Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.5% → 90.7%

Time: 17.8s

Alternatives: 22

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

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) + (z * (t - a))) / (y + (z * (b - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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) + (z * (t - a))) / (y + (z * (b - y)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 90.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6700000000000 \lor \neg \left(z \leq 19000000\right):\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{x}{z} \cdot \frac{y}{b - y} - \left(\frac{a}{b - y} + \frac{y}{\frac{z \cdot {\left(b - y\right)}^{2}}{t - a}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6700000000000.0) (not (<= z 19000000.0)))
   (+
    (/ t (- b y))
    (-
     (* (/ x z) (/ y (- b y)))
     (+ (/ a (- b y)) (/ y (/ (* z (pow (- b y) 2.0)) (- t a))))))
   (/ (fma x y (* z (- t a))) (fma z (- b y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6700000000000.0) || !(z <= 19000000.0)) {
		tmp = (t / (b - y)) + (((x / z) * (y / (b - y))) - ((a / (b - y)) + (y / ((z * pow((b - y), 2.0)) / (t - a)))));
	} else {
		tmp = fma(x, y, (z * (t - a))) / fma(z, (b - y), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6700000000000.0) || !(z <= 19000000.0))
		tmp = Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) - Float64(Float64(a / Float64(b - y)) + Float64(y / Float64(Float64(z * (Float64(b - y) ^ 2.0)) / Float64(t - a))))));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / fma(z, Float64(b - y), y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6700000000000.0], N[Not[LessEqual[z, 19000000.0]], $MachinePrecision]], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.7e12 or 1.9e7 < z

   1. Initial program 36.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. times-frac 84.1%

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

      3. associate-/l* 97.5%

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

   4. Simplified 97.5%

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

   if -6.7e12 < z < 1.9e7

   1. Initial program 92.1%

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

      1. fma-def 92.1%

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

      2. +-commutative 92.1%

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

      3. fma-def 92.1%

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

   3. Simplified 92.1%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6700000000000 \lor \neg \left(z \leq 19000000\right):\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{x}{z} \cdot \frac{y}{b - y} - \left(\frac{a}{b - y} + \frac{y}{\frac{z \cdot {\left(b - y\right)}^{2}}{t - a}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \]

Alternative 2: 90.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -29000000000000 \lor \neg \left(z \leq 31000000\right):\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{x}{z} \cdot \frac{y}{b - y} - \left(\frac{a}{b - y} + \frac{y}{\frac{z \cdot {\left(b - y\right)}^{2}}{t - a}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -29000000000000.0) (not (<= z 31000000.0)))
   (+
    (/ t (- b y))
    (-
     (* (/ x z) (/ y (- b y)))
     (+ (/ a (- b y)) (/ y (/ (* z (pow (- b y) 2.0)) (- t a))))))
   (/ (fma x y (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -29000000000000.0) || !(z <= 31000000.0)) {
		tmp = (t / (b - y)) + (((x / z) * (y / (b - y))) - ((a / (b - y)) + (y / ((z * pow((b - y), 2.0)) / (t - a)))));
	} else {
		tmp = fma(x, y, (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -29000000000000.0) || !(z <= 31000000.0))
		tmp = Float64(Float64(t / Float64(b - y)) + Float64(Float64(Float64(x / z) * Float64(y / Float64(b - y))) - Float64(Float64(a / Float64(b - y)) + Float64(y / Float64(Float64(z * (Float64(b - y) ^ 2.0)) / Float64(t - a))))));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -29000000000000.0], N[Not[LessEqual[z, 31000000.0]], $MachinePrecision]], N[(N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(a / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.9e13 or 3.1e7 < z

   1. Initial program 36.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 75.8%

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

      1. associate--l+ 75.8%

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

      2. times-frac 84.1%

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

      3. associate-/l* 97.5%

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

   4. Simplified 97.5%

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

   if -2.9e13 < z < 3.1e7

   1. Initial program 92.1%

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

      1. fma-def 92.1%

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

   3. Simplified 92.1%

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

4. Final simplification 94.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -29000000000000 \lor \neg \left(z \leq 31000000\right):\\ \;\;\;\;\frac{t}{b - y} + \left(\frac{x}{z} \cdot \frac{y}{b - y} - \left(\frac{a}{b - y} + \frac{y}{\frac{z \cdot {\left(b - y\right)}^{2}}{t - a}}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 3: 86.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+16} \lor \neg \left(z \leq 4.35 \cdot 10^{+24}\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.6e+16) (not (<= z 4.35e+24)))
   (+
    (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
    (* (/ y z) (/ (- a t) (pow (- b y) 2.0))))
   (/ (fma x y (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -2.6e+16) || !(z <= 4.35e+24)) {
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + ((y / z) * ((a - t) / pow((b - y), 2.0)));
	} else {
		tmp = fma(x, y, (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -2.6e+16) || !(z <= 4.35e+24))
		tmp = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(Float64(y / z) * Float64(Float64(a - t) / (Float64(b - y) ^ 2.0))));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -2.6e+16], N[Not[LessEqual[z, 4.35e+24]], $MachinePrecision]], N[(N[(N[(N[(y / z), $MachinePrecision] * N[(x / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / z), $MachinePrecision] * N[(N[(a - t), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.6e16 or 4.34999999999999995e24 < z

   1. Initial program 34.1%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 74.8%

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

      1. associate--r+ 74.8%

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

      2. +-commutative 74.8%

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

      3. associate--l+ 74.8%

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

      4. *-commutative 74.8%

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

      5. times-frac 83.1%

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

      6. div-sub 84.0%

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

      7. times-frac 89.3%

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

   4. Simplified 89.3%

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

   if -2.6e16 < z < 4.34999999999999995e24

   1. Initial program 92.4%

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

      1. fma-def 92.4%

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

   3. Simplified 92.4%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+16} \lor \neg \left(z \leq 4.35 \cdot 10^{+24}\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + \frac{y}{z} \cdot \frac{a - t}{{\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 4: 84.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+76} \lor \neg \left(z \leq 1.5 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.3e+76) (not (<= z 1.5e+68)))
   (/ (- t a) (- b y))
   (/ (fma x y (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.3e+76) || !(z <= 1.5e+68)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = fma(x, y, (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.3e+76) || !(z <= 1.5e+68))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.3e+76], N[Not[LessEqual[z, 1.5e+68]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e76 or 1.5000000000000001e68 < z

