Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 67.1% → 87.7%

Time: 14.5s

Alternatives: 13

Speedup: 1.0×

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: 67.1% 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: 87.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t\_3 + y \cdot x}{t\_1}\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;y \cdot \frac{x - a \cdot \frac{z}{y}}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;t\_4 \leq -5 \cdot 10^{-273}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t\_3\right)}{t\_1}\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;t\_2 - \frac{x \cdot \frac{y}{y - b} + \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{t\_1}\\ \mathbf{elif}\;t\_4 \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{t\_3}{x \cdot t\_1}\right)\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (/ (- t a) (- b y)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ t_3 (* y x)) t_1)))
   (if (<= t_4 (- INFINITY))
     (* y (/ (- x (* a (/ z y))) (fma z (- b y) y)))
     (if (<= t_4 -5e-273)
       (/ (fma x y t_3) t_1)
       (if (<= t_4 0.0)
         (-
          t_2
          (/ (+ (* x (/ y (- y b))) (/ (* y (- t a)) (pow (- b y) 2.0))) z))
         (if (<= t_4 2e+292)
           (/ (+ (* y x) (- (* z t) (* z a))) t_1)
           (if (<= t_4 INFINITY)
             (* x (+ (/ y t_1) (/ t_3 (* x t_1))))
             t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (t - a) / (b - y);
	double t_3 = z * (t - a);
	double t_4 = (t_3 + (y * x)) / t_1;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = y * ((x - (a * (z / y))) / fma(z, (b - y), y));
	} else if (t_4 <= -5e-273) {
		tmp = fma(x, y, t_3) / t_1;
	} else if (t_4 <= 0.0) {
		tmp = t_2 - (((x * (y / (y - b))) + ((y * (t - a)) / pow((b - y), 2.0))) / z);
	} else if (t_4 <= 2e+292) {
		tmp = ((y * x) + ((z * t) - (z * a))) / t_1;
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = x * ((y / t_1) + (t_3 / (x * t_1)));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(t_3 + Float64(y * x)) / t_1)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = Float64(y * Float64(Float64(x - Float64(a * Float64(z / y))) / fma(z, Float64(b - y), y)));
	elseif (t_4 <= -5e-273)
		tmp = Float64(fma(x, y, t_3) / t_1);
	elseif (t_4 <= 0.0)
		tmp = Float64(t_2 - Float64(Float64(Float64(x * Float64(y / Float64(y - b))) + Float64(Float64(y * Float64(t - a)) / (Float64(b - y) ^ 2.0))) / z));
	elseif (t_4 <= 2e+292)
		tmp = Float64(Float64(Float64(y * x) + Float64(Float64(z * t) - Float64(z * a))) / t_1);
	elseif (t_4 <= Inf)
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(t_3 / Float64(x * t_1))));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], N[(y * N[(N[(x - N[(a * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -5e-273], N[(N[(x * y + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$4, 0.0], N[(t$95$2 - N[(N[(N[(x * N[(y / N[(y - b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+292], N[(N[(N[(y * x), $MachinePrecision] + N[(N[(z * t), $MachinePrecision] - N[(z * a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], If[LessEqual[t$95$4, Infinity], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(t$95$3 / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 6 regimes

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

   1. Initial program 37.2%

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

      1. fma-define 37.2%

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

   3. Simplified 37.2%

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

   5. Taylor expanded in y around inf 37.2%

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

   6. Taylor expanded in t around 0 27.8%

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

      1. associate-/l* 59.1%

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

      2. mul-1-neg 59.1%

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

      3. unsub-neg 59.1%

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

      4. associate-/l* 72.5%

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

      5. +-commutative 72.5%

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

      6. fma-undefine 72.4%

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

   8. Simplified 72.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -4.99999999999999965e-273

   1. Initial program 99.6%

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

      1. fma-define 99.6%

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

   3. Simplified 99.6%

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

   if -4.99999999999999965e-273 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 26.5%

