Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.2% → 96.3%

Time: 22.5s

Alternatives: 17

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: 66.2% 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: 96.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t\_3}{t\_1}\\ t_5 := \frac{x}{1 - z} + t\_2\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq -4 \cdot 10^{-271}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;t\_2 + \frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t\_3\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

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 (/ (+ (* x y) t_3) t_1))
        (t_5 (+ (/ x (- 1.0 z)) t_2)))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -4e-271)
       t_4
       (if (<= t_4 0.0)
         (+
          t_2
          (/ (- (* x (/ y (- b y))) (* y (/ (- t a) (pow (- b y) 2.0)))) z))
         (if (<= t_4 5e+285) (/ (fma x y t_3) t_1) t_5))))))

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 = ((x * y) + t_3) / t_1;
	double t_5 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -4e-271) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_2 + (((x * (y / (b - y))) - (y * ((t - a) / pow((b - y), 2.0)))) / z);
	} else if (t_4 <= 5e+285) {
		tmp = fma(x, y, t_3) / t_1;
	} else {
		tmp = t_5;
	}
	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(Float64(x * y) + t_3) / t_1)
	t_5 = Float64(Float64(x / Float64(1.0 - z)) + t_2)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -4e-271)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = Float64(t_2 + Float64(Float64(Float64(x * Float64(y / Float64(b - y))) - Float64(y * Float64(Float64(t - a) / (Float64(b - y) ^ 2.0)))) / z));
	elseif (t_4 <= 5e+285)
		tmp = Float64(fma(x, y, t_3) / t_1);
	else
		tmp = t_5;
	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[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -4e-271], t$95$4, If[LessEqual[t$95$4, 0.0], N[(t$95$2 + N[(N[(N[(x * N[(y / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(y * N[(N[(t - a), $MachinePrecision] / N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 5e+285], N[(N[(x * y + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$5]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 5.00000000000000016e285 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 27.1%

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

   3. Taylor expanded in x around 0 27.1%

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

   4. Taylor expanded in y around inf 44.6%

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

      1. neg-mul-1 44.6%

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

      2. sub-neg 44.6%

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

   6. Simplified 44.6%

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

   7. Taylor expanded in z around inf 98.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -3.99999999999999985e-271

   1. Initial program 99.6%

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

   if -3.99999999999999985e-271 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 33.8%

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

   3. Taylor expanded in z around -inf 92.7%

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

      1. associate--l+ 92.7%

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

      2. mul-1-neg 92.7%

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

      3. distribute-lft-out-- 92.7%

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

      4. associate-/l* 89.6%

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

      5. associate-/l* 96.7%

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

      6. div-sub 96.7%

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

   5. Simplified 96.7%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000016e285

   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
3. Recombined 4 regimes into one program.

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -\infty:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq -4 \cdot 10^{-271}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 0:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{x \cdot \frac{y}{b - y} - y \cdot \frac{t - a}{{\left(b - y\right)}^{2}}}{z}\\ \mathbf{elif}\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 94.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{x \cdot y + t\_3}{t\_1}\\ t_5 := \frac{x}{1 - z} + t\_2\\ \mathbf{if}\;t\_4 \leq -\infty:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq -4 \cdot 10^{-271}:\\ \;\;\;\;t\_4\\ \mathbf{elif}\;t\_4 \leq 0:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_4 \leq 5 \cdot 10^{+285}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t\_3\right)}{t\_1}\\ \mathbf{else}:\\ \;\;\;\;t\_5\\ \end{array} \end{array} \]

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 (/ (+ (* x y) t_3) t_1))
        (t_5 (+ (/ x (- 1.0 z)) t_2)))
   (if (<= t_4 (- INFINITY))
     t_5
     (if (<= t_4 -4e-271)
       t_4
       (if (<= t_4 0.0) t_2 (if (<= t_4 5e+285) (/ (fma x y t_3) t_1) t_5))))))

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 = ((x * y) + t_3) / t_1;
	double t_5 = (x / (1.0 - z)) + t_2;
	double tmp;
	if (t_4 <= -((double) INFINITY)) {
		tmp = t_5;
	} else if (t_4 <= -4e-271) {
		tmp = t_4;
	} else if (t_4 <= 0.0) {
		tmp = t_2;
	} else if (t_4 <= 5e+285) {
		tmp = fma(x, y, t_3) / t_1;
	} else {
		tmp = t_5;
	}
	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(Float64(x * y) + t_3) / t_1)
	t_5 = Float64(Float64(x / Float64(1.0 - z)) + t_2)
	tmp = 0.0
	if (t_4 <= Float64(-Inf))
		tmp = t_5;
	elseif (t_4 <= -4e-271)
		tmp = t_4;
	elseif (t_4 <= 0.0)
		tmp = t_2;
	elseif (t_4 <= 5e+285)
		tmp = Float64(fma(x, y, t_3) / t_1);
	else
		tmp = t_5;
	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[(N[(x * y), $MachinePrecision] + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, (-Infinity)], t$95$5, If[LessEqual[t$95$4, -4e-271], t$95$4, If[LessEqual[t$95$4, 0.0], t$95$2, If[LessEqual[t$95$4, 5e+285], N[(N[(x * y + t$95$3), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$5]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 5.00000000000000016e285 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 27.1%

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

   3. Taylor expanded in x around 0 27.1%

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

   4. Taylor expanded in y around inf 44.6%

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

      1. neg-mul-1 44.6%

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

      2. sub-neg 44.6%

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

   6. Simplified 44.6%

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

   7. Taylor expanded in z around inf 98.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -3.99999999999999985e-271

   1. Initial program 99.6%

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

   if -3.99999999999999985e-271 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 33.8%

