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

Percentage Accurate: 89.2% → 98.6%

Time: 10.3s

Alternatives: 13

Speedup: 0.5×

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: 89.2% 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: 98.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{t_1}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, \frac{z}{t_1}, x - \frac{x}{t_1}\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(y * N[(z / t$95$1), $MachinePrecision] + N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $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 (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < +inf.0

   1. Initial program 94.5%

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

      1. *-commutative 94.5%

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

   3. Simplified 94.5%

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

      1. +-commutative 94.5%

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

      2. div-sub 94.5%

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

      3. associate-+l- 94.5%

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

      4. *-un-lft-identity 94.5%

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

      5. times-frac 99.2%

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

      6. fma-neg 99.2%

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

   5. Applied egg-rr 99.2%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 99.3%

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

Alternative 2: 94.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t_1 \leq 5 \cdot 10^{+290}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 5e+290) t_1 (/ (+ x (/ y t)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 5e+290) {
		tmp = t_1;
	} 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) :: tmp
    t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    if (t_1 <= 5d+290) then
        tmp = t_1
    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 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 5e+290) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= 5e+290:
		tmp = t_1
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= 5e+290)
		tmp = t_1;
	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 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= 5e+290)
		tmp = t_1;
	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[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+290], t$95$1, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 4.9999999999999998e290

   1. Initial program 97.5%

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

   if 4.9999999999999998e290 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 33.2%

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

      1. *-commutative 33.2%

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

   3. Simplified 33.2%

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

   4. Taylor expanded in z around inf 97.2%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 5 \cdot 10^{+290}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 3: 78.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ t_2 := z \cdot t - x\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-173}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \mathbf{elif}\;t \leq 10^{-78}:\\ \;\;\;\;\frac{y \cdot z}{t_2 \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{x - \frac{x}{t_2}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))) (t_2 (- (* z t) x)))
   (if (<= t -5.8e+22)
     t_1
     (if (<= t 2.5e-173)
       (- 1.0 (* (/ y (+ x 1.0)) (/ z x)))
       (if (<= t 1e-78)
         (/ (* y z) (* t_2 (+ x 1.0)))
         (if (<= t 7.5e-34) (/ (- x (/ x t_2)) (+ x 1.0)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (z * t) - x;
	double tmp;
	if (t <= -5.8e+22) {
		tmp = t_1;
	} else if (t <= 2.5e-173) {
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	} else if (t <= 1e-78) {
		tmp = (y * z) / (t_2 * (x + 1.0));
	} else if (t <= 7.5e-34) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    t_2 = (z * t) - x
    if (t <= (-5.8d+22)) then
        tmp = t_1
    else if (t <= 2.5d-173) then
        tmp = 1.0d0 - ((y / (x + 1.0d0)) * (z / x))
    else if (t <= 1d-78) then
        tmp = (y * z) / (t_2 * (x + 1.0d0))
    else if (t <= 7.5d-34) then
        tmp = (x - (x / t_2)) / (x + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double t_2 = (z * t) - x;
	double tmp;
	if (t <= -5.8e+22) {
		tmp = t_1;
	} else if (t <= 2.5e-173) {
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	} else if (t <= 1e-78) {
		tmp = (y * z) / (t_2 * (x + 1.0));
	} else if (t <= 7.5e-34) {
		tmp = (x - (x / t_2)) / (x + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	t_2 = (z * t) - x
	tmp = 0
	if t <= -5.8e+22:
		tmp = t_1
	elif t <= 2.5e-173:
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x))
	elif t <= 1e-78:
		tmp = (y * z) / (t_2 * (x + 1.0))
	elif t <= 7.5e-34:
		tmp = (x - (x / t_2)) / (x + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	t_2 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (t <= -5.8e+22)
		tmp = t_1;
	elseif (t <= 2.5e-173)
		tmp = Float64(1.0 - Float64(Float64(y / Float64(x + 1.0)) * Float64(z / x)));
	elseif (t <= 1e-78)
		tmp = Float64(Float64(y * z) / Float64(t_2 * Float64(x + 1.0)));
	elseif (t <= 7.5e-34)
		tmp = Float64(Float64(x - Float64(x / t_2)) / Float64(x + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	t_2 = (z * t) - x;
	tmp = 0.0;
	if (t <= -5.8e+22)
		tmp = t_1;
	elseif (t <= 2.5e-173)
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	elseif (t <= 1e-78)
		tmp = (y * z) / (t_2 * (x + 1.0));
	elseif (t <= 7.5e-34)
		tmp = (x - (x / t_2)) / (x + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[t, -5.8e+22], t$95$1, If[LessEqual[t, 2.5e-173], N[(1.0 - N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-78], N[(N[(y * z), $MachinePrecision] / N[(t$95$2 * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.5e-34], N[(N[(x - N[(x / t$95$2), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -5.8e22 or 7.5000000000000004e-34 < t