   1. Initial program 29.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 87.2%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -1.3e76 < z < 1.5000000000000001e68

   1. Initial program 89.9%

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

      1. fma-def 89.9%

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

   3. Simplified 89.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+76} \lor \neg \left(z \leq 1.5 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 5: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := x + \frac{t_1}{y}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := \frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{if}\;z \leq -2.3 \cdot 10^{-29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-202}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+16}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ x (/ t_1 y)))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (/ t_1 (+ y (* z (- b y))))))
   (if (<= z -2.3e-29)
     t_3
     (if (<= z -2.25e-144)
       t_2
       (if (<= z -8.2e-202)
         t_4
         (if (<= z 2.45e-83)
           t_2
           (if (<= z 3.9e+16)
             t_4
             (if (<= z 1.45e+68) (- (/ a y) (/ x (+ z -1.0))) t_3))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = x + (t_1 / y);
	double t_3 = (t - a) / (b - y);
	double t_4 = t_1 / (y + (z * (b - y)));
	double tmp;
	if (z <= -2.3e-29) {
		tmp = t_3;
	} else if (z <= -2.25e-144) {
		tmp = t_2;
	} else if (z <= -8.2e-202) {
		tmp = t_4;
	} else if (z <= 2.45e-83) {
		tmp = t_2;
	} else if (z <= 3.9e+16) {
		tmp = t_4;
	} else if (z <= 1.45e+68) {
		tmp = (a / y) - (x / (z + -1.0));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = x + (t_1 / y)
    t_3 = (t - a) / (b - y)
    t_4 = t_1 / (y + (z * (b - y)))
    if (z <= (-2.3d-29)) then
        tmp = t_3
    else if (z <= (-2.25d-144)) then
        tmp = t_2
    else if (z <= (-8.2d-202)) then
        tmp = t_4
    else if (z <= 2.45d-83) then
        tmp = t_2
    else if (z <= 3.9d+16) then
        tmp = t_4
    else if (z <= 1.45d+68) then
        tmp = (a / y) - (x / (z + (-1.0d0)))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = x + (t_1 / y);
	double t_3 = (t - a) / (b - y);
	double t_4 = t_1 / (y + (z * (b - y)));
	double tmp;
	if (z <= -2.3e-29) {
		tmp = t_3;
	} else if (z <= -2.25e-144) {
		tmp = t_2;
	} else if (z <= -8.2e-202) {
		tmp = t_4;
	} else if (z <= 2.45e-83) {
		tmp = t_2;
	} else if (z <= 3.9e+16) {
		tmp = t_4;
	} else if (z <= 1.45e+68) {
		tmp = (a / y) - (x / (z + -1.0));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = x + (t_1 / y)
	t_3 = (t - a) / (b - y)
	t_4 = t_1 / (y + (z * (b - y)))
	tmp = 0
	if z <= -2.3e-29:
		tmp = t_3
	elif z <= -2.25e-144:
		tmp = t_2
	elif z <= -8.2e-202:
		tmp = t_4
	elif z <= 2.45e-83:
		tmp = t_2
	elif z <= 3.9e+16:
		tmp = t_4
	elif z <= 1.45e+68:
		tmp = (a / y) - (x / (z + -1.0))
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(x + Float64(t_1 / y))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))))
	tmp = 0.0
	if (z <= -2.3e-29)
		tmp = t_3;
	elseif (z <= -2.25e-144)
		tmp = t_2;
	elseif (z <= -8.2e-202)
		tmp = t_4;
	elseif (z <= 2.45e-83)
		tmp = t_2;
	elseif (z <= 3.9e+16)
		tmp = t_4;
	elseif (z <= 1.45e+68)
		tmp = Float64(Float64(a / y) - Float64(x / Float64(z + -1.0)));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = x + (t_1 / y);
	t_3 = (t - a) / (b - y);
	t_4 = t_1 / (y + (z * (b - y)));
	tmp = 0.0;
	if (z <= -2.3e-29)
		tmp = t_3;
	elseif (z <= -2.25e-144)
		tmp = t_2;
	elseif (z <= -8.2e-202)
		tmp = t_4;
	elseif (z <= 2.45e-83)
		tmp = t_2;
	elseif (z <= 3.9e+16)
		tmp = t_4;
	elseif (z <= 1.45e+68)
		tmp = (a / y) - (x / (z + -1.0));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.3e-29], t$95$3, If[LessEqual[z, -2.25e-144], t$95$2, If[LessEqual[z, -8.2e-202], t$95$4, If[LessEqual[z, 2.45e-83], t$95$2, If[LessEqual[z, 3.9e+16], t$95$4, If[LessEqual[z, 1.45e+68], N[(N[(a / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.29999999999999991e-29 or 1.45000000000000006e68 < z

   1. Initial program 35.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 83.7%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -2.29999999999999991e-29 < z < -2.2499999999999999e-144 or -8.2000000000000008e-202 < z < 2.45e-83

   1. Initial program 91.5%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 76.6%

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

   3. Taylor expanded in x around 0 82.9%

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

   if -2.2499999999999999e-144 < z < -8.2000000000000008e-202 or 2.45e-83 < z < 3.9e16

   1. Initial program 94.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in x around 0 67.9%

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

   if 3.9e16 < z < 1.45000000000000006e68

   1. Initial program 70.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. associate-*r/ 80.0%

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

      4. neg-mul-1 80.0%

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

      5. sub-neg 80.0%

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

      6. metadata-eval 80.0%

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

   4. Simplified 90.0%

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

   5. Taylor expanded in z around inf 90.0%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{t - a}{y}} \]

   6. Taylor expanded in t around 0 90.0%

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

      1. +-commutative 90.0%

         \[\leadsto \color{blue}{\frac{a}{y} + -1 \cdot \frac{x}{z - 1}} \]

      2. mul-1-neg 90.0%

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

      3. sub-neg 90.0%

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

      4. metadata-eval 90.0%

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

      5. unsub-neg 90.0%

         \[\leadsto \color{blue}{\frac{a}{y} - \frac{x}{z + -1}} \]

   8. Simplified 90.0%

      \[\leadsto \color{blue}{\frac{a}{y} - \frac{x}{z + -1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-29}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-144}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-202}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+16}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 6: 84.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+76} \lor \neg \left(z \leq 9.2 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.3e+76) (not (<= z 9.2e+68)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* y x)) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.3e+76) || !(z <= 9.2e+68)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.3d+76)) .or. (.not. (z <= 9.2d+68))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.3e+76) || !(z <= 9.2e+68)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.3e+76) or not (z <= 9.2e+68):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.3e+76) || !(z <= 9.2e+68))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.3e+76) || ~((z <= 9.2e+68)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * (b - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.3e+76], N[Not[LessEqual[z, 9.2e+68]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e76 or 9.1999999999999999e68 < z