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

   3. Taylor expanded in z around inf 80.2%

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

   if 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000016e285

   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
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 94.8% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := \frac{x \cdot y + z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ t_3 := \frac{x}{1 - z} + t\_1\\ \mathbf{if}\;t\_2 \leq -\infty:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq -4 \cdot 10^{-271}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_2 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+285}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y)))
        (t_2 (/ (+ (* x y) (* z (- t a))) (+ y (* z (- b y)))))
        (t_3 (+ (/ x (- 1.0 z)) t_1)))
   (if (<= t_2 (- INFINITY))
     t_3
     (if (<= t_2 -4e-271)
       t_2
       (if (<= t_2 0.0) t_1 (if (<= t_2 5e+285) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_3 = (x / (1.0 - z)) + t_1;
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_3;
	} else if (t_2 <= -4e-271) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+285) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

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 t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	double t_3 = (x / (1.0 - z)) + t_1;
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else if (t_2 <= -4e-271) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 5e+285) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)))
	t_3 = (x / (1.0 - z)) + t_1
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_3
	elif t_2 <= -4e-271:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 5e+285:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))))
	t_3 = Float64(Float64(x / Float64(1.0 - z)) + t_1)
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_3;
	elseif (t_2 <= -4e-271)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 5e+285)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = ((x * y) + (z * (t - a))) / (y + (z * (b - y)));
	t_3 = (x / (1.0 - z)) + t_1;
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_3;
	elseif (t_2 <= -4e-271)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 5e+285)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = 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]}, Block[{t$95$3 = N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$3, If[LessEqual[t$95$2, -4e-271], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 5e+285], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -inf.0 or 5.00000000000000016e285 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y))))

   1. Initial program 27.1%

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

   3. Taylor expanded in x around 0 27.1%

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

   4. Taylor expanded in y around inf 44.6%

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

      1. neg-mul-1 44.6%

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

      2. sub-neg 44.6%

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

   6. Simplified 44.6%

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

   7. Taylor expanded in z around inf 98.4%

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

   if -inf.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < -3.99999999999999985e-271 or 0.0 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 5.00000000000000016e285

   1. Initial program 99.6%

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

   if -3.99999999999999985e-271 < (/.f64 (+.f64 (*.f64 x y) (*.f64 z (-.f64 t a))) (+.f64 y (*.f64 z (-.f64 b y)))) < 0.0

   1. Initial program 33.8%

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

   3. Taylor expanded in z around inf 80.2%

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

Alternative 4: 78.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := t\_1 + \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -0.27:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-123}:\\ \;\;\;\;t\_1 + \frac{t\_3}{y \cdot \left(1 - z\right)}\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-139}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-151}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-12}:\\ \;\;\;\;t\_1 + \frac{t\_3}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z)))
        (t_2 (+ t_1 (/ (- t a) (- b y))))
        (t_3 (* z (- t a))))
   (if (<= z -0.27)
     t_2
     (if (<= z -8.5e-123)
       (+ t_1 (/ t_3 (* y (- 1.0 z))))
       (if (<= z -6.6e-139)
         (/ (- t a) b)
         (if (<= z -3.8e-151)
           (/ (+ (* x y) (* z t)) y)
           (if (<= z 6e-12) (+ t_1 (/ t_3 y)) t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = t_1 + ((t - a) / (b - y));
	double t_3 = z * (t - a);
	double tmp;
	if (z <= -0.27) {
		tmp = t_2;
	} else if (z <= -8.5e-123) {
		tmp = t_1 + (t_3 / (y * (1.0 - z)));
	} else if (z <= -6.6e-139) {
		tmp = (t - a) / b;
	} else if (z <= -3.8e-151) {
		tmp = ((x * y) + (z * t)) / y;
	} else if (z <= 6e-12) {
		tmp = t_1 + (t_3 / y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    t_2 = t_1 + ((t - a) / (b - y))
    t_3 = z * (t - a)
    if (z <= (-0.27d0)) then
        tmp = t_2
    else if (z <= (-8.5d-123)) then
        tmp = t_1 + (t_3 / (y * (1.0d0 - z)))
    else if (z <= (-6.6d-139)) then
        tmp = (t - a) / b
    else if (z <= (-3.8d-151)) then
        tmp = ((x * y) + (z * t)) / y
    else if (z <= 6d-12) then
        tmp = t_1 + (t_3 / y)
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = t_1 + ((t - a) / (b - y));
	double t_3 = z * (t - a);
	double tmp;
	if (z <= -0.27) {
		tmp = t_2;
	} else if (z <= -8.5e-123) {
		tmp = t_1 + (t_3 / (y * (1.0 - z)));
	} else if (z <= -6.6e-139) {
		tmp = (t - a) / b;
	} else if (z <= -3.8e-151) {
		tmp = ((x * y) + (z * t)) / y;
	} else if (z <= 6e-12) {
		tmp = t_1 + (t_3 / y);
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	t_2 = t_1 + ((t - a) / (b - y))
	t_3 = z * (t - a)
	tmp = 0
	if z <= -0.27:
		tmp = t_2
	elif z <= -8.5e-123:
		tmp = t_1 + (t_3 / (y * (1.0 - z)))
	elif z <= -6.6e-139:
		tmp = (t - a) / b
	elif z <= -3.8e-151:
		tmp = ((x * y) + (z * t)) / y
	elif z <= 6e-12:
		tmp = t_1 + (t_3 / y)
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	t_2 = Float64(t_1 + Float64(Float64(t - a) / Float64(b - y)))
	t_3 = Float64(z * Float64(t - a))
	tmp = 0.0
	if (z <= -0.27)
		tmp = t_2;
	elseif (z <= -8.5e-123)
		tmp = Float64(t_1 + Float64(t_3 / Float64(y * Float64(1.0 - z))));
	elseif (z <= -6.6e-139)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= -3.8e-151)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / y);
	elseif (z <= 6e-12)
		tmp = Float64(t_1 + Float64(t_3 / y));
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	t_2 = t_1 + ((t - a) / (b - y));
	t_3 = z * (t - a);
	tmp = 0.0;
	if (z <= -0.27)
		tmp = t_2;
	elseif (z <= -8.5e-123)
		tmp = t_1 + (t_3 / (y * (1.0 - z)));
	elseif (z <= -6.6e-139)
		tmp = (t - a) / b;
	elseif (z <= -3.8e-151)
		tmp = ((x * y) + (z * t)) / y;
	elseif (z <= 6e-12)
		tmp = t_1 + (t_3 / y);
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.27], t$95$2, If[LessEqual[z, -8.5e-123], N[(t$95$1 + N[(t$95$3 / N[(y * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.6e-139], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, -3.8e-151], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 6e-12], N[(t$95$1 + N[(t$95$3 / y), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.27000000000000002 or 6.0000000000000003e-12 < z

