Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 65.9% → 89.7%

Time: 26.9s

Alternatives: 16

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 65.9% 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: 89.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{b - y}{y} \cdot \frac{z}{x}} + \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := \mathsf{fma}\left(z, b - y, y\right)\\ \mathbf{if}\;z \leq -7600:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-268}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_2\right)}{t_3}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{\frac{t_3}{x}} + z \cdot \frac{t}{t_3}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{t_2 + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ 1.0 (* (/ (- b y) y) (/ z x))) (/ (- t a) (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (fma z (- b y) y)))
   (if (<= z -7600.0)
     t_1
     (if (<= z 7e-268)
       (/ (fma x y t_2) t_3)
       (if (<= z 3.9e-100)
         (+ (/ y (/ t_3 x)) (* z (/ t t_3)))
         (if (<= z 1.2e+14) (/ (+ t_2 (* y x)) (+ y (* z (- b y)))) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 / (((b - y) / y) * (z / x))) + ((t - a) / (b - y));
	double t_2 = z * (t - a);
	double t_3 = fma(z, (b - y), y);
	double tmp;
	if (z <= -7600.0) {
		tmp = t_1;
	} else if (z <= 7e-268) {
		tmp = fma(x, y, t_2) / t_3;
	} else if (z <= 3.9e-100) {
		tmp = (y / (t_3 / x)) + (z * (t / t_3));
	} else if (z <= 1.2e+14) {
		tmp = (t_2 + (y * x)) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 / Float64(Float64(Float64(b - y) / y) * Float64(z / x))) + Float64(Float64(t - a) / Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = fma(z, Float64(b - y), y)
	tmp = 0.0
	if (z <= -7600.0)
		tmp = t_1;
	elseif (z <= 7e-268)
		tmp = Float64(fma(x, y, t_2) / t_3);
	elseif (z <= 3.9e-100)
		tmp = Float64(Float64(y / Float64(t_3 / x)) + Float64(z * Float64(t / t_3)));
	elseif (z <= 1.2e+14)
		tmp = Float64(Float64(t_2 + Float64(y * x)) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 / N[(N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]}, If[LessEqual[z, -7600.0], t$95$1, If[LessEqual[z, 7e-268], N[(N[(x * y + t$95$2), $MachinePrecision] / t$95$3), $MachinePrecision], If[LessEqual[z, 3.9e-100], N[(N[(y / N[(t$95$3 / x), $MachinePrecision]), $MachinePrecision] + N[(z * N[(t / t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+14], N[(N[(t$95$2 + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7600 or 1.2e14 < z

   1. Initial program 40.7%

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

   2. Taylor expanded in z around -inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate--l+ 68.9%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in x around inf 85.3%

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

      1. clear-num 85.3%

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

      2. inv-pow 85.3%

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

   7. Applied egg-rr 85.3%

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

      1. unpow-1 85.3%

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

      2. times-frac 99.9%

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

   9. Simplified 99.9%

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

   if -7600 < z < 7.00000000000000011e-268

   1. Initial program 94.8%

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

      1. fma-def 94.8%

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

      2. +-commutative 94.8%

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

      3. fma-def 94.8%

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

   3. Simplified 94.8%

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

   if 7.00000000000000011e-268 < z < 3.89999999999999977e-100

   1. Initial program 68.7%

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

   2. Taylor expanded in x around inf 68.8%

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

   3. Taylor expanded in a around 0 62.8%

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

      1. associate-/l* 90.7%

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

      2. +-commutative 90.7%

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

      3. *-commutative 90.7%

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

      4. fma-def 90.7%

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

      5. associate-/l* 87.6%

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

      6. +-commutative 87.6%

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

      7. *-commutative 87.6%

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

      8. fma-def 87.6%

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

      9. associate-/r/ 87.7%

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

   5. Simplified 87.7%

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

   if 3.89999999999999977e-100 < z < 1.2e14

   1. Initial program 92.1%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7600:\\ \;\;\;\;\frac{1}{\frac{b - y}{y} \cdot \frac{z}{x}} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-268}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-100}:\\ \;\;\;\;\frac{y}{\frac{\mathsf{fma}\left(z, b - y, y\right)}{x}} + z \cdot \frac{t}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{b - y}{y} \cdot \frac{z}{x}} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 2: 92.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + z \cdot \left(b - y\right)\\ t_2 := \frac{1}{\frac{b - y}{y} \cdot \frac{z}{x}} + \frac{t - a}{b - y}\\ t_3 := z \cdot \left(t - a\right)\\ \mathbf{if}\;z \leq -7200:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-291}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, t_3\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{t_3}{t_1}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{t_3 + y \cdot x}{t_1}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ y (* z (- b y))))
        (t_2 (+ (/ 1.0 (* (/ (- b y) y) (/ z x))) (/ (- t a) (- b y))))
        (t_3 (* z (- t a))))
   (if (<= z -7200.0)
     t_2
     (if (<= z 8e-291)
       (/ (fma x y t_3) (fma z (- b y) y))
       (if (<= z 1.3e-101)
         (+ x (/ t_3 t_1))
         (if (<= z 1.2e+14) (/ (+ t_3 (* y x)) t_1) t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = y + (z * (b - y));
	double t_2 = (1.0 / (((b - y) / y) * (z / x))) + ((t - a) / (b - y));
	double t_3 = z * (t - a);
	double tmp;
	if (z <= -7200.0) {
		tmp = t_2;
	} else if (z <= 8e-291) {
		tmp = fma(x, y, t_3) / fma(z, (b - y), y);
	} else if (z <= 1.3e-101) {
		tmp = x + (t_3 / t_1);
	} else if (z <= 1.2e+14) {
		tmp = (t_3 + (y * x)) / t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(y + Float64(z * Float64(b - y)))
	t_2 = Float64(Float64(1.0 / Float64(Float64(Float64(b - y) / y) * Float64(z / x))) + Float64(Float64(t - a) / Float64(b - y)))
	t_3 = Float64(z * Float64(t - a))
	tmp = 0.0
	if (z <= -7200.0)
		tmp = t_2;
	elseif (z <= 8e-291)
		tmp = Float64(fma(x, y, t_3) / fma(z, Float64(b - y), y));
	elseif (z <= 1.3e-101)
		tmp = Float64(x + Float64(t_3 / t_1));
	elseif (z <= 1.2e+14)
		tmp = Float64(Float64(t_3 + Float64(y * x)) / t_1);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(1.0 / N[(N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + 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, -7200.0], t$95$2, If[LessEqual[z, 8e-291], N[(N[(x * y + t$95$3), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.3e-101], N[(x + N[(t$95$3 / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.2e+14], N[(N[(t$95$3 + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$1), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7200 or 1.2e14 < z

