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

Percentage Accurate: 89.3% → 96.0%

Time: 11.6s

Alternatives: 13

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: 96.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{t_1} \cdot \frac{z}{x + 1}\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+176}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

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 (- INFINITY))
     (* (/ y t_1) (/ z (+ x 1.0)))
     (if (<= t_2 2e+176) 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 <= -((double) INFINITY)) {
		tmp = (y / t_1) * (z / (x + 1.0));
	} else if (t_2 <= 2e+176) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = (y / t_1) * (z / (x + 1.0));
	} else if (t_2 <= 2e+176) {
		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 <= -math.inf:
		tmp = (y / t_1) * (z / (x + 1.0))
	elif t_2 <= 2e+176:
		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 <= Float64(-Inf))
		tmp = Float64(Float64(y / t_1) * Float64(z / Float64(x + 1.0)));
	elseif (t_2 <= 2e+176)
		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 <= -Inf)
		tmp = (y / t_1) * (z / (x + 1.0));
	elseif (t_2 <= 2e+176)
		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, (-Infinity)], N[(N[(y / t$95$1), $MachinePrecision] * N[(z / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 2e+176], 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)) < -inf.0

   1. Initial program 45.3%

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

      1. *-commutative 45.3%

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

   3. Simplified 45.3%

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

   4. Taylor expanded in y around inf 44.5%

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

      1. *-commutative 44.5%

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

      2. *-commutative 44.5%

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

      3. times-frac 98.6%

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

      4. *-commutative 98.6%

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

      5. +-commutative 98.6%

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

   6. Simplified 98.6%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 2e176

   1. Initial program 99.1%

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

   if 2e176 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 28.2%

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

      1. *-commutative 28.2%

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

   3. Simplified 28.2%

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

   4. Taylor expanded in z around inf 87.3%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{y}{z \cdot t - x} \cdot \frac{z}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+176}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 2: 80.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{t}\\ \mathbf{if}\;t \leq -1.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{t_1}{x + 1}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-80}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+17} \lor \neg \left(t \leq 2.7 \cdot 10^{+106}\right):\\ \;\;\;\;\frac{t_1 - \frac{x}{z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ y t))))
   (if (<= t -1.4e-120)
     (/ t_1 (+ x 1.0))
     (if (<= t 4.8e-80)
       (/ (+ 1.0 (- x (/ y (/ x z)))) (+ x 1.0))
       (if (or (<= t 2.2e+17) (not (<= t 2.7e+106)))
         (/ (- t_1 (/ 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 t_1 = x + (y / t);
	double tmp;
	if (t <= -1.4e-120) {
		tmp = t_1 / (x + 1.0);
	} else if (t <= 4.8e-80) {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	} else if ((t <= 2.2e+17) || !(t <= 2.7e+106)) {
		tmp = (t_1 - (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) :: t_1
    real(8) :: tmp
    t_1 = x + (y / t)
    if (t <= (-1.4d-120)) then
        tmp = t_1 / (x + 1.0d0)
    else if (t <= 4.8d-80) then
        tmp = (1.0d0 + (x - (y / (x / z)))) / (x + 1.0d0)
    else if ((t <= 2.2d+17) .or. (.not. (t <= 2.7d+106))) then
        tmp = (t_1 - (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 t_1 = x + (y / t);
	double tmp;
	if (t <= -1.4e-120) {
		tmp = t_1 / (x + 1.0);
	} else if (t <= 4.8e-80) {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	} else if ((t <= 2.2e+17) || !(t <= 2.7e+106)) {
		tmp = (t_1 - (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):
	t_1 = x + (y / t)
	tmp = 0
	if t <= -1.4e-120:
		tmp = t_1 / (x + 1.0)
	elif t <= 4.8e-80:
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0)
	elif (t <= 2.2e+17) or not (t <= 2.7e+106):
		tmp = (t_1 - (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)
	t_1 = Float64(x + Float64(y / t))
	tmp = 0.0
	if (t <= -1.4e-120)
		tmp = Float64(t_1 / Float64(x + 1.0));
	elseif (t <= 4.8e-80)
		tmp = Float64(Float64(1.0 + Float64(x - Float64(y / Float64(x / z)))) / Float64(x + 1.0));
	elseif ((t <= 2.2e+17) || !(t <= 2.7e+106))
		tmp = Float64(Float64(t_1 - 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)
	t_1 = x + (y / t);
	tmp = 0.0;
	if (t <= -1.4e-120)
		tmp = t_1 / (x + 1.0);
	elseif (t <= 4.8e-80)
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	elseif ((t <= 2.2e+17) || ~((t <= 2.7e+106)))
		tmp = (t_1 - (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_] := Block[{t$95$1 = N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.4e-120], N[(t$95$1 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.8e-80], N[(N[(1.0 + N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 2.2e+17], N[Not[LessEqual[t, 2.7e+106]], $MachinePrecision]], N[(N[(t$95$1 - 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 4 regimes

