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

Percentage Accurate: 89.3% → 97.1%

Time: 17.6s

Alternatives: 17

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: 89.3% 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: 97.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ t_2 := \mathsf{fma}\left(t, z, -x\right)\\ \left(t\_1 + \frac{y}{x + 1} \cdot \frac{z}{t\_2}\right) - \frac{t\_1}{t\_2} \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))) (t_2 (fma t z (- x))))
   (- (+ t_1 (* (/ y (+ x 1.0)) (/ z t_2))) (/ t_1 t_2))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double t_2 = fma(t, z, -x);
	return (t_1 + ((y / (x + 1.0)) * (z / t_2))) - (t_1 / t_2);
}

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	t_2 = fma(t, z, Float64(-x))
	return Float64(Float64(t_1 + Float64(Float64(y / Float64(x + 1.0)) * Float64(z / t_2))) - Float64(t_1 / t_2))
end

Wolfram

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

Derivation

1. Initial program 91.4%

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

   1. *-commutative 91.4%

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

3. Simplified 91.4%

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

5. Taylor expanded in y around 0 91.4%

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

   1. +-commutative 91.4%

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

   2. times-frac 98.6%

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

   3. +-commutative 98.6%

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

   4. fma-neg 98.6%

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

   5. associate-/r* 98.6%

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

   6. +-commutative 98.6%

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

   7. fma-neg 98.6%

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

7. Simplified 98.6%

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

8. Final simplification 98.6%

   \[\leadsto \left(\frac{x}{x + 1} + \frac{y}{x + 1} \cdot \frac{z}{\mathsf{fma}\left(t, z, -x\right)}\right) - \frac{\frac{x}{x + 1}}{\mathsf{fma}\left(t, z, -x\right)} \]
9. Add Preprocessing

Alternative 2: 96.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t\_1}}{x + 1}\\ \mathbf{if}\;t\_2 \leq -20000:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{t\_1}\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{+271}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)) (t_2 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_2 -20000.0)
     (* (/ y (+ x 1.0)) (/ z t_1))
     (if (<= t_2 2e+271) 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 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -20000.0) {
		tmp = (y / (x + 1.0)) * (z / t_1);
	} else if (t_2 <= 2e+271) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (z * t) - x
    t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0d0)
    if (t_2 <= (-20000.0d0)) then
        tmp = (y / (x + 1.0d0)) * (z / t_1)
    else if (t_2 <= 2d+271) then
        tmp = t_2
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -20000.0) {
		tmp = (y / (x + 1.0)) * (z / t_1);
	} else if (t_2 <= 2e+271) {
		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 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_2 <= -20000.0:
		tmp = (y / (x + 1.0)) * (z / t_1)
	elif t_2 <= 2e+271:
		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(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_2 <= -20000.0)
		tmp = Float64(Float64(y / Float64(x + 1.0)) * Float64(z / t_1));
	elseif (t_2 <= 2e+271)
		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 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_2 <= -20000.0)
		tmp = (y / (x + 1.0)) * (z / t_1);
	elseif (t_2 <= 2e+271)
		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[(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$2, -20000.0], N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+271], 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)) < -2e4

   1. Initial program 82.9%

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

      1. *-commutative 82.9%

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

   3. Simplified 82.9%

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

      1. clear-num 82.9%

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

      2. associate-/r/ 83.0%

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

      3. fma-neg 83.0%

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

   6. Applied egg-rr 83.0%

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

   7. Taylor expanded in y around inf 82.8%

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

      1. times-frac 97.0%

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

      2. +-commutative 97.0%

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

   9. Simplified 97.0%

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

   if -2e4 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 1.99999999999999991e271

   1. Initial program 98.7%

      \[\frac{x + \frac{y \cdot z - x}{t \cdot z - x}}{x + 1} \]
   2. Add Preprocessing

   if 1.99999999999999991e271 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 38.3%

