Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, A

Percentage Accurate: 89.1% → 96.3%

Time: 11.1s

Alternatives: 14

Speedup: 0.3×

Specification

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 89.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(t * z) - x))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + (((y * z) - x) / ((t * z) - x))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot z - x\\ t_2 := z \cdot t - x\\ t_3 := \frac{y}{\frac{t_2 \cdot \left(x + 1\right)}{z}}\\ t_4 := \frac{x + \frac{t_1}{t_2}}{x + 1}\\ \mathbf{if}\;t_4 \leq -400:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_4 \leq 50000:\\ \;\;\;\;\frac{x + \frac{1}{\frac{t_2}{t_1}}}{x + 1}\\ \mathbf{elif}\;t_4 \leq \infty:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* y z) x))
        (t_2 (- (* z t) x))
        (t_3 (/ y (/ (* t_2 (+ x 1.0)) z)))
        (t_4 (/ (+ x (/ t_1 t_2)) (+ x 1.0))))
   (if (<= t_4 -400.0)
     t_3
     (if (<= t_4 50000.0)
       (/ (+ x (/ 1.0 (/ t_2 t_1))) (+ x 1.0))
       (if (<= t_4 INFINITY) t_3 (/ (+ x (/ y t)) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double t_2 = (z * t) - x;
	double t_3 = y / ((t_2 * (x + 1.0)) / z);
	double t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -400.0) {
		tmp = t_3;
	} else if (t_4 <= 50000.0) {
		tmp = (x + (1.0 / (t_2 / t_1))) / (x + 1.0);
	} else if (t_4 <= ((double) INFINITY)) {
		tmp = t_3;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y * z) - x;
	double t_2 = (z * t) - x;
	double t_3 = y / ((t_2 * (x + 1.0)) / z);
	double t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	double tmp;
	if (t_4 <= -400.0) {
		tmp = t_3;
	} else if (t_4 <= 50000.0) {
		tmp = (x + (1.0 / (t_2 / t_1))) / (x + 1.0);
	} else if (t_4 <= Double.POSITIVE_INFINITY) {
		tmp = t_3;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y * z) - x
	t_2 = (z * t) - x
	t_3 = y / ((t_2 * (x + 1.0)) / z)
	t_4 = (x + (t_1 / t_2)) / (x + 1.0)
	tmp = 0
	if t_4 <= -400.0:
		tmp = t_3
	elif t_4 <= 50000.0:
		tmp = (x + (1.0 / (t_2 / t_1))) / (x + 1.0)
	elif t_4 <= math.inf:
		tmp = t_3
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y * z) - x)
	t_2 = Float64(Float64(z * t) - x)
	t_3 = Float64(y / Float64(Float64(t_2 * Float64(x + 1.0)) / z))
	t_4 = Float64(Float64(x + Float64(t_1 / t_2)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_4 <= -400.0)
		tmp = t_3;
	elseif (t_4 <= 50000.0)
		tmp = Float64(Float64(x + Float64(1.0 / Float64(t_2 / t_1))) / Float64(x + 1.0));
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y * z) - x;
	t_2 = (z * t) - x;
	t_3 = y / ((t_2 * (x + 1.0)) / z);
	t_4 = (x + (t_1 / t_2)) / (x + 1.0);
	tmp = 0.0;
	if (t_4 <= -400.0)
		tmp = t_3;
	elseif (t_4 <= 50000.0)
		tmp = (x + (1.0 / (t_2 / t_1))) / (x + 1.0);
	elseif (t_4 <= Inf)
		tmp = t_3;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$3 = N[(y / N[(N[(t$95$2 * N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(x + N[(t$95$1 / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, -400.0], t$95$3, If[LessEqual[t$95$4, 50000.0], N[(N[(x + N[(1.0 / N[(t$95$2 / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, Infinity], t$95$3, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -400 or 5e4 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < +inf.0

   1. Initial program 79.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in y around inf 79.1%

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

      1. associate-/l* 96.8%

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

      2. *-commutative 96.8%

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

      3. +-commutative 96.8%

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

   6. Simplified 96.8%

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

   if -400 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 5e4

   1. Initial program 98.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 98.9%

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

   3. Simplified 98.9%

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

      1. clear-num 98.9%

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

      2. inv-pow 98.9%

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

   5. Applied egg-rr 98.9%

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

      1. unpow-1 98.9%

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

      2. *-commutative 98.9%

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

      3. *-commutative 98.9%

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

   7. Simplified 98.9%

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

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -400:\\ \;\;\;\;\frac{y}{\frac{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 50000:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{y \cdot z - x}}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 2: 96.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{y}{\frac{t_1 \cdot \left(x + 1\right)}{z}}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_3 \leq -400:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 50000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2 (/ y (/ (* t_1 (+ x 1.0)) z)))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -400.0)
     t_2
     (if (<= t_3 50000.0)
       t_3
       (if (<= t_3 INFINITY) t_2 (/ (+ x (/ y t)) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = y / ((t_1 * (x + 1.0)) / z);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -400.0) {
		tmp = t_2;
	} else if (t_3 <= 50000.0) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = y / ((t_1 * (x + 1.0)) / z);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -400.0) {
		tmp = t_2;
	} else if (t_3 <= 50000.0) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = y / ((t_1 * (x + 1.0)) / z)
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -400.0:
		tmp = t_2
	elif t_3 <= 50000.0:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(y / Float64(Float64(t_1 * Float64(x + 1.0)) / z))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -400.0)
		tmp = t_2;
	elseif (t_3 <= 50000.0)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = y / ((t_1 * (x + 1.0)) / z);
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -400.0)
		tmp = t_2;
	elseif (t_3 <= 50000.0)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(y / N[(N[(t$95$1 * N[(x + 1.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -400.0], t$95$2, If[LessEqual[t$95$3, 50000.0], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -400 or 5e4 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < +inf.0

