1.3e-72) {
		tmp = y * b;
	} else if (a <= 3.2e-216) {
		tmp = x + z;
	} else if (a <= 3.55e-106) {
		tmp = b * (y - 2.0);
	} else if (a <= 1.02e+65) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-750000.0d0)) then
        tmp = t_1
    else if (a <= (-1.3d-72)) then
        tmp = y * b
    else if (a <= 3.2d-216) then
        tmp = x + z
    else if (a <= 3.55d-106) then
        tmp = b * (y - 2.0d0)
    else if (a <= 1.02d+65) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -750000.0) {
		tmp = t_1;
	} else if (a <= -1.3e-72) {
		tmp = y * b;
	} else if (a <= 3.2e-216) {
		tmp = x + z;
	} else if (a <= 3.55e-106) {
		tmp = b * (y - 2.0);
	} else if (a <= 1.02e+65) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -750000.0:
		tmp = t_1
	elif a <= -1.3e-72:
		tmp = y * b
	elif a <= 3.2e-216:
		tmp = x + z
	elif a <= 3.55e-106:
		tmp = b * (y - 2.0)
	elif a <= 1.02e+65:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -750000.0)
		tmp = t_1;
	elseif (a <= -1.3e-72)
		tmp = Float64(y * b);
	elseif (a <= 3.2e-216)
		tmp = Float64(x + z);
	elseif (a <= 3.55e-106)
		tmp = Float64(b * Float64(y - 2.0));
	elseif (a <= 1.02e+65)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -750000.0)
		tmp = t_1;
	elseif (a <= -1.3e-72)
		tmp = y * b;
	elseif (a <= 3.2e-216)
		tmp = x + z;
	elseif (a <= 3.55e-106)
		tmp = b * (y - 2.0);
	elseif (a <= 1.02e+65)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -750000.0], t$95$1, If[LessEqual[a, -1.3e-72], N[(y * b), $MachinePrecision], If[LessEqual[a, 3.2e-216], N[(x + z), $MachinePrecision], If[LessEqual[a, 3.55e-106], N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.02e+65], N[(x + z), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -7.5e5 or 1.02000000000000005e65 < a

   1. Initial program 90.0%

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

   2. Taylor expanded in a around inf 57.5%

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

   if -7.5e5 < a < -1.29999999999999998e-72

   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 71.8%

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

   3. Taylor expanded in b around inf 65.3%

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

   if -1.29999999999999998e-72 < a < 3.20000000000000026e-216 or 3.5499999999999998e-106 < a < 1.02000000000000005e65

