Development.Shake.Progress:decay from shake-0.15.5

Percentage Accurate: 66.5% → 89.3%

Time: 19.1s

Alternatives: 15

Speedup: 1.5×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 89.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6700000000000 \lor \neg \left(z \leq 1.25 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -6700000000000.0) (not (<= z 1.25e+14)))
   (+
    (/ (- (/ x (/ (- b y) y)) (/ y (/ (pow (- b y) 2.0) (- t a)))) z)
    (/ (- t a) (- b y)))
   (/ (fma x y (* z (- t a))) (fma z (- b y) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -6700000000000.0) || !(z <= 1.25e+14)) {
		tmp = (((x / ((b - y) / y)) - (y / (pow((b - y), 2.0) / (t - a)))) / z) + ((t - a) / (b - y));
	} else {
		tmp = fma(x, y, (z * (t - a))) / fma(z, (b - y), y);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -6700000000000.0) || !(z <= 1.25e+14))
		tmp = Float64(Float64(Float64(Float64(x / Float64(Float64(b - y) / y)) - Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(t - a)))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / fma(z, Float64(b - y), y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -6700000000000.0], N[Not[LessEqual[z, 1.25e+14]], $MachinePrecision]], N[(N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(z * N[(b - y), $MachinePrecision] + y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.7e12 or 1.25e14 < z

   1. Initial program 35.8%

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

   2. Taylor expanded in z around -inf 78.0%

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

      1. associate--l+ 78.0%

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

      2. mul-1-neg 78.0%

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

      3. distribute-lft-out-- 78.0%

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

      4. associate-/l* 82.0%

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

      5. associate-/l* 93.1%

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

      6. div-sub 93.9%

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

   4. Simplified 93.9%

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

   if -6.7e12 < z < 1.25e14

   1. Initial program 92.2%

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

      1. fma-def 92.2%

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

      2. +-commutative 92.2%

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

      3. fma-def 92.2%

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

   3. Simplified 92.2%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6700000000000 \lor \neg \left(z \leq 1.25 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{\mathsf{fma}\left(z, b - y, y\right)}\\ \end{array} \]

Alternative 2: 89.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+14} \lor \neg \left(z \leq 1.3 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.6e+14) (not (<= z 1.3e+14)))
   (+
    (/ (- (/ x (/ (- b y) y)) (/ y (/ (pow (- b y) 2.0) (- t a)))) z)
    (/ (- t a) (- b y)))
   (/ (fma x y (* z (- t a))) (+ y (* z (- b y))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -3.6e+14) || !(z <= 1.3e+14)) {
		tmp = (((x / ((b - y) / y)) - (y / (pow((b - y), 2.0) / (t - a)))) / z) + ((t - a) / (b - y));
	} else {
		tmp = fma(x, y, (z * (t - a))) / (y + (z * (b - y)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -3.6e+14) || !(z <= 1.3e+14))
		tmp = Float64(Float64(Float64(Float64(x / Float64(Float64(b - y) / y)) - Float64(y / Float64((Float64(b - y) ^ 2.0) / Float64(t - a)))) / z) + Float64(Float64(t - a) / Float64(b - y)));
	else
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / Float64(y + Float64(z * Float64(b - y))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -3.6e+14], N[Not[LessEqual[z, 1.3e+14]], $MachinePrecision]], N[(N[(N[(N[(x / N[(N[(b - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(N[Power[N[(b - y), $MachinePrecision], 2.0], $MachinePrecision] / N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] + N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.6e14 or 1.3e14 < z

   1. Initial program 35.8%

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

   2. Taylor expanded in z around -inf 78.0%

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

      1. associate--l+ 78.0%

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

      2. mul-1-neg 78.0%

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

      3. distribute-lft-out-- 78.0%

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

      4. associate-/l* 82.0%

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

      5. associate-/l* 93.1%

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

      6. div-sub 93.9%

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

   4. Simplified 93.9%

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

   if -3.6e14 < z < 1.3e14

   1. Initial program 92.2%

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

      1. fma-def 92.2%

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

   3. Simplified 92.2%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+14} \lor \neg \left(z \leq 1.3 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{\frac{x}{\frac{b - y}{y}} - \frac{y}{\frac{{\left(b - y\right)}^{2}}{t - a}}}{z} + \frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \end{array} \]

Alternative 3: 85.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+55}:\\ \;\;\;\;t_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.25e+55)
     (- t_1 (/ x z))
     (if (<= z 2.2e+68) (/ (fma x y (* z (- t a))) (+ y (* z (- b y)))) t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.25e+55) {
		tmp = t_1 - (x / z);
	} else if (z <= 2.2e+68) {
		tmp = fma(x, y, (z * (t - a))) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.25e+55)
		tmp = Float64(t_1 - Float64(x / z));
	elseif (z <= 2.2e+68)
		tmp = Float64(fma(x, y, Float64(z * Float64(t - a))) / 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[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+55], N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e+68], N[(N[(x * y + N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.24999999999999999e55