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in z around inf 93.8%

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

   if -5.8e22 < t < 2.5000000000000001e-173

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in t around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. unsub-neg 79.9%

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

      4. associate-/l* 83.9%

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

      5. +-commutative 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in y around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

      3. times-frac 84.0%

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

      4. +-commutative 84.0%

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

   9. Simplified 84.0%

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

   if 2.5000000000000001e-173 < t < 9.99999999999999999e-79

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 79.7%

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

      1. *-commutative 79.7%

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

      2. *-commutative 79.7%

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

      3. +-commutative 79.7%

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

   6. Simplified 79.7%

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

   if 9.99999999999999999e-79 < t < 7.5000000000000004e-34

   1. Initial program 93.2%

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

      1. *-commutative 93.2%

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

   3. Simplified 93.2%

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

   4. Taylor expanded in y around 0 93.0%

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

      1. +-commutative 93.0%

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

   6. Simplified 93.0%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.8 \cdot 10^{+22}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-173}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \mathbf{elif}\;t \leq 10^{-78}:\\ \;\;\;\;\frac{y \cdot z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 4: 78.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -6.1 \cdot 10^{+22}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-173}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \mathbf{elif}\;t \leq 10^{-78}:\\ \;\;\;\;\frac{y \cdot z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-60}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -6.1e+22)
     t_1
     (if (<= t 2.5e-173)
       (- 1.0 (* (/ y (+ x 1.0)) (/ z x)))
       (if (<= t 1e-78)
         (/ (* y z) (* (- (* z t) x) (+ x 1.0)))
         (if (<= t 3.2e-60) 1.0 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -6.1e+22) {
		tmp = t_1;
	} else if (t <= 2.5e-173) {
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	} else if (t <= 1e-78) {
		tmp = (y * z) / (((z * t) - x) * (x + 1.0));
	} else if (t <= 3.2e-60) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-6.1d+22)) then
        tmp = t_1
    else if (t <= 2.5d-173) then
        tmp = 1.0d0 - ((y / (x + 1.0d0)) * (z / x))
    else if (t <= 1d-78) then
        tmp = (y * z) / (((z * t) - x) * (x + 1.0d0))
    else if (t <= 3.2d-60) then
        tmp = 1.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -6.1e+22) {
		tmp = t_1;
	} else if (t <= 2.5e-173) {
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	} else if (t <= 1e-78) {
		tmp = (y * z) / (((z * t) - x) * (x + 1.0));
	} else if (t <= 3.2e-60) {
		tmp = 1.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -6.1e+22:
		tmp = t_1
	elif t <= 2.5e-173:
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x))
	elif t <= 1e-78:
		tmp = (y * z) / (((z * t) - x) * (x + 1.0))
	elif t <= 3.2e-60:
		tmp = 1.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -6.1e+22)
		tmp = t_1;
	elseif (t <= 2.5e-173)
		tmp = Float64(1.0 - Float64(Float64(y / Float64(x + 1.0)) * Float64(z / x)));
	elseif (t <= 1e-78)
		tmp = Float64(Float64(y * z) / Float64(Float64(Float64(z * t) - x) * Float64(x + 1.0)));
	elseif (t <= 3.2e-60)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -6.1e+22)
		tmp = t_1;
	elseif (t <= 2.5e-173)
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	elseif (t <= 1e-78)
		tmp = (y * z) / (((z * t) - x) * (x + 1.0));
	elseif (t <= 3.2e-60)
		tmp = 1.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.1e+22], t$95$1, If[LessEqual[t, 2.5e-173], N[(1.0 - N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-78], N[(N[(y * z), $MachinePrecision] / N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.2e-60], 1.0, t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -6.0999999999999998e22 or 3.2000000000000001e-60 < t

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around inf 92.9%

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

   if -6.0999999999999998e22 < t < 2.5000000000000001e-173

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in t around 0 79.9%

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

      1. +-commutative 79.9%

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

      2. mul-1-neg 79.9%

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

      3. unsub-neg 79.9%

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

      4. associate-/l* 83.9%

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

      5. +-commutative 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in y around 0 79.8%