2. if t < -1.39999999999999997e-120

   1. Initial program 87.0%

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

      1. *-commutative 87.0%

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

   3. Simplified 87.0%

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

   4. Taylor expanded in z around inf 87.5%

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

   if -1.39999999999999997e-120 < t < 4.7999999999999998e-80

   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. Taylor expanded in t around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. unsub-neg 84.4%

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

      3. associate-/l* 86.6%

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

      4. +-commutative 86.6%

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

   6. Simplified 86.6%

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

   if 4.7999999999999998e-80 < t < 2.2e17 or 2.70000000000000006e106 < t

   1. Initial program 82.1%

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

      1. *-commutative 82.1%

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

   3. Simplified 82.1%

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

   4. Taylor expanded in t around inf 85.7%

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

   if 2.2e17 < t < 2.70000000000000006e106

   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. Taylor expanded in y around 0 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 87.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-80}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{+17} \lor \neg \left(t \leq 2.7 \cdot 10^{+106}\right):\\ \;\;\;\;\frac{\left(x + \frac{y}{t}\right) - \frac{x}{z \cdot t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 3: 81.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -4 \cdot 10^{-120}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-80}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+14} \lor \neg \left(t \leq 4 \cdot 10^{+105}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -4e-120)
     t_1
     (if (<= t 4e-80)
       (/ (+ 1.0 (- x (/ y (/ x z)))) (+ x 1.0))
       (if (or (<= t 8.2e+14) (not (<= t 4e+105)))
         t_1
         (/ (- x (/ x (- (* z t) x))) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -4e-120) {
		tmp = t_1;
	} else if (t <= 4e-80) {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	} else if ((t <= 8.2e+14) || !(t <= 4e+105)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-4d-120)) then
        tmp = t_1
    else if (t <= 4d-80) then
        tmp = (1.0d0 + (x - (y / (x / z)))) / (x + 1.0d0)
    else if ((t <= 8.2d+14) .or. (.not. (t <= 4d+105))) then
        tmp = t_1
    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 t_1 = (x + (y / t)) / (x + 1.0);
	double tmp;
	if (t <= -4e-120) {
		tmp = t_1;
	} else if (t <= 4e-80) {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	} else if ((t <= 8.2e+14) || !(t <= 4e+105)) {
		tmp = t_1;
	} else {
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (y / t)) / (x + 1.0)
	tmp = 0
	if t <= -4e-120:
		tmp = t_1
	elif t <= 4e-80:
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0)
	elif (t <= 8.2e+14) or not (t <= 4e+105):
		tmp = t_1
	else:
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0)
	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 <= -4e-120)
		tmp = t_1;
	elseif (t <= 4e-80)
		tmp = Float64(Float64(1.0 + Float64(x - Float64(y / Float64(x / z)))) / Float64(x + 1.0));
	elseif ((t <= 8.2e+14) || !(t <= 4e+105))
		tmp = t_1;
	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)
	t_1 = (x + (y / t)) / (x + 1.0);
	tmp = 0.0;
	if (t <= -4e-120)
		tmp = t_1;
	elseif (t <= 4e-80)
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	elseif ((t <= 8.2e+14) || ~((t <= 4e+105)))
		tmp = t_1;
	else
		tmp = (x - (x / ((z * t) - x))) / (x + 1.0);
	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, -4e-120], t$95$1, If[LessEqual[t, 4e-80], N[(N[(1.0 + N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t, 8.2e+14], N[Not[LessEqual[t, 4e+105]], $MachinePrecision]], t$95$1, 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 t < -3.99999999999999991e-120 or 3.99999999999999985e-80 < t < 8.2e14 or 3.9999999999999998e105 < t