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

      1. *-commutative 38.3%

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

   3. Simplified 38.3%

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

   5. Taylor expanded in z around inf 82.7%

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

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -20000:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+271}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 80.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-54}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-155}:\\ \;\;\;\;\frac{\left(x + \frac{y}{t}\right) - \frac{x}{z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + 1} \cdot \left(x + \frac{y \cdot z}{z \cdot t - x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.55e-54)
   (/ (- (+ x 1.0) (/ y (/ x z))) (+ x 1.0))
   (if (<= x 7.2e-155)
     (/ (- (+ x (/ y t)) (/ x (* z t))) (+ x 1.0))
     (* (/ 1.0 (+ x 1.0)) (+ x (/ (* y z) (- (* z t) x)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e-54) {
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	} else if (x <= 7.2e-155) {
		tmp = ((x + (y / t)) - (x / (z * t))) / (x + 1.0);
	} else {
		tmp = (1.0 / (x + 1.0)) * (x + ((y * z) / ((z * t) - 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 <= (-1.55d-54)) then
        tmp = ((x + 1.0d0) - (y / (x / z))) / (x + 1.0d0)
    else if (x <= 7.2d-155) then
        tmp = ((x + (y / t)) - (x / (z * t))) / (x + 1.0d0)
    else
        tmp = (1.0d0 / (x + 1.0d0)) * (x + ((y * z) / ((z * t) - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e-54) {
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	} else if (x <= 7.2e-155) {
		tmp = ((x + (y / t)) - (x / (z * t))) / (x + 1.0);
	} else {
		tmp = (1.0 / (x + 1.0)) * (x + ((y * z) / ((z * t) - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.55e-54:
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0)
	elif x <= 7.2e-155:
		tmp = ((x + (y / t)) - (x / (z * t))) / (x + 1.0)
	else:
		tmp = (1.0 / (x + 1.0)) * (x + ((y * z) / ((z * t) - x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.55e-54)
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	elseif (x <= 7.2e-155)
		tmp = Float64(Float64(Float64(x + Float64(y / t)) - Float64(x / Float64(z * t))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(1.0 / Float64(x + 1.0)) * Float64(x + Float64(Float64(y * z) / Float64(Float64(z * t) - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.55e-54)
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	elseif (x <= 7.2e-155)
		tmp = ((x + (y / t)) - (x / (z * t))) / (x + 1.0);
	else
		tmp = (1.0 / (x + 1.0)) * (x + ((y * z) / ((z * t) - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.55e-54], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e-155], N[(N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(x + N[(N[(y * z), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.55000000000000002e-54

   1. Initial program 81.2%

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

      1. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in t around 0 78.1%

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

      1. associate-+r+ 78.1%

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

      2. mul-1-neg 78.1%

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

      3. unsub-neg 78.1%

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

      4. +-commutative 78.1%

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

      5. associate-/l* 86.2%

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

      6. +-commutative 86.2%

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

   7. Simplified 86.2%

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

   if -1.55000000000000002e-54 < x < 7.19999999999999977e-155

   1. Initial program 94.1%

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

      1. *-commutative 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in t around inf 82.2%

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

   if 7.19999999999999977e-155 < x

   1. Initial program 96.8%

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

      1. *-commutative 96.8%

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

   3. Simplified 96.8%

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

      1. clear-num 96.8%

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

      2. associate-/r/ 96.7%

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

      3. fma-neg 96.7%

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

   6. Applied egg-rr 96.7%

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

   7. Taylor expanded in y around inf 92.2%

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

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-54}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-155}:\\ \;\;\;\;\frac{\left(x + \frac{y}{t}\right) - \frac{x}{z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{x + 1} \cdot \left(x + \frac{y \cdot z}{z \cdot t - x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-55}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-27}:\\ \;\;\;\;\frac{x + \left(\frac{y}{t} - \frac{\frac{x}{t}}{z}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1e-55)
   (/ (- (+ x 1.0) (/ y (/ x z))) (+ x 1.0))
   (if (<= x 2.85e-27)
     (/ (+ x (- (/ y t) (/ (/ x t) z))) (+ x 1.0))
     (/ (- x (/ x (- (* z t) x))) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1e-55) {
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	} else if (x <= 2.85e-27) {
		tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 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 <= (-1d-55)) then
        tmp = ((x + 1.0d0) - (y / (x / z))) / (x + 1.0d0)
    else if (x <= 2.85d-27) then
        tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0d0)
    else
        tmp = (x - (x / ((z * t) - x))) / (x + 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 <= -1e-55) {
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	} else if (x <= 2.85e-27) {
		tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1e-55:
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0)
	elif x <= 2.85e-27:
		tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0)
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1e-55)
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	elseif (x <= 2.85e-27)
		tmp = Float64(Float64(x + Float64(Float64(y / t) - Float64(Float64(x / t) / z))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1e-55)
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	elseif (x <= 2.85e-27)
		tmp = (x + ((y / t) - ((x / t) / z))) / (x + 1.0);
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1e-55], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.85e-27], N[(N[(x + N[(N[(y / t), $MachinePrecision] - N[(N[(x / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.99999999999999995e-56