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

      1. mul-1-neg 79.8%

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

      2. unsub-neg 79.8%

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

      3. times-frac 84.0%

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

      4. +-commutative 84.0%

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

   9. Simplified 84.0%

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

   if 2.5000000000000001e-173 < t < 9.99999999999999999e-79

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 79.7%

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

      1. *-commutative 79.7%

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

      2. *-commutative 79.7%

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

      3. +-commutative 79.7%

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

   6. Simplified 79.7%

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

   if 9.99999999999999999e-79 < t < 3.2000000000000001e-60

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in t around inf 27.6%

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

      1. +-commutative 27.6%

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

   6. Simplified 27.6%

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

   7. Taylor expanded in x around inf 75.5%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.1 \cdot 10^{+22}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-173}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \mathbf{elif}\;t \leq 10^{-78}:\\ \;\;\;\;\frac{y \cdot z}{\left(z \cdot t - x\right) \cdot \left(x + 1\right)}\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{-60}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 5: 68.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 + \frac{-1}{\frac{x}{y \cdot z}}\\ \mathbf{if}\;x \leq -0.98:\\ \;\;\;\;1 - z \cdot \frac{\frac{y}{x}}{x}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-136}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-53}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ 1.0 (/ -1.0 (/ x (* y z))))))
   (if (<= x -0.98)
     (- 1.0 (* z (/ (/ y x) x)))
     (if (<= x -2.3e-151)
       t_1
       (if (<= x 3.1e-136)
         (/ y t)
         (if (<= x 4e-76) t_1 (if (<= x 5e-53) (/ y t) 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (-1.0 / (x / (y * z)));
	double tmp;
	if (x <= -0.98) {
		tmp = 1.0 - (z * ((y / x) / x));
	} else if (x <= -2.3e-151) {
		tmp = t_1;
	} else if (x <= 3.1e-136) {
		tmp = y / t;
	} else if (x <= 4e-76) {
		tmp = t_1;
	} else if (x <= 5e-53) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 + ((-1.0d0) / (x / (y * z)))
    if (x <= (-0.98d0)) then
        tmp = 1.0d0 - (z * ((y / x) / x))
    else if (x <= (-2.3d-151)) then
        tmp = t_1
    else if (x <= 3.1d-136) then
        tmp = y / t
    else if (x <= 4d-76) then
        tmp = t_1
    else if (x <= 5d-53) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 + (-1.0 / (x / (y * z)));
	double tmp;
	if (x <= -0.98) {
		tmp = 1.0 - (z * ((y / x) / x));
	} else if (x <= -2.3e-151) {
		tmp = t_1;
	} else if (x <= 3.1e-136) {
		tmp = y / t;
	} else if (x <= 4e-76) {
		tmp = t_1;
	} else if (x <= 5e-53) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 + (-1.0 / (x / (y * z)))
	tmp = 0
	if x <= -0.98:
		tmp = 1.0 - (z * ((y / x) / x))
	elif x <= -2.3e-151:
		tmp = t_1
	elif x <= 3.1e-136:
		tmp = y / t
	elif x <= 4e-76:
		tmp = t_1
	elif x <= 5e-53:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 + Float64(-1.0 / Float64(x / Float64(y * z))))
	tmp = 0.0
	if (x <= -0.98)
		tmp = Float64(1.0 - Float64(z * Float64(Float64(y / x) / x)));
	elseif (x <= -2.3e-151)
		tmp = t_1;
	elseif (x <= 3.1e-136)
		tmp = Float64(y / t);
	elseif (x <= 4e-76)
		tmp = t_1;
	elseif (x <= 5e-53)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 + (-1.0 / (x / (y * z)));
	tmp = 0.0;
	if (x <= -0.98)
		tmp = 1.0 - (z * ((y / x) / x));
	elseif (x <= -2.3e-151)
		tmp = t_1;
	elseif (x <= 3.1e-136)
		tmp = y / t;
	elseif (x <= 4e-76)
		tmp = t_1;
	elseif (x <= 5e-53)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 + N[(-1.0 / N[(x / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.98], N[(1.0 - N[(z * N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.3e-151], t$95$1, If[LessEqual[x, 3.1e-136], N[(y / t), $MachinePrecision], If[LessEqual[x, 4e-76], t$95$1, If[LessEqual[x, 5e-53], N[(y / t), $MachinePrecision], 1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.97999999999999998

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in t around 0 92.9%

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

      1. +-commutative 92.9%

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

      2. mul-1-neg 92.9%

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

      3. unsub-neg 92.9%

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

      4. associate-/l* 97.1%

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

      5. +-commutative 97.1%

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

   6. Simplified 97.1%

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

   7. Taylor expanded in y around 0 92.8%

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

      1. mul-1-neg 92.8%

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

      2. unsub-neg 92.8%

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

      3. times-frac 97.1%

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

      4. +-commutative 97.1%

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

   9. Simplified 97.1%

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

   10. Taylor expanded in x around inf 92.8%

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

       1. unpow2 92.8%

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

       2. *-commutative 92.8%

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

       3. associate-*r/ 95.7%

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

       4. associate-/r* 97.1%

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

   12. Simplified 97.1%

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

   if -0.97999999999999998 < x < -2.29999999999999996e-151 or 3.1e-136 < x < 3.99999999999999971e-76