   1. Initial program 30.4%

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

   2. Taylor expanded in z around -inf 73.9%

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

      1. associate--l+ 73.9%

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

      2. mul-1-neg 73.9%

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

      3. distribute-lft-out-- 73.9%

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

      4. associate-/l* 78.8%

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

      5. associate-/l* 91.1%

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

      6. div-sub 92.8%

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

   4. Simplified 92.8%

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

   5. Taylor expanded in y around inf 88.1%

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

   if -2.24999999999999999e55 < z < 2.19999999999999987e68

   1. Initial program 90.9%

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

      1. fma-def 90.9%

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

   3. Simplified 90.9%

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

   if 2.19999999999999987e68 < z

   1. Initial program 31.0%

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

   2. Taylor expanded in z around inf 89.3%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+55}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+68}:\\ \;\;\;\;\frac{\mathsf{fma}\left(x, y, z \cdot \left(t - a\right)\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 4: 75.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot \left(t - a\right)\\ t_2 := x + \frac{t_1}{y}\\ t_3 := \frac{t - a}{b - y}\\ t_4 := t_3 - \frac{x}{z}\\ \mathbf{if}\;z \leq -1.5 \cdot 10^{-25}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-202}:\\ \;\;\;\;\frac{t_1}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+100}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (* z (- t a)))
        (t_2 (+ x (/ t_1 y)))
        (t_3 (/ (- t a) (- b y)))
        (t_4 (- t_3 (/ x z))))
   (if (<= z -1.5e-25)
     t_4
     (if (<= z -1.45e-141)
       t_2
       (if (<= z -8.2e-202)
         (/ t_1 (+ y (* z (- b y))))
         (if (<= z 1e-21) t_2 (if (<= z 1.6e+100) t_4 t_3)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = x + (t_1 / y);
	double t_3 = (t - a) / (b - y);
	double t_4 = t_3 - (x / z);
	double tmp;
	if (z <= -1.5e-25) {
		tmp = t_4;
	} else if (z <= -1.45e-141) {
		tmp = t_2;
	} else if (z <= -8.2e-202) {
		tmp = t_1 / (y + (z * (b - y)));
	} else if (z <= 1e-21) {
		tmp = t_2;
	} else if (z <= 1.6e+100) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_1 = z * (t - a)
    t_2 = x + (t_1 / y)
    t_3 = (t - a) / (b - y)
    t_4 = t_3 - (x / z)
    if (z <= (-1.5d-25)) then
        tmp = t_4
    else if (z <= (-1.45d-141)) then
        tmp = t_2
    else if (z <= (-8.2d-202)) then
        tmp = t_1 / (y + (z * (b - y)))
    else if (z <= 1d-21) then
        tmp = t_2
    else if (z <= 1.6d+100) then
        tmp = t_4
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = z * (t - a);
	double t_2 = x + (t_1 / y);
	double t_3 = (t - a) / (b - y);
	double t_4 = t_3 - (x / z);
	double tmp;
	if (z <= -1.5e-25) {
		tmp = t_4;
	} else if (z <= -1.45e-141) {
		tmp = t_2;
	} else if (z <= -8.2e-202) {
		tmp = t_1 / (y + (z * (b - y)));
	} else if (z <= 1e-21) {
		tmp = t_2;
	} else if (z <= 1.6e+100) {
		tmp = t_4;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = z * (t - a)
	t_2 = x + (t_1 / y)
	t_3 = (t - a) / (b - y)
	t_4 = t_3 - (x / z)
	tmp = 0
	if z <= -1.5e-25:
		tmp = t_4
	elif z <= -1.45e-141:
		tmp = t_2
	elif z <= -8.2e-202:
		tmp = t_1 / (y + (z * (b - y)))
	elif z <= 1e-21:
		tmp = t_2
	elif z <= 1.6e+100:
		tmp = t_4
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(z * Float64(t - a))
	t_2 = Float64(x + Float64(t_1 / y))
	t_3 = Float64(Float64(t - a) / Float64(b - y))
	t_4 = Float64(t_3 - Float64(x / z))
	tmp = 0.0
	if (z <= -1.5e-25)
		tmp = t_4;
	elseif (z <= -1.45e-141)
		tmp = t_2;
	elseif (z <= -8.2e-202)
		tmp = Float64(t_1 / Float64(y + Float64(z * Float64(b - y))));
	elseif (z <= 1e-21)
		tmp = t_2;
	elseif (z <= 1.6e+100)
		tmp = t_4;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = z * (t - a);
	t_2 = x + (t_1 / y);
	t_3 = (t - a) / (b - y);
	t_4 = t_3 - (x / z);
	tmp = 0.0;
	if (z <= -1.5e-25)
		tmp = t_4;
	elseif (z <= -1.45e-141)
		tmp = t_2;
	elseif (z <= -8.2e-202)
		tmp = t_1 / (y + (z * (b - y)));
	elseif (z <= 1e-21)
		tmp = t_2;
	elseif (z <= 1.6e+100)
		tmp = t_4;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(t$95$1 / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$3 - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.5e-25], t$95$4, If[LessEqual[z, -1.45e-141], t$95$2, If[LessEqual[z, -8.2e-202], N[(t$95$1 / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1e-21], t$95$2, If[LessEqual[z, 1.6e+100], t$95$4, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4999999999999999e-25 or 9.99999999999999908e-22 < z < 1.5999999999999999e100

   1. Initial program 51.4%

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

   2. Taylor expanded in z around -inf 71.3%

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

      1. associate--l+ 71.3%

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

      2. mul-1-neg 71.3%

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

      3. distribute-lft-out-- 71.3%

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

      4. associate-/l* 74.4%

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

      5. associate-/l* 86.1%

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

      6. div-sub 87.2%

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

   4. Simplified 87.2%

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

   5. Taylor expanded in y around inf 81.9%

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

   if -1.4999999999999999e-25 < z < -1.45e-141 or -8.2000000000000008e-202 < z < 9.99999999999999908e-22