   1. Initial program 48.9%

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

   3. Taylor expanded in x around 0 48.8%

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

   4. Taylor expanded in y around inf 46.0%

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

      1. neg-mul-1 46.0%

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

      2. sub-neg 46.0%

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

   6. Simplified 46.0%

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

   7. Taylor expanded in z around inf 88.1%

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

   if -0.27000000000000002 < z < -8.4999999999999995e-123

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0 91.0%

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

   4. Taylor expanded in y around inf 87.8%

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

      1. neg-mul-1 87.8%

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

      2. sub-neg 87.8%

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

   6. Simplified 87.8%

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

   7. Taylor expanded in y around inf 67.5%

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

      1. mul-1-neg 67.5%

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

      2. unsub-neg 67.5%

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

   9. Simplified 67.5%

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

   if -8.4999999999999995e-123 < z < -6.5999999999999999e-139

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 100.0%

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

   if -6.5999999999999999e-139 < z < -3.7999999999999997e-151

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 76.2%

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

   4. Taylor expanded in t around inf 100.0%

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

   if -3.7999999999999997e-151 < z < 6.0000000000000003e-12

   1. Initial program 90.8%

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

   3. Taylor expanded in x around 0 90.8%

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

   4. Taylor expanded in y around inf 80.3%

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

      1. neg-mul-1 80.3%

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

      2. sub-neg 80.3%

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

   6. Simplified 80.3%

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

   7. Taylor expanded in z around 0 72.3%

      \[\leadsto \frac{x}{1 - z} + \color{blue}{\frac{z \cdot \left(t - a\right)}{y}} \]
3. Recombined 5 regimes into one program.
4. Add Preprocessing

Alternative 5: 78.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ t_2 := t\_1 + \frac{z \cdot \left(t - a\right)}{y}\\ t_3 := t\_1 + \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{-41}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-96}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-139}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;z \leq -2.75 \cdot 10^{-157}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y}\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-13}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z)))
        (t_2 (+ t_1 (/ (* z (- t a)) y)))
        (t_3 (+ t_1 (/ (- t a) (- b y)))))
   (if (<= z -2.25e-41)
     t_3
     (if (<= z -1.3e-96)
       t_2
       (if (<= z -1.5e-139)
         t_3
         (if (<= z -2.75e-157)
           (/ (+ (* x y) (* z t)) y)
           (if (<= z 1.25e-13) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = t_1 + ((z * (t - a)) / y);
	double t_3 = t_1 + ((t - a) / (b - y));
	double tmp;
	if (z <= -2.25e-41) {
		tmp = t_3;
	} else if (z <= -1.3e-96) {
		tmp = t_2;
	} else if (z <= -1.5e-139) {
		tmp = t_3;
	} else if (z <= -2.75e-157) {
		tmp = ((x * y) + (z * t)) / y;
	} else if (z <= 1.25e-13) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    t_2 = t_1 + ((z * (t - a)) / y)
    t_3 = t_1 + ((t - a) / (b - y))
    if (z <= (-2.25d-41)) then
        tmp = t_3
    else if (z <= (-1.3d-96)) then
        tmp = t_2
    else if (z <= (-1.5d-139)) then
        tmp = t_3
    else if (z <= (-2.75d-157)) then
        tmp = ((x * y) + (z * t)) / y
    else if (z <= 1.25d-13) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double t_2 = t_1 + ((z * (t - a)) / y);
	double t_3 = t_1 + ((t - a) / (b - y));
	double tmp;
	if (z <= -2.25e-41) {
		tmp = t_3;
	} else if (z <= -1.3e-96) {
		tmp = t_2;
	} else if (z <= -1.5e-139) {
		tmp = t_3;
	} else if (z <= -2.75e-157) {
		tmp = ((x * y) + (z * t)) / y;
	} else if (z <= 1.25e-13) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	t_2 = t_1 + ((z * (t - a)) / y)
	t_3 = t_1 + ((t - a) / (b - y))
	tmp = 0
	if z <= -2.25e-41:
		tmp = t_3
	elif z <= -1.3e-96:
		tmp = t_2
	elif z <= -1.5e-139:
		tmp = t_3
	elif z <= -2.75e-157:
		tmp = ((x * y) + (z * t)) / y
	elif z <= 1.25e-13:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	t_2 = Float64(t_1 + Float64(Float64(z * Float64(t - a)) / y))
	t_3 = Float64(t_1 + Float64(Float64(t - a) / Float64(b - y)))
	tmp = 0.0
	if (z <= -2.25e-41)
		tmp = t_3;
	elseif (z <= -1.3e-96)
		tmp = t_2;
	elseif (z <= -1.5e-139)
		tmp = t_3;
	elseif (z <= -2.75e-157)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / y);
	elseif (z <= 1.25e-13)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	t_2 = t_1 + ((z * (t - a)) / y);
	t_3 = t_1 + ((t - a) / (b - y));
	tmp = 0.0;
	if (z <= -2.25e-41)
		tmp = t_3;
	elseif (z <= -1.3e-96)
		tmp = t_2;
	elseif (z <= -1.5e-139)
		tmp = t_3;
	elseif (z <= -2.75e-157)
		tmp = ((x * y) + (z * t)) / y;
	elseif (z <= 1.25e-13)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$1 + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e-41], t$95$3, If[LessEqual[z, -1.3e-96], t$95$2, If[LessEqual[z, -1.5e-139], t$95$3, If[LessEqual[z, -2.75e-157], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.25e-13], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.25e-41 or -1.3000000000000001e-96 < z < -1.5e-139 or 1.24999999999999997e-13 < z