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in t around 0 59.8%

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

      1. +-commutative 59.8%

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

      2. mul-1-neg 59.8%

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

      3. unsub-neg 59.8%

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

      4. associate-/l* 59.7%

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

      5. +-commutative 59.7%

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

   6. Simplified 59.7%

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

   7. Taylor expanded in y around 0 59.8%

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

      1. mul-1-neg 59.8%

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

      2. unsub-neg 59.8%

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

      3. times-frac 59.8%

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

      4. +-commutative 59.8%

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

   9. Simplified 59.8%

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

   10. Taylor expanded in x around 0 58.3%

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

       1. clear-num 58.4%

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

       2. inv-pow 58.4%

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

   12. Applied egg-rr 58.4%

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

       1. unpow-1 58.4%

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

   14. Simplified 58.4%

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

   if -2.29999999999999996e-151 < x < 3.1e-136 or 3.99999999999999971e-76 < x < 5e-53

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in z around inf 78.4%

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

      1. div-inv 78.4%

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

      2. +-commutative 78.4%

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

   6. Applied egg-rr 78.4%

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

   7. Taylor expanded in x around 0 58.8%

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

   if 5e-53 < x

   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. Taylor expanded in t around inf 82.1%

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

      1. +-commutative 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in x around inf 84.7%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.98:\\ \;\;\;\;1 - z \cdot \frac{\frac{y}{x}}{x}\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-151}:\\ \;\;\;\;1 + \frac{-1}{\frac{x}{y \cdot z}}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-136}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-76}:\\ \;\;\;\;1 + \frac{-1}{\frac{x}{y \cdot z}}\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-53}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 68.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 1 - \frac{y \cdot z}{x}\\ \mathbf{if}\;x \leq -0.36:\\ \;\;\;\;1 - z \cdot \frac{\frac{y}{x}}{x}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-151}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-136}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- 1.0 (/ (* y z) x))))
   (if (<= x -0.36)
     (- 1.0 (* z (/ (/ y x) x)))
     (if (<= x -3.2e-151)
       t_1
       (if (<= x 2.9e-136)
         (/ y t)
         (if (<= x 3.8e-76) t_1 (if (<= x 2.2e-53) (/ y t) 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - ((y * z) / x);
	double tmp;
	if (x <= -0.36) {
		tmp = 1.0 - (z * ((y / x) / x));
	} else if (x <= -3.2e-151) {
		tmp = t_1;
	} else if (x <= 2.9e-136) {
		tmp = y / t;
	} else if (x <= 3.8e-76) {
		tmp = t_1;
	} else if (x <= 2.2e-53) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 1.0d0 - ((y * z) / x)
    if (x <= (-0.36d0)) then
        tmp = 1.0d0 - (z * ((y / x) / x))
    else if (x <= (-3.2d-151)) then
        tmp = t_1
    else if (x <= 2.9d-136) then
        tmp = y / t
    else if (x <= 3.8d-76) then
        tmp = t_1
    else if (x <= 2.2d-53) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 1.0 - ((y * z) / x);
	double tmp;
	if (x <= -0.36) {
		tmp = 1.0 - (z * ((y / x) / x));
	} else if (x <= -3.2e-151) {
		tmp = t_1;
	} else if (x <= 2.9e-136) {
		tmp = y / t;
	} else if (x <= 3.8e-76) {
		tmp = t_1;
	} else if (x <= 2.2e-53) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 1.0 - ((y * z) / x)
	tmp = 0
	if x <= -0.36:
		tmp = 1.0 - (z * ((y / x) / x))
	elif x <= -3.2e-151:
		tmp = t_1
	elif x <= 2.9e-136:
		tmp = y / t
	elif x <= 3.8e-76:
		tmp = t_1
	elif x <= 2.2e-53:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(1.0 - Float64(Float64(y * z) / x))
	tmp = 0.0
	if (x <= -0.36)
		tmp = Float64(1.0 - Float64(z * Float64(Float64(y / x) / x)));
	elseif (x <= -3.2e-151)
		tmp = t_1;
	elseif (x <= 2.9e-136)
		tmp = Float64(y / t);
	elseif (x <= 3.8e-76)
		tmp = t_1;
	elseif (x <= 2.2e-53)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 1.0 - ((y * z) / x);
	tmp = 0.0;
	if (x <= -0.36)
		tmp = 1.0 - (z * ((y / x) / x));
	elseif (x <= -3.2e-151)
		tmp = t_1;
	elseif (x <= 2.9e-136)
		tmp = y / t;
	elseif (x <= 3.8e-76)
		tmp = t_1;
	elseif (x <= 2.2e-53)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(1.0 - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -0.36], N[(1.0 - N[(z * N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3.2e-151], t$95$1, If[LessEqual[x, 2.9e-136], N[(y / t), $MachinePrecision], If[LessEqual[x, 3.8e-76], t$95$1, If[LessEqual[x, 2.2e-53], N[(y / t), $MachinePrecision], 1.0]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -0.35999999999999999