   1. Initial program 29.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 87.2%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -1.3e76 < z < 9.1999999999999999e68

   1. Initial program 89.9%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+76} \lor \neg \left(z \leq 9.2 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 7: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -1.2 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 0.0074:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -1.2e-25)
     t_1
     (if (<= z 1.3e-66)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 0.0074)
         (/ (- (+ t (/ (* y x) z)) a) b)
         (if (<= z 1.45e+68) (- (/ (- a t) y) (/ x (+ z -1.0))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.2e-25) {
		tmp = t_1;
	} else if (z <= 1.3e-66) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 0.0074) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if (z <= 1.45e+68) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-1.2d-25)) then
        tmp = t_1
    else if (z <= 1.3d-66) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 0.0074d0) then
        tmp = ((t + ((y * x) / z)) - a) / b
    else if (z <= 1.45d+68) then
        tmp = ((a - t) / y) - (x / (z + (-1.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -1.2e-25) {
		tmp = t_1;
	} else if (z <= 1.3e-66) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 0.0074) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if (z <= 1.45e+68) {
		tmp = ((a - t) / y) - (x / (z + -1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -1.2e-25:
		tmp = t_1
	elif z <= 1.3e-66:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 0.0074:
		tmp = ((t + ((y * x) / z)) - a) / b
	elif z <= 1.45e+68:
		tmp = ((a - t) / y) - (x / (z + -1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -1.2e-25)
		tmp = t_1;
	elseif (z <= 1.3e-66)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 0.0074)
		tmp = Float64(Float64(Float64(t + Float64(Float64(y * x) / z)) - a) / b);
	elseif (z <= 1.45e+68)
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / Float64(z + -1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -1.2e-25)
		tmp = t_1;
	elseif (z <= 1.3e-66)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 0.0074)
		tmp = ((t + ((y * x) / z)) - a) / b;
	elseif (z <= 1.45e+68)
		tmp = ((a - t) / y) - (x / (z + -1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.2e-25], t$95$1, If[LessEqual[z, 1.3e-66], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0074], N[(N[(N[(t + N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 1.45e+68], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.20000000000000005e-25 or 1.45000000000000006e68 < z

   1. Initial program 35.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 83.7%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -1.20000000000000005e-25 < z < 1.2999999999999999e-66

   1. Initial program 92.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 71.0%

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

   3. Taylor expanded in x around 0 76.3%

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

   if 1.2999999999999999e-66 < z < 0.0074000000000000003

   1. Initial program 89.0%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 66.3%

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

      1. associate--r+ 66.3%

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

      2. +-commutative 66.3%

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

      3. associate--l+ 66.3%

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

      4. *-commutative 66.3%

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

      5. times-frac 66.2%

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

      6. div-sub 66.2%

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

      7. times-frac 66.3%

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

   4. Simplified 66.3%

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

   5. Taylor expanded in b around inf 66.7%

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

   if 0.0074000000000000003 < z < 1.45000000000000006e68

   1. Initial program 82.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around -inf 77.0%

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

      1. mul-1-neg 77.0%

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

      2. unsub-neg 77.0%

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

      3. associate-*r/ 77.0%

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

      4. neg-mul-1 77.0%

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

      5. sub-neg 77.0%

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

      6. metadata-eval 77.0%

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

   4. Simplified 82.8%

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

   5. Taylor expanded in z around inf 74.4%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{t - a}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 0.0074:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z + -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+16} \lor \neg \left(z \leq 1.45 \cdot 10^{+68}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z + -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.1e-24)
     t_1
     (if (<= z 7.2e-22)
       (+ x (/ (* z (- t a)) y))
       (if (or (<= z 3.9e+16) (not (<= z 1.45e+68)))
         t_1
         (- (/ a y) (/ x (+ z -1.0))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.1e-24) {
		tmp = t_1;
	} else if (z <= 7.2e-22) {
		tmp = x + ((z * (t - a)) / y);
	} else if ((z <= 3.9e+16) || !(z <= 1.45e+68)) {
		tmp = t_1;
	} else {
		tmp = (a / y) - (x / (z + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.1d-24)) then
        tmp = t_1
    else if (z <= 7.2d-22) then
        tmp = x + ((z * (t - a)) / y)
    else if ((z <= 3.9d+16) .or. (.not. (z <= 1.45d+68))) then
        tmp = t_1
    else
        tmp = (a / y) - (x / (z + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.1e-24) {
		tmp = t_1;
	} else if (z <= 7.2e-22) {
		tmp = x + ((z * (t - a)) / y);
	} else if ((z <= 3.9e+16) || !(z <= 1.45e+68)) {
		tmp = t_1;
	} else {
		tmp = (a / y) - (x / (z + -1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.1e-24:
		tmp = t_1
	elif z <= 7.2e-22:
		tmp = x + ((z * (t - a)) / y)
	elif (z <= 3.9e+16) or not (z <= 1.45e+68):
		tmp = t_1
	else:
		tmp = (a / y) - (x / (z + -1.0))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.1e-24)
		tmp = t_1;
	elseif (z <= 7.2e-22)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif ((z <= 3.9e+16) || !(z <= 1.45e+68))
		tmp = t_1;
	else
		tmp = Float64(Float64(a / y) - Float64(x / Float64(z + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.1e-24)
		tmp = t_1;
	elseif (z <= 7.2e-22)
		tmp = x + ((z * (t - a)) / y);
	elseif ((z <= 3.9e+16) || ~((z <= 1.45e+68)))
		tmp = t_1;
	else
		tmp = (a / y) - (x / (z + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e-24], t$95$1, If[LessEqual[z, 7.2e-22], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 3.9e+16], N[Not[LessEqual[z, 1.45e+68]], $MachinePrecision]], t$95$1, N[(N[(a / y), $MachinePrecision] - N[(x / N[(z + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.0999999999999999e-24 or 7.1999999999999996e-22 < z < 3.9e16 or 1.45000000000000006e68 < z

   1. Initial program 42.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 81.4%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -2.0999999999999999e-24 < z < 7.1999999999999996e-22