   1. Initial program 55.5%

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

   3. Taylor expanded in x around 0 55.5%

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

   4. Taylor expanded in y around inf 51.8%

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

      1. neg-mul-1 51.8%

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

      2. sub-neg 51.8%

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

   6. Simplified 51.8%

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

   7. Taylor expanded in z around inf 85.1%

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

   if -2.25e-41 < z < -1.3000000000000001e-96 or -2.7499999999999999e-157 < z < 1.24999999999999997e-13

   1. Initial program 90.1%

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

   3. Taylor expanded in x around 0 90.1%

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

   4. Taylor expanded in y around inf 81.1%

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

      1. neg-mul-1 81.1%

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

      2. sub-neg 81.1%

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

   6. Simplified 81.1%

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

   7. Taylor expanded in z around 0 72.3%

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

   if -1.5e-139 < z < -2.7499999999999999e-157

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 81.0%

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

   4. Taylor expanded in t around inf 100.0%

      \[\leadsto \frac{x \cdot y + z \cdot \color{blue}{t}}{y} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 6: 68.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{z \cdot t}{y}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-123}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-139}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-151}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y}\\ \mathbf{elif}\;z \leq 10^{-85}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ x (/ (* z t) y))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -5.6e-52)
     t_2
     (if (<= z -8.5e-123)
       t_1
       (if (<= z -8.2e-139)
         (/ (- t a) b)
         (if (<= z -3e-151)
           (/ (+ (* x y) (* z t)) y)
           (if (<= z 1e-85) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((z * t) / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.6e-52) {
		tmp = t_2;
	} else if (z <= -8.5e-123) {
		tmp = t_1;
	} else if (z <= -8.2e-139) {
		tmp = (t - a) / b;
	} else if (z <= -3e-151) {
		tmp = ((x * y) + (z * t)) / y;
	} else if (z <= 1e-85) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + ((z * t) / y)
    t_2 = (t - a) / (b - y)
    if (z <= (-5.6d-52)) then
        tmp = t_2
    else if (z <= (-8.5d-123)) then
        tmp = t_1
    else if (z <= (-8.2d-139)) then
        tmp = (t - a) / b
    else if (z <= (-3d-151)) then
        tmp = ((x * y) + (z * t)) / y
    else if (z <= 1d-85) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x + ((z * t) / y);
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -5.6e-52) {
		tmp = t_2;
	} else if (z <= -8.5e-123) {
		tmp = t_1;
	} else if (z <= -8.2e-139) {
		tmp = (t - a) / b;
	} else if (z <= -3e-151) {
		tmp = ((x * y) + (z * t)) / y;
	} else if (z <= 1e-85) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x + ((z * t) / y)
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -5.6e-52:
		tmp = t_2
	elif z <= -8.5e-123:
		tmp = t_1
	elif z <= -8.2e-139:
		tmp = (t - a) / b
	elif z <= -3e-151:
		tmp = ((x * y) + (z * t)) / y
	elif z <= 1e-85:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x + Float64(Float64(z * t) / y))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -5.6e-52)
		tmp = t_2;
	elseif (z <= -8.5e-123)
		tmp = t_1;
	elseif (z <= -8.2e-139)
		tmp = Float64(Float64(t - a) / b);
	elseif (z <= -3e-151)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * t)) / y);
	elseif (z <= 1e-85)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x + ((z * t) / y);
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -5.6e-52)
		tmp = t_2;
	elseif (z <= -8.5e-123)
		tmp = t_1;
	elseif (z <= -8.2e-139)
		tmp = (t - a) / b;
	elseif (z <= -3e-151)
		tmp = ((x * y) + (z * t)) / y;
	elseif (z <= 1e-85)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e-52], t$95$2, If[LessEqual[z, -8.5e-123], t$95$1, If[LessEqual[z, -8.2e-139], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, -3e-151], N[(N[(N[(x * y), $MachinePrecision] + N[(z * t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1e-85], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.59999999999999989e-52 or 9.9999999999999998e-86 < z