   1. Initial program 84.8%

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

      1. *-commutative 84.8%

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

   3. Simplified 84.8%

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

   4. Taylor expanded in z around inf 85.9%

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

   if -3.99999999999999991e-120 < t < 3.99999999999999985e-80

   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. Taylor expanded in t around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. unsub-neg 84.4%

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

      3. associate-/l* 86.6%

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

      4. +-commutative 86.6%

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

   6. Simplified 86.6%

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

   if 8.2e14 < t < 3.9999999999999998e105

   1. Initial program 90.9%

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

      1. *-commutative 90.9%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in y around 0 91.0%

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

      1. +-commutative 91.0%

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

   6. Simplified 91.0%

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

4. Final simplification 86.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4 \cdot 10^{-120}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-80}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \mathbf{elif}\;t \leq 8.2 \cdot 10^{+14} \lor \neg \left(t \leq 4 \cdot 10^{+105}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 4: 69.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{if}\;x \leq -1.36 \cdot 10^{-46}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z (- (* z t) x)))))
   (if (<= x -1.36e-46)
     1.0
     (if (<= x 4e-144)
       t_1
       (if (<= x 1.1e-101)
         (* x (+ 1.0 (/ -1.0 (* z t))))
         (if (<= x 2.8e-21) t_1 (/ 1.0 (/ (+ x 1.0) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -1.36e-46) {
		tmp = 1.0;
	} else if (x <= 4e-144) {
		tmp = t_1;
	} else if (x <= 1.1e-101) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 2.8e-21) {
		tmp = t_1;
	} else {
		tmp = 1.0 / ((x + 1.0) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * (z / ((z * t) - x))
    if (x <= (-1.36d-46)) then
        tmp = 1.0d0
    else if (x <= 4d-144) then
        tmp = t_1
    else if (x <= 1.1d-101) then
        tmp = x * (1.0d0 + ((-1.0d0) / (z * t)))
    else if (x <= 2.8d-21) then
        tmp = t_1
    else
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -1.36e-46) {
		tmp = 1.0;
	} else if (x <= 4e-144) {
		tmp = t_1;
	} else if (x <= 1.1e-101) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 2.8e-21) {
		tmp = t_1;
	} else {
		tmp = 1.0 / ((x + 1.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / ((z * t) - x))
	tmp = 0
	if x <= -1.36e-46:
		tmp = 1.0
	elif x <= 4e-144:
		tmp = t_1
	elif x <= 1.1e-101:
		tmp = x * (1.0 + (-1.0 / (z * t)))
	elif x <= 2.8e-21:
		tmp = t_1
	else:
		tmp = 1.0 / ((x + 1.0) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(z / Float64(Float64(z * t) - x)))
	tmp = 0.0
	if (x <= -1.36e-46)
		tmp = 1.0;
	elseif (x <= 4e-144)
		tmp = t_1;
	elseif (x <= 1.1e-101)
		tmp = Float64(x * Float64(1.0 + Float64(-1.0 / Float64(z * t))));
	elseif (x <= 2.8e-21)
		tmp = t_1;
	else
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (z / ((z * t) - x));
	tmp = 0.0;
	if (x <= -1.36e-46)
		tmp = 1.0;
	elseif (x <= 4e-144)
		tmp = t_1;
	elseif (x <= 1.1e-101)
		tmp = x * (1.0 + (-1.0 / (z * t)));
	elseif (x <= 2.8e-21)
		tmp = t_1;
	else
		tmp = 1.0 / ((x + 1.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.36e-46], 1.0, If[LessEqual[x, 4e-144], t$95$1, If[LessEqual[x, 1.1e-101], N[(x * N[(1.0 + N[(-1.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e-21], t$95$1, N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.3600000000000001e-46

   1. Initial program 92.3%

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

      1. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around inf 70.9%

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

   5. Taylor expanded in x around inf 82.2%

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

   if -1.3600000000000001e-46 < x < 3.9999999999999998e-144 or 1.0999999999999999e-101 < x < 2.80000000000000004e-21