   1. Initial program 81.2%

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

      1. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in t around 0 78.1%

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

      1. associate-+r+ 78.1%

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

      2. mul-1-neg 78.1%

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

      3. unsub-neg 78.1%

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

      4. +-commutative 78.1%

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

      5. associate-/l* 86.2%

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

      6. +-commutative 86.2%

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

   7. Simplified 86.2%

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

   if -9.99999999999999995e-56 < x < 2.8499999999999998e-27

   1. Initial program 95.4%

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

      1. *-commutative 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in t around inf 77.9%

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

      1. associate--l+ 77.9%

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

      2. associate-/r* 73.9%

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

   7. Applied egg-rr 73.9%

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

   if 2.8499999999999998e-27 < x

   1. Initial program 95.5%

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

      1. *-commutative 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around 0 95.7%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \cdot 10^{-55}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 2.85 \cdot 10^{-27}:\\ \;\;\;\;\frac{x + \left(\frac{y}{t} - \frac{\frac{x}{t}}{z}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\left(x + \frac{y}{t}\right) - \frac{x}{z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9.5e-55)
   (/ (- (+ x 1.0) (/ y (/ x z))) (+ x 1.0))
   (if (<= x 1.5e-29)
     (/ (- (+ x (/ y t)) (/ x (* z t))) (+ x 1.0))
     (/ (- x (/ x (- (* z t) x))) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.5e-55) {
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	} else if (x <= 1.5e-29) {
		tmp = ((x + (y / t)) - (x / (z * t))) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 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 <= (-9.5d-55)) then
        tmp = ((x + 1.0d0) - (y / (x / z))) / (x + 1.0d0)
    else if (x <= 1.5d-29) then
        tmp = ((x + (y / t)) - (x / (z * t))) / (x + 1.0d0)
    else
        tmp = (x - (x / ((z * t) - x))) / (x + 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 <= -9.5e-55) {
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	} else if (x <= 1.5e-29) {
		tmp = ((x + (y / t)) - (x / (z * t))) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9.5e-55:
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0)
	elif x <= 1.5e-29:
		tmp = ((x + (y / t)) - (x / (z * t))) / (x + 1.0)
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9.5e-55)
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	elseif (x <= 1.5e-29)
		tmp = Float64(Float64(Float64(x + Float64(y / t)) - Float64(x / Float64(z * t))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9.5e-55)
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	elseif (x <= 1.5e-29)
		tmp = ((x + (y / t)) - (x / (z * t))) / (x + 1.0);
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9.5e-55], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e-29], N[(N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] - N[(x / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5000000000000006e-55

   1. Initial program 81.2%

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

      1. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in t around 0 78.1%

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

      1. associate-+r+ 78.1%

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

      2. mul-1-neg 78.1%

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

      3. unsub-neg 78.1%

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

      4. +-commutative 78.1%

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

      5. associate-/l* 86.2%

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

      6. +-commutative 86.2%

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

   7. Simplified 86.2%

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

   if -9.5000000000000006e-55 < x < 1.5000000000000001e-29

   1. Initial program 95.4%

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

      1. *-commutative 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in t around inf 77.9%

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

   if 1.5000000000000001e-29 < x

   1. Initial program 95.5%

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

      1. *-commutative 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around 0 95.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\left(x + \frac{y}{t}\right) - \frac{x}{z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-153} \lor \neg \left(z \leq 3.15 \cdot 10^{-83}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.25e-153) (not (<= z 3.15e-83)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (- x (/ x (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e-153) || !(z <= 3.15e-83)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 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 ((z <= (-1.25d-153)) .or. (.not. (z <= 3.15d-83))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x - (x / ((z * t) - x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.25e-153) || !(z <= 3.15e-83)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.25e-153) or not (z <= 3.15e-83):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.25e-153) || !(z <= 3.15e-83))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.25e-153) || ~((z <= 3.15e-83)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.25e-153], N[Not[LessEqual[z, 3.15e-83]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.25000000000000008e-153 or 3.14999999999999983e-83 < z