   1. Initial program 56.9%

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

   3. Taylor expanded in z around inf 77.4%

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

   if -5.59999999999999989e-52 < z < -8.4999999999999995e-123 or -3e-151 < z < 9.9999999999999998e-86

   1. Initial program 88.4%

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

   3. Taylor expanded in z around 0 61.2%

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

   4. Taylor expanded in t around inf 53.4%

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

   5. Taylor expanded in x around 0 64.8%

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

   if -8.4999999999999995e-123 < z < -8.20000000000000028e-139

   1. Initial program 98.8%

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

   3. Taylor expanded in y around 0 100.0%

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

   if -8.20000000000000028e-139 < z < -3e-151

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 76.2%

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

   4. Taylor expanded in t around inf 100.0%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-52}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-123}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-139}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-151}:\\ \;\;\;\;\frac{x \cdot y + z \cdot t}{y}\\ \mathbf{elif}\;z \leq 10^{-85}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -0.0037:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(z \cdot \frac{t - a}{x \cdot y} + 1\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-82}:\\ \;\;\;\;\frac{t + \left(x \cdot \frac{y}{z} - a\right)}{b}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -0.0037)
     t_1
     (if (<= z -7.8e-70)
       (* x (+ (* z (/ (- t a) (* x y))) 1.0))
       (if (<= z -3.9e-82)
         (/ (+ t (- (* x (/ y z)) a)) b)
         (if (<= z 4.5e-15) (* x (/ y (+ y (* z (- b y))))) 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 <= -0.0037) {
		tmp = t_1;
	} else if (z <= -7.8e-70) {
		tmp = x * ((z * ((t - a) / (x * y))) + 1.0);
	} else if (z <= -3.9e-82) {
		tmp = (t + ((x * (y / z)) - a)) / b;
	} else if (z <= 4.5e-15) {
		tmp = x * (y / (y + (z * (b - y))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-0.0037d0)) then
        tmp = t_1
    else if (z <= (-7.8d-70)) then
        tmp = x * ((z * ((t - a) / (x * y))) + 1.0d0)
    else if (z <= (-3.9d-82)) then
        tmp = (t + ((x * (y / z)) - a)) / b
    else if (z <= 4.5d-15) then
        tmp = x * (y / (y + (z * (b - y))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -0.0037) {
		tmp = t_1;
	} else if (z <= -7.8e-70) {
		tmp = x * ((z * ((t - a) / (x * y))) + 1.0);
	} else if (z <= -3.9e-82) {
		tmp = (t + ((x * (y / z)) - a)) / b;
	} else if (z <= 4.5e-15) {
		tmp = x * (y / (y + (z * (b - y))));
	} 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 <= -0.0037:
		tmp = t_1
	elif z <= -7.8e-70:
		tmp = x * ((z * ((t - a) / (x * y))) + 1.0)
	elif z <= -3.9e-82:
		tmp = (t + ((x * (y / z)) - a)) / b
	elif z <= 4.5e-15:
		tmp = x * (y / (y + (z * (b - y))))
	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 <= -0.0037)
		tmp = t_1;
	elseif (z <= -7.8e-70)
		tmp = Float64(x * Float64(Float64(z * Float64(Float64(t - a) / Float64(x * y))) + 1.0));
	elseif (z <= -3.9e-82)
		tmp = Float64(Float64(t + Float64(Float64(x * Float64(y / z)) - a)) / b);
	elseif (z <= 4.5e-15)
		tmp = Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -0.0037)
		tmp = t_1;
	elseif (z <= -7.8e-70)
		tmp = x * ((z * ((t - a) / (x * y))) + 1.0);
	elseif (z <= -3.9e-82)
		tmp = (t + ((x * (y / z)) - a)) / b;
	elseif (z <= 4.5e-15)
		tmp = x * (y / (y + (z * (b - y))));
	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, -0.0037], t$95$1, If[LessEqual[z, -7.8e-70], N[(x * N[(N[(z * N[(N[(t - a), $MachinePrecision] / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.9e-82], N[(N[(t + N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision]), $MachinePrecision] / b), $MachinePrecision], If[LessEqual[z, 4.5e-15], N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.0037000000000000002 or 4.4999999999999998e-15 < z