   1. Initial program 40.7%

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

   2. Taylor expanded in z around -inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate--l+ 68.9%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in x around inf 85.3%

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

      1. clear-num 85.3%

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

      2. inv-pow 85.3%

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

   7. Applied egg-rr 85.3%

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

      1. unpow-1 85.3%

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

      2. times-frac 99.9%

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

   9. Simplified 99.9%

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

   if -7200 < z < 7.9999999999999997e-291

   1. Initial program 93.8%

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

      1. fma-def 93.9%

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

      2. +-commutative 93.9%

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

      3. fma-def 93.9%

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

   3. Simplified 93.9%

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

   if 7.9999999999999997e-291 < z < 1.3000000000000001e-101

   1. Initial program 79.1%

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

   2. Taylor expanded in x around inf 79.1%

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

   3. Taylor expanded in z around 0 93.1%

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

   if 1.3000000000000001e-101 < z < 1.2e14

   1. Initial program 88.6%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7200:\\ \;\;\;\;\frac{1}{\frac{b - y}{y} \cdot \frac{z}{x}} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-291}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{b - y}{y} \cdot \frac{z}{x}} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 3: 92.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{b - y}{y} \cdot \frac{z}{x}} + \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := y + z \cdot \left(b - y\right)\\ t_4 := \frac{t_2}{t_3}\\ \mathbf{if}\;z \leq -7600:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-291}:\\ \;\;\;\;t_4 + \frac{y \cdot x}{t_3}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-101}:\\ \;\;\;\;x + t_4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{t_2 + y \cdot x}{t_3}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ 1.0 (* (/ (- b y) y) (/ z x))) (/ (- t a) (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (+ y (* z (- b y))))
        (t_4 (/ t_2 t_3)))
   (if (<= z -7600.0)
     t_1
     (if (<= z 7.4e-291)
       (+ t_4 (/ (* y x) t_3))
       (if (<= z 9.2e-101)
         (+ x t_4)
         (if (<= z 1.2e+14) (/ (+ t_2 (* y x)) t_3) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 / (((b - y) / y) * (z / x))) + ((t - a) / (b - y));
	double t_2 = z * (t - a);
	double t_3 = y + (z * (b - y));
	double t_4 = t_2 / t_3;
	double tmp;
	if (z <= -7600.0) {
		tmp = t_1;
	} else if (z <= 7.4e-291) {
		tmp = t_4 + ((y * x) / t_3);
	} else if (z <= 9.2e-101) {
		tmp = x + t_4;
	} else if (z <= 1.2e+14) {
		tmp = (t_2 + (y * x)) / t_3;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (1.0d0 / (((b - y) / y) * (z / x))) + ((t - a) / (b - y))
    t_2 = z * (t - a)
    t_3 = y + (z * (b - y))
    t_4 = t_2 / t_3
    if (z <= (-7600.0d0)) then
        tmp = t_1
    else if (z <= 7.4d-291) then
        tmp = t_4 + ((y * x) / t_3)
    else if (z <= 9.2d-101) then
        tmp = x + t_4
    else if (z <= 1.2d+14) then
        tmp = (t_2 + (y * x)) / t_3
    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 = (1.0 / (((b - y) / y) * (z / x))) + ((t - a) / (b - y));
	double t_2 = z * (t - a);
	double t_3 = y + (z * (b - y));
	double t_4 = t_2 / t_3;
	double tmp;
	if (z <= -7600.0) {
		tmp = t_1;
	} else if (z <= 7.4e-291) {
		tmp = t_4 + ((y * x) / t_3);
	} else if (z <= 9.2e-101) {
		tmp = x + t_4;
	} else if (z <= 1.2e+14) {
		tmp = (t_2 + (y * x)) / t_3;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 / (((b - y) / y) * (z / x))) + ((t - a) / (b - y))
	t_2 = z * (t - a)
	t_3 = y + (z * (b - y))
	t_4 = t_2 / t_3
	tmp = 0
	if z <= -7600.0:
		tmp = t_1
	elif z <= 7.4e-291:
		tmp = t_4 + ((y * x) / t_3)
	elif z <= 9.2e-101:
		tmp = x + t_4
	elif z <= 1.2e+14:
		tmp = (t_2 + (y * x)) / t_3
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 / Float64(Float64(Float64(b - y) / y) * Float64(z / x))) + Float64(Float64(t - a) / Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(y + Float64(z * Float64(b - y)))
	t_4 = Float64(t_2 / t_3)
	tmp = 0.0
	if (z <= -7600.0)
		tmp = t_1;
	elseif (z <= 7.4e-291)
		tmp = Float64(t_4 + Float64(Float64(y * x) / t_3));
	elseif (z <= 9.2e-101)
		tmp = Float64(x + t_4);
	elseif (z <= 1.2e+14)
		tmp = Float64(Float64(t_2 + Float64(y * x)) / t_3);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 / (((b - y) / y) * (z / x))) + ((t - a) / (b - y));
	t_2 = z * (t - a);
	t_3 = y + (z * (b - y));
	t_4 = t_2 / t_3;
	tmp = 0.0;
	if (z <= -7600.0)
		tmp = t_1;
	elseif (z <= 7.4e-291)
		tmp = t_4 + ((y * x) / t_3);
	elseif (z <= 9.2e-101)
		tmp = x + t_4;
	elseif (z <= 1.2e+14)
		tmp = (t_2 + (y * x)) / t_3;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 / N[(N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$2 / t$95$3), $MachinePrecision]}, If[LessEqual[z, -7600.0], t$95$1, If[LessEqual[z, 7.4e-291], N[(t$95$4 + N[(N[(y * x), $MachinePrecision] / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.2e-101], N[(x + t$95$4), $MachinePrecision], If[LessEqual[z, 1.2e+14], N[(N[(t$95$2 + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision], t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7600 or 1.2e14 < z