   1. Initial program 87.5%

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

      1. *-commutative 87.5%

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

   3. Simplified 87.5%

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

   5. Taylor expanded in z around inf 78.9%

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

   if -1.25000000000000008e-153 < z < 3.14999999999999983e-83

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 85.4%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.25 \cdot 10^{-153} \lor \neg \left(z \leq 3.15 \cdot 10^{-83}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-40} \lor \neg \left(t \leq 1.15 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.6e-40) (not (<= t 1.15e-11)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (- (+ x 1.0) (/ y (/ x z))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.6e-40) || !(t <= 1.15e-11)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 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 ((t <= (-4.6d-40)) .or. (.not. (t <= 1.15d-11))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = ((x + 1.0d0) - (y / (x / z))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.6e-40) || !(t <= 1.15e-11)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.6e-40) or not (t <= 1.15e-11):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.6e-40) || !(t <= 1.15e-11))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.6e-40) || ~((t <= 1.15e-11)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.6e-40], N[Not[LessEqual[t, 1.15e-11]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.6e-40 or 1.15000000000000007e-11 < t

   1. Initial program 88.5%

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

      1. *-commutative 88.5%

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

   3. Simplified 88.5%

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

   5. Taylor expanded in z around inf 89.6%

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

   if -4.6e-40 < t < 1.15000000000000007e-11

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

   3. Simplified 94.2%

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

   5. Taylor expanded in t around 0 72.7%

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

      1. associate-+r+ 72.7%

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

      2. mul-1-neg 72.7%

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

      3. unsub-neg 72.7%

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

      4. +-commutative 72.7%

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

      5. associate-/l* 74.8%

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

      6. +-commutative 74.8%

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

   7. Simplified 74.8%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.6 \cdot 10^{-40} \lor \neg \left(t \leq 1.15 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-55}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.6e-55)
   (/ (- (+ x 1.0) (/ y (/ x z))) (+ x 1.0))
   (if (<= x 1.5e-29)
     (/ (- x (/ (- (/ x z) y) t)) (+ x 1.0))
     (/ (- x (/ x (- (* z t) x))) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.6e-55) {
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	} else if (x <= 1.5e-29) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 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 <= (-4.6d-55)) then
        tmp = ((x + 1.0d0) - (y / (x / z))) / (x + 1.0d0)
    else if (x <= 1.5d-29) then
        tmp = (x - (((x / z) - y) / t)) / (x + 1.0d0)
    else
        tmp = (x - (x / ((z * t) - x))) / (x + 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 <= -4.6e-55) {
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	} else if (x <= 1.5e-29) {
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.6e-55:
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0)
	elif x <= 1.5e-29:
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0)
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.6e-55)
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	elseif (x <= 1.5e-29)
		tmp = Float64(Float64(x - Float64(Float64(Float64(x / z) - y) / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.6e-55)
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	elseif (x <= 1.5e-29)
		tmp = (x - (((x / z) - y) / t)) / (x + 1.0);
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.6e-55], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e-29], N[(N[(x - N[(N[(N[(x / z), $MachinePrecision] - y), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.60000000000000023e-55

   1. Initial program 81.2%

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

      1. *-commutative 81.2%

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

   3. Simplified 81.2%

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

   5. Taylor expanded in t around 0 78.1%

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

      1. associate-+r+ 78.1%

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

      2. mul-1-neg 78.1%

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

      3. unsub-neg 78.1%

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

      4. +-commutative 78.1%

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

      5. associate-/l* 86.2%

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

      6. +-commutative 86.2%

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

   7. Simplified 86.2%

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

   if -4.60000000000000023e-55 < x < 1.5000000000000001e-29

   1. Initial program 95.4%

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

      1. *-commutative 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in t around -inf 77.9%