   1. Initial program 91.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 67.2%

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

   3. Taylor expanded in x around 0 73.6%

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

   if 3.9e16 < z < 1.45000000000000006e68

   1. Initial program 70.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around -inf 80.0%

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

      1. mul-1-neg 80.0%

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

      2. unsub-neg 80.0%

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

      3. associate-*r/ 80.0%

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

      4. neg-mul-1 80.0%

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

      5. sub-neg 80.0%

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

      6. metadata-eval 80.0%

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

   4. Simplified 90.0%

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

   5. Taylor expanded in z around inf 90.0%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{t - a}{y}} \]

   6. Taylor expanded in t around 0 90.0%

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

      1. +-commutative 90.0%

         \[\leadsto \color{blue}{\frac{a}{y} + -1 \cdot \frac{x}{z - 1}} \]

      2. mul-1-neg 90.0%

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

      3. sub-neg 90.0%

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

      4. metadata-eval 90.0%

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

      5. unsub-neg 90.0%

         \[\leadsto \color{blue}{\frac{a}{y} - \frac{x}{z + -1}} \]

   8. Simplified 90.0%

      \[\leadsto \color{blue}{\frac{a}{y} - \frac{x}{z + -1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-24}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-22}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+16} \lor \neg \left(z \leq 1.45 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y} - \frac{x}{z + -1}\\ \end{array} \]

Alternative 9: 74.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 43000000000000 \lor \neg \left(z \leq 3.6 \cdot 10^{+68}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -5.4e-30)
     t_1
     (if (<= z 6e-23)
       (+ x (/ (* z (- t a)) y))
       (if (or (<= z 43000000000000.0) (not (<= z 3.6e+68)))
         t_1
         (- (/ (- a t) y) (/ x z)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.4e-30) {
		tmp = t_1;
	} else if (z <= 6e-23) {
		tmp = x + ((z * (t - a)) / y);
	} else if ((z <= 43000000000000.0) || !(z <= 3.6e+68)) {
		tmp = t_1;
	} else {
		tmp = ((a - t) / y) - (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) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-5.4d-30)) then
        tmp = t_1
    else if (z <= 6d-23) then
        tmp = x + ((z * (t - a)) / y)
    else if ((z <= 43000000000000.0d0) .or. (.not. (z <= 3.6d+68))) then
        tmp = t_1
    else
        tmp = ((a - t) / y) - (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 t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.4e-30) {
		tmp = t_1;
	} else if (z <= 6e-23) {
		tmp = x + ((z * (t - a)) / y);
	} else if ((z <= 43000000000000.0) || !(z <= 3.6e+68)) {
		tmp = t_1;
	} else {
		tmp = ((a - t) / y) - (x / z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -5.4e-30:
		tmp = t_1
	elif z <= 6e-23:
		tmp = x + ((z * (t - a)) / y)
	elif (z <= 43000000000000.0) or not (z <= 3.6e+68):
		tmp = t_1
	else:
		tmp = ((a - t) / y) - (x / z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5.4e-30)
		tmp = t_1;
	elseif (z <= 6e-23)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif ((z <= 43000000000000.0) || !(z <= 3.6e+68))
		tmp = t_1;
	else
		tmp = Float64(Float64(Float64(a - t) / y) - Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -5.4e-30)
		tmp = t_1;
	elseif (z <= 6e-23)
		tmp = x + ((z * (t - a)) / y);
	elseif ((z <= 43000000000000.0) || ~((z <= 3.6e+68)))
		tmp = t_1;
	else
		tmp = ((a - t) / y) - (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e-30], t$95$1, If[LessEqual[z, 6e-23], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 43000000000000.0], N[Not[LessEqual[z, 3.6e+68]], $MachinePrecision]], t$95$1, N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.39999999999999975e-30 or 6.00000000000000006e-23 < z < 4.3e13 or 3.5999999999999999e68 < z

   1. Initial program 42.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 81.4%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -5.39999999999999975e-30 < z < 6.00000000000000006e-23

   1. Initial program 91.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 67.2%

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

   3. Taylor expanded in x around 0 73.6%

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

   if 4.3e13 < z < 3.5999999999999999e68

   1. Initial program 73.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around -inf 81.8%

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

      1. mul-1-neg 81.8%

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

      2. unsub-neg 81.8%

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

      3. associate-*r/ 81.8%

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

      4. neg-mul-1 81.8%

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

      5. sub-neg 81.8%

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

      6. metadata-eval 81.8%

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

   4. Simplified 90.9%

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

   5. Taylor expanded in z around inf 89.9%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{t - a}{y}} \]

   6. Taylor expanded in z around inf 89.9%

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

      1. associate--l+ 89.9%

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

      2. mul-1-neg 89.9%

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

      3. div-sub 89.9%

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

   8. Simplified 89.9%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-30}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-23}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 43000000000000 \lor \neg \left(z \leq 3.6 \cdot 10^{+68}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \end{array} \]

Alternative 10: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 19500000000:\\ \;\;\;\;\frac{z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2e-24)
     t_1
     (if (<= z 1.55e-33)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 19500000000.0)
         (/ (* z t) (+ y (* z (- b y))))
         (if (<= z 1.45e+68) (- (/ (- a t) y) (/ x z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2e-24) {
		tmp = t_1;
	} else if (z <= 1.55e-33) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 19500000000.0) {
		tmp = (z * t) / (y + (z * (b - y)));
	} else if (z <= 1.45e+68) {
		tmp = ((a - t) / y) - (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 - a) / (b - y)
    if (z <= (-2d-24)) then
        tmp = t_1
    else if (z <= 1.55d-33) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 19500000000.0d0) then
        tmp = (z * t) / (y + (z * (b - y)))
    else if (z <= 1.45d+68) then
        tmp = ((a - t) / y) - (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 - a) / (b - y);
	double tmp;
	if (z <= -2e-24) {
		tmp = t_1;
	} else if (z <= 1.55e-33) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 19500000000.0) {
		tmp = (z * t) / (y + (z * (b - y)));
	} else if (z <= 1.45e+68) {
		tmp = ((a - t) / y) - (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2e-24:
		tmp = t_1
	elif z <= 1.55e-33:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 19500000000.0:
		tmp = (z * t) / (y + (z * (b - y)))
	elif z <= 1.45e+68:
		tmp = ((a - t) / y) - (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2e-24)
		tmp = t_1;
	elseif (z <= 1.55e-33)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 19500000000.0)
		tmp = Float64(Float64(z * t) / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 1.45e+68)
		tmp = Float64(Float64(Float64(a - t) / y) - 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 - a) / (b - y);
	tmp = 0.0;
	if (z <= -2e-24)
		tmp = t_1;
	elseif (z <= 1.55e-33)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 19500000000.0)
		tmp = (z * t) / (y + (z * (b - y)));
	elseif (z <= 1.45e+68)
		tmp = ((a - t) / y) - (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2e-24], t$95$1, If[LessEqual[z, 1.55e-33], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 19500000000.0], N[(N[(z * t), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e+68], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.99999999999999985e-24 or 1.45000000000000006e68 < z