   1. Initial program 40.7%

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

   2. Taylor expanded in z around -inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate--l+ 68.9%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in x around inf 85.3%

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

      1. clear-num 85.3%

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

      2. inv-pow 85.3%

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

   7. Applied egg-rr 85.3%

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

      1. unpow-1 85.3%

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

      2. times-frac 99.9%

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

   9. Simplified 99.9%

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

   if -7600 < z < 7.4000000000000001e-291

   1. Initial program 93.8%

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

   2. Taylor expanded in x around inf 93.9%

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

   if 7.4000000000000001e-291 < z < 9.1999999999999998e-101

   1. Initial program 79.1%

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

   2. Taylor expanded in x around inf 79.1%

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

   3. Taylor expanded in z around 0 93.1%

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

   if 9.1999999999999998e-101 < z < 1.2e14

   1. Initial program 88.6%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7600:\\ \;\;\;\;\frac{1}{\frac{b - y}{y} \cdot \frac{z}{x}} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-291}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)} + \frac{y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{+14}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{b - y}{y} \cdot \frac{z}{x}} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 92.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{\frac{b - y}{y} \cdot \frac{z}{x}} + \frac{t - a}{b - y}\\ t_2 := z \cdot \left(t - a\right)\\ t_3 := y + z \cdot \left(b - y\right)\\ t_4 := \frac{t_2 + y \cdot x}{t_3}\\ \mathbf{if}\;z \leq -7600:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-291}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{t_2}{t_3}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+14}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (/ 1.0 (* (/ (- b y) y) (/ z x))) (/ (- t a) (- b y))))
        (t_2 (* z (- t a)))
        (t_3 (+ y (* z (- b y))))
        (t_4 (/ (+ t_2 (* y x)) t_3)))
   (if (<= z -7600.0)
     t_1
     (if (<= z 5.4e-291)
       t_4
       (if (<= z 1.6e-101) (+ x (/ t_2 t_3)) (if (<= z 3.4e+14) t_4 t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (1.0 / (((b - y) / y) * (z / x))) + ((t - a) / (b - y));
	double t_2 = z * (t - a);
	double t_3 = y + (z * (b - y));
	double t_4 = (t_2 + (y * x)) / t_3;
	double tmp;
	if (z <= -7600.0) {
		tmp = t_1;
	} else if (z <= 5.4e-291) {
		tmp = t_4;
	} else if (z <= 1.6e-101) {
		tmp = x + (t_2 / t_3);
	} else if (z <= 3.4e+14) {
		tmp = t_4;
	} 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) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = (1.0d0 / (((b - y) / y) * (z / x))) + ((t - a) / (b - y))
    t_2 = z * (t - a)
    t_3 = y + (z * (b - y))
    t_4 = (t_2 + (y * x)) / t_3
    if (z <= (-7600.0d0)) then
        tmp = t_1
    else if (z <= 5.4d-291) then
        tmp = t_4
    else if (z <= 1.6d-101) then
        tmp = x + (t_2 / t_3)
    else if (z <= 3.4d+14) then
        tmp = t_4
    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 = (1.0 / (((b - y) / y) * (z / x))) + ((t - a) / (b - y));
	double t_2 = z * (t - a);
	double t_3 = y + (z * (b - y));
	double t_4 = (t_2 + (y * x)) / t_3;
	double tmp;
	if (z <= -7600.0) {
		tmp = t_1;
	} else if (z <= 5.4e-291) {
		tmp = t_4;
	} else if (z <= 1.6e-101) {
		tmp = x + (t_2 / t_3);
	} else if (z <= 3.4e+14) {
		tmp = t_4;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (1.0 / (((b - y) / y) * (z / x))) + ((t - a) / (b - y))
	t_2 = z * (t - a)
	t_3 = y + (z * (b - y))
	t_4 = (t_2 + (y * x)) / t_3
	tmp = 0
	if z <= -7600.0:
		tmp = t_1
	elif z <= 5.4e-291:
		tmp = t_4
	elif z <= 1.6e-101:
		tmp = x + (t_2 / t_3)
	elif z <= 3.4e+14:
		tmp = t_4
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(1.0 / Float64(Float64(Float64(b - y) / y) * Float64(z / x))) + Float64(Float64(t - a) / Float64(b - y)))
	t_2 = Float64(z * Float64(t - a))
	t_3 = Float64(y + Float64(z * Float64(b - y)))
	t_4 = Float64(Float64(t_2 + Float64(y * x)) / t_3)
	tmp = 0.0
	if (z <= -7600.0)
		tmp = t_1;
	elseif (z <= 5.4e-291)
		tmp = t_4;
	elseif (z <= 1.6e-101)
		tmp = Float64(x + Float64(t_2 / t_3));
	elseif (z <= 3.4e+14)
		tmp = t_4;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (1.0 / (((b - y) / y) * (z / x))) + ((t - a) / (b - y));
	t_2 = z * (t - a);
	t_3 = y + (z * (b - y));
	t_4 = (t_2 + (y * x)) / t_3;
	tmp = 0.0;
	if (z <= -7600.0)
		tmp = t_1;
	elseif (z <= 5.4e-291)
		tmp = t_4;
	elseif (z <= 1.6e-101)
		tmp = x + (t_2 / t_3);
	elseif (z <= 3.4e+14)
		tmp = t_4;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(1.0 / N[(N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$2 + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$3), $MachinePrecision]}, If[LessEqual[z, -7600.0], t$95$1, If[LessEqual[z, 5.4e-291], t$95$4, If[LessEqual[z, 1.6e-101], N[(x + N[(t$95$2 / t$95$3), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.4e+14], t$95$4, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7600 or 3.4e14 < z

   1. Initial program 40.7%

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

   2. Taylor expanded in z around -inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate--l+ 68.9%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in x around inf 85.3%