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

      1. mul-1-neg 77.9%

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

      2. distribute-lft-out-- 77.9%

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

   7. Simplified 77.9%

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

   if 1.5000000000000001e-29 < x

   1. Initial program 95.5%

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

      1. *-commutative 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in y around 0 95.7%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-55}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{x - \frac{\frac{x}{z} - y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 67.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-56}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-143} \lor \neg \left(x \leq 1.7 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.9e-56)
   1.0
   (if (or (<= x -7e-143) (not (<= x 1.7e-25)))
     (/ x (+ x 1.0))
     (/ y (* (+ x 1.0) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.9e-56) {
		tmp = 1.0;
	} else if ((x <= -7e-143) || !(x <= 1.7e-25)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / ((x + 1.0) * 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 <= (-1.9d-56)) then
        tmp = 1.0d0
    else if ((x <= (-7d-143)) .or. (.not. (x <= 1.7d-25))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / ((x + 1.0d0) * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.9e-56) {
		tmp = 1.0;
	} else if ((x <= -7e-143) || !(x <= 1.7e-25)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / ((x + 1.0) * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.9e-56:
		tmp = 1.0
	elif (x <= -7e-143) or not (x <= 1.7e-25):
		tmp = x / (x + 1.0)
	else:
		tmp = y / ((x + 1.0) * t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.9e-56)
		tmp = 1.0;
	elseif ((x <= -7e-143) || !(x <= 1.7e-25))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / Float64(Float64(x + 1.0) * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.9e-56)
		tmp = 1.0;
	elseif ((x <= -7e-143) || ~((x <= 1.7e-25)))
		tmp = x / (x + 1.0);
	else
		tmp = y / ((x + 1.0) * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.9e-56], 1.0, If[Or[LessEqual[x, -7e-143], N[Not[LessEqual[x, 1.7e-25]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / N[(N[(x + 1.0), $MachinePrecision] * t), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.9000000000000001e-56

   1. Initial program 81.5%

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

      1. *-commutative 81.5%

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

   3. Simplified 81.5%

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

      1. clear-num 81.4%

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

      2. associate-/r/ 81.4%

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

      3. fma-neg 81.4%

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

   6. Applied egg-rr 81.4%

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

   7. Taylor expanded in y around inf 72.0%

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

   8. Taylor expanded in x around inf 78.1%

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

   if -1.9000000000000001e-56 < x < -7.00000000000000011e-143 or 1.70000000000000001e-25 < x

   1. Initial program 96.2%

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

      1. *-commutative 96.2%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around inf 88.9%

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

      1. +-commutative 88.9%

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

   7. Simplified 88.9%

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

   if -7.00000000000000011e-143 < x < 1.70000000000000001e-25

   1. Initial program 94.8%

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

      1. *-commutative 94.8%

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

   3. Simplified 94.8%

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

   5. Taylor expanded in t around inf 77.5%

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

   6. Taylor expanded in t around 0 64.2%

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

      1. +-commutative 64.2%

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

   8. Simplified 64.2%

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

   9. Taylor expanded in y around inf 56.3%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-56}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-143} \lor \neg \left(x \leq 1.7 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\left(x + 1\right) \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 78.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-56} \lor \neg \left(x \leq 1.45 \cdot 10^{+44}\right):\\ \;\;\;\;1 - z \cdot \frac{y}{x \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -1.6e-56) (not (<= x 1.45e+44)))
   (- 1.0 (* z (/ y (* x (+ x 1.0)))))
   (/ (+ x (/ y t)) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -1.6e-56) || !(x <= 1.45e+44)) {
		tmp = 1.0 - (z * (y / (x * (x + 1.0))));
	} else {
		tmp = (x + (y / t)) / (x + 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 <= (-1.6d-56)) .or. (.not. (x <= 1.45d+44))) then
        tmp = 1.0d0 - (z * (y / (x * (x + 1.0d0))))
    else
        tmp = (x + (y / t)) / (x + 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 <= -1.6e-56) || !(x <= 1.45e+44)) {
		tmp = 1.0 - (z * (y / (x * (x + 1.0))));
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -1.6e-56) or not (x <= 1.45e+44):
		tmp = 1.0 - (z * (y / (x * (x + 1.0))))
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -1.6e-56) || !(x <= 1.45e+44))
		tmp = Float64(1.0 - Float64(z * Float64(y / Float64(x * Float64(x + 1.0)))));
	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)
	tmp = 0.0;
	if ((x <= -1.6e-56) || ~((x <= 1.45e+44)))
		tmp = 1.0 - (z * (y / (x * (x + 1.0))));
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -1.6e-56], N[Not[LessEqual[x, 1.45e+44]], $MachinePrecision]], N[(1.0 - N[(z * N[(y / N[(x * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.59999999999999993e-56 or 1.4500000000000001e44 < x