   1. Initial program 79.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 79.2%

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

   3. Simplified 79.2%

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

   4. Taylor expanded in y around inf 79.1%

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

      1. associate-/l* 96.8%

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

      2. *-commutative 96.8%

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

      3. +-commutative 96.8%

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

   6. Simplified 96.8%

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

   if -400 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 5e4

   1. Initial program 98.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]

   if +inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 0.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -400:\\ \;\;\;\;\frac{y}{\frac{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}{z}}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 50000:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{y}{\frac{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 3: 73.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;x \leq -23.5:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;1 - \frac{y}{\frac{x}{z}}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{z}{x}}{\frac{x}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= x -23.5)
     (- 1.0 (* (/ z x) (/ y x)))
     (if (<= x -1.15e-51)
       t_1
       (if (<= x -3.8e-210)
         (- 1.0 (/ y (/ x z)))
         (if (<= x 3.7e+15) t_1 (- 1.0 (/ (/ z x) (/ x y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (x <= -23.5) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= -1.15e-51) {
		tmp = t_1;
	} else if (x <= -3.8e-210) {
		tmp = 1.0 - (y / (x / z));
	} else if (x <= 3.7e+15) {
		tmp = t_1;
	} else {
		tmp = 1.0 - ((z / x) / (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (x <= (-23.5d0)) then
        tmp = 1.0d0 - ((z / x) * (y / x))
    else if (x <= (-1.15d-51)) then
        tmp = t_1
    else if (x <= (-3.8d-210)) then
        tmp = 1.0d0 - (y / (x / z))
    else if (x <= 3.7d+15) then
        tmp = t_1
    else
        tmp = 1.0d0 - ((z / x) / (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (x <= -23.5) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= -1.15e-51) {
		tmp = t_1;
	} else if (x <= -3.8e-210) {
		tmp = 1.0 - (y / (x / z));
	} else if (x <= 3.7e+15) {
		tmp = t_1;
	} else {
		tmp = 1.0 - ((z / x) / (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if x <= -23.5:
		tmp = 1.0 - ((z / x) * (y / x))
	elif x <= -1.15e-51:
		tmp = t_1
	elif x <= -3.8e-210:
		tmp = 1.0 - (y / (x / z))
	elif x <= 3.7e+15:
		tmp = t_1
	else:
		tmp = 1.0 - ((z / x) / (x / y))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -23.5)
		tmp = Float64(1.0 - Float64(Float64(z / x) * Float64(y / x)));
	elseif (x <= -1.15e-51)
		tmp = t_1;
	elseif (x <= -3.8e-210)
		tmp = Float64(1.0 - Float64(y / Float64(x / z)));
	elseif (x <= 3.7e+15)
		tmp = t_1;
	else
		tmp = Float64(1.0 - Float64(Float64(z / x) / Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (x <= -23.5)
		tmp = 1.0 - ((z / x) * (y / x));
	elseif (x <= -1.15e-51)
		tmp = t_1;
	elseif (x <= -3.8e-210)
		tmp = 1.0 - (y / (x / z));
	elseif (x <= 3.7e+15)
		tmp = t_1;
	else
		tmp = 1.0 - ((z / x) / (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -23.5], N[(1.0 - N[(N[(z / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.15e-51], t$95$1, If[LessEqual[x, -3.8e-210], N[(1.0 - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e+15], t$95$1, N[(1.0 - N[(N[(z / x), $MachinePrecision] / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -23.5

   1. Initial program 92.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 92.4%

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

   3. Simplified 92.4%

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

   4. Taylor expanded in x around -inf 77.4%

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

      1. mul-1-neg 77.4%

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

      2. unsub-neg 77.4%

         \[\leadsto \color{blue}{1 - \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]

      3. distribute-rgt-out-- 77.4%

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

      4. unpow2 77.4%

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

      5. times-frac 87.1%

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

   6. Simplified 87.1%

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

   7. Taylor expanded in y around inf 98.1%

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

   if -23.5 < x < -1.15000000000000001e-51 or -3.80000000000000003e-210 < x < 3.7e15

   1. Initial program 89.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 89.1%

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

   3. Simplified 89.1%

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

   4. Taylor expanded in z around inf 76.2%

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

   if -1.15000000000000001e-51 < x < -3.80000000000000003e-210

   1. Initial program 96.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around 0 65.9%

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

      1. neg-mul-1 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in y around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. unsub-neg 65.9%