   1. Initial program 35.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 83.7%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -1.99999999999999985e-24 < z < 1.54999999999999998e-33

   1. Initial program 91.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 67.8%

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

   3. Taylor expanded in x around 0 74.4%

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

   if 1.54999999999999998e-33 < z < 1.95e10

   1. Initial program 99.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in t around inf 59.3%

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

      1. *-commutative 59.3%

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

   4. Simplified 59.3%

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

   if 1.95e10 < z < 1.45000000000000006e68

   1. Initial program 73.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around -inf 81.8%

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

      1. mul-1-neg 81.8%

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

      2. unsub-neg 81.8%

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

      3. associate-*r/ 81.8%

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

      4. neg-mul-1 81.8%

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

      5. sub-neg 81.8%

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

      6. metadata-eval 81.8%

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

   4. Simplified 90.9%

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

   5. Taylor expanded in z around inf 89.9%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{t - a}{y}} \]

   6. Taylor expanded in z around inf 89.9%

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

      1. associate--l+ 89.9%

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

      2. mul-1-neg 89.9%

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

      3. div-sub 89.9%

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

   8. Simplified 89.9%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{-24}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-33}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 19500000000:\\ \;\;\;\;\frac{z \cdot t}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 11: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 47000000000000:\\ \;\;\;\;\frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.1e-28)
     t_1
     (if (<= z 3.6e-66)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 47000000000000.0)
         (/ (+ t (- (/ x (/ z y)) a)) b)
         (if (<= z 1.45e+68) (- (/ (- a t) y) (/ x z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.1e-28) {
		tmp = t_1;
	} else if (z <= 3.6e-66) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 47000000000000.0) {
		tmp = (t + ((x / (z / y)) - a)) / b;
	} else if (z <= 1.45e+68) {
		tmp = ((a - t) / y) - (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 - a) / (b - y)
    if (z <= (-2.1d-28)) then
        tmp = t_1
    else if (z <= 3.6d-66) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 47000000000000.0d0) then
        tmp = (t + ((x / (z / y)) - a)) / b
    else if (z <= 1.45d+68) then
        tmp = ((a - t) / y) - (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 - a) / (b - y);
	double tmp;
	if (z <= -2.1e-28) {
		tmp = t_1;
	} else if (z <= 3.6e-66) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 47000000000000.0) {
		tmp = (t + ((x / (z / y)) - a)) / b;
	} else if (z <= 1.45e+68) {
		tmp = ((a - t) / y) - (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.1e-28:
		tmp = t_1
	elif z <= 3.6e-66:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 47000000000000.0:
		tmp = (t + ((x / (z / y)) - a)) / b
	elif z <= 1.45e+68:
		tmp = ((a - t) / y) - (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.1e-28)
		tmp = t_1;
	elseif (z <= 3.6e-66)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 47000000000000.0)
		tmp = Float64(Float64(t + Float64(Float64(x / Float64(z / y)) - a)) / b);
	elseif (z <= 1.45e+68)
		tmp = Float64(Float64(Float64(a - t) / y) - 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 - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.1e-28)
		tmp = t_1;
	elseif (z <= 3.6e-66)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 47000000000000.0)
		tmp = (t + ((x / (z / y)) - a)) / b;
	elseif (z <= 1.45e+68)
		tmp = ((a - t) / y) - (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e-28], t$95$1, If[LessEqual[z, 3.6e-66], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 47000000000000.0], N[(N[(t + N[(N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 1.45e+68], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.10000000000000006e-28 or 1.45000000000000006e68 < z

   1. Initial program 35.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 83.7%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -2.10000000000000006e-28 < z < 3.60000000000000012e-66