   1. Initial program 95.8%

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

      1. *-commutative 95.8%

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

   3. Simplified 95.8%

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

   4. Taylor expanded in t around 0 92.9%

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

      1. +-commutative 92.9%

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

      2. mul-1-neg 92.9%

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

      3. unsub-neg 92.9%

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

      4. associate-/l* 97.1%

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

      5. +-commutative 97.1%

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

   6. Simplified 97.1%

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

   7. Taylor expanded in y around 0 92.8%

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

      1. mul-1-neg 92.8%

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

      2. unsub-neg 92.8%

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

      3. times-frac 97.1%

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

      4. +-commutative 97.1%

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

   9. Simplified 97.1%

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

   10. Taylor expanded in x around inf 92.8%

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

       1. unpow2 92.8%

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

       2. *-commutative 92.8%

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

       3. associate-*r/ 95.7%

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

       4. associate-/r* 97.1%

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

   12. Simplified 97.1%

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

   if -0.35999999999999999 < x < -3.20000000000000021e-151 or 2.89999999999999995e-136 < x < 3.8000000000000002e-76

   1. Initial program 88.7%

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

      1. *-commutative 88.7%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in t around 0 59.8%

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

      1. +-commutative 59.8%

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

      2. mul-1-neg 59.8%

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

      3. unsub-neg 59.8%

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

      4. associate-/l* 59.7%

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

      5. +-commutative 59.7%

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

   6. Simplified 59.7%

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

   7. Taylor expanded in y around 0 59.8%

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

      1. mul-1-neg 59.8%

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

      2. unsub-neg 59.8%

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

      3. times-frac 59.8%

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

      4. +-commutative 59.8%

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

   9. Simplified 59.8%

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

   10. Taylor expanded in x around 0 58.3%

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

   if -3.20000000000000021e-151 < x < 2.89999999999999995e-136 or 3.8000000000000002e-76 < x < 2.20000000000000018e-53

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in z around inf 78.4%

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

      1. div-inv 78.4%

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

      2. +-commutative 78.4%

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

   6. Applied egg-rr 78.4%

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

   7. Taylor expanded in x around 0 58.8%

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

   if 2.20000000000000018e-53 < x

   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. Taylor expanded in t around inf 82.1%

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

      1. +-commutative 82.1%

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

   6. Simplified 82.1%

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

   7. Taylor expanded in x around inf 84.7%

      \[\leadsto \color{blue}{1} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.36:\\ \;\;\;\;1 - z \cdot \frac{\frac{y}{x}}{x}\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-151}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-136}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-76}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-53}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 76.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -4.8 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-77}:\\ \;\;\;\;1 - z \cdot \frac{\frac{y}{x}}{x}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-173}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -4.8e-14)
     t_1
     (if (<= t -1.9e-77)
       (- 1.0 (* z (/ (/ y x) x)))
       (if (<= t 2.5e-173) (- 1.0 (/ (* y z) x)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -4.8e-14) {
		tmp = t_1;
	} else if (t <= -1.9e-77) {
		tmp = 1.0 - (z * ((y / x) / x));
	} else if (t <= 2.5e-173) {
		tmp = 1.0 - ((y * z) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-4.8d-14)) then
        tmp = t_1
    else if (t <= (-1.9d-77)) then
        tmp = 1.0d0 - (z * ((y / x) / x))
    else if (t <= 2.5d-173) then
        tmp = 1.0d0 - ((y * z) / x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -4.8e-14) {
		tmp = t_1;
	} else if (t <= -1.9e-77) {
		tmp = 1.0 - (z * ((y / x) / x));
	} else if (t <= 2.5e-173) {
		tmp = 1.0 - ((y * z) / x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -4.8e-14:
		tmp = t_1
	elif t <= -1.9e-77:
		tmp = 1.0 - (z * ((y / x) / x))
	elif t <= 2.5e-173:
		tmp = 1.0 - ((y * z) / x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0))
	tmp = 0.0
	if (t <= -4.8e-14)
		tmp = t_1;
	elseif (t <= -1.9e-77)
		tmp = Float64(1.0 - Float64(z * Float64(Float64(y / x) / x)));
	elseif (t <= 2.5e-173)
		tmp = Float64(1.0 - Float64(Float64(y * z) / x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -4.8e-14)
		tmp = t_1;
	elseif (t <= -1.9e-77)
		tmp = 1.0 - (z * ((y / x) / x));
	elseif (t <= 2.5e-173)
		tmp = 1.0 - ((y * z) / x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.8e-14], t$95$1, If[LessEqual[t, -1.9e-77], N[(1.0 - N[(z * N[(N[(y / x), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2.5e-173], N[(1.0 - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.8e-14 or 2.5000000000000001e-173 < t