   1. Initial program 48.9%

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

   3. Taylor expanded in z around inf 84.6%

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

   if -0.0037000000000000002 < z < -7.80000000000000038e-70

   1. Initial program 88.3%

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

   3. Taylor expanded in z around 0 56.3%

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

   4. Taylor expanded in x around inf 67.5%

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

      1. associate-/l* 67.5%

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

   6. Simplified 67.5%

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

   if -7.80000000000000038e-70 < z < -3.89999999999999973e-82

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.5%

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

   4. Taylor expanded in b around inf 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-/l* 100.0%

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

   6. Simplified 100.0%

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

   if -3.89999999999999973e-82 < z < 4.4999999999999998e-15

   1. Initial program 91.6%

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

   3. Taylor expanded in x around 0 91.6%

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

   4. Taylor expanded in x around inf 59.3%

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

      1. associate-/l* 66.5%

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

   6. Simplified 66.5%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0037:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-70}:\\ \;\;\;\;x \cdot \left(z \cdot \frac{t - a}{x \cdot y} + 1\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-82}:\\ \;\;\;\;\frac{t + \left(x \cdot \frac{y}{z} - a\right)}{b}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-15}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 69.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ t_2 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-52}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-304}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{-217}:\\ \;\;\;\;\frac{x \cdot y + z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* x (/ y (+ y (* z (- b y)))))) (t_2 (/ (- t a) (- b y))))
   (if (<= z -4.8e-52)
     t_2
     (if (<= z 3.9e-304)
       t_1
       (if (<= z 9.5e-217)
         (/ (+ (* x y) (* z (- t a))) y)
         (if (<= z 1.45e-14) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y / (y + (z * (b - y))));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.8e-52) {
		tmp = t_2;
	} else if (z <= 3.9e-304) {
		tmp = t_1;
	} else if (z <= 9.5e-217) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if (z <= 1.45e-14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x * (y / (y + (z * (b - y))))
    t_2 = (t - a) / (b - y)
    if (z <= (-4.8d-52)) then
        tmp = t_2
    else if (z <= 3.9d-304) then
        tmp = t_1
    else if (z <= 9.5d-217) then
        tmp = ((x * y) + (z * (t - a))) / y
    else if (z <= 1.45d-14) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x * (y / (y + (z * (b - y))));
	double t_2 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.8e-52) {
		tmp = t_2;
	} else if (z <= 3.9e-304) {
		tmp = t_1;
	} else if (z <= 9.5e-217) {
		tmp = ((x * y) + (z * (t - a))) / y;
	} else if (z <= 1.45e-14) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x * (y / (y + (z * (b - y))))
	t_2 = (t - a) / (b - y)
	tmp = 0
	if z <= -4.8e-52:
		tmp = t_2
	elif z <= 3.9e-304:
		tmp = t_1
	elif z <= 9.5e-217:
		tmp = ((x * y) + (z * (t - a))) / y
	elif z <= 1.45e-14:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x * Float64(y / Float64(y + Float64(z * Float64(b - y)))))
	t_2 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -4.8e-52)
		tmp = t_2;
	elseif (z <= 3.9e-304)
		tmp = t_1;
	elseif (z <= 9.5e-217)
		tmp = Float64(Float64(Float64(x * y) + Float64(z * Float64(t - a))) / y);
	elseif (z <= 1.45e-14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x * (y / (y + (z * (b - y))));
	t_2 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -4.8e-52)
		tmp = t_2;
	elseif (z <= 3.9e-304)
		tmp = t_1;
	elseif (z <= 9.5e-217)
		tmp = ((x * y) + (z * (t - a))) / y;
	elseif (z <= 1.45e-14)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-52], t$95$2, If[LessEqual[z, 3.9e-304], t$95$1, If[LessEqual[z, 9.5e-217], N[(N[(N[(x * y), $MachinePrecision] + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[z, 1.45e-14], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000003e-52 or 1.4500000000000001e-14 < z

   1. Initial program 53.1%

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

   3. Taylor expanded in z around inf 81.4%

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

   if -4.8000000000000003e-52 < z < 3.89999999999999975e-304 or 9.5000000000000001e-217 < z < 1.4500000000000001e-14

   1. Initial program 89.0%

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

   3. Taylor expanded in x around 0 89.0%

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

   4. Taylor expanded in x around inf 57.3%

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

      1. associate-/l* 67.1%

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

   6. Simplified 67.1%

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

   if 3.89999999999999975e-304 < z < 9.5000000000000001e-217

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 77.8%

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

Alternative 9: 53.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{+76}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.12 \cdot 10^{-35}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -7.4e+76)
     t_1
     (if (<= y -1.12e-35)
       (/ t (- b y))
       (if (<= y -1.2e-40) x (if (<= y 5.2e-24) (/ (- t a) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -7.4e+76) {
		tmp = t_1;
	} else if (y <= -1.12e-35) {
		tmp = t / (b - y);
	} else if (y <= -1.2e-40) {
		tmp = x;
	} else if (y <= 5.2e-24) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-7.4d+76)) then
        tmp = t_1
    else if (y <= (-1.12d-35)) then
        tmp = t / (b - y)
    else if (y <= (-1.2d-40)) then
        tmp = x
    else if (y <= 5.2d-24) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -7.4e+76) {
		tmp = t_1;
	} else if (y <= -1.12e-35) {
		tmp = t / (b - y);
	} else if (y <= -1.2e-40) {
		tmp = x;
	} else if (y <= 5.2e-24) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -7.4e+76:
		tmp = t_1
	elif y <= -1.12e-35:
		tmp = t / (b - y)
	elif y <= -1.2e-40:
		tmp = x
	elif y <= 5.2e-24:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -7.4e+76)
		tmp = t_1;
	elseif (y <= -1.12e-35)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= -1.2e-40)
		tmp = x;
	elseif (y <= 5.2e-24)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -7.4e+76)
		tmp = t_1;
	elseif (y <= -1.12e-35)
		tmp = t / (b - y);
	elseif (y <= -1.2e-40)
		tmp = x;
	elseif (y <= 5.2e-24)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.4e+76], t$95$1, If[LessEqual[y, -1.12e-35], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e-40], x, If[LessEqual[y, 5.2e-24], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.3999999999999999e76 or 5.2e-24 < y