   1. Initial program 87.3%

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

      1. *-commutative 87.3%

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

   3. Simplified 87.3%

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

   5. Taylor expanded in z around 0 85.8%

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

   6. Taylor expanded in y around inf 90.8%

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

      1. associate-*r/ 90.8%

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

      2. mul-1-neg 90.8%

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

      3. +-commutative 90.8%

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

   8. Simplified 90.8%

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

   if -1.59999999999999993e-56 < x < 1.4500000000000001e44

   1. Initial program 95.7%

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

      1. *-commutative 95.7%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in z around inf 70.8%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{-56} \lor \neg \left(x \leq 1.45 \cdot 10^{+44}\right):\\ \;\;\;\;1 - z \cdot \frac{y}{x \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 71.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.52e-18)
   1.0
   (if (<= x 8.5e-27) (* y (/ z (- (* z t) x))) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.52e-18) {
		tmp = 1.0;
	} else if (x <= 8.5e-27) {
		tmp = y * (z / ((z * t) - x));
	} else {
		tmp = x / (x + 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 <= (-1.52d-18)) then
        tmp = 1.0d0
    else if (x <= 8.5d-27) then
        tmp = y * (z / ((z * t) - x))
    else
        tmp = x / (x + 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 <= -1.52e-18) {
		tmp = 1.0;
	} else if (x <= 8.5e-27) {
		tmp = y * (z / ((z * t) - x));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.52e-18:
		tmp = 1.0
	elif x <= 8.5e-27:
		tmp = y * (z / ((z * t) - x))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.52e-18)
		tmp = 1.0;
	elseif (x <= 8.5e-27)
		tmp = Float64(y * Float64(z / Float64(Float64(z * t) - x)));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.52e-18)
		tmp = 1.0;
	elseif (x <= 8.5e-27)
		tmp = y * (z / ((z * t) - x));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.52e-18], 1.0, If[LessEqual[x, 8.5e-27], N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.52e-18

   1. Initial program 82.8%

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

      1. *-commutative 82.8%

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

   3. Simplified 82.8%

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

      1. clear-num 82.8%

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

      2. associate-/r/ 82.8%

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

      3. fma-neg 82.8%

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

   6. Applied egg-rr 82.8%

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

   7. Taylor expanded in y around inf 79.6%

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

   8. Taylor expanded in x around inf 85.2%

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

   if -1.52e-18 < x < 8.50000000000000033e-27

   1. Initial program 93.5%

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

      1. *-commutative 93.5%

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

   3. Simplified 93.5%

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

      1. clear-num 93.4%

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

      2. associate-/r/ 93.5%

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

      3. fma-neg 93.5%

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

   6. Applied egg-rr 93.5%

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

   7. Taylor expanded in y around inf 57.8%

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

      1. times-frac 61.5%

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

      2. +-commutative 61.5%

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

   9. Simplified 61.5%

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

   10. Taylor expanded in x around 0 61.5%

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

   if 8.50000000000000033e-27 < x

   1. Initial program 95.5%

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

      1. *-commutative 95.5%

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

   3. Simplified 95.5%

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

   5. Taylor expanded in t around inf 94.8%

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

      1. +-commutative 94.8%

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

   7. Simplified 94.8%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.52 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-56}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.00015:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.35e-56) 1.0 (if (<= x 0.00015) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.35e-56) {
		tmp = 1.0;
	} else if (x <= 0.00015) {
		tmp = (x + (y / t)) / (x + 1.0);
	} 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 <= (-2.35d-56)) then
        tmp = 1.0d0
    else if (x <= 0.00015d0) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    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 <= -2.35e-56) {
		tmp = 1.0;
	} else if (x <= 0.00015) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.35e-56:
		tmp = 1.0
	elif x <= 0.00015:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.35e-56)
		tmp = 1.0;
	elseif (x <= 0.00015)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.35e-56)
		tmp = 1.0;
	elseif (x <= 0.00015)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.35e-56], 1.0, If[LessEqual[x, 0.00015], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.35e-56 or 1.49999999999999987e-4 < x