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

      1. sub-neg 26.5%

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

      2. distribute-lft-in 26.5%

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

   4. Applied egg-rr 26.5%

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

   5. Taylor expanded in z around -inf 95.6%

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

      1. mul-1-neg 95.6%

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

      2. unsub-neg 95.6%

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

      3. mul-1-neg 95.6%

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

      4. mul-1-neg 95.6%

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

      5. unsub-neg 95.6%

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

   7. Simplified 91.6%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 2e292

   1. Initial program 99.5%

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

      1. sub-neg 99.5%

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

      2. distribute-lft-in 99.6%

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

   4. Applied egg-rr 99.6%

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

   if 2e292 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < +inf.0

   1. Initial program 36.8%

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

   3. Taylor expanded in x around inf 75.1%

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

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

   1. Initial program 0.0%

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

   3. Taylor expanded in z around inf 79.9%

      \[\leadsto \color{blue}{\frac{t - a}{b - y}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;y \cdot \frac{x - a \cdot \frac{z}{y}}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq -5 \cdot 10^{-273}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x \cdot \frac{y}{y - b} + \frac{y \cdot \left(t - a\right)}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq 2 \cdot 10^{+292}:\\ \;\;\;\;\frac{y \cdot x + \left(z \cdot t - z \cdot a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)} \leq \infty:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 90.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+30} \lor \neg \left(z \leq 175000000\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -8e+30) (not (<= z 175000000.0)))
     (+
      (+ (* (/ y z) (/ x (- b y))) (/ (- t a) (- b y)))
      (* y (/ (- a t) (* z (pow (- b y) 2.0)))))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -8e+30) || !(z <= 175000000.0)) {
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * pow((b - y), 2.0))));
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-8d+30)) .or. (.not. (z <= 175000000.0d0))) then
        tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * ((b - y) ** 2.0d0))))
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -8e+30) || !(z <= 175000000.0)) {
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * Math.pow((b - y), 2.0))));
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -8e+30) or not (z <= 175000000.0):
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * math.pow((b - y), 2.0))))
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -8e+30) || !(z <= 175000000.0))
		tmp = Float64(Float64(Float64(Float64(y / z) * Float64(x / Float64(b - y))) + Float64(Float64(t - a) / Float64(b - y))) + Float64(y * Float64(Float64(a - t) / Float64(z * (Float64(b - y) ^ 2.0)))));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -8e+30) || ~((z <= 175000000.0)))
		tmp = (((y / z) * (x / (b - y))) + ((t - a) / (b - y))) + (y * ((a - t) / (z * ((b - y) ^ 2.0))));
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -8e+30], N[Not[LessEqual[z, 175000000.0]], $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[(y * N[(N[(a - t), $MachinePrecision] / N[(z * N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -8.0000000000000002e30 or 1.75e8 < z

   1. Initial program 49.0%

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

   3. Taylor expanded in z around inf 70.8%

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

      1. associate--r+ 70.8%

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

      2. +-commutative 70.8%

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

      3. associate--l+ 70.8%

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

      4. *-commutative 70.8%

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

      5. times-frac 76.8%

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

      6. div-sub 77.7%

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

      7. associate-/l* 91.2%

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

   5. Simplified 91.2%

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

   if -8.0000000000000002e30 < z < 1.75e8

   1. Initial program 86.1%

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

   3. Taylor expanded in x around inf 88.7%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+30} \lor \neg \left(z \leq 175000000\right):\\ \;\;\;\;\left(\frac{y}{z} \cdot \frac{x}{b - y} + \frac{t - a}{b - y}\right) + y \cdot \frac{a - t}{z \cdot {\left(b - y\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+51} \lor \neg \left(z \leq 2.4 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{t\_1} + \frac{z \cdot \left(t - a\right)}{x \cdot t\_1}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y)))))
   (if (or (<= z -3.1e+51) (not (<= z 2.4e+41)))
     (/ (- t a) (- b y))
     (* x (+ (/ y t_1) (/ (* z (- t a)) (* x t_1)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -3.1e+51) || !(z <= 2.4e+41)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y + (z * (b - y))
    if ((z <= (-3.1d+51)) .or. (.not. (z <= 2.4d+41))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double tmp;
	if ((z <= -3.1e+51) || !(z <= 2.4e+41)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = y + (z * (b - y))
	tmp = 0
	if (z <= -3.1e+51) or not (z <= 2.4e+41):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)))
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	tmp = 0.0
	if ((z <= -3.1e+51) || !(z <= 2.4e+41))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(Float64(y / t_1) + Float64(Float64(z * Float64(t - a)) / Float64(x * t_1))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = y + (z * (b - y));
	tmp = 0.0;
	if ((z <= -3.1e+51) || ~((z <= 2.4e+41)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * ((y / t_1) + ((z * (t - a)) / (x * t_1)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[z, -3.1e+51], N[Not[LessEqual[z, 2.4e+41]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / t$95$1), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(x * t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -3.10000000000000011e51 or 2.4000000000000002e41 < z