   1. Initial program 91.0%

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

   2. Taylor expanded in z around 0 70.6%

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

   3. Taylor expanded in x around 0 77.6%

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

   if -1.45e-141 < z < -8.2000000000000008e-202

   1. Initial program 99.2%

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

   2. Taylor expanded in x around 0 78.4%

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

   if 1.5999999999999999e100 < z

   1. Initial program 30.8%

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

   2. Taylor expanded in z around inf 90.8%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{-25}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-202}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right)}{y + z \cdot \left(b - y\right)}\\ \mathbf{elif}\;z \leq 10^{-21}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{+100}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 5: 85.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+55}:\\ \;\;\;\;t_1 - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))))
   (if (<= z -2.2e+55)
     (- t_1 (/ x z))
     (if (<= z 1.8e+68)
       (/ (+ (* z (- t a)) (* x y)) (+ y (* z (- b y))))
       t_1))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.2e+55) {
		tmp = t_1 - (x / z);
	} else if (z <= 1.8e+68) {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t - a) / (b - y)
    if (z <= (-2.2d+55)) then
        tmp = t_1 - (x / z)
    else if (z <= 1.8d+68) then
        tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double tmp;
	if (z <= -2.2e+55) {
		tmp = t_1 - (x / z);
	} else if (z <= 1.8e+68) {
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	tmp = 0
	if z <= -2.2e+55:
		tmp = t_1 - (x / z)
	elif z <= 1.8e+68:
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	tmp = 0.0
	if (z <= -2.2e+55)
		tmp = Float64(t_1 - Float64(x / z));
	elseif (z <= 1.8e+68)
		tmp = Float64(Float64(Float64(z * Float64(t - a)) + Float64(x * y)) / Float64(y + Float64(z * Float64(b - y))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	tmp = 0.0;
	if (z <= -2.2e+55)
		tmp = t_1 - (x / z);
	elseif (z <= 1.8e+68)
		tmp = ((z * (t - a)) + (x * y)) / (y + (z * (b - y)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.2e+55], N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.8e+68], N[(N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision] / N[(y + N[(z * N[(b - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2000000000000001e55

   1. Initial program 30.4%

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

   2. Taylor expanded in z around -inf 73.9%

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

      1. associate--l+ 73.9%

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

      2. mul-1-neg 73.9%

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

      3. distribute-lft-out-- 73.9%

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

      4. associate-/l* 78.8%

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

      5. associate-/l* 91.1%

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

      6. div-sub 92.8%

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

   4. Simplified 92.8%

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

   5. Taylor expanded in y around inf 88.1%

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

   if -2.2000000000000001e55 < z < 1.7999999999999999e68

   1. Initial program 90.9%

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

   if 1.7999999999999999e68 < z

   1. Initial program 31.0%

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

   2. Taylor expanded in z around inf 89.3%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+55}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+68}:\\ \;\;\;\;\frac{z \cdot \left(t - a\right) + x \cdot y}{y + z \cdot \left(b - y\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 6: 76.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t - a}{b - y}\\ t_2 := t_1 - \frac{x}{z}\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+100}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- t a) (- b y))) (t_2 (- t_1 (/ x z))))
   (if (<= z -1.8e-28)
     t_2
     (if (<= z 3.4e-21)
       (+ x (/ (* z (- t a)) y))
       (if (<= z 1.9e+100) t_2 t_1)))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = t_1 - (x / z);
	double tmp;
	if (z <= -1.8e-28) {
		tmp = t_2;
	} else if (z <= 3.4e-21) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 1.9e+100) {
		tmp = t_2;
	} 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) :: tmp
    t_1 = (t - a) / (b - y)
    t_2 = t_1 - (x / z)
    if (z <= (-1.8d-28)) then
        tmp = t_2
    else if (z <= 3.4d-21) then
        tmp = x + ((z * (t - a)) / y)
    else if (z <= 1.9d+100) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (t - a) / (b - y);
	double t_2 = t_1 - (x / z);
	double tmp;
	if (z <= -1.8e-28) {
		tmp = t_2;
	} else if (z <= 3.4e-21) {
		tmp = x + ((z * (t - a)) / y);
	} else if (z <= 1.9e+100) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = (t - a) / (b - y)
	t_2 = t_1 - (x / z)
	tmp = 0
	if z <= -1.8e-28:
		tmp = t_2
	elif z <= 3.4e-21:
		tmp = x + ((z * (t - a)) / y)
	elif z <= 1.9e+100:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(t - a) / Float64(b - y))
	t_2 = Float64(t_1 - Float64(x / z))
	tmp = 0.0
	if (z <= -1.8e-28)
		tmp = t_2;
	elseif (z <= 3.4e-21)
		tmp = Float64(x + Float64(Float64(z * Float64(t - a)) / y));
	elseif (z <= 1.9e+100)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (t - a) / (b - y);
	t_2 = t_1 - (x / z);
	tmp = 0.0;
	if (z <= -1.8e-28)
		tmp = t_2;
	elseif (z <= 3.4e-21)
		tmp = x + ((z * (t - a)) / y);
	elseif (z <= 1.9e+100)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 - N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e-28], t$95$2, If[LessEqual[z, 3.4e-21], N[(x + N[(N[(z * N[(t - a), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+100], t$95$2, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.7999999999999999e-28 or 3.4e-21 < z < 1.89999999999999982e100