   1. Initial program 87.6%

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

      1. *-commutative 87.6%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in y around inf 56.0%

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

      1. *-commutative 56.0%

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

      2. *-commutative 56.0%

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

      3. times-frac 58.6%

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

      4. *-commutative 58.6%

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

      5. +-commutative 58.6%

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

   6. Simplified 58.6%

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

   7. Taylor expanded in x around 0 58.6%

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

   8. Taylor expanded in y around 0 56.0%

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

      1. *-commutative 56.0%

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

      2. *-commutative 56.0%

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

      3. fma-neg 56.0%

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

      4. associate-*l/ 65.4%

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

      5. *-commutative 65.4%

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

      6. fma-neg 65.4%

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

      7. *-commutative 65.4%

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

   10. Simplified 65.4%

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

   if 3.9999999999999998e-144 < x < 1.0999999999999999e-101

   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. Taylor expanded in y around 0 83.9%

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

      1. +-commutative 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in x around 0 51.5%

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

      1. *-commutative 51.5%

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

   9. Simplified 51.5%

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

   if 2.80000000000000004e-21 < x

   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. Taylor expanded in t around inf 87.3%

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

      1. +-commutative 87.3%

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

   6. Simplified 87.3%

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

      1. clear-num 87.3%

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

      2. inv-pow 87.3%

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

      3. +-commutative 87.3%

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

   8. Applied egg-rr 87.3%

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

      1. unpow-1 87.3%

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

   10. Simplified 87.3%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.36 \cdot 10^{-46}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-101}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-21}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \end{array} \]

Alternative 5: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{-48}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{z}{t_1}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)))
   (if (<= x -2.4e-48)
     1.0
     (if (<= x 7e-144)
       (* y (/ z t_1))
       (if (<= x 3e-94)
         (* x (+ 1.0 (/ -1.0 (* z t))))
         (if (<= x 3.9e-19) (* z (/ y t_1)) (/ 1.0 (/ (+ x 1.0) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (x <= -2.4e-48) {
		tmp = 1.0;
	} else if (x <= 7e-144) {
		tmp = y * (z / t_1);
	} else if (x <= 3e-94) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 3.9e-19) {
		tmp = z * (y / t_1);
	} else {
		tmp = 1.0 / ((x + 1.0) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * t) - x
    if (x <= (-2.4d-48)) then
        tmp = 1.0d0
    else if (x <= 7d-144) then
        tmp = y * (z / t_1)
    else if (x <= 3d-94) then
        tmp = x * (1.0d0 + ((-1.0d0) / (z * t)))
    else if (x <= 3.9d-19) then
        tmp = z * (y / t_1)
    else
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    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 tmp;
	if (x <= -2.4e-48) {
		tmp = 1.0;
	} else if (x <= 7e-144) {
		tmp = y * (z / t_1);
	} else if (x <= 3e-94) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 3.9e-19) {
		tmp = z * (y / t_1);
	} else {
		tmp = 1.0 / ((x + 1.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	tmp = 0
	if x <= -2.4e-48:
		tmp = 1.0
	elif x <= 7e-144:
		tmp = y * (z / t_1)
	elif x <= 3e-94:
		tmp = x * (1.0 + (-1.0 / (z * t)))
	elif x <= 3.9e-19:
		tmp = z * (y / t_1)
	else:
		tmp = 1.0 / ((x + 1.0) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (x <= -2.4e-48)
		tmp = 1.0;
	elseif (x <= 7e-144)
		tmp = Float64(y * Float64(z / t_1));
	elseif (x <= 3e-94)
		tmp = Float64(x * Float64(1.0 + Float64(-1.0 / Float64(z * t))));
	elseif (x <= 3.9e-19)
		tmp = Float64(z * Float64(y / t_1));
	else
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	tmp = 0.0;
	if (x <= -2.4e-48)
		tmp = 1.0;
	elseif (x <= 7e-144)
		tmp = y * (z / t_1);
	elseif (x <= 3e-94)
		tmp = x * (1.0 + (-1.0 / (z * t)));
	elseif (x <= 3.9e-19)
		tmp = z * (y / t_1);
	else
		tmp = 1.0 / ((x + 1.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[x, -2.4e-48], 1.0, If[LessEqual[x, 7e-144], N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3e-94], N[(x * N[(1.0 + N[(-1.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e-19], N[(z * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.4e-48