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

      3. associate-/l* 66.0%

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

      4. associate-/l* 66.0%

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

      5. +-commutative 66.0%

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

   9. Simplified 66.0%

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

   10. Taylor expanded in x around 0 66.0%

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

   if 3.7e15 < x

   1. Initial program 86.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in x around -inf 76.7%

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

      1. mul-1-neg 76.7%

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

      2. unsub-neg 76.7%

         \[\leadsto \color{blue}{1 - \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]

      3. distribute-rgt-out-- 76.7%

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

      4. unpow2 76.7%

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

      5. times-frac 90.1%

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

   6. Simplified 90.1%

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

   7. Taylor expanded in y around inf 94.7%

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

      1. clear-num 94.7%

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

      2. un-div-inv 94.7%

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

   9. Applied egg-rr 94.7%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -23.5:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-51}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;1 - \frac{y}{\frac{x}{z}}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+15}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{z}{x}}{\frac{x}{y}}\\ \end{array} \]

Alternative 4: 69.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{if}\;x \leq -1.02 \cdot 10^{-50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;1 - \frac{y}{\frac{x}{z}}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{y}{t - \frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (* (/ z x) (/ y x)))))
   (if (<= x -1.02e-50)
     t_1
     (if (<= x -3.8e-210)
       (- 1.0 (/ y (/ x z)))
       (if (<= x 2.2e-9) (/ y (- t (/ x z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - ((z / x) * (y / x));
	double tmp;
	if (x <= -1.02e-50) {
		tmp = t_1;
	} else if (x <= -3.8e-210) {
		tmp = 1.0 - (y / (x / z));
	} else if (x <= 2.2e-9) {
		tmp = y / (t - (x / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 - ((z / x) * (y / x))
    if (x <= (-1.02d-50)) then
        tmp = t_1
    else if (x <= (-3.8d-210)) then
        tmp = 1.0d0 - (y / (x / z))
    else if (x <= 2.2d-9) then
        tmp = y / (t - (x / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - ((z / x) * (y / x));
	double tmp;
	if (x <= -1.02e-50) {
		tmp = t_1;
	} else if (x <= -3.8e-210) {
		tmp = 1.0 - (y / (x / z));
	} else if (x <= 2.2e-9) {
		tmp = y / (t - (x / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - ((z / x) * (y / x))
	tmp = 0
	if x <= -1.02e-50:
		tmp = t_1
	elif x <= -3.8e-210:
		tmp = 1.0 - (y / (x / z))
	elif x <= 2.2e-9:
		tmp = y / (t - (x / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(Float64(z / x) * Float64(y / x)))
	tmp = 0.0
	if (x <= -1.02e-50)
		tmp = t_1;
	elseif (x <= -3.8e-210)
		tmp = Float64(1.0 - Float64(y / Float64(x / z)));
	elseif (x <= 2.2e-9)
		tmp = Float64(y / Float64(t - Float64(x / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - ((z / x) * (y / x));
	tmp = 0.0;
	if (x <= -1.02e-50)
		tmp = t_1;
	elseif (x <= -3.8e-210)
		tmp = 1.0 - (y / (x / z));
	elseif (x <= 2.2e-9)
		tmp = y / (t - (x / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 - N[(N[(z / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.02e-50], t$95$1, If[LessEqual[x, -3.8e-210], N[(1.0 - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.2e-9], N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.0199999999999999e-50 or 2.1999999999999998e-9 < x

   1. Initial program 88.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 88.9%

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

   3. Simplified 88.9%

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

   4. Taylor expanded in x around -inf 72.3%

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

      1. mul-1-neg 72.3%

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

      2. unsub-neg 72.3%

         \[\leadsto \color{blue}{1 - \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]

      3. distribute-rgt-out-- 72.3%

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

      4. unpow2 72.3%

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

      5. times-frac 82.9%

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

   6. Simplified 82.9%

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

   7. Taylor expanded in y around inf 90.7%

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

   if -1.0199999999999999e-50 < x < -3.80000000000000003e-210

   1. Initial program 96.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around 0 65.9%

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

      1. neg-mul-1 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in y around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. unsub-neg 65.9%

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

      3. associate-/l* 66.0%

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

      4. associate-/l* 66.0%

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

      5. +-commutative 66.0%

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

   9. Simplified 66.0%

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

   10. Taylor expanded in x around 0 66.0%

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

   if -3.80000000000000003e-210 < x < 2.1999999999999998e-9

   1. Initial program 89.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around inf 54.0%

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

      1. associate-/l* 57.9%

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

      2. *-commutative 57.9%

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

      3. +-commutative 57.9%

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

   6. Simplified 57.9%

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

   7. Taylor expanded in x around 0 63.1%

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

   8. Taylor expanded in t around 0 63.1%

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

      1. neg-mul-1 63.1%

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

      2. distribute-neg-frac 63.1%

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

   10. Simplified 63.1%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;1 - \frac{y}{\frac{x}{z}}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-9}:\\ \;\;\;\;\frac{y}{t - \frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \end{array} \]