   1. Initial program 92.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 71.0%

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

   3. Taylor expanded in x around 0 76.3%

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

   if 3.60000000000000012e-66 < z < 4.7e13

   1. Initial program 91.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 54.0%

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

      1. associate--r+ 54.0%

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

      2. +-commutative 54.0%

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

      3. associate--l+ 54.0%

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

      4. *-commutative 54.0%

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

      5. times-frac 54.0%

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

      6. div-sub 54.0%

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

      7. times-frac 58.2%

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

   4. Simplified 58.2%

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

   5. Taylor expanded in b around inf 59.0%

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

      1. associate--l+ 59.0%

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

      2. associate-/l* 58.9%

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

   7. Simplified 58.9%

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

   if 4.7e13 < z < 1.45000000000000006e68

   1. Initial program 73.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around -inf 81.8%

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

      1. mul-1-neg 81.8%

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

      2. unsub-neg 81.8%

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

      3. associate-*r/ 81.8%

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

      4. neg-mul-1 81.8%

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

      5. sub-neg 81.8%

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

      6. metadata-eval 81.8%

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

   4. Simplified 90.9%

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

   5. Taylor expanded in z around inf 89.9%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{t - a}{y}} \]

   6. Taylor expanded in z around inf 89.9%

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

      1. associate--l+ 89.9%

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

      2. mul-1-neg 89.9%

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

      3. div-sub 89.9%

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

   8. Simplified 89.9%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-28}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 47000000000000:\\ \;\;\;\;\frac{t + \left(\frac{x}{\frac{z}{y}} - a\right)}{b}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{+68}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 12: 74.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -8 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 54000000000000:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -8e-25)
     t_1
     (if (<= z 9.8e-71)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 54000000000000.0)
         (/ (- (+ t (/ (* y x) z)) a) b)
         (if (<= z 3.6e+68) (- (/ (- a t) y) (/ x z)) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -8e-25) {
		tmp = t_1;
	} else if (z <= 9.8e-71) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 54000000000000.0) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if (z <= 3.6e+68) {
		tmp = ((a - t) / y) - (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 - a) / (b - y)
    if (z <= (-8d-25)) then
        tmp = t_1
    else if (z <= 9.8d-71) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 54000000000000.0d0) then
        tmp = ((t + ((y * x) / z)) - a) / b
    else if (z <= 3.6d+68) then
        tmp = ((a - t) / y) - (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 - a) / (b - y);
	double tmp;
	if (z <= -8e-25) {
		tmp = t_1;
	} else if (z <= 9.8e-71) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 54000000000000.0) {
		tmp = ((t + ((y * x) / z)) - a) / b;
	} else if (z <= 3.6e+68) {
		tmp = ((a - t) / y) - (x / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -8e-25:
		tmp = t_1
	elif z <= 9.8e-71:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 54000000000000.0:
		tmp = ((t + ((y * x) / z)) - a) / b
	elif z <= 3.6e+68:
		tmp = ((a - t) / y) - (x / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -8e-25)
		tmp = t_1;
	elseif (z <= 9.8e-71)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 54000000000000.0)
		tmp = Float64(Float64(Float64(t + Float64(Float64(y * x) / z)) - a) / b);
	elseif (z <= 3.6e+68)
		tmp = Float64(Float64(Float64(a - t) / y) - 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 - a) / (b - y);
	tmp = 0.0;
	if (z <= -8e-25)
		tmp = t_1;
	elseif (z <= 9.8e-71)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 54000000000000.0)
		tmp = ((t + ((y * x) / z)) - a) / b;
	elseif (z <= 3.6e+68)
		tmp = ((a - t) / y) - (x / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e-25], t$95$1, If[LessEqual[z, 9.8e-71], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 54000000000000.0], N[(N[(N[(t + N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 3.6e+68], N[(N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision] - N[(x / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.00000000000000031e-25 or 3.5999999999999999e68 < z

   1. Initial program 35.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 83.7%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -8.00000000000000031e-25 < z < 9.7999999999999994e-71

   1. Initial program 92.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 71.0%

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

   3. Taylor expanded in x around 0 76.3%

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

   if 9.7999999999999994e-71 < z < 5.4e13

   1. Initial program 91.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 54.0%

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

      1. associate--r+ 54.0%

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

      2. +-commutative 54.0%

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

      3. associate--l+ 54.0%

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

      4. *-commutative 54.0%

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

      5. times-frac 54.0%

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

      6. div-sub 54.0%

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

      7. times-frac 58.2%

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

   4. Simplified 58.2%

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

   5. Taylor expanded in b around inf 59.0%

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

   if 5.4e13 < z < 3.5999999999999999e68

   1. Initial program 73.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around -inf 81.8%

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

      1. mul-1-neg 81.8%

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

      2. unsub-neg 81.8%

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

      3. associate-*r/ 81.8%

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

      4. neg-mul-1 81.8%

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

      5. sub-neg 81.8%

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

      6. metadata-eval 81.8%

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

   4. Simplified 90.9%

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

   5. Taylor expanded in z around inf 89.9%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{t - a}{y}} \]

   6. Taylor expanded in z around inf 89.9%

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

      1. associate--l+ 89.9%

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

      2. mul-1-neg 89.9%

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

      3. div-sub 89.9%

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

   8. Simplified 89.9%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{-25}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-71}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 54000000000000:\\ \;\;\;\;\frac{\left(t + \frac{y \cdot x}{z}\right) - a}{b}\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{+68}:\\ \;\;\;\;\frac{a - t}{y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 13: 72.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-27} \lor \neg \left(z \leq 2.6 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6.2e-27) (not (<= z 2.6e-21)))
   (/ (- t a) (- b y))
   (+ x (* z (/ (- t a) y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.2e-27) || !(z <= 2.6e-21)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * ((t - a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-6.2d-27)) .or. (.not. (z <= 2.6d-21))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + (z * ((t - a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6.2e-27) || !(z <= 2.6e-21)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + (z * ((t - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -6.2e-27) or not (z <= 2.6e-21):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + (z * ((t - a) / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6.2e-27) || !(z <= 2.6e-21))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(t - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -6.2e-27) || ~((z <= 2.6e-21)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + (z * ((t - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6.2e-27], N[Not[LessEqual[z, 2.6e-21]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.1999999999999997e-27 or 2.60000000000000017e-21 < z

   1. Initial program 44.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 78.6%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -6.1999999999999997e-27 < z < 2.60000000000000017e-21

   1. Initial program 91.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 67.2%

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

   3. Taylor expanded in z around 0 68.8%

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

      1. div-sub 69.7%

         \[\leadsto x + z \cdot \color{blue}{\frac{t - a}{y}} \]

   5. Simplified 69.7%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{-27} \lor \neg \left(z \leq 2.6 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{t - a}{y}\\ \end{array} \]

Alternative 14: 75.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-26} \lor \neg \left(z \leq 7 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.5e-26) (not (<= z 7e-23)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.5e-26) || !(z <= 7e-23)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.5d-26)) .or. (.not. (z <= 7d-23))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.5e-26) || !(z <= 7e-23)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.5e-26) or not (z <= 7e-23):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.5e-26) || !(z <= 7e-23))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.5e-26) || ~((z <= 7e-23)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.5e-26], N[Not[LessEqual[z, 7e-23]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.50000000000000006e-26 or 6.99999999999999987e-23 < z

   1. Initial program 44.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 78.6%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]

   if -1.50000000000000006e-26 < z < 6.99999999999999987e-23

   1. Initial program 91.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 67.2%

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

   3. Taylor expanded in x around 0 73.6%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-26} \lor \neg \left(z \leq 7 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]

Alternative 15: 59.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+40} \lor \neg \left(y \leq 7 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -1.85e+40) (not (<= y 7e+20)))
   (/ x (- 1.0 z))
   (/ (- t a) (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.85e+40) || !(y <= 7e+20)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-1.85d+40)) .or. (.not. (y <= 7d+20))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / (b - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -1.85e+40) || !(y <= 7e+20)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -1.85e+40) or not (y <= 7e+20):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -1.85e+40) || !(y <= 7e+20))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -1.85e+40) || ~((y <= 7e+20)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -1.85e+40], N[Not[LessEqual[y, 7e+20]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.85e40 or 7e20 < y

   1. Initial program 58.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around inf 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 61.5%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if -1.85e40 < y < 7e20