   1. Initial program 51.4%

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

   2. Taylor expanded in z around -inf 71.3%

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

      1. associate--l+ 71.3%

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

      2. mul-1-neg 71.3%

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

      3. distribute-lft-out-- 71.3%

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

      4. associate-/l* 74.4%

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

      5. associate-/l* 86.1%

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

      6. div-sub 87.2%

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

   4. Simplified 87.2%

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

   5. Taylor expanded in y around inf 81.9%

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

   if -1.7999999999999999e-28 < z < 3.4e-21

   1. Initial program 91.7%

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

   2. Taylor expanded in z around 0 67.2%

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

   3. Taylor expanded in x around 0 73.6%

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

   if 1.89999999999999982e100 < z

   1. Initial program 30.8%

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

   2. Taylor expanded in z around inf 90.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-28}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-21}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+100}:\\ \;\;\;\;\frac{t - a}{b - y} - \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b - y}\\ \end{array} \]

Alternative 7: 34.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-263}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-180}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)))
   (if (<= y -1.2e-47)
     x
     (if (<= y -1.45e-115)
       t_1
       (if (<= y -6e-263)
         (/ t b)
         (if (<= y 1.9e-240)
           t_1
           (if (<= y 3.2e-180) (/ t b) (if (<= y 2.95e-80) t_1 x))))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double tmp;
	if (y <= -1.2e-47) {
		tmp = x;
	} else if (y <= -1.45e-115) {
		tmp = t_1;
	} else if (y <= -6e-263) {
		tmp = t / b;
	} else if (y <= 1.9e-240) {
		tmp = t_1;
	} else if (y <= 3.2e-180) {
		tmp = t / b;
	} else if (y <= 2.95e-80) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = -a / b
    if (y <= (-1.2d-47)) then
        tmp = x
    else if (y <= (-1.45d-115)) then
        tmp = t_1
    else if (y <= (-6d-263)) then
        tmp = t / b
    else if (y <= 1.9d-240) then
        tmp = t_1
    else if (y <= 3.2d-180) then
        tmp = t / b
    else if (y <= 2.95d-80) then
        tmp = t_1
    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 t_1 = -a / b;
	double tmp;
	if (y <= -1.2e-47) {
		tmp = x;
	} else if (y <= -1.45e-115) {
		tmp = t_1;
	} else if (y <= -6e-263) {
		tmp = t / b;
	} else if (y <= 1.9e-240) {
		tmp = t_1;
	} else if (y <= 3.2e-180) {
		tmp = t / b;
	} else if (y <= 2.95e-80) {
		tmp = t_1;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	tmp = 0
	if y <= -1.2e-47:
		tmp = x
	elif y <= -1.45e-115:
		tmp = t_1
	elif y <= -6e-263:
		tmp = t / b
	elif y <= 1.9e-240:
		tmp = t_1
	elif y <= 3.2e-180:
		tmp = t / b
	elif y <= 2.95e-80:
		tmp = t_1
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	tmp = 0.0
	if (y <= -1.2e-47)
		tmp = x;
	elseif (y <= -1.45e-115)
		tmp = t_1;
	elseif (y <= -6e-263)
		tmp = Float64(t / b);
	elseif (y <= 1.9e-240)
		tmp = t_1;
	elseif (y <= 3.2e-180)
		tmp = Float64(t / b);
	elseif (y <= 2.95e-80)
		tmp = t_1;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	tmp = 0.0;
	if (y <= -1.2e-47)
		tmp = x;
	elseif (y <= -1.45e-115)
		tmp = t_1;
	elseif (y <= -6e-263)
		tmp = t / b;
	elseif (y <= 1.9e-240)
		tmp = t_1;
	elseif (y <= 3.2e-180)
		tmp = t / b;
	elseif (y <= 2.95e-80)
		tmp = t_1;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, If[LessEqual[y, -1.2e-47], x, If[LessEqual[y, -1.45e-115], t$95$1, If[LessEqual[y, -6e-263], N[(t / b), $MachinePrecision], If[LessEqual[y, 1.9e-240], t$95$1, If[LessEqual[y, 3.2e-180], N[(t / b), $MachinePrecision], If[LessEqual[y, 2.95e-80], t$95$1, x]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e-47 or 2.95e-80 < y

   1. Initial program 60.0%

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

   2. Taylor expanded in z around 0 38.3%

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

   if -1.2e-47 < y < -1.4499999999999999e-115 or -6.0000000000000001e-263 < y < 1.89999999999999994e-240 or 3.20000000000000015e-180 < y < 2.95e-80

   1. Initial program 69.5%

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

   2. Taylor expanded in y around 0 72.2%

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

   3. Taylor expanded in t around 0 56.3%

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

      1. mul-1-neg 56.3%

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

   5. Simplified 56.3%

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

   if -1.4499999999999999e-115 < y < -6.0000000000000001e-263 or 1.89999999999999994e-240 < y < 3.20000000000000015e-180