Alternative 5: 69.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;1 - \frac{y}{\frac{x}{z}}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{t - \frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{z}{x}}{\frac{x}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.4e-50)
   (- 1.0 (* (/ z x) (/ y x)))
   (if (<= x -3.8e-210)
     (- 1.0 (/ y (/ x z)))
     (if (<= x 1.3e-8) (/ y (- t (/ x z))) (- 1.0 (/ (/ z x) (/ x y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e-50) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= -3.8e-210) {
		tmp = 1.0 - (y / (x / z));
	} else if (x <= 1.3e-8) {
		tmp = y / (t - (x / z));
	} else {
		tmp = 1.0 - ((z / x) / (x / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-2.4d-50)) then
        tmp = 1.0d0 - ((z / x) * (y / x))
    else if (x <= (-3.8d-210)) then
        tmp = 1.0d0 - (y / (x / z))
    else if (x <= 1.3d-8) then
        tmp = y / (t - (x / z))
    else
        tmp = 1.0d0 - ((z / x) / (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e-50) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= -3.8e-210) {
		tmp = 1.0 - (y / (x / z));
	} else if (x <= 1.3e-8) {
		tmp = y / (t - (x / z));
	} else {
		tmp = 1.0 - ((z / x) / (x / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.4e-50:
		tmp = 1.0 - ((z / x) * (y / x))
	elif x <= -3.8e-210:
		tmp = 1.0 - (y / (x / z))
	elif x <= 1.3e-8:
		tmp = y / (t - (x / z))
	else:
		tmp = 1.0 - ((z / x) / (x / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.4e-50)
		tmp = Float64(1.0 - Float64(Float64(z / x) * Float64(y / x)));
	elseif (x <= -3.8e-210)
		tmp = Float64(1.0 - Float64(y / Float64(x / z)));
	elseif (x <= 1.3e-8)
		tmp = Float64(y / Float64(t - Float64(x / z)));
	else
		tmp = Float64(1.0 - Float64(Float64(z / x) / Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.4e-50)
		tmp = 1.0 - ((z / x) * (y / x));
	elseif (x <= -3.8e-210)
		tmp = 1.0 - (y / (x / z));
	elseif (x <= 1.3e-8)
		tmp = y / (t - (x / z));
	else
		tmp = 1.0 - ((z / x) / (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.4e-50], N[(1.0 - N[(N[(z / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.8e-210], N[(1.0 - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e-8], N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(z / x), $MachinePrecision] / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.40000000000000002e-50

   1. Initial program 91.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in x around -inf 71.2%

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

      1. mul-1-neg 71.2%

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

      2. unsub-neg 71.2%

         \[\leadsto \color{blue}{1 - \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]

      3. distribute-rgt-out-- 71.2%

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

      4. unpow2 71.2%

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

      5. times-frac 79.9%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in y around inf 90.2%

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

   if -2.40000000000000002e-50 < x < -3.80000000000000003e-210

   1. Initial program 96.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 96.3%

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

   3. Simplified 96.3%

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

   4. Taylor expanded in z around 0 65.9%

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

      1. neg-mul-1 65.9%

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

   6. Simplified 65.9%

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

   7. Taylor expanded in y around 0 65.9%

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

      1. mul-1-neg 65.9%

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

      2. unsub-neg 65.9%

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

      3. associate-/l* 66.0%

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

      4. associate-/l* 66.0%

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

      5. +-commutative 66.0%

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

   9. Simplified 66.0%

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

   10. Taylor expanded in x around 0 66.0%

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

   if -3.80000000000000003e-210 < x < 1.3000000000000001e-8

   1. Initial program 89.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 89.9%

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

   3. Simplified 89.9%

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

   4. Taylor expanded in y around inf 54.0%

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

      1. associate-/l* 57.9%

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

      2. *-commutative 57.9%

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

      3. +-commutative 57.9%

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

   6. Simplified 57.9%

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

   7. Taylor expanded in x around 0 63.1%

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

   8. Taylor expanded in t around 0 63.1%

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

      1. neg-mul-1 63.1%

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

      2. distribute-neg-frac 63.1%

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

   10. Simplified 63.1%

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

   if 1.3000000000000001e-8 < x

   1. Initial program 86.3%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in x around -inf 73.2%

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

      1. mul-1-neg 73.2%

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

      2. unsub-neg 73.2%

         \[\leadsto \color{blue}{1 - \frac{y \cdot z - t \cdot z}{{x}^{2}}} \]

      3. distribute-rgt-out-- 73.2%

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

      4. unpow2 73.2%

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

      5. times-frac 85.7%

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

   6. Simplified 85.7%

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

   7. Taylor expanded in y around inf 91.1%

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

      1. clear-num 91.0%

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

      2. un-div-inv 91.1%

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

   9. Applied egg-rr 91.1%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-50}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;1 - \frac{y}{\frac{x}{z}}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;\frac{y}{t - \frac{x}{z}}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{\frac{z}{x}}{\frac{x}{y}}\\ \end{array} \]

Alternative 6: 82.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-59} \lor \neg \left(t \leq 1.1 \cdot 10^{-99}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\frac{x + 1}{\frac{z}{x}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.2e-59) (not (<= t 1.1e-99)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (/ y (/ (+ x 1.0) (/ z x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.2e-59) || !(t <= 1.1e-99)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y / ((x + 1.0) / (z / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-6.2d-59)) .or. (.not. (t <= 1.1d-99))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - (y / ((x + 1.0d0) / (z / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.2e-59) || !(t <= 1.1e-99)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - (y / ((x + 1.0) / (z / x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.2e-59) or not (t <= 1.1e-99):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - (y / ((x + 1.0) / (z / x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.2e-59) || !(t <= 1.1e-99))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(y / Float64(Float64(x + 1.0) / Float64(z / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.2e-59) || ~((t <= 1.1e-99)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - (y / ((x + 1.0) / (z / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.2e-59], N[Not[LessEqual[t, 1.1e-99]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(y / N[(N[(x + 1.0), $MachinePrecision] / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.19999999999999998e-59 or 1.10000000000000002e-99 < t