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

      1. clear-num 88.0%

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

      2. associate-/r/ 87.9%

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

      3. fma-neg 87.9%

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

   6. Applied egg-rr 87.9%

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

   7. Taylor expanded in y around inf 82.5%

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

   8. Taylor expanded in x around inf 86.1%

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

   if -2.35e-56 < x < 1.49999999999999987e-4

   1. Initial program 95.4%

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

      1. *-commutative 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in z around inf 70.5%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.35 \cdot 10^{-56}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 0.00015:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 77.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-20}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 0.00088:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.35e-20)
   (/ (- x (/ y (/ x z))) (+ x 1.0))
   (if (<= x 0.00088) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.35e-20) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else if (x <= 0.00088) {
		tmp = (x + (y / t)) / (x + 1.0);
	} 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 <= (-1.35d-20)) then
        tmp = (x - (y / (x / z))) / (x + 1.0d0)
    else if (x <= 0.00088d0) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    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 <= -1.35e-20) {
		tmp = (x - (y / (x / z))) / (x + 1.0);
	} else if (x <= 0.00088) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.35e-20:
		tmp = (x - (y / (x / z))) / (x + 1.0)
	elif x <= 0.00088:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.35e-20)
		tmp = Float64(Float64(x - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	elseif (x <= 0.00088)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.35e-20)
		tmp = (x - (y / (x / z))) / (x + 1.0);
	elseif (x <= 0.00088)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.35e-20], N[(N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.00088], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -1.35e-20

   1. Initial program 83.3%

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

      1. *-commutative 83.3%

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

   3. Simplified 83.3%

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

      1. clear-num 83.3%

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

      2. associate-/r/ 83.3%

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

      3. fma-neg 83.3%

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

   6. Applied egg-rr 83.3%

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

   7. Taylor expanded in y around inf 80.2%

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

   8. Taylor expanded in t around 0 77.4%

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

      1. mul-1-neg 77.4%

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

      2. unsub-neg 77.4%

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

      3. associate-/l* 86.4%

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

      4. +-commutative 86.4%

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

   10. Simplified 86.4%

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

   if -1.35e-20 < x < 8.80000000000000031e-4

   1. Initial program 93.5%

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

      1. *-commutative 93.5%

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

   3. Simplified 93.5%

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

   5. Taylor expanded in z around inf 67.9%

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

   if 8.80000000000000031e-4 < x

   1. Initial program 95.4%

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

      1. *-commutative 95.4%

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

   3. Simplified 95.4%

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

      1. clear-num 95.4%

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

      2. associate-/r/ 95.2%

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

      3. fma-neg 95.2%

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

   6. Applied egg-rr 95.2%

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

   7. Taylor expanded in y around inf 94.4%

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

   8. Taylor expanded in x around inf 95.2%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-20}:\\ \;\;\;\;\frac{x - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;x \leq 0.00088:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-23} \lor \neg \left(t \leq 0.038\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.5e-23) (not (<= t 0.038))) (/ x (+ x 1.0)) 1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.5e-23) || !(t <= 0.038)) {
		tmp = x / (x + 1.0);
	} 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 ((t <= (-9.5d-23)) .or. (.not. (t <= 0.038d0))) then
        tmp = x / (x + 1.0d0)
    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 ((t <= -9.5e-23) || !(t <= 0.038)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9.5e-23) or not (t <= 0.038):
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9.5e-23) || !(t <= 0.038))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9.5e-23) || ~((t <= 0.038)))
		tmp = x / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9.5e-23], N[Not[LessEqual[t, 0.038]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if t < -9.50000000000000058e-23 or 0.0379999999999999991 < t