   1. Initial program 44.1%

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

   3. Taylor expanded in z around inf 84.0%

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

   if -3.10000000000000011e51 < z < 2.4000000000000002e41

   1. Initial program 86.6%

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

   3. Taylor expanded in x around inf 87.6%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+51} \lor \neg \left(z \leq 2.4 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{y + z \cdot \left(b - y\right)} + \frac{z \cdot \left(t - a\right)}{x \cdot \left(y + z \cdot \left(b - y\right)\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+56} \lor \neg \left(z \leq 6 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.4e+56) (not (<= z 6e+41)))
   (/ (- 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 <= -5.4e+56) || !(z <= 6e+41)) {
		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 <= (-5.4d+56)) .or. (.not. (z <= 6d+41))) 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 <= -5.4e+56) || !(z <= 6e+41)) {
		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 <= -5.4e+56) or not (z <= 6e+41):
		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 <= -5.4e+56) || !(z <= 6e+41))
		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 <= -5.4e+56) || ~((z <= 6e+41)))
		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, -5.4e+56], N[Not[LessEqual[z, 6e+41]], $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 < -5.40000000000000019e56 or 5.9999999999999997e41 < z

   1. Initial program 44.1%

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

   3. Taylor expanded in z around inf 84.0%

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

   if -5.40000000000000019e56 < z < 5.9999999999999997e41

   1. Initial program 86.6%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{+56} \lor \neg \left(z \leq 6 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+33} \lor \neg \left(z \leq 7.5 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1e+33) (not (<= z 7.5e+40)))
   (/ (- t a) (- b y))
   (/ (+ (* z (- t a)) (* y x)) (+ y (* z b)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1e+33) || !(z <= 7.5e+40)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * b));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1d+33)) .or. (.not. (z <= 7.5d+40))) then
        tmp = (t - a) / (b - y)
    else
        tmp = ((z * (t - a)) + (y * x)) / (y + (z * b))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1e+33) || !(z <= 7.5e+40)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * b));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1e+33) or not (z <= 7.5e+40):
		tmp = (t - a) / (b - y)
	else:
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * b))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1e+33) || !(z <= 7.5e+40))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(y * x)) / Float64(y + Float64(z * b)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1e+33) || ~((z <= 7.5e+40)))
		tmp = (t - a) / (b - y);
	else
		tmp = ((z * (t - a)) + (y * x)) / (y + (z * b));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1e+33], N[Not[LessEqual[z, 7.5e+40]], $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 * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9.9999999999999995e32 or 7.4999999999999996e40 < z

   1. Initial program 45.3%

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

   3. Taylor expanded in z around inf 83.6%

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

   if -9.9999999999999995e32 < z < 7.4999999999999996e40

   1. Initial program 86.9%

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

   3. Taylor expanded in b around inf 83.9%

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

      1. *-commutative 83.9%

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

   5. Simplified 83.9%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+33} \lor \neg \left(z \leq 7.5 \cdot 10^{+40}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot b}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-12} \lor \neg \left(z \leq 1.25 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{z \cdot a}{y}\right) + t \cdot \frac{z}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4e-12) (not (<= z 1.25e-16)))
   (/ (- t a) (- b y))
   (+ (- x (/ (* z a) y)) (* t (/ z y)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4e-12) || !(z <= 1.25e-16)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x - ((z * a) / y)) + (t * (z / 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 <= (-4d-12)) .or. (.not. (z <= 1.25d-16))) then
        tmp = (t - a) / (b - y)
    else
        tmp = (x - ((z * a) / y)) + (t * (z / 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 <= -4e-12) || !(z <= 1.25e-16)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x - ((z * a) / y)) + (t * (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4e-12) or not (z <= 1.25e-16):
		tmp = (t - a) / (b - y)
	else:
		tmp = (x - ((z * a) / y)) + (t * (z / y))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4e-12) || !(z <= 1.25e-16))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(x - Float64(Float64(z * a) / y)) + Float64(t * Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4e-12) || ~((z <= 1.25e-16)))
		tmp = (t - a) / (b - y);
	else
		tmp = (x - ((z * a) / y)) + (t * (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4e-12], N[Not[LessEqual[z, 1.25e-16]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(t * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.99999999999999992e-12 or 1.2500000000000001e-16 < z

   1. Initial program 52.9%

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

   3. Taylor expanded in z around inf 79.9%

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

   if -3.99999999999999992e-12 < z < 1.2500000000000001e-16

   1. Initial program 85.6%

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

      1. fma-define 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in y around inf 83.4%