   1. Initial program 92.3%

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

      1. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in z around inf 70.9%

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

   5. Taylor expanded in x around inf 82.2%

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

   if -2.4e-48 < x < 6.9999999999999997e-144

   1. Initial program 87.1%

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

      1. *-commutative 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in y around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. *-commutative 57.6%

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

      3. times-frac 59.5%

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

      4. *-commutative 59.5%

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

      5. +-commutative 59.5%

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

   6. Simplified 59.5%

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

   7. Taylor expanded in x around 0 59.5%

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

   8. Taylor expanded in y around 0 57.6%

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

      1. *-commutative 57.6%

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

      2. *-commutative 57.6%

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

      3. fma-neg 57.7%

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

      4. associate-*l/ 67.3%

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

      5. *-commutative 67.3%

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

      6. fma-neg 67.3%

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

      7. *-commutative 67.3%

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

   10. Simplified 67.3%

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

   if 6.9999999999999997e-144 < x < 3.0000000000000001e-94

   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. Taylor expanded in y around 0 83.9%

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

      1. +-commutative 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in x around 0 51.5%

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

      1. *-commutative 51.5%

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

   9. Simplified 51.5%

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

   if 3.0000000000000001e-94 < x < 3.89999999999999995e-19

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around inf 43.1%

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

      1. *-commutative 43.1%

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

      2. *-commutative 43.1%

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

      3. times-frac 51.1%

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

      4. *-commutative 51.1%

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

      5. +-commutative 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in x around 0 51.1%

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

   if 3.89999999999999995e-19 < x

   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. Taylor expanded in t around inf 87.3%

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

      1. +-commutative 87.3%

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

   6. Simplified 87.3%

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

      1. clear-num 87.3%

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

      2. inv-pow 87.3%

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

      3. +-commutative 87.3%

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

   8. Applied egg-rr 87.3%

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

      1. unpow-1 87.3%

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

   10. Simplified 87.3%

       \[\leadsto \color{blue}{\frac{1}{\frac{1 + x}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-48}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-94}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \end{array} \]

Alternative 6: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;x \leq -1.7 \cdot 10^{-46}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{z}{t_1}\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{y}{t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)))
   (if (<= x -1.7e-46)
     (- 1.0 (* (/ z x) (/ y x)))
     (if (<= x 6e-144)
       (* y (/ z t_1))
       (if (<= x 1.08e-93)
         (* x (+ 1.0 (/ -1.0 (* z t))))
         (if (<= x 1.65e-19) (* z (/ y t_1)) (/ 1.0 (/ (+ x 1.0) x))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (x <= -1.7e-46) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= 6e-144) {
		tmp = y * (z / t_1);
	} else if (x <= 1.08e-93) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 1.65e-19) {
		tmp = z * (y / t_1);
	} else {
		tmp = 1.0 / ((x + 1.0) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (z * t) - x
    if (x <= (-1.7d-46)) then
        tmp = 1.0d0 - ((z / x) * (y / x))
    else if (x <= 6d-144) then
        tmp = y * (z / t_1)
    else if (x <= 1.08d-93) then
        tmp = x * (1.0d0 + ((-1.0d0) / (z * t)))
    else if (x <= 1.65d-19) then
        tmp = z * (y / t_1)
    else
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    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 tmp;
	if (x <= -1.7e-46) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= 6e-144) {
		tmp = y * (z / t_1);
	} else if (x <= 1.08e-93) {
		tmp = x * (1.0 + (-1.0 / (z * t)));
	} else if (x <= 1.65e-19) {
		tmp = z * (y / t_1);
	} else {
		tmp = 1.0 / ((x + 1.0) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	tmp = 0
	if x <= -1.7e-46:
		tmp = 1.0 - ((z / x) * (y / x))
	elif x <= 6e-144:
		tmp = y * (z / t_1)
	elif x <= 1.08e-93:
		tmp = x * (1.0 + (-1.0 / (z * t)))
	elif x <= 1.65e-19:
		tmp = z * (y / t_1)
	else:
		tmp = 1.0 / ((x + 1.0) / x)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (x <= -1.7e-46)
		tmp = Float64(1.0 - Float64(Float64(z / x) * Float64(y / x)));
	elseif (x <= 6e-144)
		tmp = Float64(y * Float64(z / t_1));
	elseif (x <= 1.08e-93)
		tmp = Float64(x * Float64(1.0 + Float64(-1.0 / Float64(z * t))));
	elseif (x <= 1.65e-19)
		tmp = Float64(z * Float64(y / t_1));
	else
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	tmp = 0.0;
	if (x <= -1.7e-46)
		tmp = 1.0 - ((z / x) * (y / x));
	elseif (x <= 6e-144)
		tmp = y * (z / t_1);
	elseif (x <= 1.08e-93)
		tmp = x * (1.0 + (-1.0 / (z * t)));
	elseif (x <= 1.65e-19)
		tmp = z * (y / t_1);
	else
		tmp = 1.0 / ((x + 1.0) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, If[LessEqual[x, -1.7e-46], N[(1.0 - N[(N[(z / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e-144], N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.08e-93], N[(x * N[(1.0 + N[(-1.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.65e-19], N[(z * N[(y / t$95$1), $MachinePrecision]), $MachinePrecision], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -1.69999999999999998e-46