   1. Initial program 77.9%

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

   2. Taylor expanded in y around 0 67.1%

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

   3. Taylor expanded in t around inf 47.7%

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

4. Final simplification 44.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-47}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-115}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq -6 \cdot 10^{-263}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-240}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-180}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{-80}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 41.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-a}{b}\\ t_2 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-265}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-241}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-180}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ (- a) b)) (t_2 (/ x (- 1.0 z))))
   (if (<= y -4.8e-99)
     t_2
     (if (<= y -4.2e-265)
       (/ t b)
       (if (<= y 8.6e-241)
         t_1
         (if (<= y 2.5e-180) (/ t b) (if (<= y 8.6e-81) t_1 t_2)))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -4.8e-99) {
		tmp = t_2;
	} else if (y <= -4.2e-265) {
		tmp = t / b;
	} else if (y <= 8.6e-241) {
		tmp = t_1;
	} else if (y <= 2.5e-180) {
		tmp = t / b;
	} else if (y <= 8.6e-81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -a / b
    t_2 = x / (1.0d0 - z)
    if (y <= (-4.8d-99)) then
        tmp = t_2
    else if (y <= (-4.2d-265)) then
        tmp = t / b
    else if (y <= 8.6d-241) then
        tmp = t_1
    else if (y <= 2.5d-180) then
        tmp = t / b
    else if (y <= 8.6d-81) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = -a / b;
	double t_2 = x / (1.0 - z);
	double tmp;
	if (y <= -4.8e-99) {
		tmp = t_2;
	} else if (y <= -4.2e-265) {
		tmp = t / b;
	} else if (y <= 8.6e-241) {
		tmp = t_1;
	} else if (y <= 2.5e-180) {
		tmp = t / b;
	} else if (y <= 8.6e-81) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = -a / b
	t_2 = x / (1.0 - z)
	tmp = 0
	if y <= -4.8e-99:
		tmp = t_2
	elif y <= -4.2e-265:
		tmp = t / b
	elif y <= 8.6e-241:
		tmp = t_1
	elif y <= 2.5e-180:
		tmp = t / b
	elif y <= 8.6e-81:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(-a) / b)
	t_2 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -4.8e-99)
		tmp = t_2;
	elseif (y <= -4.2e-265)
		tmp = Float64(t / b);
	elseif (y <= 8.6e-241)
		tmp = t_1;
	elseif (y <= 2.5e-180)
		tmp = Float64(t / b);
	elseif (y <= 8.6e-81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = -a / b;
	t_2 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -4.8e-99)
		tmp = t_2;
	elseif (y <= -4.2e-265)
		tmp = t / b;
	elseif (y <= 8.6e-241)
		tmp = t_1;
	elseif (y <= 2.5e-180)
		tmp = t / b;
	elseif (y <= 8.6e-81)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[((-a) / b), $MachinePrecision]}, Block[{t$95$2 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e-99], t$95$2, If[LessEqual[y, -4.2e-265], N[(t / b), $MachinePrecision], If[LessEqual[y, 8.6e-241], t$95$1, If[LessEqual[y, 2.5e-180], N[(t / b), $MachinePrecision], If[LessEqual[y, 8.6e-81], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.8000000000000001e-99 or 8.6000000000000006e-81 < y

   1. Initial program 60.3%

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

      1. fma-def 60.4%

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

   3. Simplified 60.4%

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

      1. fma-def 60.3%

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

      2. sub-neg 60.3%

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

      3. distribute-lft-in 60.3%

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

      4. *-commutative 60.3%

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

      5. associate-+r+ 60.3%

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

      6. *-commutative 60.3%

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

   5. Applied egg-rr 60.3%

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

   6. Taylor expanded in y around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. sub-neg 51.8%

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

   8. Simplified 51.8%

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

   if -4.8000000000000001e-99 < y < -4.20000000000000007e-265 or 8.5999999999999997e-241 < y < 2.5000000000000001e-180

   1. Initial program 78.8%

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

   2. Taylor expanded in y around 0 65.0%

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

   3. Taylor expanded in t around inf 45.7%

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

   if -4.20000000000000007e-265 < y < 8.5999999999999997e-241 or 2.5000000000000001e-180 < y < 8.6000000000000006e-81

   1. Initial program 68.6%

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

   2. Taylor expanded in y around 0 77.7%

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

   3. Taylor expanded in t around 0 59.1%

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

      1. mul-1-neg 59.1%

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

   5. Simplified 59.1%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{-265}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-241}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-180}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{elif}\;y \leq 8.6 \cdot 10^{-81}:\\ \;\;\;\;\frac{-a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 9: 53.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-39}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-39}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -1.7e+146)
     t_1
     (if (<= y -7.5e-39)
       (+ x (* z (/ t y)))
       (if (<= y -7e-39) (/ (- x) z) (if (<= y 5.2e-24) (/ (- t a) b) t_1))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.7e+146) {
		tmp = t_1;
	} else if (y <= -7.5e-39) {
		tmp = x + (z * (t / y));
	} else if (y <= -7e-39) {
		tmp = -x / z;
	} else if (y <= 5.2e-24) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (1.0d0 - z)
    if (y <= (-1.7d+146)) then
        tmp = t_1
    else if (y <= (-7.5d-39)) then
        tmp = x + (z * (t / y))
    else if (y <= (-7d-39)) then
        tmp = -x / z
    else if (y <= 5.2d-24) then
        tmp = (t - a) / b
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = x / (1.0 - z);
	double tmp;
	if (y <= -1.7e+146) {
		tmp = t_1;
	} else if (y <= -7.5e-39) {
		tmp = x + (z * (t / y));
	} else if (y <= -7e-39) {
		tmp = -x / z;
	} else if (y <= 5.2e-24) {
		tmp = (t - a) / b;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	t_1 = x / (1.0 - z)
	tmp = 0
	if y <= -1.7e+146:
		tmp = t_1
	elif y <= -7.5e-39:
		tmp = x + (z * (t / y))
	elif y <= -7e-39:
		tmp = -x / z
	elif y <= 5.2e-24:
		tmp = (t - a) / b
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a, b)
	t_1 = Float64(x / Float64(1.0 - z))
	tmp = 0.0
	if (y <= -1.7e+146)
		tmp = t_1;
	elseif (y <= -7.5e-39)
		tmp = Float64(x + Float64(z * Float64(t / y)));
	elseif (y <= -7e-39)
		tmp = Float64(Float64(-x) / z);
	elseif (y <= 5.2e-24)
		tmp = Float64(Float64(t - a) / b);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = x / (1.0 - z);
	tmp = 0.0;
	if (y <= -1.7e+146)
		tmp = t_1;
	elseif (y <= -7.5e-39)
		tmp = x + (z * (t / y));
	elseif (y <= -7e-39)
		tmp = -x / z;
	elseif (y <= 5.2e-24)
		tmp = (t - a) / b;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e+146], t$95$1, If[LessEqual[y, -7.5e-39], N[(x + N[(z * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-39], N[((-x) / z), $MachinePrecision], If[LessEqual[y, 5.2e-24], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.69999999999999995e146 or 5.2e-24 < y