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

      1. clear-num 85.3%

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

      2. inv-pow 85.3%

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

   7. Applied egg-rr 85.3%

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

      1. unpow-1 85.3%

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

      2. times-frac 99.9%

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

   9. Simplified 99.9%

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

   if -7600 < z < 5.39999999999999983e-291 or 1.59999999999999989e-101 < z < 3.4e14

   1. Initial program 92.3%

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

   if 5.39999999999999983e-291 < z < 1.59999999999999989e-101

   1. Initial program 79.1%

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

   2. Taylor expanded in x around inf 79.1%

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

   3. Taylor expanded in z around 0 93.1%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7600:\\ \;\;\;\;\frac{1}{\frac{b - y}{y} \cdot \frac{z}{x}} + \frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-291}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{+14}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{b - y}{y} \cdot \frac{z}{x}} + \frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 84.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y} + \frac{y \cdot x}{t_1}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := \frac{t_3 + y \cdot x}{y + z \cdot b}\\ \mathbf{if}\;z \leq -0.62:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-290}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{t_3}{y + t_1}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- b y)))
        (t_2 (+ (/ (- t a) (- b y)) (/ (* y x) t_1)))
        (t_3 (* z (- t a)))
        (t_4 (/ (+ t_3 (* y x)) (+ y (* z b)))))
   (if (<= z -0.62)
     t_2
     (if (<= z 1.16e-290)
       t_4
       (if (<= z 9.2e-101) (+ x (/ t_3 (+ y t_1))) (if (<= z 1.0) t_4 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (b - y);
	double t_2 = ((t - a) / (b - y)) + ((y * x) / t_1);
	double t_3 = z * (t - a);
	double t_4 = (t_3 + (y * x)) / (y + (z * b));
	double tmp;
	if (z <= -0.62) {
		tmp = t_2;
	} else if (z <= 1.16e-290) {
		tmp = t_4;
	} else if (z <= 9.2e-101) {
		tmp = x + (t_3 / (y + t_1));
	} else if (z <= 1.0) {
		tmp = t_4;
	} 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) :: t_4
    real(8) :: tmp
    t_1 = z * (b - y)
    t_2 = ((t - a) / (b - y)) + ((y * x) / t_1)
    t_3 = z * (t - a)
    t_4 = (t_3 + (y * x)) / (y + (z * b))
    if (z <= (-0.62d0)) then
        tmp = t_2
    else if (z <= 1.16d-290) then
        tmp = t_4
    else if (z <= 9.2d-101) then
        tmp = x + (t_3 / (y + t_1))
    else if (z <= 1.0d0) then
        tmp = t_4
    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 = z * (b - y);
	double t_2 = ((t - a) / (b - y)) + ((y * x) / t_1);
	double t_3 = z * (t - a);
	double t_4 = (t_3 + (y * x)) / (y + (z * b));
	double tmp;
	if (z <= -0.62) {
		tmp = t_2;
	} else if (z <= 1.16e-290) {
		tmp = t_4;
	} else if (z <= 9.2e-101) {
		tmp = x + (t_3 / (y + t_1));
	} else if (z <= 1.0) {
		tmp = t_4;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (b - y)
	t_2 = ((t - a) / (b - y)) + ((y * x) / t_1)
	t_3 = z * (t - a)
	t_4 = (t_3 + (y * x)) / (y + (z * b))
	tmp = 0
	if z <= -0.62:
		tmp = t_2
	elif z <= 1.16e-290:
		tmp = t_4
	elif z <= 9.2e-101:
		tmp = x + (t_3 / (y + t_1))
	elif z <= 1.0:
		tmp = t_4
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(b - y))
	t_2 = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(y * x) / t_1))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(Float64(t_3 + Float64(y * x)) / Float64(y + Float64(z * b)))
	tmp = 0.0
	if (z <= -0.62)
		tmp = t_2;
	elseif (z <= 1.16e-290)
		tmp = t_4;
	elseif (z <= 9.2e-101)
		tmp = Float64(x + Float64(t_3 / Float64(y + t_1)));
	elseif (z <= 1.0)
		tmp = t_4;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (b - y);
	t_2 = ((t - a) / (b - y)) + ((y * x) / t_1);
	t_3 = z * (t - a);
	t_4 = (t_3 + (y * x)) / (y + (z * b));
	tmp = 0.0;
	if (z <= -0.62)
		tmp = t_2;
	elseif (z <= 1.16e-290)
		tmp = t_4;
	elseif (z <= 9.2e-101)
		tmp = x + (t_3 / (y + t_1));
	elseif (z <= 1.0)
		tmp = t_4;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(t$95$3 + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.62], t$95$2, If[LessEqual[z, 1.16e-290], t$95$4, If[LessEqual[z, 9.2e-101], N[(x + N[(t$95$3 / N[(y + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], t$95$4, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.619999999999999996 or 1 < z

   1. Initial program 42.1%

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

   2. Taylor expanded in z around -inf 68.3%

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

      1. +-commutative 68.3%

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

      2. associate--l+ 68.3%

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

   4. Simplified 83.8%

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

   5. Taylor expanded in x around inf 84.4%

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

   if -0.619999999999999996 < z < 1.16000000000000001e-290 or 9.1999999999999998e-101 < z < 1