   1. Initial program 92.3%

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

      1. *-commutative 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in x around -inf 76.8%

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

      1. mul-1-neg 76.8%

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

      2. unsub-neg 76.8%

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

      3. distribute-rgt-out-- 76.8%

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

      4. unpow2 76.8%

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

      5. times-frac 82.0%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in y around inf 89.2%

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

   if -1.69999999999999998e-46 < x < 5.9999999999999997e-144

   1. Initial program 87.1%

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

      1. *-commutative 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in y around inf 57.6%

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

      1. *-commutative 57.6%

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

      2. *-commutative 57.6%

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

      3. times-frac 59.5%

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

      4. *-commutative 59.5%

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

      5. +-commutative 59.5%

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

   6. Simplified 59.5%

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

   7. Taylor expanded in x around 0 59.5%

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

   8. Taylor expanded in y around 0 57.6%

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

      1. *-commutative 57.6%

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

      2. *-commutative 57.6%

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

      3. fma-neg 57.7%

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

      4. associate-*l/ 67.3%

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

      5. *-commutative 67.3%

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

      6. fma-neg 67.3%

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

      7. *-commutative 67.3%

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

   10. Simplified 67.3%

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

   if 5.9999999999999997e-144 < x < 1.08e-93

   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. Taylor expanded in y around 0 83.9%

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

      1. +-commutative 83.9%

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

   6. Simplified 83.9%

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

   7. Taylor expanded in x around 0 51.5%

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

      1. *-commutative 51.5%

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

   9. Simplified 51.5%

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

   if 1.08e-93 < x < 1.6499999999999999e-19

   1. Initial program 91.8%

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

      1. *-commutative 91.8%

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

   3. Simplified 91.8%

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

   4. Taylor expanded in y around inf 43.1%

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

      1. *-commutative 43.1%

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

      2. *-commutative 43.1%

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

      3. times-frac 51.1%

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

      4. *-commutative 51.1%

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

      5. +-commutative 51.1%

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

   6. Simplified 51.1%

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

   7. Taylor expanded in x around 0 51.1%

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

   if 1.6499999999999999e-19 < x

   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. Taylor expanded in t around inf 87.3%

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

      1. +-commutative 87.3%

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

   6. Simplified 87.3%

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

      1. clear-num 87.3%

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

      2. inv-pow 87.3%

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

      3. +-commutative 87.3%

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

   8. Applied egg-rr 87.3%

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

      1. unpow-1 87.3%

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

   10. Simplified 87.3%

       \[\leadsto \color{blue}{\frac{1}{\frac{1 + x}{x}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{-46}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-144}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 1.08 \cdot 10^{-93}:\\ \;\;\;\;x \cdot \left(1 + \frac{-1}{z \cdot t}\right)\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-19}:\\ \;\;\;\;z \cdot \frac{y}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \end{array} \]