   1. Initial program 59.0%

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

      1. fma-def 59.0%

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

   3. Simplified 59.0%

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

      1. fma-def 59.0%

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

      2. sub-neg 59.0%

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

      3. distribute-lft-in 59.0%

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

      4. *-commutative 59.0%

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

      5. associate-+r+ 59.0%

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

      6. *-commutative 59.0%

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

   5. Applied egg-rr 59.0%

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

   6. Taylor expanded in y around inf 62.4%

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

      1. mul-1-neg 62.4%

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

      2. sub-neg 62.4%

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

   8. Simplified 62.4%

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

   if -1.69999999999999995e146 < y < -7.49999999999999971e-39

   1. Initial program 62.1%

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

   2. Taylor expanded in z around 0 54.4%

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

   3. Taylor expanded in x around 0 57.1%

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

   4. Taylor expanded in t around inf 52.5%

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

      1. associate-/l* 50.0%

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

      2. associate-/r/ 52.5%

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

   6. Simplified 52.5%

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

   if -7.49999999999999971e-39 < y < -6.99999999999999999e-39

   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 z around -inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. mul-1-neg 100.0%

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

      3. distribute-lft-out-- 100.0%

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

      4. associate-/l* 100.0%

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

      5. associate-/l* 100.0%

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

      6. div-sub 100.0%

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

   4. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. sqr-pow 0.0%

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

   6. Applied egg-rr 0.0%

      \[\leadsto \left(-\color{blue}{{\left(\frac{z}{-\mathsf{fma}\left(y, \frac{x}{b - y}, \left(-y\right) \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}\right)}^{-0.5} \cdot {\left(\frac{z}{-\mathsf{fma}\left(y, \frac{x}{b - y}, \left(-y\right) \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}\right)}^{-0.5}}\right) + \frac{t - a}{b - y} \]
   7. Step-by-step derivation

      1. pow-sqr 100.0%

         \[\leadsto \left(-\color{blue}{{\left(\frac{z}{-\mathsf{fma}\left(y, \frac{x}{b - y}, \left(-y\right) \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}\right)}^{\left(2 \cdot -0.5\right)}}\right) + \frac{t - a}{b - y} \]

      2. metadata-eval 100.0%

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

      3. unpow-1 100.0%

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

      4. fma-udef 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-*r/ 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. associate-/r/ 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in y around inf 100.0%

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

       1. associate-*r/ 100.0%

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

       2. mul-1-neg 100.0%

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

   11. Simplified 100.0%

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

   if -6.99999999999999999e-39 < y < 5.2e-24

   1. Initial program 72.6%

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

   2. Taylor expanded in y around 0 67.9%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+146}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-39}:\\ \;\;\;\;x + z \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-39}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 10: 53.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{1 - z}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-39}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (/ x (- 1.0 z))))
   (if (<= y -3.4e+148)
     t_1
     (if (<= y -7.2e-39)
       (+ x (/ (* z t) y))
       (if (<= y -7e-39) (/ (- x) z) (if (<= y 4.1e-16) (/ (- 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 <= -3.4e+148) {
		tmp = t_1;
	} else if (y <= -7.2e-39) {
		tmp = x + ((z * t) / y);
	} else if (y <= -7e-39) {
		tmp = -x / z;
	} else if (y <= 4.1e-16) {
		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 <= (-3.4d+148)) then
        tmp = t_1
    else if (y <= (-7.2d-39)) then
        tmp = x + ((z * t) / y)
    else if (y <= (-7d-39)) then
        tmp = -x / z
    else if (y <= 4.1d-16) 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 <= -3.4e+148) {
		tmp = t_1;
	} else if (y <= -7.2e-39) {
		tmp = x + ((z * t) / y);
	} else if (y <= -7e-39) {
		tmp = -x / z;
	} else if (y <= 4.1e-16) {
		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 <= -3.4e+148:
		tmp = t_1
	elif y <= -7.2e-39:
		tmp = x + ((z * t) / y)
	elif y <= -7e-39:
		tmp = -x / z
	elif y <= 4.1e-16:
		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 <= -3.4e+148)
		tmp = t_1;
	elseif (y <= -7.2e-39)
		tmp = Float64(x + Float64(Float64(z * t) / y));
	elseif (y <= -7e-39)
		tmp = Float64(Float64(-x) / z);
	elseif (y <= 4.1e-16)
		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 <= -3.4e+148)
		tmp = t_1;
	elseif (y <= -7.2e-39)
		tmp = x + ((z * t) / y);
	elseif (y <= -7e-39)
		tmp = -x / z;
	elseif (y <= 4.1e-16)
		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, -3.4e+148], t$95$1, If[LessEqual[y, -7.2e-39], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7e-39], N[((-x) / z), $MachinePrecision], If[LessEqual[y, 4.1e-16], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.4000000000000003e148 or 4.10000000000000006e-16 < y