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

   6. Taylor expanded in z around 0 57.6%

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

   7. Taylor expanded in t around 0 71.0%

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

      1. associate-+r+ 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. associate-*r/ 71.0%

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

   9. Simplified 71.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{-12} \lor \neg \left(z \leq 1.25 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{z \cdot a}{y}\right) + t \cdot \frac{z}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-12} \lor \neg \left(z \leq 4 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.8e-12) (not (<= z 4e-16)))
   (/ (- t a) (- b y))
   (- x (/ (* z a) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.8e-12) || !(z <= 4e-16)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * 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 <= (-3.8d-12)) .or. (.not. (z <= 4d-16))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x - ((z * 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 <= -3.8e-12) || !(z <= 4e-16)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x - ((z * a) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.8e-12) or not (z <= 4e-16):
		tmp = (t - a) / (b - y)
	else:
		tmp = x - ((z * a) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.8e-12) || !(z <= 4e-16))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x - Float64(Float64(z * a) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -3.8e-12) || ~((z <= 4e-16)))
		tmp = (t - a) / (b - y);
	else
		tmp = x - ((z * a) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.8e-12], N[Not[LessEqual[z, 4e-16]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z * a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.79999999999999996e-12 or 3.9999999999999999e-16 < z

   1. Initial program 52.9%

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

   3. Taylor expanded in z around inf 79.9%

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

   if -3.79999999999999996e-12 < z < 3.9999999999999999e-16

   1. Initial program 85.6%

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

      1. fma-define 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in y around inf 83.4%

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

   6. Taylor expanded in z around 0 57.6%

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

   7. Taylor expanded in t around 0 62.3%

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

      1. mul-1-neg 62.3%

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

      2. unsub-neg 62.3%

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

   9. Simplified 62.3%

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

4. Final simplification 71.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-12} \lor \neg \left(z \leq 4 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z \cdot a}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0003 \lor \neg \left(y \leq 3.9 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -0.0003) (not (<= y 3.9e-50))) (/ 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 <= -0.0003) || !(y <= 3.9e-50)) {
		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 <= (-0.0003d0)) .or. (.not. (y <= 3.9d-50))) 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 <= -0.0003) || !(y <= 3.9e-50)) {
		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 <= -0.0003) or not (y <= 3.9e-50):
		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 <= -0.0003) || !(y <= 3.9e-50))
		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 <= -0.0003) || ~((y <= 3.9e-50)))
		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, -0.0003], N[Not[LessEqual[y, 3.9e-50]], $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 < -2.99999999999999974e-4 or 3.90000000000000021e-50 < y

   1. Initial program 54.9%

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

   3. Taylor expanded in y around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. unsub-neg 57.5%

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

   5. Simplified 57.5%

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

   if -2.99999999999999974e-4 < y < 3.90000000000000021e-50

   1. Initial program 82.4%

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

   3. Taylor expanded in y around 0 60.9%

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

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0003 \lor \neg \left(y \leq 3.9 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-10} \lor \neg \left(y \leq 4.1 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -3e-10) (not (<= y 4.1e-50))) (/ x (- 1.0 z)) (/ t (- b y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -3e-10) || !(y <= 4.1e-50)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (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 <= (-3d-10)) .or. (.not. (y <= 4.1d-50))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = t / (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 <= -3e-10) || !(y <= 4.1e-50)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = t / (b - y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -3e-10) or not (y <= 4.1e-50):
		tmp = x / (1.0 - z)
	else:
		tmp = t / (b - y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -3e-10) || !(y <= 4.1e-50))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(t / Float64(b - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -3e-10) || ~((y <= 4.1e-50)))
		tmp = x / (1.0 - z);
	else
		tmp = t / (b - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -3e-10], N[Not[LessEqual[y, 4.1e-50]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e-10 or 4.09999999999999985e-50 < y