   1. Initial program 58.3%

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

   3. Taylor expanded in y around inf 56.3%

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

      1. mul-1-neg 56.3%

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

      2. unsub-neg 56.3%

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

   5. Simplified 56.3%

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

   if -7.3999999999999999e76 < y < -1.12e-35

   1. Initial program 78.9%

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

   3. Taylor expanded in t around inf 31.3%

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

      1. *-commutative 31.3%

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

   5. Simplified 31.3%

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

   6. Taylor expanded in z around inf 43.2%

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

   if -1.12e-35 < y < -1.19999999999999996e-40

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 68.4%

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

   if -1.19999999999999996e-40 < y < 5.2e-24

   1. Initial program 77.2%

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

   3. Taylor expanded in y around 0 65.9%

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

Alternative 10: 75.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{+16} \lor \neg \left(z \leq 0.0015\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.35e+16) (not (<= z 0.0015)))
   (/ (- t a) (- b y))
   (+ (/ x (- 1.0 z)) (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.35e+16) || !(z <= 0.0015)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x / (1.0 - z)) + ((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 <= (-3.35d+16)) .or. (.not. (z <= 0.0015d0))) then
        tmp = (t - a) / (b - y)
    else
        tmp = (x / (1.0d0 - z)) + ((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 <= -3.35e+16) || !(z <= 0.0015)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = (x / (1.0 - z)) + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -3.35e+16) or not (z <= 0.0015):
		tmp = (t - a) / (b - y)
	else:
		tmp = (x / (1.0 - z)) + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.35e+16) || !(z <= 0.0015))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(Float64(x / Float64(1.0 - z)) + 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 <= -3.35e+16) || ~((z <= 0.0015)))
		tmp = (t - a) / (b - y);
	else
		tmp = (x / (1.0 - z)) + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.35e+16], N[Not[LessEqual[z, 0.0015]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision] + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.35e16 or 0.0015 < z

   1. Initial program 47.3%

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

   3. Taylor expanded in z around inf 85.7%

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

   if -3.35e16 < z < 0.0015

   1. Initial program 91.6%

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

   3. Taylor expanded in x around 0 91.6%

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

   4. Taylor expanded in y around inf 81.8%

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

      1. neg-mul-1 81.8%

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

      2. sub-neg 81.8%

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

   6. Simplified 81.8%

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

   7. Taylor expanded in z around 0 68.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{+16} \lor \neg \left(z \leq 0.0015\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z} + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-52} \lor \neg \left(z \leq 2.4 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.5e-52) (not (<= z 2.4e-8)))
   (/ (- t a) (- b y))
   (* x (/ y (+ y (* z (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.5e-52) || !(z <= 2.4e-8)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * (y / (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 <= (-4.5d-52)) .or. (.not. (z <= 2.4d-8))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x * (y / (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 <= -4.5e-52) || !(z <= 2.4e-8)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x * (y / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.5e-52) or not (z <= 2.4e-8):
		tmp = (t - a) / (b - y)
	else:
		tmp = x * (y / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.5e-52) || !(z <= 2.4e-8))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x * Float64(y / 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 <= -4.5e-52) || ~((z <= 2.4e-8)))
		tmp = (t - a) / (b - y);
	else
		tmp = x * (y / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.5e-52], N[Not[LessEqual[z, 2.4e-8]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(y / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.5e-52 or 2.39999999999999998e-8 < z

   1. Initial program 53.1%

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

   3. Taylor expanded in z around inf 81.4%

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

   if -4.5e-52 < z < 2.39999999999999998e-8

   1. Initial program 90.5%

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

   3. Taylor expanded in x around 0 90.5%

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

   4. Taylor expanded in x around inf 56.5%

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

      1. associate-/l* 64.9%

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

   6. Simplified 64.9%

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

4. Final simplification 74.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{-52} \lor \neg \left(z \leq 2.4 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{y + z \cdot \left(b - y\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 35.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-45}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-288}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-105}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -7e-45)
   x
   (if (<= y -1.1e-288) (/ (- a) b) (if (<= y 9e-105) (/ t b) x))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -7e-45) {
		tmp = x;
	} else if (y <= -1.1e-288) {
		tmp = -a / b;
	} else if (y <= 9e-105) {
		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 <= (-7d-45)) then
        tmp = x
    else if (y <= (-1.1d-288)) then
        tmp = -a / b
    else if (y <= 9d-105) 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 <= -7e-45) {
		tmp = x;
	} else if (y <= -1.1e-288) {
		tmp = -a / b;
	} else if (y <= 9e-105) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -7e-45:
		tmp = x
	elif y <= -1.1e-288:
		tmp = -a / b
	elif y <= 9e-105:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -7e-45)
		tmp = x;
	elseif (y <= -1.1e-288)
		tmp = Float64(Float64(-a) / b);
	elseif (y <= 9e-105)
		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 <= -7e-45)
		tmp = x;
	elseif (y <= -1.1e-288)
		tmp = -a / b;
	elseif (y <= 9e-105)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -7e-45], x, If[LessEqual[y, -1.1e-288], N[((-a) / b), $MachinePrecision], If[LessEqual[y, 9e-105], N[(t / b), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -7e-45 or 8.9999999999999995e-105 < y

   1. Initial program 66.1%

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

   3. Taylor expanded in z around 0 35.4%

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

   if -7e-45 < y < -1.1000000000000001e-288

   1. Initial program 73.4%

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

   3. Taylor expanded in y around 0 64.9%

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

   4. Taylor expanded in t around 0 50.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{a}{b}} \]
   5. Step-by-step derivation