   1. Initial program 92.1%

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

   2. Taylor expanded in b around inf 89.7%

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

   if 1.16000000000000001e-290 < z < 9.1999999999999998e-101

   1. Initial program 79.1%

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

   2. Taylor expanded in x around inf 79.1%

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

   3. Taylor expanded in z around 0 93.1%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.62:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y \cdot x}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-290}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y \cdot x}{z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 6: 84.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(b - y\right)\\ t_2 := \frac{t - a}{b - y} + \frac{y \cdot x}{t_1}\\ t_3 := z \cdot \left(t - a\right)\\ t_4 := y + t_1\\ t_5 := \frac{t_3 + y \cdot x}{t_4}\\ \mathbf{if}\;z \leq -7600:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-290}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{t_3}{t_4}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+14}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- b y)))
        (t_2 (+ (/ (- t a) (- b y)) (/ (* y x) t_1)))
        (t_3 (* z (- t a)))
        (t_4 (+ y t_1))
        (t_5 (/ (+ t_3 (* y x)) t_4)))
   (if (<= z -7600.0)
     t_2
     (if (<= z 1.3e-290)
       t_5
       (if (<= z 1.06e-101) (+ x (/ t_3 t_4)) (if (<= z 5.5e+14) t_5 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (b - y);
	double t_2 = ((t - a) / (b - y)) + ((y * x) / t_1);
	double t_3 = z * (t - a);
	double t_4 = y + t_1;
	double t_5 = (t_3 + (y * x)) / t_4;
	double tmp;
	if (z <= -7600.0) {
		tmp = t_2;
	} else if (z <= 1.3e-290) {
		tmp = t_5;
	} else if (z <= 1.06e-101) {
		tmp = x + (t_3 / t_4);
	} else if (z <= 5.5e+14) {
		tmp = t_5;
	} 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) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_1 = z * (b - y)
    t_2 = ((t - a) / (b - y)) + ((y * x) / t_1)
    t_3 = z * (t - a)
    t_4 = y + t_1
    t_5 = (t_3 + (y * x)) / t_4
    if (z <= (-7600.0d0)) then
        tmp = t_2
    else if (z <= 1.3d-290) then
        tmp = t_5
    else if (z <= 1.06d-101) then
        tmp = x + (t_3 / t_4)
    else if (z <= 5.5d+14) then
        tmp = t_5
    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 = z * (b - y);
	double t_2 = ((t - a) / (b - y)) + ((y * x) / t_1);
	double t_3 = z * (t - a);
	double t_4 = y + t_1;
	double t_5 = (t_3 + (y * x)) / t_4;
	double tmp;
	if (z <= -7600.0) {
		tmp = t_2;
	} else if (z <= 1.3e-290) {
		tmp = t_5;
	} else if (z <= 1.06e-101) {
		tmp = x + (t_3 / t_4);
	} else if (z <= 5.5e+14) {
		tmp = t_5;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (b - y)
	t_2 = ((t - a) / (b - y)) + ((y * x) / t_1)
	t_3 = z * (t - a)
	t_4 = y + t_1
	t_5 = (t_3 + (y * x)) / t_4
	tmp = 0
	if z <= -7600.0:
		tmp = t_2
	elif z <= 1.3e-290:
		tmp = t_5
	elif z <= 1.06e-101:
		tmp = x + (t_3 / t_4)
	elif z <= 5.5e+14:
		tmp = t_5
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(b - y))
	t_2 = Float64(Float64(Float64(t - a) / Float64(b - y)) + Float64(Float64(y * x) / t_1))
	t_3 = Float64(z * Float64(t - a))
	t_4 = Float64(y + t_1)
	t_5 = Float64(Float64(t_3 + Float64(y * x)) / t_4)
	tmp = 0.0
	if (z <= -7600.0)
		tmp = t_2;
	elseif (z <= 1.3e-290)
		tmp = t_5;
	elseif (z <= 1.06e-101)
		tmp = Float64(x + Float64(t_3 / t_4));
	elseif (z <= 5.5e+14)
		tmp = t_5;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (b - y);
	t_2 = ((t - a) / (b - y)) + ((y * x) / t_1);
	t_3 = z * (t - a);
	t_4 = y + t_1;
	t_5 = (t_3 + (y * x)) / t_4;
	tmp = 0.0;
	if (z <= -7600.0)
		tmp = t_2;
	elseif (z <= 1.3e-290)
		tmp = t_5;
	elseif (z <= 1.06e-101)
		tmp = x + (t_3 / t_4);
	elseif (z <= 5.5e+14)
		tmp = t_5;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(y + t$95$1), $MachinePrecision]}, Block[{t$95$5 = N[(N[(t$95$3 + N[(y * x), $MachinePrecision]), $MachinePrecision] / t$95$4), $MachinePrecision]}, If[LessEqual[z, -7600.0], t$95$2, If[LessEqual[z, 1.3e-290], t$95$5, If[LessEqual[z, 1.06e-101], N[(x + N[(t$95$3 / t$95$4), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.5e+14], t$95$5, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7600 or 5.5e14 < z