   1. Initial program 54.9%

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

   3. Taylor expanded in y around inf 57.5%

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

      1. mul-1-neg 57.5%

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

      2. unsub-neg 57.5%

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

   5. Simplified 57.5%

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

   if -3e-10 < y < 4.09999999999999985e-50

   1. Initial program 82.4%

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

   3. Taylor expanded in z around inf 68.6%

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

   4. Taylor expanded in t around inf 32.3%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{-10} \lor \neg \left(y \leq 4.1 \cdot 10^{-50}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 45.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-27} \lor \neg \left(z \leq 4.5 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.05e-27) (not (<= z 4.5e-17))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-27) || !(z <= 4.5e-17)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.05d-27)) .or. (.not. (z <= 4.5d-17))) then
        tmp = t / (b - y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.05e-27) || !(z <= 4.5e-17)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.05e-27) or not (z <= 4.5e-17):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.05e-27) || !(z <= 4.5e-17))
		tmp = Float64(t / Float64(b - y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.05e-27) || ~((z <= 4.5e-17)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.05e-27], N[Not[LessEqual[z, 4.5e-17]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.05000000000000008e-27 or 4.49999999999999978e-17 < z

   1. Initial program 53.6%

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

   3. Taylor expanded in z around inf 78.4%

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

   4. Taylor expanded in t around inf 36.3%

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

   if -1.05000000000000008e-27 < z < 4.49999999999999978e-17

   1. Initial program 85.9%

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

   3. Taylor expanded in z around 0 51.2%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{-27} \lor \neg \left(z \leq 4.5 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 34.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -360000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-50}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -360000000000.0) x (if (<= y 3e-50) (/ t b) (+ x (* z x)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -360000000000.0) {
		tmp = x;
	} else if (y <= 3e-50) {
		tmp = t / b;
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-360000000000.0d0)) then
        tmp = x
    else if (y <= 3d-50) then
        tmp = t / b
    else
        tmp = x + (z * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -360000000000.0) {
		tmp = x;
	} else if (y <= 3e-50) {
		tmp = t / b;
	} else {
		tmp = x + (z * x);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -360000000000.0:
		tmp = x
	elif y <= 3e-50:
		tmp = t / b
	else:
		tmp = x + (z * x)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -360000000000.0)
		tmp = x;
	elseif (y <= 3e-50)
		tmp = Float64(t / b);
	else
		tmp = Float64(x + Float64(z * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -360000000000.0)
		tmp = x;
	elseif (y <= 3e-50)
		tmp = t / b;
	else
		tmp = x + (z * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -360000000000.0], x, If[LessEqual[y, 3e-50], N[(t / b), $MachinePrecision], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6e11

   1. Initial program 53.8%

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

   3. Taylor expanded in z around 0 58.3%

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

   if -3.6e11 < y < 2.9999999999999999e-50

   1. Initial program 82.6%

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

      1. fma-define 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around inf 73.7%

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

   6. Taylor expanded in t around inf 47.6%

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

      1. associate-/l* 44.8%

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

   8. Simplified 44.8%

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

   9. Taylor expanded in y around 0 27.6%

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

   if 2.9999999999999999e-50 < y

   1. Initial program 55.4%

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

   3. Taylor expanded in y around inf 48.6%

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

      1. mul-1-neg 48.6%

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

      2. unsub-neg 48.6%

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

   5. Simplified 48.6%

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

   6. Taylor expanded in z around 0 33.6%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -360000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-50}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 34.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -480000000000:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-50}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -480000000000.0) x (if (<= y 4.1e-50) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -480000000000.0) {
		tmp = x;
	} else if (y <= 4.1e-50) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-480000000000.0d0)) then
        tmp = x
    else if (y <= 4.1d-50) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -480000000000.0) {
		tmp = x;
	} else if (y <= 4.1e-50) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -480000000000.0:
		tmp = x
	elif y <= 4.1e-50:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -480000000000.0)
		tmp = x;
	elseif (y <= 4.1e-50)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -480000000000.0)
		tmp = x;
	elseif (y <= 4.1e-50)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -480000000000.0], x, If[LessEqual[y, 4.1e-50], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -4.8e11 or 4.09999999999999985e-50 < y

   1. Initial program 54.6%

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

   3. Taylor expanded in z around 0 45.9%

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

   if -4.8e11 < y < 4.09999999999999985e-50

   1. Initial program 82.6%

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

      1. fma-define 82.6%

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

   3. Simplified 82.6%

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

   5. Taylor expanded in y around inf 73.7%

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

   6. Taylor expanded in t around inf 47.6%

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

      1. associate-/l* 44.8%

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

   8. Simplified 44.8%

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

   9. Taylor expanded in y around 0 27.6%

      \[\leadsto \color{blue}{\frac{t}{b}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 13: 25.6% 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 69.0%

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

3. Taylor expanded in z around 0 26.5%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer Target 1: 74.7% 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 2024170 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (* z t) (* y x)) (+ y (* z (- b y)))) (/ a (+ (- b y) (/ y z)))))

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