   1. Initial program 98.9%

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

   2. Taylor expanded in a around 0 94.8%

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

   3. Taylor expanded in y around 0 62.0%

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

      1. associate--l+ 62.0%

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

      2. sub-neg 62.0%

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

      3. metadata-eval 62.0%

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

      4. neg-mul-1 62.0%

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

   5. Simplified 62.0%

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

   6. Taylor expanded in b around 0 39.3%

      \[\leadsto \color{blue}{x + z} \]
   7. Step-by-step derivation

      1. +-commutative 39.3%

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

   8. Simplified 39.3%

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

   if 3.20000000000000026e-216 < a < 3.5499999999999998e-106

   1. Initial program 95.9%

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

   2. Taylor expanded in t around inf 65.4%

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

      1. associate-*r* 65.4%

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

      2. neg-mul-1 65.4%

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

   4. Simplified 65.4%

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

   5. Taylor expanded in t around 0 53.9%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -750000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-72}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 3.2 \cdot 10^{-216}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;a \leq 3.55 \cdot 10^{-106}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+65}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 15: 48.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -0.00047:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-122}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+69}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -0.00047)
     t_1
     (if (<= y -2.4e-122)
       (+ x z)
       (if (<= y 8.5e-60)
         (* t (- b a))
         (if (<= y 1.15e+69)
           (* z (- 1.0 y))
           (if (<= y 5.5e+89) (* a (- 1.0 t)) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -0.00047) {
		tmp = t_1;
	} else if (y <= -2.4e-122) {
		tmp = x + z;
	} else if (y <= 8.5e-60) {
		tmp = t * (b - a);
	} else if (y <= 1.15e+69) {
		tmp = z * (1.0 - y);
	} else if (y <= 5.5e+89) {
		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 = y * (b - z)
    if (y <= (-0.00047d0)) then
        tmp = t_1
    else if (y <= (-2.4d-122)) then
        tmp = x + z
    else if (y <= 8.5d-60) then
        tmp = t * (b - a)
    else if (y <= 1.15d+69) then
        tmp = z * (1.0d0 - y)
    else if (y <= 5.5d+89) 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 = y * (b - z);
	double tmp;
	if (y <= -0.00047) {
		tmp = t_1;
	} else if (y <= -2.4e-122) {
		tmp = x + z;
	} else if (y <= 8.5e-60) {
		tmp = t * (b - a);
	} else if (y <= 1.15e+69) {
		tmp = z * (1.0 - y);
	} else if (y <= 5.5e+89) {
		tmp = a * (1.0 - t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -0.00047:
		tmp = t_1
	elif y <= -2.4e-122:
		tmp = x + z
	elif y <= 8.5e-60:
		tmp = t * (b - a)
	elif y <= 1.15e+69:
		tmp = z * (1.0 - y)
	elif y <= 5.5e+89:
		tmp = a * (1.0 - t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -0.00047)
		tmp = t_1;
	elseif (y <= -2.4e-122)
		tmp = Float64(x + z);
	elseif (y <= 8.5e-60)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 1.15e+69)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (y <= 5.5e+89)
		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 = y * (b - z);
	tmp = 0.0;
	if (y <= -0.00047)
		tmp = t_1;
	elseif (y <= -2.4e-122)
		tmp = x + z;
	elseif (y <= 8.5e-60)
		tmp = t * (b - a);
	elseif (y <= 1.15e+69)
		tmp = z * (1.0 - y);
	elseif (y <= 5.5e+89)
		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[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.00047], t$95$1, If[LessEqual[y, -2.4e-122], N[(x + z), $MachinePrecision], If[LessEqual[y, 8.5e-60], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e+69], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+89], N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.69999999999999986e-4 or 5.49999999999999976e89 < y