   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. Add Preprocessing

   5. Taylor expanded in t around inf 66.9%

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

      1. +-commutative 66.9%

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

   7. Simplified 66.9%

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

   if -9.50000000000000058e-23 < t < 0.0379999999999999991

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

   3. Simplified 94.2%

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

      1. clear-num 94.2%

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

      2. associate-/r/ 94.2%

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

      3. fma-neg 94.2%

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

   6. Applied egg-rr 94.2%

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

   7. Taylor expanded in y around inf 81.5%

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

   8. Taylor expanded in x around inf 53.6%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-23} \lor \neg \left(t \leq 0.038\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-25}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.7e-25)
   (/ 1.0 (/ (+ x 1.0) x))
   (if (<= t 9.5e-6) 1.0 (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e-25) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (t <= 9.5e-6) {
		tmp = 1.0;
	} else {
		tmp = x / (x + 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 (t <= (-1.7d-25)) then
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    else if (t <= 9.5d-6) then
        tmp = 1.0d0
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.7e-25) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (t <= 9.5e-6) {
		tmp = 1.0;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.7e-25:
		tmp = 1.0 / ((x + 1.0) / x)
	elif t <= 9.5e-6:
		tmp = 1.0
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.7e-25)
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	elseif (t <= 9.5e-6)
		tmp = 1.0;
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.7e-25)
		tmp = 1.0 / ((x + 1.0) / x);
	elseif (t <= 9.5e-6)
		tmp = 1.0;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.7e-25], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 9.5e-6], 1.0, N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.70000000000000001e-25

   1. Initial program 91.5%

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

      1. *-commutative 91.5%

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

   3. Simplified 91.5%

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

   5. Taylor expanded in t around inf 66.6%

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

      1. +-commutative 66.6%

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

   7. Simplified 66.6%

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

      1. clear-num 66.7%

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

      2. inv-pow 66.7%

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

   9. Applied egg-rr 66.7%

      \[\leadsto \color{blue}{{\left(\frac{x + 1}{x}\right)}^{-1}} \]
   10. Step-by-step derivation

       1. unpow-1 66.7%

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

   11. Simplified 66.7%

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

   if -1.70000000000000001e-25 < t < 9.5000000000000005e-6

   1. Initial program 94.2%

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

      1. *-commutative 94.2%

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

   3. Simplified 94.2%

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

      1. clear-num 94.2%

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

      2. associate-/r/ 94.2%

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

      3. fma-neg 94.2%

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

   6. Applied egg-rr 94.2%

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

   7. Taylor expanded in y around inf 81.5%

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

   8. Taylor expanded in x around inf 53.6%

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

   if 9.5000000000000005e-6 < t

   1. Initial program 85.6%

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

      1. *-commutative 85.6%

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

   3. Simplified 85.6%

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

   5. Taylor expanded in t around inf 67.2%

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

      1. +-commutative 67.2%

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

   7. Simplified 67.2%

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

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.7 \cdot 10^{-25}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;t \leq 9.5 \cdot 10^{-6}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 55.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-56}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2e-56) 1.0 (if (<= x 4.8e-5) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2e-56) {
		tmp = 1.0;
	} else if (x <= 4.8e-5) {
		tmp = x;
	} 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 <= (-2d-56)) then
        tmp = 1.0d0
    else if (x <= 4.8d-5) then
        tmp = x
    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 <= -2e-56) {
		tmp = 1.0;
	} else if (x <= 4.8e-5) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2e-56:
		tmp = 1.0
	elif x <= 4.8e-5:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2e-56)
		tmp = 1.0;
	elseif (x <= 4.8e-5)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2e-56)
		tmp = 1.0;
	elseif (x <= 4.8e-5)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2e-56], 1.0, If[LessEqual[x, 4.8e-5], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.0000000000000001e-56 or 4.8000000000000001e-5 < x

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

      1. clear-num 88.0%

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

      2. associate-/r/ 87.9%

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

      3. fma-neg 87.9%

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

   6. Applied egg-rr 87.9%

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

   7. Taylor expanded in y around inf 82.5%

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

   8. Taylor expanded in x around inf 86.1%

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

   if -2.0000000000000001e-56 < x < 4.8000000000000001e-5

   1. Initial program 95.4%

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

      1. *-commutative 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in t around inf 22.2%

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

      1. +-commutative 22.2%

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

   7. Simplified 22.2%

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

   8. Taylor expanded in x around 0 21.8%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{-56}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 52.9% 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 91.4%

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

   1. *-commutative 91.4%

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

3. Simplified 91.4%

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

   1. clear-num 91.4%

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

   2. associate-/r/ 91.4%

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

   3. fma-neg 91.4%

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

6. Applied egg-rr 91.4%

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

7. Taylor expanded in y around inf 80.5%

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

8. Taylor expanded in x around inf 52.2%

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

9. Final simplification 52.2%

   \[\leadsto 1 \]
10. Add Preprocessing

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 2024040 
(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)))