   1. Initial program 71.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around inf 67.7%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+40} \lor \neg \left(y \leq 7 \cdot 10^{+20}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 16: 41.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+79} \lor \neg \left(z \leq 9.4 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.6e+79) (not (<= z 9.4e+61))) (/ (- a t) y) (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.6e+79) || !(z <= 9.4e+61)) {
		tmp = (a - t) / y;
	} else {
		tmp = x / (1.0 - 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 ((z <= (-5.6d+79)) .or. (.not. (z <= 9.4d+61))) then
        tmp = (a - t) / y
    else
        tmp = x / (1.0d0 - 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 ((z <= -5.6e+79) || !(z <= 9.4e+61)) {
		tmp = (a - t) / y;
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.6e+79) or not (z <= 9.4e+61):
		tmp = (a - t) / y
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.6e+79) || !(z <= 9.4e+61))
		tmp = Float64(Float64(a - t) / y);
	else
		tmp = Float64(x / Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.6e+79) || ~((z <= 9.4e+61)))
		tmp = (a - t) / y;
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.6e+79], N[Not[LessEqual[z, 9.4e+61]], $MachinePrecision]], N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.6000000000000002e79 or 9.3999999999999997e61 < z

   1. Initial program 29.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around -inf 21.9%

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

      1. mul-1-neg 21.9%

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

      2. unsub-neg 21.9%

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

      3. associate-*r/ 21.9%

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

      4. neg-mul-1 21.9%

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

      5. sub-neg 21.9%

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

      6. metadata-eval 21.9%

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

   4. Simplified 38.4%

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

   5. Taylor expanded in z around inf 46.6%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{t - a}{y}} \]

   6. Taylor expanded in x around 0 34.9%

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

      1. div-sub 35.0%

         \[\leadsto \color{blue}{\frac{a - t}{y}} \]

   8. Simplified 35.0%

      \[\leadsto \color{blue}{\frac{a - t}{y}} \]

   if -5.6000000000000002e79 < z < 9.3999999999999997e61

   1. Initial program 89.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around inf 45.3%

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

      1. mul-1-neg 45.3%

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

      2. unsub-neg 45.3%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 45.3%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+79} \lor \neg \left(z \leq 9.4 \cdot 10^{+61}\right):\\ \;\;\;\;\frac{a - t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 17: 53.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-39} \lor \neg \left(y \leq 1.1 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -5.6e-39) (not (<= y 1.1e-15))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -5.6e-39) || !(y <= 1.1e-15)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / 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 <= (-5.6d-39)) .or. (.not. (y <= 1.1d-15))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / 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 <= -5.6e-39) || !(y <= 1.1e-15)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -5.6e-39) or not (y <= 1.1e-15):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -5.6e-39) || !(y <= 1.1e-15))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -5.6e-39) || ~((y <= 1.1e-15)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -5.6e-39], N[Not[LessEqual[y, 1.1e-15]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.6000000000000003e-39 or 1.09999999999999993e-15 < y

   1. Initial program 60.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around inf 56.2%

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

      1. mul-1-neg 56.2%

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

      2. unsub-neg 56.2%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 56.2%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if -5.6000000000000003e-39 < y < 1.09999999999999993e-15

   1. Initial program 72.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around 0 67.9%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.6 \cdot 10^{-39} \lor \neg \left(y \leq 1.1 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 18: 33.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00027:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 12:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.00027) (/ (- x) z) (if (<= z 12.0) (+ x (* z x)) (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.00027) {
		tmp = -x / z;
	} else if (z <= 12.0) {
		tmp = x + (z * x);
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.00027d0)) then
        tmp = -x / z
    else if (z <= 12.0d0) then
        tmp = x + (z * x)
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.00027) {
		tmp = -x / z;
	} else if (z <= 12.0) {
		tmp = x + (z * x);
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.00027:
		tmp = -x / z
	elif z <= 12.0:
		tmp = x + (z * x)
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.00027)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= 12.0)
		tmp = Float64(x + Float64(z * x));
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.00027)
		tmp = -x / z;
	elseif (z <= 12.0)
		tmp = x + (z * x);
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.00027], N[((-x) / z), $MachinePrecision], If[LessEqual[z, 12.0], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], N[(a / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.70000000000000003e-4

   1. Initial program 36.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around inf 22.6%

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

      1. mul-1-neg 22.6%

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

      2. unsub-neg 22.6%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 22.6%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   5. Taylor expanded in z around inf 22.4%

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

      1. associate-*r/ 22.4%

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

      2. mul-1-neg 22.4%

         \[\leadsto \frac{\color{blue}{-x}}{z} \]

   7. Simplified 22.4%

      \[\leadsto \color{blue}{\frac{-x}{z}} \]

   if -2.70000000000000003e-4 < z < 12

   1. Initial program 91.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around inf 45.8%

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

      1. mul-1-neg 45.8%

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

      2. unsub-neg 45.8%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 45.8%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   5. Taylor expanded in z around 0 45.3%

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

   if 12 < z

   1. Initial program 42.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around -inf 36.2%

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

      1. mul-1-neg 36.2%

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

      2. unsub-neg 36.2%

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

      3. associate-*r/ 36.2%

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

      4. neg-mul-1 36.2%

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

      5. sub-neg 36.2%

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

      6. metadata-eval 36.2%

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

   4. Simplified 44.7%

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

   5. Taylor expanded in x around 0 36.1%

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

      1. times-frac 48.4%

         \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{z}{y} \cdot \frac{t - a}{z - 1}} \]

      2. sub-neg 48.4%

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

      3. metadata-eval 48.4%

         \[\leadsto \frac{-x}{z + -1} - \frac{z}{y} \cdot \frac{t - a}{z + \color{blue}{-1}} \]

   7. Simplified 48.4%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{z}{y} \cdot \frac{t - a}{z + -1}} \]

   8. Taylor expanded in a around inf 20.0%

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

   9. Taylor expanded in z around inf 27.6%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00027:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 12:\\ \;\;\;\;x + z \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]

Alternative 19: 32.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 10.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.2e+89) (/ a y) (if (<= z 10.5) x (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.2e+89) {
		tmp = a / y;
	} else if (z <= 10.5) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.2d+89)) then
        tmp = a / y
    else if (z <= 10.5d0) then
        tmp = x
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.2e+89) {
		tmp = a / y;
	} else if (z <= 10.5) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.2e+89:
		tmp = a / y
	elif z <= 10.5:
		tmp = x
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.2e+89)
		tmp = Float64(a / y);
	elseif (z <= 10.5)
		tmp = x;
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.2e+89)
		tmp = a / y;
	elseif (z <= 10.5)
		tmp = x;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.2e+89], N[(a / y), $MachinePrecision], If[LessEqual[z, 10.5], x, N[(a / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.19999999999999987e89 or 10.5 < z