   1. Initial program 87.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in z around inf 88.4%

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

   if -6.19999999999999998e-59 < t < 1.10000000000000002e-99

   1. Initial program 92.9%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in z around 0 84.2%

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

      1. neg-mul-1 84.2%

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

   6. Simplified 84.2%

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

   7. Taylor expanded in y around 0 84.2%

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

      1. mul-1-neg 84.2%

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

      2. unsub-neg 84.2%

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

      3. associate-/l* 90.3%

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

      4. associate-/l* 90.3%

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

      5. +-commutative 90.3%

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

   9. Simplified 90.3%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.2 \cdot 10^{-59} \lor \neg \left(t \leq 1.1 \cdot 10^{-99}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{\frac{x + 1}{\frac{z}{x}}}\\ \end{array} \]

Alternative 7: 63.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \frac{-z}{x}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-153}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= x -2.2e-66)
     t_1
     (if (<= x -1.6e-179)
       (* y (/ (- z) x))
       (if (<= x -3.8e-210) 1.0 (if (<= x 2.15e-153) (/ y t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -2.2e-66) {
		tmp = t_1;
	} else if (x <= -1.6e-179) {
		tmp = y * (-z / x);
	} else if (x <= -3.8e-210) {
		tmp = 1.0;
	} else if (x <= 2.15e-153) {
		tmp = y / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    if (x <= (-2.2d-66)) then
        tmp = t_1
    else if (x <= (-1.6d-179)) then
        tmp = y * (-z / x)
    else if (x <= (-3.8d-210)) then
        tmp = 1.0d0
    else if (x <= 2.15d-153) then
        tmp = y / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -2.2e-66) {
		tmp = t_1;
	} else if (x <= -1.6e-179) {
		tmp = y * (-z / x);
	} else if (x <= -3.8e-210) {
		tmp = 1.0;
	} else if (x <= 2.15e-153) {
		tmp = y / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -2.2e-66:
		tmp = t_1
	elif x <= -1.6e-179:
		tmp = y * (-z / x)
	elif x <= -3.8e-210:
		tmp = 1.0
	elif x <= 2.15e-153:
		tmp = y / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -2.2e-66)
		tmp = t_1;
	elseif (x <= -1.6e-179)
		tmp = Float64(y * Float64(Float64(-z) / x));
	elseif (x <= -3.8e-210)
		tmp = 1.0;
	elseif (x <= 2.15e-153)
		tmp = Float64(y / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -2.2e-66)
		tmp = t_1;
	elseif (x <= -1.6e-179)
		tmp = y * (-z / x);
	elseif (x <= -3.8e-210)
		tmp = 1.0;
	elseif (x <= 2.15e-153)
		tmp = y / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.2e-66], t$95$1, If[LessEqual[x, -1.6e-179], N[(y * N[((-z) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.8e-210], 1.0, If[LessEqual[x, 2.15e-153], N[(y / t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.2000000000000001e-66 or 2.15e-153 < x

   1. Initial program 90.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in t around inf 75.8%

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

      1. +-commutative 75.8%

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

   6. Simplified 75.8%

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

   if -2.2000000000000001e-66 < x < -1.6e-179

   1. Initial program 99.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 51.8%

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

      1. associate-/l* 51.9%

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

      2. *-commutative 51.9%

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

      3. +-commutative 51.9%

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

   6. Simplified 51.9%

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

   7. Taylor expanded in t around 0 45.5%

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

      1. mul-1-neg 45.5%

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

      2. times-frac 45.6%

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

      3. distribute-rgt-neg-in 45.6%

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

      4. +-commutative 45.6%

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

   9. Simplified 45.6%

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

   10. Taylor expanded in x around 0 45.5%

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

       1. associate-*r/ 45.6%

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

       2. neg-mul-1 45.6%

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

       3. distribute-lft-neg-in 45.6%

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

   12. Simplified 45.6%

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

   if -1.6e-179 < x < -3.80000000000000003e-210

   1. Initial program 84.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 84.4%

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

   3. Simplified 84.4%

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

   4. Taylor expanded in z around 0 60.2%

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

      1. neg-mul-1 60.2%

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

   6. Simplified 60.2%

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

   7. Taylor expanded in y around 0 60.2%

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

      1. mul-1-neg 60.2%

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

      2. unsub-neg 60.2%

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

      3. associate-/l* 60.1%

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

      4. associate-/l* 60.1%

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

      5. +-commutative 60.1%

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

   9. Simplified 60.1%

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

   10. Taylor expanded in y around 0 49.4%

       \[\leadsto \color{blue}{1} \]