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around inf 86.8%

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

   if -4.8e-14 < t < -1.8999999999999999e-77

   1. Initial program 78.3%

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

      1. *-commutative 78.3%

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

   3. Simplified 78.3%

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

   4. Taylor expanded in t around 0 72.9%

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

      1. +-commutative 72.9%

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

      2. mul-1-neg 72.9%

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

      3. unsub-neg 72.9%

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

      4. associate-/l* 89.0%

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

      5. +-commutative 89.0%

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

   6. Simplified 89.0%

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

   7. Taylor expanded in y around 0 72.5%

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

      1. mul-1-neg 72.5%

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

      2. unsub-neg 72.5%

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

      3. times-frac 89.1%

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

      4. +-commutative 89.1%

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

   9. Simplified 89.1%

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

   10. Taylor expanded in x around inf 55.8%

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

       1. unpow2 55.8%

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

       2. *-commutative 55.8%

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

       3. associate-*r/ 67.6%

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

       4. associate-/r* 78.1%

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

   12. Simplified 78.1%

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

   if -1.8999999999999999e-77 < t < 2.5000000000000001e-173

   1. Initial program 98.5%

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

      1. *-commutative 98.5%

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

   3. Simplified 98.5%

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

   4. Taylor expanded in t around 0 84.6%

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

      1. +-commutative 84.6%

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

      2. mul-1-neg 84.6%

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

      3. unsub-neg 84.6%

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

      4. associate-/l* 84.7%

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

      5. +-commutative 84.7%

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

   6. Simplified 84.7%

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

   7. Taylor expanded in y around 0 84.6%

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

      1. mul-1-neg 84.6%

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

      2. unsub-neg 84.6%

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

      3. times-frac 84.7%

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

      4. +-commutative 84.7%

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

   9. Simplified 84.7%

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

   10. Taylor expanded in x around 0 77.5%

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

4. Final simplification 83.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-77}:\\ \;\;\;\;1 - z \cdot \frac{\frac{y}{x}}{x}\\ \mathbf{elif}\;t \leq 2.5 \cdot 10^{-173}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 8: 81.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+24} \lor \neg \left(t \leq 1.08 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.2e+24) (not (<= t 1.08e-60)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (* (/ y (+ x 1.0)) (/ z x)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.2e+24) || !(t <= 1.08e-60)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.2d+24)) .or. (.not. (t <= 1.08d-60))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y / (x + 1.0d0)) * (z / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.2e+24) || !(t <= 1.08e-60)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.2e+24) or not (t <= 1.08e-60):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.2e+24) || !(t <= 1.08e-60))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y / Float64(x + 1.0)) * Float64(z / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.2e+24) || ~((t <= 1.08e-60)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((y / (x + 1.0)) * (z / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.2e+24], N[Not[LessEqual[t, 1.08e-60]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.2e24 or 1.07999999999999997e-60 < t

   1. Initial program 88.1%

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

      1. *-commutative 88.1%

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

   3. Simplified 88.1%

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

   4. Taylor expanded in z around inf 92.9%

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

   if -1.2e24 < t < 1.07999999999999997e-60

   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. Taylor expanded in t around 0 75.6%

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

      1. +-commutative 75.6%

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

      2. mul-1-neg 75.6%

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

      3. unsub-neg 75.6%

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

      4. associate-/l* 79.0%

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

      5. +-commutative 79.0%

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

   6. Simplified 79.0%

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

   7. Taylor expanded in y around 0 75.5%

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

      1. mul-1-neg 75.5%

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

      2. unsub-neg 75.5%

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

      3. times-frac 79.0%

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

      4. +-commutative 79.0%

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

   9. Simplified 79.0%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.2 \cdot 10^{+24} \lor \neg \left(t \leq 1.08 \cdot 10^{-60}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y}{x + 1} \cdot \frac{z}{x}\\ \end{array} \]