   1. Initial program 86.7%

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

   2. Taylor expanded in y around inf 75.4%

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

   if -4.69999999999999986e-4 < y < -2.39999999999999987e-122

   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 0 68.0%

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

   3. Taylor expanded in y around 0 68.0%

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

      1. associate--l+ 68.0%

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

      2. sub-neg 68.0%

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

      3. metadata-eval 68.0%

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

      4. neg-mul-1 68.0%

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

   5. Simplified 68.0%

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

   6. Taylor expanded in b around 0 49.7%

      \[\leadsto \color{blue}{x + z} \]
   7. Step-by-step derivation

      1. +-commutative 49.7%

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

   8. Simplified 49.7%

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

   if -2.39999999999999987e-122 < y < 8.50000000000000044e-60

   1. Initial program 98.8%

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

   2. Taylor expanded in t around inf 45.9%

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

   if 8.50000000000000044e-60 < y < 1.15000000000000008e69

   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 49.8%

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

   if 1.15000000000000008e69 < y < 5.49999999999999976e89

   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 47.0%

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

4. Final simplification 58.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00047:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-122}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+69}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+89}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 16: 47.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -0.00047:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-127}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+69}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+89}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* y (- b z))))
   (if (<= y -0.00047)
     t_1
     (if (<= y -1.3e-127)
       (+ x z)
       (if (<= y 4.4e-60)
         (* t (- b a))
         (if (<= y 1.36e+69)
           (* z (- 1.0 y))
           (if (<= y 6e+89) (+ x a) t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -0.00047) {
		tmp = t_1;
	} else if (y <= -1.3e-127) {
		tmp = x + z;
	} else if (y <= 4.4e-60) {
		tmp = t * (b - a);
	} else if (y <= 1.36e+69) {
		tmp = z * (1.0 - y);
	} else if (y <= 6e+89) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (b - z)
    if (y <= (-0.00047d0)) then
        tmp = t_1
    else if (y <= (-1.3d-127)) then
        tmp = x + z
    else if (y <= 4.4d-60) then
        tmp = t * (b - a)
    else if (y <= 1.36d+69) then
        tmp = z * (1.0d0 - y)
    else if (y <= 6d+89) then
        tmp = x + a
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y * (b - z);
	double tmp;
	if (y <= -0.00047) {
		tmp = t_1;
	} else if (y <= -1.3e-127) {
		tmp = x + z;
	} else if (y <= 4.4e-60) {
		tmp = t * (b - a);
	} else if (y <= 1.36e+69) {
		tmp = z * (1.0 - y);
	} else if (y <= 6e+89) {
		tmp = x + a;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y * (b - z)
	tmp = 0
	if y <= -0.00047:
		tmp = t_1
	elif y <= -1.3e-127:
		tmp = x + z
	elif y <= 4.4e-60:
		tmp = t * (b - a)
	elif y <= 1.36e+69:
		tmp = z * (1.0 - y)
	elif y <= 6e+89:
		tmp = x + a
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y * Float64(b - z))
	tmp = 0.0
	if (y <= -0.00047)
		tmp = t_1;
	elseif (y <= -1.3e-127)
		tmp = Float64(x + z);
	elseif (y <= 4.4e-60)
		tmp = Float64(t * Float64(b - a));
	elseif (y <= 1.36e+69)
		tmp = Float64(z * Float64(1.0 - y));
	elseif (y <= 6e+89)
		tmp = Float64(x + a);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y * (b - z);
	tmp = 0.0;
	if (y <= -0.00047)
		tmp = t_1;
	elseif (y <= -1.3e-127)
		tmp = x + z;
	elseif (y <= 4.4e-60)
		tmp = t * (b - a);
	elseif (y <= 1.36e+69)
		tmp = z * (1.0 - y);
	elseif (y <= 6e+89)
		tmp = x + a;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y * N[(b - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.00047], t$95$1, If[LessEqual[y, -1.3e-127], N[(x + z), $MachinePrecision], If[LessEqual[y, 4.4e-60], N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.36e+69], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6e+89], N[(x + a), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.69999999999999986e-4 or 6.00000000000000025e89 < y

   1. Initial program 86.7%

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

   2. Taylor expanded in y around inf 75.4%

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

   if -4.69999999999999986e-4 < y < -1.29999999999999995e-127

   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 0 68.0%

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

   3. Taylor expanded in y around 0 68.0%

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

      1. associate--l+ 68.0%

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

      2. sub-neg 68.0%

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

      3. metadata-eval 68.0%

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

      4. neg-mul-1 68.0%

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

   5. Simplified 68.0%

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

   6. Taylor expanded in b around 0 49.7%

      \[\leadsto \color{blue}{x + z} \]
   7. Step-by-step derivation

      1. +-commutative 49.7%

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

   8. Simplified 49.7%

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

   if -1.29999999999999995e-127 < y < 4.3999999999999998e-60

   1. Initial program 98.8%

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

   2. Taylor expanded in t around inf 45.9%

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

   if 4.3999999999999998e-60 < y < 1.36000000000000006e69

   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 49.8%

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

   if 1.36000000000000006e69 < y < 6.00000000000000025e89

   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 99.9%

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

   3. Taylor expanded in z around 0 87.5%

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

   4. Taylor expanded in x around inf 59.6%

      \[\leadsto \color{blue}{x} - -1 \cdot a \]
3. Recombined 5 regimes into one program.