   1. Initial program 40.7%

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

   2. Taylor expanded in z around -inf 69.0%

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

      1. +-commutative 69.0%

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

      2. associate--l+ 68.9%

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

   4. Simplified 84.6%

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

   5. Taylor expanded in x around inf 85.3%

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

   if -7600 < z < 1.3e-290 or 1.0600000000000001e-101 < z < 5.5e14

   1. Initial program 92.3%

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

   if 1.3e-290 < z < 1.0600000000000001e-101

   1. Initial program 79.1%

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

   2. Taylor expanded in x around inf 79.1%

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

   3. Taylor expanded in z around 0 93.1%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7600:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y \cdot x}{z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-290}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{+14}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y} + \frac{y \cdot x}{z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 7: 82.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := \frac{t_1 + y \cdot x}{y + z \cdot b}\\ t_3 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -4.2:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 6000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (/ (+ t_1 (* y x)) (+ y (* z b))))
        (t_3 (/ (- t a) (- b y))))
   (if (<= z -4.2)
     t_3
     (if (<= z 2.1e-290)
       t_2
       (if (<= z 2.45e-101)
         (+ x (/ t_1 (+ y (* z (- b y)))))
         (if (<= z 6000000.0) t_2 t_3))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = (t_1 + (y * x)) / (y + (z * b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.2) {
		tmp = t_3;
	} else if (z <= 2.1e-290) {
		tmp = t_2;
	} else if (z <= 2.45e-101) {
		tmp = x + (t_1 / (y + (z * (b - y))));
	} else if (z <= 6000000.0) {
		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 = z * (t - a)
    t_2 = (t_1 + (y * x)) / (y + (z * b))
    t_3 = (t - a) / (b - y)
    if (z <= (-4.2d0)) then
        tmp = t_3
    else if (z <= 2.1d-290) then
        tmp = t_2
    else if (z <= 2.45d-101) then
        tmp = x + (t_1 / (y + (z * (b - y))))
    else if (z <= 6000000.0d0) 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 = z * (t - a);
	double t_2 = (t_1 + (y * x)) / (y + (z * b));
	double t_3 = (t - a) / (b - y);
	double tmp;
	if (z <= -4.2) {
		tmp = t_3;
	} else if (z <= 2.1e-290) {
		tmp = t_2;
	} else if (z <= 2.45e-101) {
		tmp = x + (t_1 / (y + (z * (b - y))));
	} else if (z <= 6000000.0) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = (t_1 + (y * x)) / (y + (z * b))
	t_3 = (t - a) / (b - y)
	tmp = 0
	if z <= -4.2:
		tmp = t_3
	elif z <= 2.1e-290:
		tmp = t_2
	elif z <= 2.45e-101:
		tmp = x + (t_1 / (y + (z * (b - y))))
	elif z <= 6000000.0:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(Float64(t_1 + Float64(y * x)) / Float64(y + Float64(z * b)))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -4.2)
		tmp = t_3;
	elseif (z <= 2.1e-290)
		tmp = t_2;
	elseif (z <= 2.45e-101)
		tmp = Float64(x + Float64(t_1 / Float64(y + Float64(z * Float64(b - y)))));
	elseif (z <= 6000000.0)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = (t_1 + (y * x)) / (y + (z * b));
	t_3 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -4.2)
		tmp = t_3;
	elseif (z <= 2.1e-290)
		tmp = t_2;
	elseif (z <= 2.45e-101)
		tmp = x + (t_1 / (y + (z * (b - y))));
	elseif (z <= 6000000.0)
		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[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(t$95$1 + N[(y * x), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.2], t$95$3, If[LessEqual[z, 2.1e-290], t$95$2, If[LessEqual[z, 2.45e-101], N[(x + N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6000000.0], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000018 or 6e6 < z

   1. Initial program 42.1%

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

   2. Taylor expanded in z around inf 79.7%

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

   if -4.20000000000000018 < z < 2.1000000000000001e-290 or 2.45e-101 < z < 6e6

   1. Initial program 92.1%

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

   2. Taylor expanded in b around inf 89.7%

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

   if 2.1000000000000001e-290 < z < 2.45e-101

   1. Initial program 79.1%

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

   2. Taylor expanded in x around inf 79.1%

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

   3. Taylor expanded in z around 0 93.1%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2:\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-290}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot b}\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{-101}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 6000000:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + y \cdot x}{y + z \cdot b}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 8: 80.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -44 \lor \neg \left(z \leq 1.2 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -44.0) (not (<= z 1.2e+14)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) (+ y (* z (- b y)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -44.0) || !(z <= 1.2e+14)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / (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 <= (-44.0d0)) .or. (.not. (z <= 1.2d+14))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) / (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 <= -44.0) || !(z <= 1.2e+14)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -44.0) or not (z <= 1.2e+14):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))))
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -44.0) || !(z <= 1.2e+14))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / 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 <= -44.0) || ~((z <= 1.2e+14)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / (y + (z * (b - y))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -44.0], N[Not[LessEqual[z, 1.2e+14]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -44 or 1.2e14 < z

   1. Initial program 40.7%

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

   2. Taylor expanded in z around inf 80.5%

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

   if -44 < z < 1.2e14

   1. Initial program 88.0%

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

   2. Taylor expanded in x around inf 88.0%

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

   3. Taylor expanded in z around 0 78.6%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -44 \lor \neg \left(z \leq 1.2 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 9: 43.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{b - y}\\ t_2 := \frac{-a}{b}\\ t_3 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-212}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-51}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ t (- b y))) (t_2 (/ (- a) b)) (t_3 (/ x (- 1.0 z))))
   (if (<= y -2.9e+77)
     t_3
     (if (<= y -2.9e-212)
       t_1
       (if (<= y 1.4e-281)
         t_2
         (if (<= y 1.55e-230) t_1 (if (<= y 1.05e-51) t_2 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = t / (b - y);
	double t_2 = -a / b;
	double t_3 = x / (1.0 - z);
	double tmp;
	if (y <= -2.9e+77) {
		tmp = t_3;
	} else if (y <= -2.9e-212) {
		tmp = t_1;
	} else if (y <= 1.4e-281) {
		tmp = t_2;
	} else if (y <= 1.55e-230) {
		tmp = t_1;
	} else if (y <= 1.05e-51) {
		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 = t / (b - y)
    t_2 = -a / b
    t_3 = x / (1.0d0 - z)
    if (y <= (-2.9d+77)) then
        tmp = t_3
    else if (y <= (-2.9d-212)) then
        tmp = t_1
    else if (y <= 1.4d-281) then
        tmp = t_2
    else if (y <= 1.55d-230) then
        tmp = t_1
    else if (y <= 1.05d-51) 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 = t / (b - y);
	double t_2 = -a / b;
	double t_3 = x / (1.0 - z);
	double tmp;
	if (y <= -2.9e+77) {
		tmp = t_3;
	} else if (y <= -2.9e-212) {
		tmp = t_1;
	} else if (y <= 1.4e-281) {
		tmp = t_2;
	} else if (y <= 1.55e-230) {
		tmp = t_1;
	} else if (y <= 1.05e-51) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = t / (b - y)
	t_2 = -a / b
	t_3 = x / (1.0 - z)
	tmp = 0
	if y <= -2.9e+77:
		tmp = t_3
	elif y <= -2.9e-212:
		tmp = t_1
	elif y <= 1.4e-281:
		tmp = t_2
	elif y <= 1.55e-230:
		tmp = t_1
	elif y <= 1.05e-51:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(t / Float64(b - y))
	t_2 = Float64(Float64(-a) / b)
	t_3 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -2.9e+77)
		tmp = t_3;
	elseif (y <= -2.9e-212)
		tmp = t_1;
	elseif (y <= 1.4e-281)
		tmp = t_2;
	elseif (y <= 1.55e-230)
		tmp = t_1;
	elseif (y <= 1.05e-51)
		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 / (b - y);
	t_2 = -a / b;
	t_3 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -2.9e+77)
		tmp = t_3;
	elseif (y <= -2.9e-212)
		tmp = t_1;
	elseif (y <= 1.4e-281)
		tmp = t_2;
	elseif (y <= 1.55e-230)
		tmp = t_1;
	elseif (y <= 1.05e-51)
		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[(t / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[((-a) / b), $MachinePrecision]}, Block[{t$95$3 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.9e+77], t$95$3, If[LessEqual[y, -2.9e-212], t$95$1, If[LessEqual[y, 1.4e-281], t$95$2, If[LessEqual[y, 1.55e-230], t$95$1, If[LessEqual[y, 1.05e-51], t$95$2, t$95$3]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.9000000000000002e77 or 1.05000000000000001e-51 < y