Alternative 9: 65.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \frac{-y}{x}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{-137}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.32e-5)
   1.0
   (if (<= x -2.8e-61)
     (* z (/ (- y) x))
     (if (<= x -7e-151) 1.0 (if (<= x 1e-137) (/ y t) (/ x (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.32e-5) {
		tmp = 1.0;
	} else if (x <= -2.8e-61) {
		tmp = z * (-y / x);
	} else if (x <= -7e-151) {
		tmp = 1.0;
	} else if (x <= 1e-137) {
		tmp = y / t;
	} 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 <= (-1.32d-5)) then
        tmp = 1.0d0
    else if (x <= (-2.8d-61)) then
        tmp = z * (-y / x)
    else if (x <= (-7d-151)) then
        tmp = 1.0d0
    else if (x <= 1d-137) then
        tmp = y / t
    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 <= -1.32e-5) {
		tmp = 1.0;
	} else if (x <= -2.8e-61) {
		tmp = z * (-y / x);
	} else if (x <= -7e-151) {
		tmp = 1.0;
	} else if (x <= 1e-137) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.32e-5:
		tmp = 1.0
	elif x <= -2.8e-61:
		tmp = z * (-y / x)
	elif x <= -7e-151:
		tmp = 1.0
	elif x <= 1e-137:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.32e-5)
		tmp = 1.0;
	elseif (x <= -2.8e-61)
		tmp = Float64(z * Float64(Float64(-y) / x));
	elseif (x <= -7e-151)
		tmp = 1.0;
	elseif (x <= 1e-137)
		tmp = Float64(y / t);
	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 <= -1.32e-5)
		tmp = 1.0;
	elseif (x <= -2.8e-61)
		tmp = z * (-y / x);
	elseif (x <= -7e-151)
		tmp = 1.0;
	elseif (x <= 1e-137)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.32e-5], 1.0, If[LessEqual[x, -2.8e-61], N[(z * N[((-y) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7e-151], 1.0, If[LessEqual[x, 1e-137], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.32000000000000007e-5 or -2.8000000000000001e-61 < x < -6.99999999999999991e-151

   1. Initial program 96.5%

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

      1. *-commutative 96.5%

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

   3. Simplified 96.5%

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

   4. Taylor expanded in t around inf 79.6%

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

      1. +-commutative 79.6%

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

   6. Simplified 79.6%

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

   7. Taylor expanded in x around inf 83.4%

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

   if -1.32000000000000007e-5 < x < -2.8000000000000001e-61

   1. Initial program 77.6%

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

      1. *-commutative 77.6%

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

   3. Simplified 77.6%

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

   4. Taylor expanded in y around inf 55.7%

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

      1. times-frac 68.8%

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

      2. +-commutative 68.8%

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

   6. Simplified 68.8%

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

   7. Taylor expanded in t around 0 50.8%

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

      1. mul-1-neg 50.8%

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

      2. times-frac 50.7%

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

      3. distribute-rgt-neg-in 50.7%

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

      4. +-commutative 50.7%

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

      5. distribute-frac-neg 50.7%

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

   9. Simplified 50.7%

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

   10. Taylor expanded in x around 0 47.9%

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

       1. mul-1-neg 47.9%

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

       2. associate-*l/ 48.0%

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

   12. Simplified 48.0%

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

   if -6.99999999999999991e-151 < x < 9.99999999999999978e-138

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around inf 75.9%

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

      1. div-inv 75.9%

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

      2. +-commutative 75.9%

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

   6. Applied egg-rr 75.9%

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

   7. Taylor expanded in x around 0 60.3%

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

   if 9.99999999999999978e-138 < x

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in t around inf 73.4%

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

      1. +-commutative 73.4%

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

   6. Simplified 73.4%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.32 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{-61}:\\ \;\;\;\;z \cdot \frac{-y}{x}\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 10^{-137}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 10: 64.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-77} \lor \neg \left(t \leq 2.6 \cdot 10^{-59}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.2e-77) (not (<= t 2.6e-59)))
   (/ x (+ x 1.0))
   (- 1.0 (/ (* y z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.2e-77) || !(t <= 2.6e-59)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0 - ((y * z) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.2d-77)) .or. (.not. (t <= 2.6d-59))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y * z) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.2e-77) || !(t <= 2.6e-59)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = 1.0 - ((y * z) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.2e-77) or not (t <= 2.6e-59):
		tmp = x / (x + 1.0)
	else:
		tmp = 1.0 - ((y * z) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.2e-77) || !(t <= 2.6e-59))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y * z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.2e-77) || ~((t <= 2.6e-59)))
		tmp = x / (x + 1.0);
	else
		tmp = 1.0 - ((y * z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.2e-77], N[Not[LessEqual[t, 2.6e-59]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.20000000000000007e-77 or 2.59999999999999998e-59 < t