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00047:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;y \leq -1.3 \cdot 10^{-127}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.36 \cdot 10^{+69}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+89}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 17: 32.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(-t\right)\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+39}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-195}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-135}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-69}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- t))))
   (if (<= b -2.6e+39)
     (* y b)
     (if (<= b 2.6e-195)
       (+ x z)
       (if (<= b 3.7e-135)
         t_1
         (if (<= b 3.9e-69) (+ x z) (if (<= b 6.1e+75) t_1 (* y b))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * -t;
	double tmp;
	if (b <= -2.6e+39) {
		tmp = y * b;
	} else if (b <= 2.6e-195) {
		tmp = x + z;
	} else if (b <= 3.7e-135) {
		tmp = t_1;
	} else if (b <= 3.9e-69) {
		tmp = x + z;
	} else if (b <= 6.1e+75) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * -t
    if (b <= (-2.6d+39)) then
        tmp = y * b
    else if (b <= 2.6d-195) then
        tmp = x + z
    else if (b <= 3.7d-135) then
        tmp = t_1
    else if (b <= 3.9d-69) then
        tmp = x + z
    else if (b <= 6.1d+75) then
        tmp = t_1
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * -t;
	double tmp;
	if (b <= -2.6e+39) {
		tmp = y * b;
	} else if (b <= 2.6e-195) {
		tmp = x + z;
	} else if (b <= 3.7e-135) {
		tmp = t_1;
	} else if (b <= 3.9e-69) {
		tmp = x + z;
	} else if (b <= 6.1e+75) {
		tmp = t_1;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * -t
	tmp = 0
	if b <= -2.6e+39:
		tmp = y * b
	elif b <= 2.6e-195:
		tmp = x + z
	elif b <= 3.7e-135:
		tmp = t_1
	elif b <= 3.9e-69:
		tmp = x + z
	elif b <= 6.1e+75:
		tmp = t_1
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(-t))
	tmp = 0.0
	if (b <= -2.6e+39)
		tmp = Float64(y * b);
	elseif (b <= 2.6e-195)
		tmp = Float64(x + z);
	elseif (b <= 3.7e-135)
		tmp = t_1;
	elseif (b <= 3.9e-69)
		tmp = Float64(x + z);
	elseif (b <= 6.1e+75)
		tmp = t_1;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * -t;
	tmp = 0.0;
	if (b <= -2.6e+39)
		tmp = y * b;
	elseif (b <= 2.6e-195)
		tmp = x + z;
	elseif (b <= 3.7e-135)
		tmp = t_1;
	elseif (b <= 3.9e-69)
		tmp = x + z;
	elseif (b <= 6.1e+75)
		tmp = t_1;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * (-t)), $MachinePrecision]}, If[LessEqual[b, -2.6e+39], N[(y * b), $MachinePrecision], If[LessEqual[b, 2.6e-195], N[(x + z), $MachinePrecision], If[LessEqual[b, 3.7e-135], t$95$1, If[LessEqual[b, 3.9e-69], N[(x + z), $MachinePrecision], If[LessEqual[b, 6.1e+75], t$95$1, N[(y * b), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if b < -2.6e39 or 6.10000000000000009e75 < b

   1. Initial program 87.1%

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

   2. Taylor expanded in y around inf 48.9%

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

   3. Taylor expanded in b around inf 39.2%

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

   if -2.6e39 < b < 2.6000000000000002e-195 or 3.6999999999999997e-135 < b < 3.89999999999999981e-69

   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 a around 0 67.4%

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

   3. Taylor expanded in y around 0 41.9%

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

      1. associate--l+ 41.9%

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

      2. sub-neg 41.9%

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

      3. metadata-eval 41.9%

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

      4. neg-mul-1 41.9%

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

   5. Simplified 41.9%

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

   6. Taylor expanded in b around 0 40.9%

      \[\leadsto \color{blue}{x + z} \]
   7. Step-by-step derivation

      1. +-commutative 40.9%

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

   8. Simplified 40.9%

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

   if 2.6000000000000002e-195 < b < 3.6999999999999997e-135 or 3.89999999999999981e-69 < b < 6.10000000000000009e75