   if -3.80000000000000003e-210 < x < 2.15e-153

   1. Initial program 87.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 87.0%

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

   3. Simplified 87.0%

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

      1. clear-num 87.0%

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

      2. inv-pow 87.0%

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

   5. Applied egg-rr 87.0%

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

      1. unpow-1 87.0%

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

      2. *-commutative 87.0%

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

      3. *-commutative 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in x around 0 64.2%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \frac{-z}{x}\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-153}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 8: 65.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -5.4 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-210}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-153}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= x -5.4e-41)
     t_1
     (if (<= x -3.7e-210)
       (- 1.0 (* y (/ z x)))
       (if (<= x 2.35e-153) (/ y t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -5.4e-41) {
		tmp = t_1;
	} else if (x <= -3.7e-210) {
		tmp = 1.0 - (y * (z / x));
	} else if (x <= 2.35e-153) {
		tmp = y / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    if (x <= (-5.4d-41)) then
        tmp = t_1
    else if (x <= (-3.7d-210)) then
        tmp = 1.0d0 - (y * (z / x))
    else if (x <= 2.35d-153) then
        tmp = y / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -5.4e-41) {
		tmp = t_1;
	} else if (x <= -3.7e-210) {
		tmp = 1.0 - (y * (z / x));
	} else if (x <= 2.35e-153) {
		tmp = y / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -5.4e-41:
		tmp = t_1
	elif x <= -3.7e-210:
		tmp = 1.0 - (y * (z / x))
	elif x <= 2.35e-153:
		tmp = y / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -5.4e-41)
		tmp = t_1;
	elseif (x <= -3.7e-210)
		tmp = Float64(1.0 - Float64(y * Float64(z / x)));
	elseif (x <= 2.35e-153)
		tmp = Float64(y / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -5.4e-41)
		tmp = t_1;
	elseif (x <= -3.7e-210)
		tmp = 1.0 - (y * (z / x));
	elseif (x <= 2.35e-153)
		tmp = y / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -5.4e-41], t$95$1, If[LessEqual[x, -3.7e-210], N[(1.0 - N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.35e-153], N[(y / t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.4e-41 or 2.35e-153 < x

   1. Initial program 90.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in t around inf 77.6%

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

      1. +-commutative 77.6%

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

   6. Simplified 77.6%

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

   if -5.4e-41 < x < -3.7000000000000003e-210

   1. Initial program 93.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in z around 0 61.5%

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

      1. neg-mul-1 61.5%

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

   6. Simplified 61.5%

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

   7. Taylor expanded in y around 0 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

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

      3. associate-/l* 61.6%

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

      4. associate-/l* 61.6%

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

      5. +-commutative 61.6%

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

   9. Simplified 61.6%

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

   10. Taylor expanded in x around 0 61.5%

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

       1. associate-*r/ 61.6%

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

   12. Simplified 61.6%

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

   if -3.7000000000000003e-210 < x < 2.35e-153

   1. Initial program 87.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 87.0%

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

   3. Simplified 87.0%

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

      1. clear-num 87.0%

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

      2. inv-pow 87.0%

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

   5. Applied egg-rr 87.0%

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

      1. unpow-1 87.0%

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

      2. *-commutative 87.0%

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

      3. *-commutative 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in x around 0 64.2%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-210}:\\ \;\;\;\;1 - y \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq 2.35 \cdot 10^{-153}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 9: 65.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -2.7 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-210}:\\ \;\;\;\;1 - \frac{y}{\frac{x}{z}}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-153}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= x -2.7e-41)
     t_1
     (if (<= x -3.7e-210)
       (- 1.0 (/ y (/ x z)))
       (if (<= x 2.8e-153) (/ y t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -2.7e-41) {
		tmp = t_1;
	} else if (x <= -3.7e-210) {
		tmp = 1.0 - (y / (x / z));
	} else if (x <= 2.8e-153) {
		tmp = y / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x / (x + 1.0d0)
    if (x <= (-2.7d-41)) then
        tmp = t_1
    else if (x <= (-3.7d-210)) then
        tmp = 1.0d0 - (y / (x / z))
    else if (x <= 2.8d-153) then
        tmp = y / t
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -2.7e-41) {
		tmp = t_1;
	} else if (x <= -3.7e-210) {
		tmp = 1.0 - (y / (x / z));
	} else if (x <= 2.8e-153) {
		tmp = y / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -2.7e-41:
		tmp = t_1
	elif x <= -3.7e-210:
		tmp = 1.0 - (y / (x / z))
	elif x <= 2.8e-153:
		tmp = y / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -2.7e-41)
		tmp = t_1;
	elseif (x <= -3.7e-210)
		tmp = Float64(1.0 - Float64(y / Float64(x / z)));
	elseif (x <= 2.8e-153)
		tmp = Float64(y / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -2.7e-41)
		tmp = t_1;
	elseif (x <= -3.7e-210)
		tmp = 1.0 - (y / (x / z));
	elseif (x <= 2.8e-153)
		tmp = y / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.7e-41], t$95$1, If[LessEqual[x, -3.7e-210], N[(1.0 - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e-153], N[(y / t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.7e-41 or 2.8000000000000001e-153 < x

   1. Initial program 90.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 90.4%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in t around inf 77.6%