   1. Initial program 52.1%

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

   2. Taylor expanded in y around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

   4. Simplified 47.6%

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

   if -2.9000000000000002e77 < y < -2.8999999999999999e-212 or 1.40000000000000003e-281 < y < 1.55e-230

   1. Initial program 82.0%

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

   2. Taylor expanded in z around -inf 60.8%

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

      1. +-commutative 60.8%

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

      2. associate--l+ 60.8%

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

   4. Simplified 63.5%

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

   5. Taylor expanded in x around inf 70.8%

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

   6. Taylor expanded in t around inf 46.4%

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

   if -2.8999999999999999e-212 < y < 1.40000000000000003e-281 or 1.55e-230 < y < 1.05000000000000001e-51

   1. Initial program 69.4%

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

   2. Taylor expanded in b around inf 53.9%

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

   3. Taylor expanded in a around inf 56.0%

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

      1. mul-1-neg 56.0%

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

   5. Simplified 56.0%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-212}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-281}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-230}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-51}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 10: 54.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -7.8 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-47}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -7.8e+77)
     t_1
     (if (<= y -2.1e-40)
       (/ t (- b y))
       (if (<= y -1.2e-47)
         (+ x (* z x))
         (if (<= y 5.7e-49) (/ (- 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 <= -7.8e+77) {
		tmp = t_1;
	} else if (y <= -2.1e-40) {
		tmp = t / (b - y);
	} else if (y <= -1.2e-47) {
		tmp = x + (z * x);
	} else if (y <= 5.7e-49) {
		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 <= (-7.8d+77)) then
        tmp = t_1
    else if (y <= (-2.1d-40)) then
        tmp = t / (b - y)
    else if (y <= (-1.2d-47)) then
        tmp = x + (z * x)
    else if (y <= 5.7d-49) 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 <= -7.8e+77) {
		tmp = t_1;
	} else if (y <= -2.1e-40) {
		tmp = t / (b - y);
	} else if (y <= -1.2e-47) {
		tmp = x + (z * x);
	} else if (y <= 5.7e-49) {
		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 <= -7.8e+77:
		tmp = t_1
	elif y <= -2.1e-40:
		tmp = t / (b - y)
	elif y <= -1.2e-47:
		tmp = x + (z * x)
	elif y <= 5.7e-49:
		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 <= -7.8e+77)
		tmp = t_1;
	elseif (y <= -2.1e-40)
		tmp = Float64(t / Float64(b - y));
	elseif (y <= -1.2e-47)
		tmp = Float64(x + Float64(z * x));
	elseif (y <= 5.7e-49)
		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 <= -7.8e+77)
		tmp = t_1;
	elseif (y <= -2.1e-40)
		tmp = t / (b - y);
	elseif (y <= -1.2e-47)
		tmp = x + (z * x);
	elseif (y <= 5.7e-49)
		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, -7.8e+77], t$95$1, If[LessEqual[y, -2.1e-40], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.2e-47], N[(x + N[(z * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.7e-49], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -7.7999999999999995e77 or 5.7000000000000003e-49 < y

   1. Initial program 52.1%

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

   2. Taylor expanded in y around inf 47.6%

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

      1. +-commutative 47.6%

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

      2. mul-1-neg 47.6%

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

      3. unsub-neg 47.6%

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

   4. Simplified 47.6%

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

   if -7.7999999999999995e77 < y < -2.10000000000000018e-40

   1. Initial program 75.2%

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

   2. Taylor expanded in z around -inf 54.5%

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

      1. +-commutative 54.5%

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

      2. associate--l+ 54.5%

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

   4. Simplified 62.7%

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

   5. Taylor expanded in x around inf 63.1%

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

   6. Taylor expanded in t around inf 35.8%

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

   if -2.10000000000000018e-40 < y < -1.2e-47

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 75.2%

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

      1. +-commutative 75.2%

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

      2. mul-1-neg 75.2%

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

      3. unsub-neg 75.2%

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

   4. Simplified 75.2%

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

   5. Taylor expanded in z around 0 76.8%

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

   if -1.2e-47 < y < 5.7000000000000003e-49

   1. Initial program 75.4%

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

   2. Taylor expanded in y around 0 71.9%

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

4. Final simplification 57.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-40}:\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{elif}\;y \leq -1.2 \cdot 10^{-47}:\\ \;\;\;\;x + z \cdot x\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{-49}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 11: 73.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-25} \lor \neg \left(z \leq 4.8 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -5.8e-25) (not (<= z 4.8e-73)))
   (/ (- t a) (- b y))
   (+ x (/ (* z (- t a)) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.8e-25) || !(z <= 4.8e-73)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-5.8d-25)) .or. (.not. (z <= 4.8d-73))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * (t - a)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -5.8e-25) || !(z <= 4.8e-73)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * (t - a)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -5.8e-25) or not (z <= 4.8e-73):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * (t - a)) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -5.8e-25) || !(z <= 4.8e-73))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -5.8e-25) || ~((z <= 4.8e-73)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * (t - a)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -5.8e-25], N[Not[LessEqual[z, 4.8e-73]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000001e-25 or 4.80000000000000011e-73 < z

   1. Initial program 49.8%

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

   2. Taylor expanded in z around inf 75.4%

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

   if -5.8000000000000001e-25 < z < 4.80000000000000011e-73

   1. Initial program 86.1%

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

   2. Taylor expanded in x around inf 86.2%

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

   3. Taylor expanded in z around 0 81.4%

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

   4. Taylor expanded in z around 0 70.1%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-25} \lor \neg \left(z \leq 4.8 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]