   1. Initial program 97.9%

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

   2. Taylor expanded in t around inf 58.2%

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

      1. associate-*r* 58.2%

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

      2. neg-mul-1 58.2%

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

   4. Simplified 58.2%

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

   5. Taylor expanded in a around inf 43.5%

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

      1. associate-*r* 43.5%

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

      2. neg-mul-1 43.5%

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

      3. *-commutative 43.5%

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

   7. Simplified 43.5%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -2.6 \cdot 10^{+39}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{-195}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{-135}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{elif}\;b \leq 3.9 \cdot 10^{-69}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 6.1 \cdot 10^{+75}:\\ \;\;\;\;a \cdot \left(-t\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 18: 60.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+57} \lor \neg \left(z \leq 6.7 \cdot 10^{+111}\right):\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.1e+57) (not (<= z 6.7e+111)))
   (* z (- 1.0 y))
   (+ x (* (- (+ y t) 2.0) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.1e+57) || !(z <= 6.7e+111)) {
		tmp = z * (1.0 - y);
	} else {
		tmp = x + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.1d+57)) .or. (.not. (z <= 6.7d+111))) then
        tmp = z * (1.0d0 - y)
    else
        tmp = x + (((y + t) - 2.0d0) * b)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.1e+57) || !(z <= 6.7e+111)) {
		tmp = z * (1.0 - y);
	} else {
		tmp = x + (((y + t) - 2.0) * b);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.1e+57) or not (z <= 6.7e+111):
		tmp = z * (1.0 - y)
	else:
		tmp = x + (((y + t) - 2.0) * b)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.1e+57) || !(z <= 6.7e+111))
		tmp = Float64(z * Float64(1.0 - y));
	else
		tmp = Float64(x + Float64(Float64(Float64(y + t) - 2.0) * b));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.1e+57) || ~((z <= 6.7e+111)))
		tmp = z * (1.0 - y);
	else
		tmp = x + (((y + t) - 2.0) * b);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.1e+57], N[Not[LessEqual[z, 6.7e+111]], $MachinePrecision]], N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.1e57 or 6.7000000000000003e111 < z

   1. Initial program 91.5%

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

   2. Taylor expanded in z around inf 64.2%

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

   if -1.1e57 < z < 6.7000000000000003e111

   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 a around 0 62.9%

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

   3. Taylor expanded in z around 0 59.9%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+57} \lor \neg \left(z \leq 6.7 \cdot 10^{+111}\right):\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 19: 41.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -860000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-73}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+63}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* a (- 1.0 t))))
   (if (<= a -860000.0)
     t_1
     (if (<= a -5e-73) (* y b) (if (<= a 1.25e+63) (+ x z) t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -860000.0) {
		tmp = t_1;
	} else if (a <= -5e-73) {
		tmp = y * b;
	} else if (a <= 1.25e+63) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = a * (1.0d0 - t)
    if (a <= (-860000.0d0)) then
        tmp = t_1
    else if (a <= (-5d-73)) then
        tmp = y * b
    else if (a <= 1.25d+63) then
        tmp = x + z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = a * (1.0 - t);
	double tmp;
	if (a <= -860000.0) {
		tmp = t_1;
	} else if (a <= -5e-73) {
		tmp = y * b;
	} else if (a <= 1.25e+63) {
		tmp = x + z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = a * (1.0 - t)
	tmp = 0
	if a <= -860000.0:
		tmp = t_1
	elif a <= -5e-73:
		tmp = y * b
	elif a <= 1.25e+63:
		tmp = x + z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(a * Float64(1.0 - t))
	tmp = 0.0
	if (a <= -860000.0)
		tmp = t_1;
	elseif (a <= -5e-73)
		tmp = Float64(y * b);
	elseif (a <= 1.25e+63)
		tmp = Float64(x + z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = a * (1.0 - t);
	tmp = 0.0;
	if (a <= -860000.0)
		tmp = t_1;
	elseif (a <= -5e-73)
		tmp = y * b;
	elseif (a <= 1.25e+63)
		tmp = x + z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -860000.0], t$95$1, If[LessEqual[a, -5e-73], N[(y * b), $MachinePrecision], If[LessEqual[a, 1.25e+63], N[(x + z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -8.6e5 or 1.25000000000000003e63 < a