      1. neg-mul-1 50.7%

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

      2. distribute-neg-frac 50.7%

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

   6. Simplified 50.7%

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

   if -1.1000000000000001e-288 < y < 8.9999999999999995e-105

   1. Initial program 76.8%

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

   3. Taylor expanded in t around inf 35.5%

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

      1. *-commutative 35.5%

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

   5. Simplified 35.5%

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

   6. Taylor expanded in y around 0 49.3%

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

Alternative 13: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-52} \lor \neg \left(z \leq 1.3 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.3e-52) (not (<= z 1.3e-85)))
   (/ (- t a) (- b y))
   (+ x (/ (* z t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.3e-52) || !(z <= 1.3e-85)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / 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 <= (-4.3d-52)) .or. (.not. (z <= 1.3d-85))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * t) / 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 <= -4.3e-52) || !(z <= 1.3e-85)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.3e-52) or not (z <= 1.3e-85):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.3e-52) || !(z <= 1.3e-85))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -4.3e-52) || ~((z <= 1.3e-85)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.3e-52], N[Not[LessEqual[z, 1.3e-85]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.3000000000000003e-52 or 1.30000000000000006e-85 < z

   1. Initial program 56.9%

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

   3. Taylor expanded in z around inf 77.4%

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

   if -4.3000000000000003e-52 < z < 1.30000000000000006e-85

   1. Initial program 89.3%

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

   3. Taylor expanded in z around 0 59.4%

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

   4. Taylor expanded in t around inf 53.3%

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

   5. Taylor expanded in x around 0 62.8%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{-52} \lor \neg \left(z \leq 1.3 \cdot 10^{-85}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-44} \lor \neg \left(z \leq 1360000000\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -4.8e-44) (not (<= z 1360000000.0)))
   (/ t (- b y))
   (/ x (- 1.0 z))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -4.8e-44) || !(z <= 1360000000.0)) {
		tmp = t / (b - 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 <= (-4.8d-44)) .or. (.not. (z <= 1360000000.0d0))) then
        tmp = t / (b - 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 <= -4.8e-44) || !(z <= 1360000000.0)) {
		tmp = t / (b - y);
	} else {
		tmp = x / (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -4.8e-44) or not (z <= 1360000000.0):
		tmp = t / (b - y)
	else:
		tmp = x / (1.0 - z)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -4.8e-44) || !(z <= 1360000000.0))
		tmp = Float64(t / Float64(b - 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 <= -4.8e-44) || ~((z <= 1360000000.0)))
		tmp = t / (b - y);
	else
		tmp = x / (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -4.8e-44], N[Not[LessEqual[z, 1360000000.0]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.80000000000000017e-44 or 1.36e9 < z

   1. Initial program 51.0%

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

   3. Taylor expanded in t around inf 27.6%

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

      1. *-commutative 27.6%

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

   5. Simplified 27.6%

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

   6. Taylor expanded in z around inf 47.3%

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

   if -4.80000000000000017e-44 < z < 1.36e9

   1. Initial program 91.0%

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

   3. Taylor expanded in y around inf 49.9%

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

      1. mul-1-neg 49.9%

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

      2. unsub-neg 49.9%

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

   5. Simplified 49.9%

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

4. Final simplification 48.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-44} \lor \neg \left(z \leq 1360000000\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 45.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-44} \lor \neg \left(z \leq 9.2 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.95e-44) (not (<= z 9.2e-39))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.95e-44) || !(z <= 9.2e-39)) {
		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 <= (-1.95d-44)) .or. (.not. (z <= 9.2d-39))) 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 <= -1.95e-44) || !(z <= 9.2e-39)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.95e-44) or not (z <= 9.2e-39):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.95e-44) || !(z <= 9.2e-39))
		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 <= -1.95e-44) || ~((z <= 9.2e-39)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.95e-44], N[Not[LessEqual[z, 9.2e-39]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.9500000000000001e-44 or 9.20000000000000033e-39 < z

   1. Initial program 54.0%

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

   3. Taylor expanded in t around inf 26.0%

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

      1. *-commutative 26.0%

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

   5. Simplified 26.0%

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

   6. Taylor expanded in z around inf 44.7%

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

   if -1.9500000000000001e-44 < z < 9.20000000000000033e-39

   1. Initial program 90.2%

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

   3. Taylor expanded in z around 0 53.0%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{-44} \lor \neg \left(z \leq 9.2 \cdot 10^{-39}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 37.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-52} \lor \neg \left(z \leq 9.6 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.9e-52) (not (<= z 9.6e-30))) (/ t b) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.9e-52) || !(z <= 9.6e-30)) {
		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 ((z <= (-5.9d-52)) .or. (.not. (z <= 9.6d-30))) 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 ((z <= -5.9e-52) || !(z <= 9.6e-30)) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.9e-52) or not (z <= 9.6e-30):
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.9e-52) || !(z <= 9.6e-30))
		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 ((z <= -5.9e-52) || ~((z <= 9.6e-30)))
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.9e-52], N[Not[LessEqual[z, 9.6e-30]], $MachinePrecision]], N[(t / b), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -5.90000000000000019e-52 or 9.5999999999999994e-30 < z

   1. Initial program 54.3%

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

   3. Taylor expanded in t around inf 25.9%

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

      1. *-commutative 25.9%

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

   5. Simplified 25.9%

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

   6. Taylor expanded in y around 0 25.8%

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

   if -5.90000000000000019e-52 < z < 9.5999999999999994e-30

   1. Initial program 90.1%

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

   3. Taylor expanded in z around 0 53.4%

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

4. Final simplification 37.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.9 \cdot 10^{-52} \lor \neg \left(z \leq 9.6 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.4% 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 69.4%

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

3. Taylor expanded in z around 0 25.0%

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

Developer target: 73.1% 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 2024110 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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