   1. Initial program 59.0%

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

      1. fma-def 59.0%

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

   3. Simplified 59.0%

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

      1. fma-def 59.0%

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

      2. sub-neg 59.0%

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

      3. distribute-lft-in 59.0%

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

      4. *-commutative 59.0%

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

      5. associate-+r+ 59.0%

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

      6. *-commutative 59.0%

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

   5. Applied egg-rr 59.0%

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

   6. Taylor expanded in y around inf 62.4%

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

      1. mul-1-neg 62.4%

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

      2. sub-neg 62.4%

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

   8. Simplified 62.4%

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

   if -3.4000000000000003e148 < y < -7.2000000000000001e-39

   1. Initial program 62.1%

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

   2. Taylor expanded in z around 0 54.4%

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

   3. Taylor expanded in x around 0 57.1%

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

   4. Taylor expanded in t around inf 52.5%

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

   if -7.2000000000000001e-39 < y < -6.99999999999999999e-39

   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 z around -inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. mul-1-neg 100.0%

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

      3. distribute-lft-out-- 100.0%

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

      4. associate-/l* 100.0%

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

      5. associate-/l* 100.0%

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

      6. div-sub 100.0%

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

   4. Simplified 100.0%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

      3. sqr-pow 0.0%

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

   6. Applied egg-rr 0.0%

      \[\leadsto \left(-\color{blue}{{\left(\frac{z}{-\mathsf{fma}\left(y, \frac{x}{b - y}, \left(-y\right) \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}\right)}^{-0.5} \cdot {\left(\frac{z}{-\mathsf{fma}\left(y, \frac{x}{b - y}, \left(-y\right) \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}\right)}^{-0.5}}\right) + \frac{t - a}{b - y} \]
   7. Step-by-step derivation

      1. pow-sqr 100.0%

         \[\leadsto \left(-\color{blue}{{\left(\frac{z}{-\mathsf{fma}\left(y, \frac{x}{b - y}, \left(-y\right) \cdot \frac{t - a}{{\left(b - y\right)}^{2}}\right)}\right)}^{\left(2 \cdot -0.5\right)}}\right) + \frac{t - a}{b - y} \]

      2. metadata-eval 100.0%

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

      3. unpow-1 100.0%

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

      4. fma-udef 100.0%

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

      5. cancel-sign-sub-inv 100.0%

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

      6. associate-*r/ 100.0%

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

      7. associate-/l* 100.0%

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

      8. *-commutative 100.0%

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

      9. associate-/r/ 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in y around inf 100.0%

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

       1. associate-*r/ 100.0%

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

       2. mul-1-neg 100.0%

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

   11. Simplified 100.0%

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

   if -6.99999999999999999e-39 < y < 4.10000000000000006e-16

   1. Initial program 72.6%

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

   2. Taylor expanded in y around 0 67.9%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+148}:\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \mathbf{elif}\;y \leq -7 \cdot 10^{-39}:\\ \;\;\;\;\frac{-x}{z}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{-16}:\\ \;\;\;\;\frac{t - a}{b}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{1 - z}\\ \end{array} \]

Alternative 11: 75.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-26} \lor \neg \left(z \leq 1.5 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -2.1e-26) (not (<= z 1.5e-22)))
   (/ (- 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 <= -2.1e-26) || !(z <= 1.5e-22)) {
		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 <= (-2.1d-26)) .or. (.not. (z <= 1.5d-22))) 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 <= -2.1e-26) || !(z <= 1.5e-22)) {
		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 <= -2.1e-26) or not (z <= 1.5e-22):
		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 <= -2.1e-26) || !(z <= 1.5e-22))
		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 <= -2.1e-26) || ~((z <= 1.5e-22)))
		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, -2.1e-26], N[Not[LessEqual[z, 1.5e-22]], $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 < -2.10000000000000008e-26 or 1.5e-22 < z

   1. Initial program 44.8%

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

   2. Taylor expanded in z around inf 78.6%

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

   if -2.10000000000000008e-26 < z < 1.5e-22

   1. Initial program 91.7%

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

   2. Taylor expanded in z around 0 67.2%

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

   3. Taylor expanded in x around 0 73.6%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{-26} \lor \neg \left(z \leq 1.5 \cdot 10^{-22}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot \left(t - a\right)}{y}\\ \end{array} \]