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

      1. +-commutative 77.6%

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

   6. Simplified 77.6%

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

   if -2.7e-41 < x < -3.7000000000000003e-210

   1. Initial program 93.1%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in z around 0 61.5%

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

      1. neg-mul-1 61.5%

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

   6. Simplified 61.5%

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

   7. Taylor expanded in y around 0 61.5%

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

      1. mul-1-neg 61.5%

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

      2. unsub-neg 61.5%

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

      3. associate-/l* 61.6%

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

      4. associate-/l* 61.6%

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

      5. +-commutative 61.6%

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

   9. Simplified 61.6%

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

   10. Taylor expanded in x around 0 61.6%

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

   if -3.7000000000000003e-210 < x < 2.8000000000000001e-153

   1. Initial program 87.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 87.0%

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

   3. Simplified 87.0%

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

      1. clear-num 87.0%

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

      2. inv-pow 87.0%

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

   5. Applied egg-rr 87.0%

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

      1. unpow-1 87.0%

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

      2. *-commutative 87.0%

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

      3. *-commutative 87.0%

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

   7. Simplified 87.0%

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

   8. Taylor expanded in x around 0 64.2%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-41}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{-210}:\\ \;\;\;\;1 - \frac{y}{\frac{x}{z}}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-153}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 10: 72.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-40} \lor \neg \left(x \leq 0.00195\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t - \frac{x}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.8e-40) (not (<= x 0.00195)))
   (/ x (+ x 1.0))
   (/ y (- t (/ x z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.8e-40) || !(x <= 0.00195)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / (t - (x / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5.8d-40)) .or. (.not. (x <= 0.00195d0))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / (t - (x / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.8e-40) || !(x <= 0.00195)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / (t - (x / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.8e-40) or not (x <= 0.00195):
		tmp = x / (x + 1.0)
	else:
		tmp = y / (t - (x / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.8e-40) || !(x <= 0.00195))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / Float64(t - Float64(x / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.8e-40) || ~((x <= 0.00195)))
		tmp = x / (x + 1.0);
	else
		tmp = y / (t - (x / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.8e-40], N[Not[LessEqual[x, 0.00195]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.7999999999999998e-40 or 0.0019499999999999999 < x

   1. Initial program 89.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 89.4%

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

   3. Simplified 89.4%

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

   4. Taylor expanded in t around inf 84.8%

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

      1. +-commutative 84.8%

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

   6. Simplified 84.8%

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

   if -5.7999999999999998e-40 < x < 0.0019499999999999999

   1. Initial program 90.8%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in y around inf 50.5%

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

      1. associate-/l* 54.3%

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

      2. *-commutative 54.3%

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

      3. +-commutative 54.3%

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

   6. Simplified 54.3%

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

   7. Taylor expanded in x around 0 58.9%

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

   8. Taylor expanded in t around 0 58.9%

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

      1. neg-mul-1 58.9%

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

      2. distribute-neg-frac 58.9%

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

   10. Simplified 58.9%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-40} \lor \neg \left(x \leq 0.00195\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t - \frac{x}{z}}\\ \end{array} \]

Alternative 11: 66.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-90} \lor \neg \left(x \leq 2.35 \cdot 10^{-153}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -5.4e-90) (not (<= x 2.35e-153))) (/ x (+ x 1.0)) (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.4e-90) || !(x <= 2.35e-153)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-5.4d-90)) .or. (.not. (x <= 2.35d-153))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -5.4e-90) || !(x <= 2.35e-153)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -5.4e-90) or not (x <= 2.35e-153):
		tmp = x / (x + 1.0)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -5.4e-90) || !(x <= 2.35e-153))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -5.4e-90) || ~((x <= 2.35e-153)))
		tmp = x / (x + 1.0);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -5.4e-90], N[Not[LessEqual[x, 2.35e-153]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.39999999999999993e-90 or 2.35e-153 < x

   1. Initial program 90.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in t around inf 74.1%

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

      1. +-commutative 74.1%

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

   6. Simplified 74.1%

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

   if -5.39999999999999993e-90 < x < 2.35e-153

   1. Initial program 88.4%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 88.4%

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

   3. Simplified 88.4%

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

      1. clear-num 88.4%

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

      2. inv-pow 88.4%

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

   5. Applied egg-rr 88.4%

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

      1. unpow-1 88.4%

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

      2. *-commutative 88.4%

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

      3. *-commutative 88.4%

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

   7. Simplified 88.4%

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

   8. Taylor expanded in x around 0 56.2%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-90} \lor \neg \left(x \leq 2.35 \cdot 10^{-153}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]

Alternative 12: 63.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{-9}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.8e-210) 1.0 (if (<= x 1.16e-9) (/ y t) (+ 1.0 (/ -1.0 x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.8e-210) {
		tmp = 1.0;
	} else if (x <= 1.16e-9) {
		tmp = y / t;
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.8d-210)) then
        tmp = 1.0d0
    else if (x <= 1.16d-9) then
        tmp = y / t
    else
        tmp = 1.0d0 + ((-1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.8e-210) {
		tmp = 1.0;
	} else if (x <= 1.16e-9) {
		tmp = y / t;
	} else {
		tmp = 1.0 + (-1.0 / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.8e-210:
		tmp = 1.0
	elif x <= 1.16e-9:
		tmp = y / t
	else:
		tmp = 1.0 + (-1.0 / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.8e-210)
		tmp = 1.0;
	elseif (x <= 1.16e-9)
		tmp = Float64(y / t);
	else
		tmp = Float64(1.0 + Float64(-1.0 / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.8e-210)
		tmp = 1.0;
	elseif (x <= 1.16e-9)
		tmp = y / t;
	else
		tmp = 1.0 + (-1.0 / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.8e-210], 1.0, If[LessEqual[x, 1.16e-9], N[(y / t), $MachinePrecision], N[(1.0 + N[(-1.0 / x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.80000000000000003e-210