   1. Initial program 90.0%

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

   2. Taylor expanded in a around inf 57.5%

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

   if -8.6e5 < a < -4.9999999999999998e-73

   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 71.8%

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

   3. Taylor expanded in b around inf 65.3%

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

   if -4.9999999999999998e-73 < a < 1.25000000000000003e63

   1. Initial program 98.3%

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

   2. Taylor expanded in a around 0 94.3%

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

   3. Taylor expanded in y around 0 59.4%

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

      1. associate--l+ 59.4%

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

      2. sub-neg 59.4%

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

      3. metadata-eval 59.4%

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

      4. neg-mul-1 59.4%

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

   5. Simplified 59.4%

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

   6. Taylor expanded in b around 0 34.9%

      \[\leadsto \color{blue}{x + z} \]
   7. Step-by-step derivation

      1. +-commutative 34.9%

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

   8. Simplified 34.9%

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

4. Final simplification 47.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -860000:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \mathbf{elif}\;a \leq -5 \cdot 10^{-73}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+63}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 20: 26.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+33}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-15}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= t -2.7e+33)
   (* t b)
   (if (<= t 4e-15) a (if (<= t 1.12e+70) x (* t b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.7e+33) {
		tmp = t * b;
	} else if (t <= 4e-15) {
		tmp = a;
	} else if (t <= 1.12e+70) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (t <= (-2.7d+33)) then
        tmp = t * b
    else if (t <= 4d-15) then
        tmp = a
    else if (t <= 1.12d+70) then
        tmp = x
    else
        tmp = t * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (t <= -2.7e+33) {
		tmp = t * b;
	} else if (t <= 4e-15) {
		tmp = a;
	} else if (t <= 1.12e+70) {
		tmp = x;
	} else {
		tmp = t * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if t <= -2.7e+33:
		tmp = t * b
	elif t <= 4e-15:
		tmp = a
	elif t <= 1.12e+70:
		tmp = x
	else:
		tmp = t * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (t <= -2.7e+33)
		tmp = Float64(t * b);
	elseif (t <= 4e-15)
		tmp = a;
	elseif (t <= 1.12e+70)
		tmp = x;
	else
		tmp = Float64(t * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (t <= -2.7e+33)
		tmp = t * b;
	elseif (t <= 4e-15)
		tmp = a;
	elseif (t <= 1.12e+70)
		tmp = x;
	else
		tmp = t * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[t, -2.7e+33], N[(t * b), $MachinePrecision], If[LessEqual[t, 4e-15], a, If[LessEqual[t, 1.12e+70], x, N[(t * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.69999999999999991e33 or 1.11999999999999993e70 < t

   1. Initial program 92.2%

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

   2. Taylor expanded in t around inf 65.9%

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

      1. associate-*r* 65.9%

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

      2. neg-mul-1 65.9%

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

   4. Simplified 65.9%

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

   5. Taylor expanded in t around inf 63.4%

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

   6. Taylor expanded in a around 0 31.3%

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

   if -2.69999999999999991e33 < t < 4.0000000000000003e-15

   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 a around inf 24.2%

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

   3. Taylor expanded in t around 0 22.0%

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

   if 4.0000000000000003e-15 < t < 1.11999999999999993e70

   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 x around inf 29.7%

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

4. Final simplification 26.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+33}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-15}:\\ \;\;\;\;a\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 21: 25.0% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-205}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+91}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -8.2e+30)
   (* y b)
   (if (<= y 1.4e-205) x (if (<= y 2.2e+91) a (* y b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.2e+30) {
		tmp = y * b;
	} else if (y <= 1.4e-205) {
		tmp = x;
	} else if (y <= 2.2e+91) {
		tmp = a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-8.2d+30)) then
        tmp = y * b
    else if (y <= 1.4d-205) then
        tmp = x
    else if (y <= 2.2d+91) then
        tmp = a
    else
        tmp = y * b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -8.2e+30) {
		tmp = y * b;
	} else if (y <= 1.4e-205) {
		tmp = x;
	} else if (y <= 2.2e+91) {
		tmp = a;
	} else {
		tmp = y * b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -8.2e+30:
		tmp = y * b
	elif y <= 1.4e-205:
		tmp = x
	elif y <= 2.2e+91:
		tmp = a
	else:
		tmp = y * b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -8.2e+30)
		tmp = Float64(y * b);
	elseif (y <= 1.4e-205)
		tmp = x;
	elseif (y <= 2.2e+91)
		tmp = a;
	else
		tmp = Float64(y * b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -8.2e+30)
		tmp = y * b;
	elseif (y <= 1.4e-205)
		tmp = x;
	elseif (y <= 2.2e+91)
		tmp = a;
	else
		tmp = y * b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -8.2e+30], N[(y * b), $MachinePrecision], If[LessEqual[y, 1.4e-205], x, If[LessEqual[y, 2.2e+91], a, N[(y * b), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.20000000000000011e30 or 2.19999999999999999e91 < y

   1. Initial program 86.2%

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

   2. Taylor expanded in y around inf 76.3%

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

   3. Taylor expanded in b around inf 43.7%

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

   if -8.20000000000000011e30 < y < 1.39999999999999996e-205

   1. Initial program 98.8%

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

   2. Taylor expanded in x around inf 20.3%

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

   if 1.39999999999999996e-205 < y < 2.19999999999999999e91

   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 39.2%

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

   3. Taylor expanded in t around 0 22.4%

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

4. Final simplification 30.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{+30}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-205}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+91}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;y \cdot b\\ \end{array} \]