Alternative 12: 63.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-26} \lor \neg \left(z \leq 8.4 \cdot 10^{-92}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.8e-26) (not (<= z 8.4e-92))) (/ (- t a) (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.8e-26) || !(z <= 8.4e-92)) {
		tmp = (t - a) / (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 <= (-1.8d-26)) .or. (.not. (z <= 8.4d-92))) then
        tmp = (t - a) / (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 <= -1.8e-26) || !(z <= 8.4e-92)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.8e-26) or not (z <= 8.4e-92):
		tmp = (t - a) / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.8e-26) || !(z <= 8.4e-92))
		tmp = Float64(Float64(t - a) / 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 <= -1.8e-26) || ~((z <= 8.4e-92)))
		tmp = (t - a) / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.8e-26], N[Not[LessEqual[z, 8.4e-92]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.8000000000000001e-26 or 8.4e-92 < z

   1. Initial program 50.8%

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

   2. Taylor expanded in z around inf 74.7%

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

   if -1.8000000000000001e-26 < z < 8.4e-92

   1. Initial program 85.7%

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

   2. Taylor expanded in z around 0 50.2%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-26} \lor \neg \left(z \leq 8.4 \cdot 10^{-92}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 44.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-23} \lor \neg \left(z \leq 7 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.3e-23) (not (<= z 7e-89))) (/ t (- b y)) x))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.3e-23) || !(z <= 7e-89)) {
		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 <= (-1.3d-23)) .or. (.not. (z <= 7d-89))) 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 <= -1.3e-23) || !(z <= 7e-89)) {
		tmp = t / (b - y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.3e-23) or not (z <= 7e-89):
		tmp = t / (b - y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.3e-23) || !(z <= 7e-89))
		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 <= -1.3e-23) || ~((z <= 7e-89)))
		tmp = t / (b - y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.3e-23], N[Not[LessEqual[z, 7e-89]], $MachinePrecision]], N[(t / N[(b - y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e-23 or 6.9999999999999994e-89 < z

   1. Initial program 50.8%

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

   2. Taylor expanded in z around -inf 67.1%

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

      1. +-commutative 67.1%

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

      2. associate--l+ 67.1%

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

   4. Simplified 80.1%

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

   5. Taylor expanded in x around inf 80.7%

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

   6. Taylor expanded in t around inf 39.0%

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

   if -1.3e-23 < z < 6.9999999999999994e-89

   1. Initial program 85.7%

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

   2. Taylor expanded in z around 0 50.2%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-23} \lor \neg \left(z \leq 7 \cdot 10^{-89}\right):\\ \;\;\;\;\frac{t}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 36.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.75 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -3.75e-25) (/ t b) (if (<= z 2.25e-74) x (/ (- a) b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.75e-25) {
		tmp = t / b;
	} else if (z <= 2.25e-74) {
		tmp = x;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-3.75d-25)) then
        tmp = t / b
    else if (z <= 2.25d-74) then
        tmp = x
    else
        tmp = -a / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -3.75e-25) {
		tmp = t / b;
	} else if (z <= 2.25e-74) {
		tmp = x;
	} else {
		tmp = -a / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -3.75e-25:
		tmp = t / b
	elif z <= 2.25e-74:
		tmp = x
	else:
		tmp = -a / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -3.75e-25)
		tmp = Float64(t / b);
	elseif (z <= 2.25e-74)
		tmp = x;
	else
		tmp = Float64(Float64(-a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -3.75e-25)
		tmp = t / b;
	elseif (z <= 2.25e-74)
		tmp = x;
	else
		tmp = -a / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -3.75e-25], N[(t / b), $MachinePrecision], If[LessEqual[z, 2.25e-74], x, N[((-a) / b), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.74999999999999994e-25

   1. Initial program 47.0%

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

   2. Taylor expanded in b around inf 28.5%

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

   3. Taylor expanded in t around inf 35.2%

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

   if -3.74999999999999994e-25 < z < 2.25e-74

   1. Initial program 85.9%

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

   2. Taylor expanded in z around 0 49.8%

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

   if 2.25e-74 < z

   1. Initial program 53.4%

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

   2. Taylor expanded in b around inf 34.7%

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

   3. Taylor expanded in a around inf 27.9%

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

      1. mul-1-neg 27.9%

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

   5. Simplified 27.9%

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

4. Final simplification 38.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.75 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-a}{b}\\ \end{array} \]

Alternative 15: 36.5% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= z -2.2e-25) (/ t b) (if (<= z 6.8e-89) x (/ t b))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.2e-25) {
		tmp = t / b;
	} else if (z <= 6.8e-89) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (z <= (-2.2d-25)) then
        tmp = t / b
    else if (z <= 6.8d-89) then
        tmp = x
    else
        tmp = t / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (z <= -2.2e-25) {
		tmp = t / b;
	} else if (z <= 6.8e-89) {
		tmp = x;
	} else {
		tmp = t / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if z <= -2.2e-25:
		tmp = t / b
	elif z <= 6.8e-89:
		tmp = x
	else:
		tmp = t / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (z <= -2.2e-25)
		tmp = Float64(t / b);
	elseif (z <= 6.8e-89)
		tmp = x;
	else
		tmp = Float64(t / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (z <= -2.2e-25)
		tmp = t / b;
	elseif (z <= 6.8e-89)
		tmp = x;
	else
		tmp = t / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[z, -2.2e-25], N[(t / b), $MachinePrecision], If[LessEqual[z, 6.8e-89], x, N[(t / b), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if z < -2.2000000000000002e-25 or 6.8000000000000001e-89 < z

   1. Initial program 50.8%

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

   2. Taylor expanded in b around inf 32.3%

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

   3. Taylor expanded in t around inf 30.4%

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

   if -2.2000000000000002e-25 < z < 6.8000000000000001e-89

   1. Initial program 85.7%

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

   2. Taylor expanded in z around 0 50.2%

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

4. Final simplification 38.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-25}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-89}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{b}\\ \end{array} \]

Alternative 16: 25.4% 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 64.6%

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

2. Taylor expanded in z around 0 22.9%

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

3. Final simplification 22.9%

   \[\leadsto x \]

Developer target: 72.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023279 
(FPCore (x y z t a b)
  :name "Development.Shake.Progress:decay from shake-0.15.5"
  :precision binary64

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

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