   1. Initial program 93.0%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in z around 0 79.9%

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

      1. neg-mul-1 79.9%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in y around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

      3. associate-/l* 83.7%

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

      4. associate-/l* 83.8%

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

      5. +-commutative 83.8%

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

   9. Simplified 83.8%

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

   10. Taylor expanded in y around 0 66.6%

       \[\leadsto \color{blue}{1} \]

   if -3.80000000000000003e-210 < x < 1.15999999999999992e-9

   1. Initial program 89.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 89.6%

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

   3. Simplified 89.6%

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

      1. clear-num 89.7%

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

      2. inv-pow 89.7%

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

   5. Applied egg-rr 89.7%

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

      1. unpow-1 89.7%

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

      2. *-commutative 89.7%

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

      3. *-commutative 89.7%

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

   7. Simplified 89.7%

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

   8. Taylor expanded in x around 0 56.1%

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

   if 1.15999999999999992e-9 < x

   1. Initial program 86.6%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 86.6%

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

   3. Simplified 86.6%

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

   4. Taylor expanded in t around inf 83.7%

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

      1. +-commutative 83.7%

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

   6. Simplified 83.7%

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

   7. Taylor expanded in x around inf 83.0%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{-9}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{x}\\ \end{array} \]

Alternative 13: 64.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.8e-210) 1.0 (if (<= x 5.5e-16) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.8e-210) {
		tmp = 1.0;
	} else if (x <= 5.5e-16) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.8d-210)) then
        tmp = 1.0d0
    else if (x <= 5.5d-16) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.8e-210) {
		tmp = 1.0;
	} else if (x <= 5.5e-16) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.8e-210:
		tmp = 1.0
	elif x <= 5.5e-16:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.8e-210)
		tmp = 1.0;
	elseif (x <= 5.5e-16)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.8e-210)
		tmp = 1.0;
	elseif (x <= 5.5e-16)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.8e-210], 1.0, If[LessEqual[x, 5.5e-16], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.80000000000000003e-210 or 5.49999999999999964e-16 < x

   1. Initial program 90.2%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   4. Taylor expanded in z around 0 80.8%

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

      1. neg-mul-1 80.8%

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

   6. Simplified 80.8%

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

   7. Taylor expanded in y around 0 80.7%

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

      1. mul-1-neg 80.7%

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

      2. unsub-neg 80.7%

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

      3. associate-/l* 87.7%

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

      4. associate-/l* 86.6%

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

      5. +-commutative 86.6%

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

   9. Simplified 86.6%

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

   10. Taylor expanded in y around 0 73.4%

       \[\leadsto \color{blue}{1} \]

   if -3.80000000000000003e-210 < x < 5.49999999999999964e-16

   1. Initial program 89.5%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 89.5%

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

   3. Simplified 89.5%

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

      1. clear-num 89.5%

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

      2. inv-pow 89.5%

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

   5. Applied egg-rr 89.5%

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

      1. unpow-1 89.5%

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

      2. *-commutative 89.5%

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

      3. *-commutative 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in x around 0 56.8%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-210}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-16}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 14: 53.0% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 1.0)

C

double code(double x, double y, double z, double t) {
	return 1.0;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = 1.0d0
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0;
}

Python

def code(x, y, z, t):
	return 1.0

Julia

function code(x, y, z, t)
	return 1.0
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0;
end

Wolfram

code[x_, y_, z_, t_] := 1.0

Derivation

1. Initial program 90.0%

   \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
2. Step-by-step derivation

   1. *-commutative 90.0%

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

3. Simplified 90.0%

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

4. Taylor expanded in z around 0 65.2%

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

   1. neg-mul-1 65.2%

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

6. Simplified 65.2%

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

7. Taylor expanded in y around 0 65.2%

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

   1. mul-1-neg 65.2%

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

   2. unsub-neg 65.2%

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

   3. associate-/l* 70.1%

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

   4. associate-/l* 69.4%

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

   5. +-commutative 69.4%

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

9. Simplified 69.4%

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

10. Taylor expanded in y around 0 56.3%

    \[\leadsto \color{blue}{1} \]

11. Final simplification 56.3%

    \[\leadsto 1 \]

Developer target: 99.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x + \left(\frac{y}{t - \frac{x}{z}} - \frac{x}{t \cdot z - x}\right)}{x + 1} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0)))

C

double code(double x, double y, double z, double t) {
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0d0)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
}

Python

def code(x, y, z, t):
	return (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(x + Float64(Float64(y / Float64(t - Float64(x / z))) - Float64(x / Float64(Float64(t * z) - x)))) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x + ((y / (t - (x / z))) - (x / ((t * z) - x)))) / (x + 1.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x + N[(N[(y / N[(t - N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(N[(t * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023213 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))