   1. Initial program 86.9%

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

      1. *-commutative 86.9%

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

   3. Simplified 86.9%

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

   4. Taylor expanded in t around inf 68.3%

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

      1. +-commutative 68.3%

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

   6. Simplified 68.3%

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

   if -2.20000000000000007e-77 < t < 2.59999999999999998e-59

   1. Initial program 98.7%

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

      1. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in t around 0 78.2%

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

      1. +-commutative 78.2%

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

      2. mul-1-neg 78.2%

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

      3. unsub-neg 78.2%

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

      4. associate-/l* 78.3%

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

      5. +-commutative 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in y around 0 78.2%

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

      1. mul-1-neg 78.2%

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

      2. unsub-neg 78.2%

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

      3. times-frac 78.3%

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

      4. +-commutative 78.3%

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

   9. Simplified 78.3%

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

   10. Taylor expanded in x around 0 71.6%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.2 \cdot 10^{-77} \lor \neg \left(t \leq 2.6 \cdot 10^{-59}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \end{array} \]

Alternative 11: 66.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-141}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7e-151) 1.0 (if (<= x 3.4e-141) (/ y t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7e-151) {
		tmp = 1.0;
	} else if (x <= 3.4e-141) {
		tmp = y / t;
	} 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 <= (-7d-151)) then
        tmp = 1.0d0
    else if (x <= 3.4d-141) then
        tmp = y / t
    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 <= -7e-151) {
		tmp = 1.0;
	} else if (x <= 3.4e-141) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7e-151:
		tmp = 1.0
	elif x <= 3.4e-141:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7e-151)
		tmp = 1.0;
	elseif (x <= 3.4e-141)
		tmp = Float64(y / t);
	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 <= -7e-151)
		tmp = 1.0;
	elseif (x <= 3.4e-141)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7e-151], 1.0, If[LessEqual[x, 3.4e-141], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.99999999999999991e-151

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   4. Taylor expanded in t around inf 66.7%

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

      1. +-commutative 66.7%

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

   6. Simplified 66.7%

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

   7. Taylor expanded in x around inf 69.0%

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

   if -6.99999999999999991e-151 < x < 3.3999999999999998e-141

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

   3. Simplified 89.3%

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

   4. Taylor expanded in z around inf 75.9%

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

      1. div-inv 75.9%

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

      2. +-commutative 75.9%

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

   6. Applied egg-rr 75.9%

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

   7. Taylor expanded in x around 0 60.3%

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

   if 3.3999999999999998e-141 < x

   1. Initial program 91.0%

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

      1. *-commutative 91.0%

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

   3. Simplified 91.0%

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

   4. Taylor expanded in t around inf 73.4%

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

      1. +-commutative 73.4%

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

   6. Simplified 73.4%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{-141}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 12: 66.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-52}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.5e-151) 1.0 (if (<= x 2.8e-52) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e-151) {
		tmp = 1.0;
	} else if (x <= 2.8e-52) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.5d-151)) then
        tmp = 1.0d0
    else if (x <= 2.8d-52) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.5e-151) {
		tmp = 1.0;
	} else if (x <= 2.8e-52) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.5e-151:
		tmp = 1.0
	elif x <= 2.8e-52:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.5e-151)
		tmp = 1.0;
	elseif (x <= 2.8e-52)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.5e-151)
		tmp = 1.0;
	elseif (x <= 2.8e-52)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.5e-151], 1.0, If[LessEqual[x, 2.8e-52], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -4.5000000000000002e-151 or 2.79999999999999995e-52 < x

   1. Initial program 91.2%

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

      1. *-commutative 91.2%

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

   3. Simplified 91.2%

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

   4. Taylor expanded in t around inf 72.1%

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

      1. +-commutative 72.1%

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

   6. Simplified 72.1%

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

   7. Taylor expanded in x around inf 74.6%

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

   if -4.5000000000000002e-151 < x < 2.79999999999999995e-52

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in z around inf 74.7%

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

      1. div-inv 74.7%

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

      2. +-commutative 74.7%

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

   6. Applied egg-rr 74.7%

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

   7. Taylor expanded in x around 0 54.5%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{-151}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-52}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 52.8% 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 91.2%

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

   1. *-commutative 91.2%

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

3. Simplified 91.2%

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

4. Taylor expanded in t around inf 55.1%

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

   1. +-commutative 55.1%

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

6. Simplified 55.1%

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

7. Taylor expanded in x around inf 52.9%

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

8. Final simplification 52.9%

   \[\leadsto 1 \]

Developer target: 99.4% 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 2023229 
(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)))