Alternative 12: 70.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-27} \lor \neg \left(z \leq 3.2 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -1.4e-27) (not (<= z 3.2e-23)))
   (/ (- t a) (- b y))
   (+ x (/ (* z t) y))))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e-27) || !(z <= 3.2e-23)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((z <= (-1.4d-27)) .or. (.not. (z <= 3.2d-23))) then
        tmp = (t - a) / (b - y)
    else
        tmp = x + ((z * t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -1.4e-27) || !(z <= 3.2e-23)) {
		tmp = (t - a) / (b - y);
	} else {
		tmp = x + ((z * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (z <= -1.4e-27) or not (z <= 3.2e-23):
		tmp = (t - a) / (b - y)
	else:
		tmp = x + ((z * t) / y)
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((z <= -1.4e-27) || !(z <= 3.2e-23))
		tmp = Float64(Float64(t - a) / Float64(b - y));
	else
		tmp = Float64(x + Float64(Float64(z * t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((z <= -1.4e-27) || ~((z <= 3.2e-23)))
		tmp = (t - a) / (b - y);
	else
		tmp = x + ((z * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[z, -1.4e-27], N[Not[LessEqual[z, 3.2e-23]], $MachinePrecision]], N[(N[(t - a), $MachinePrecision] / N[(b - y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(z * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.4e-27 or 3.19999999999999976e-23 < z

   1. Initial program 44.8%

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

   2. Taylor expanded in z around inf 78.6%

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

   if -1.4e-27 < z < 3.19999999999999976e-23

   1. Initial program 91.7%

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

   2. Taylor expanded in z around 0 67.2%

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

   3. Taylor expanded in x around 0 73.6%

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

   4. Taylor expanded in t around inf 62.0%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{-27} \lor \neg \left(z \leq 3.2 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{t - a}{b - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z \cdot t}{y}\\ \end{array} \]

Alternative 13: 53.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-39} \lor \neg \left(y \leq 6.5 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= y -7e-39) (not (<= y 6.5e-17))) (/ x (- 1.0 z)) (/ (- t a) b)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7e-39) || !(y <= 6.5e-17)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if ((y <= (-7d-39)) .or. (.not. (y <= 6.5d-17))) then
        tmp = x / (1.0d0 - z)
    else
        tmp = (t - a) / b
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((y <= -7e-39) || !(y <= 6.5e-17)) {
		tmp = x / (1.0 - z);
	} else {
		tmp = (t - a) / b;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if (y <= -7e-39) or not (y <= 6.5e-17):
		tmp = x / (1.0 - z)
	else:
		tmp = (t - a) / b
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if ((y <= -7e-39) || !(y <= 6.5e-17))
		tmp = Float64(x / Float64(1.0 - z));
	else
		tmp = Float64(Float64(t - a) / b);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if ((y <= -7e-39) || ~((y <= 6.5e-17)))
		tmp = x / (1.0 - z);
	else
		tmp = (t - a) / b;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[Or[LessEqual[y, -7e-39], N[Not[LessEqual[y, 6.5e-17]], $MachinePrecision]], N[(x / N[(1.0 - z), $MachinePrecision]), $MachinePrecision], N[(N[(t - a), $MachinePrecision] / b), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.99999999999999999e-39 or 6.4999999999999996e-17 < y

   1. Initial program 60.3%

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

      1. fma-def 60.3%

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

   3. Simplified 60.3%

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

      1. fma-def 60.3%

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

      2. sub-neg 60.3%

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

      3. distribute-lft-in 60.3%

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

      4. *-commutative 60.3%

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

      5. associate-+r+ 60.3%

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

      6. *-commutative 60.3%

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

   5. Applied egg-rr 60.3%

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

   6. Taylor expanded in y around inf 56.2%

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

      1. mul-1-neg 56.2%

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

      2. sub-neg 56.2%

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

   8. Simplified 56.2%

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

   if -6.99999999999999999e-39 < y < 6.4999999999999996e-17

   1. Initial program 72.6%

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

   2. Taylor expanded in y around 0 67.9%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-39} \lor \neg \left(y \leq 6.5 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x}{1 - z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t - a}{b}\\ \end{array} \]

Alternative 14: 34.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-23}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (if (<= y -1.62e-115) x (if (<= y 1.4e-23) (/ t b) x)))

C

double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.62e-115) {
		tmp = x;
	} else if (y <= 1.4e-23) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: tmp
    if (y <= (-1.62d-115)) then
        tmp = x
    else if (y <= 1.4d-23) then
        tmp = t / b
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (y <= -1.62e-115) {
		tmp = x;
	} else if (y <= 1.4e-23) {
		tmp = t / b;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	tmp = 0
	if y <= -1.62e-115:
		tmp = x
	elif y <= 1.4e-23:
		tmp = t / b
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a, b)
	tmp = 0.0
	if (y <= -1.62e-115)
		tmp = x;
	elseif (y <= 1.4e-23)
		tmp = Float64(t / b);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a, b)
	tmp = 0.0;
	if (y <= -1.62e-115)
		tmp = x;
	elseif (y <= 1.4e-23)
		tmp = t / b;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := If[LessEqual[y, -1.62e-115], x, If[LessEqual[y, 1.4e-23], N[(t / b), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1.62e-115 or 1.3999999999999999e-23 < y

   1. Initial program 62.0%

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

   2. Taylor expanded in z around 0 37.6%

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

   if -1.62e-115 < y < 1.3999999999999999e-23

   1. Initial program 72.2%

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

   2. Taylor expanded in y around 0 69.8%

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

   3. Taylor expanded in t around inf 39.6%

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

4. Final simplification 38.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.62 \cdot 10^{-115}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-23}:\\ \;\;\;\;\frac{t}{b}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 25.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.4%

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

2. Taylor expanded in z around 0 24.6%

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

3. Final simplification 24.6%

   \[\leadsto x \]

Developer target: 73.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

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

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

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