   1. Initial program 35.4%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around -inf 28.1%

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

      1. mul-1-neg 28.1%

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

      2. unsub-neg 28.1%

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

      3. associate-*r/ 28.1%

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

      4. neg-mul-1 28.1%

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

      5. sub-neg 28.1%

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

      6. metadata-eval 28.1%

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

   4. Simplified 43.1%

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

   5. Taylor expanded in x around 0 31.0%

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

      1. times-frac 45.0%

         \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{z}{y} \cdot \frac{t - a}{z - 1}} \]

      2. sub-neg 45.0%

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

      3. metadata-eval 45.0%

         \[\leadsto \frac{-x}{z + -1} - \frac{z}{y} \cdot \frac{t - a}{z + \color{blue}{-1}} \]

   7. Simplified 45.0%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{z}{y} \cdot \frac{t - a}{z + -1}} \]

   8. Taylor expanded in a around inf 15.4%

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

   9. Taylor expanded in z around inf 24.4%

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

   if -3.19999999999999987e89 < z < 10.5

   1. Initial program 89.8%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 40.9%

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

4. Final simplification 33.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+89}:\\ \;\;\;\;\frac{a}{y}\\ \mathbf{elif}\;z \leq 10.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]

Alternative 20: 33.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00062:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 10.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -0.00062) (/ (- x) z) (if (<= z 10.5) x (/ a y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.00062) {
		tmp = -x / z;
	} else if (z <= 10.5) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-0.00062d0)) then
        tmp = -x / z
    else if (z <= 10.5d0) then
        tmp = x
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -0.00062) {
		tmp = -x / z;
	} else if (z <= 10.5) {
		tmp = x;
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -0.00062:
		tmp = -x / z
	elif z <= 10.5:
		tmp = x
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -0.00062)
		tmp = Float64(Float64(-x) / z);
	elseif (z <= 10.5)
		tmp = x;
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -0.00062)
		tmp = -x / z;
	elseif (z <= 10.5)
		tmp = x;
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -0.00062], N[((-x) / z), $MachinePrecision], If[LessEqual[z, 10.5], x, N[(a / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -6.2e-4

   1. Initial program 36.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around inf 22.6%

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

      1. mul-1-neg 22.6%

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

      2. unsub-neg 22.6%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 22.6%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   5. Taylor expanded in z around inf 22.4%

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

      1. associate-*r/ 22.4%

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

      2. mul-1-neg 22.4%

         \[\leadsto \frac{\color{blue}{-x}}{z} \]

   7. Simplified 22.4%

      \[\leadsto \color{blue}{\frac{-x}{z}} \]

   if -6.2e-4 < z < 10.5

   1. Initial program 91.7%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in z around 0 44.9%

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

   if 10.5 < z

   1. Initial program 42.9%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around -inf 36.2%

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

      1. mul-1-neg 36.2%

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

      2. unsub-neg 36.2%

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

      3. associate-*r/ 36.2%

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

      4. neg-mul-1 36.2%

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

      5. sub-neg 36.2%

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

      6. metadata-eval 36.2%

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

   4. Simplified 44.7%

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

   5. Taylor expanded in x around 0 36.1%

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

      1. times-frac 48.4%

         \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{z}{y} \cdot \frac{t - a}{z - 1}} \]

      2. sub-neg 48.4%

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

      3. metadata-eval 48.4%

         \[\leadsto \frac{-x}{z + -1} - \frac{z}{y} \cdot \frac{t - a}{z + \color{blue}{-1}} \]

   7. Simplified 48.4%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{z}{y} \cdot \frac{t - a}{z + -1}} \]

   8. Taylor expanded in a around inf 20.0%

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

   9. Taylor expanded in z around inf 27.6%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00062:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;z \leq 10.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]

Alternative 21: 33.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z 5e+46) (/ x (- 1.0 z)) (/ a y)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 5e+46) {
		tmp = x / (1.0 - z);
	} else {
		tmp = a / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= 5d+46) then
        tmp = x / (1.0d0 - z)
    else
        tmp = a / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= 5e+46) {
		tmp = x / (1.0 - z);
	} else {
		tmp = a / y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= 5e+46:
		tmp = x / (1.0 - z)
	else:
		tmp = a / y
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= 5e+46)
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(a / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= 5e+46)
		tmp = x / (1.0 - z);
	else
		tmp = a / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, 5e+46], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(a / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.0000000000000002e46

   1. Initial program 74.3%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around inf 38.9%

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

      1. mul-1-neg 38.9%

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

      2. unsub-neg 38.9%

         \[\leadsto \frac{x}{\color{blue}{1 - z}} \]

   4. Simplified 38.9%

      \[\leadsto \color{blue}{\frac{x}{1 - z}} \]

   if 5.0000000000000002e46 < z

   1. Initial program 35.6%

      \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

   2. Taylor expanded in y around -inf 27.6%

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

      1. mul-1-neg 27.6%

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

      2. unsub-neg 27.6%

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

      3. associate-*r/ 27.6%

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

      4. neg-mul-1 27.6%

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

      5. sub-neg 27.6%

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

      6. metadata-eval 27.6%

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

   4. Simplified 37.8%

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

   5. Taylor expanded in x around 0 27.5%

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

      1. times-frac 42.1%

         \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{z}{y} \cdot \frac{t - a}{z - 1}} \]

      2. sub-neg 42.1%

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

      3. metadata-eval 42.1%

         \[\leadsto \frac{-x}{z + -1} - \frac{z}{y} \cdot \frac{t - a}{z + \color{blue}{-1}} \]

   7. Simplified 42.1%

      \[\leadsto \frac{-x}{z + -1} - \color{blue}{\frac{z}{y} \cdot \frac{t - a}{z + -1}} \]

   8. Taylor expanded in a around inf 19.3%

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

   9. Taylor expanded in z around inf 29.5%

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

4. Final simplification 37.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{+46}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{a}{y}\\ \end{array} \]

Alternative 22: 25.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.4%

   \[\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \]

2. Taylor expanded in z around 0 24.6%

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

3. Final simplification 24.6%

   \[\leadsto x \]

Developer target: 73.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

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 = (((z * t) + (y * x)) / (y + (z * (b - y)))) - (a / ((b - y) + (y / z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023297 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :herbie-target
  (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z))))

  (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))