Alternative 22: 32.8% accurate, 2.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+38} \lor \neg \left(b \leq 0.000105\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= b -6.2e+38) (not (<= b 0.000105))) (* y b) (+ x z)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((b <= -6.2e+38) || !(b <= 0.000105)) {
		tmp = y * b;
	} else {
		tmp = x + 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 ((b <= (-6.2d+38)) .or. (.not. (b <= 0.000105d0))) then
        tmp = y * b
    else
        tmp = x + 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 ((b <= -6.2e+38) || !(b <= 0.000105)) {
		tmp = y * b;
	} else {
		tmp = x + z;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (b <= -6.2e+38) or not (b <= 0.000105):
		tmp = y * b
	else:
		tmp = x + z
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((b <= -6.2e+38) || !(b <= 0.000105))
		tmp = Float64(y * b);
	else
		tmp = Float64(x + z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((b <= -6.2e+38) || ~((b <= 0.000105)))
		tmp = y * b;
	else
		tmp = x + z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[b, -6.2e+38], N[Not[LessEqual[b, 0.000105]], $MachinePrecision]], N[(y * b), $MachinePrecision], N[(x + z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if b < -6.20000000000000035e38 or 1.05e-4 < b

   1. Initial program 88.8%

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

   2. Taylor expanded in y around inf 46.8%

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

   3. Taylor expanded in b around inf 36.7%

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

   if -6.20000000000000035e38 < b < 1.05e-4

   1. Initial program 98.5%

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

   2. Taylor expanded in a around 0 60.3%

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

   3. Taylor expanded in y around 0 35.8%

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

      1. associate--l+ 35.8%

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

      2. sub-neg 35.8%

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

      3. metadata-eval 35.8%

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

      4. neg-mul-1 35.8%

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

   5. Simplified 35.8%

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

   6. Taylor expanded in b around 0 33.6%

      \[\leadsto \color{blue}{x + z} \]
   7. Step-by-step derivation

      1. +-commutative 33.6%

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

   8. Simplified 33.6%

      \[\leadsto \color{blue}{z + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;b \leq -6.2 \cdot 10^{+38} \lor \neg \left(b \leq 0.000105\right):\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 23: 20.9% accurate, 4.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+131}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= x -6.6e-13) x (if (<= x 1.8e+131) a x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.6e-13) {
		tmp = x;
	} else if (x <= 1.8e+131) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (x <= (-6.6d-13)) then
        tmp = x
    else if (x <= 1.8d+131) then
        tmp = a
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (x <= -6.6e-13) {
		tmp = x;
	} else if (x <= 1.8e+131) {
		tmp = a;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if x <= -6.6e-13:
		tmp = x
	elif x <= 1.8e+131:
		tmp = a
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (x <= -6.6e-13)
		tmp = x;
	elseif (x <= 1.8e+131)
		tmp = a;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (x <= -6.6e-13)
		tmp = x;
	elseif (x <= 1.8e+131)
		tmp = a;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[x, -6.6e-13], x, If[LessEqual[x, 1.8e+131], a, x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.6000000000000001e-13 or 1.80000000000000016e131 < x

   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 x around inf 30.9%

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

   if -6.6000000000000001e-13 < x < 1.80000000000000016e131

   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 a around inf 36.4%

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

   3. Taylor expanded in t around 0 18.0%

      \[\leadsto \color{blue}{a} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+131}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24: 11.1% accurate, 21.0× speedup

Math

\[\begin{array}{l} \\ a \end{array} \]

FPCore

(FPCore (x y z t a b) :precision binary64 a)

C

double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = a
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return a;
}

Python

def code(x, y, z, t, a, b):
	return a

Julia

function code(x, y, z, t, a, b)
	return a
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = a;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := a

Derivation

1. Initial program 94.1%

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

2. Taylor expanded in a around inf 30.2%

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

3. Taylor expanded in t around 0 12.5%

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

4. Final simplification 12.5%

   \[\leadsto a \]

Reproduce

herbie shell --seed 2023308 
(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)))