Alternative 7: 82.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-121} \lor \neg \left(t \leq 9 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7.5e-121) (not (<= t 9e-80)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ 1.0 (- x (/ y (/ x z)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.5e-121) || !(t <= 9e-80)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (1.0 + (x - (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 <= (-7.5d-121)) .or. (.not. (t <= 9d-80))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (1.0d0 + (x - (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 <= -7.5e-121) || !(t <= 9e-80)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7.5e-121) or not (t <= 9e-80):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7.5e-121) || !(t <= 9e-80))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(1.0 + Float64(x - 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 <= -7.5e-121) || ~((t <= 9e-80)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (1.0 + (x - (y / (x / z)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7.5e-121], N[Not[LessEqual[t, 9e-80]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 + N[(x - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.50000000000000027e-121 or 9.0000000000000006e-80 < t

   1. Initial program 85.2%

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

      1. *-commutative 85.2%

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

   3. Simplified 85.2%

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

   4. Taylor expanded in z around inf 82.9%

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

   if -7.50000000000000027e-121 < t < 9.0000000000000006e-80

   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. Taylor expanded in t around 0 84.4%

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

      1. mul-1-neg 84.4%

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

      2. unsub-neg 84.4%

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

      3. associate-/l* 86.6%

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

      4. +-commutative 86.6%

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

   6. Simplified 86.6%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.5 \cdot 10^{-121} \lor \neg \left(t \leq 9 \cdot 10^{-80}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \left(x - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \]

Alternative 8: 77.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-18}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 17200000000000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.2e-18)
   (- 1.0 (* (/ z x) (/ y x)))
   (if (<= x 17200000000000.0) (/ (+ x (/ y t)) (+ x 1.0)) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.2e-18) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= 17200000000000.0) {
		tmp = (x + (y / t)) / (x + 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 (x <= (-2.2d-18)) then
        tmp = 1.0d0 - ((z / x) * (y / x))
    else if (x <= 17200000000000.0d0) then
        tmp = (x + (y / t)) / (x + 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 (x <= -2.2e-18) {
		tmp = 1.0 - ((z / x) * (y / x));
	} else if (x <= 17200000000000.0) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.2e-18:
		tmp = 1.0 - ((z / x) * (y / x))
	elif x <= 17200000000000.0:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.2e-18)
		tmp = Float64(1.0 - Float64(Float64(z / x) * Float64(y / x)));
	elseif (x <= 17200000000000.0)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 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 (x <= -2.2e-18)
		tmp = 1.0 - ((z / x) * (y / x));
	elseif (x <= 17200000000000.0)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.2e-18], N[(1.0 - N[(N[(z / x), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 17200000000000.0], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.1999999999999998e-18

   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 x around -inf 80.7%

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

      1. mul-1-neg 80.7%

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

      2. unsub-neg 80.7%

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

      3. distribute-rgt-out-- 80.7%

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

      4. unpow2 80.7%

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

      5. times-frac 86.3%

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

   6. Simplified 86.3%

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

   7. Taylor expanded in y around inf 92.6%

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

   if -2.1999999999999998e-18 < x < 1.72e13

   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. Taylor expanded in z around inf 66.8%

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

   if 1.72e13 < x

   1. Initial program 90.6%

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

      1. *-commutative 90.6%

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

   3. Simplified 90.6%

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

   4. Taylor expanded in t around inf 94.5%

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

      1. +-commutative 94.5%

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

   6. Simplified 94.5%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-18}:\\ \;\;\;\;1 - \frac{z}{x} \cdot \frac{y}{x}\\ \mathbf{elif}\;x \leq 17200000000000:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 9: 66.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-68}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.48 \cdot 10^{-139}:\\ \;\;\;\;\frac{y}{t + x \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8e-68)
   1.0
   (if (<= x 1.48e-139) (/ y (+ t (* x t))) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8e-68) {
		tmp = 1.0;
	} else if (x <= 1.48e-139) {
		tmp = y / (t + (x * 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 <= (-8d-68)) then
        tmp = 1.0d0
    else if (x <= 1.48d-139) then
        tmp = y / (t + (x * 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 <= -8e-68) {
		tmp = 1.0;
	} else if (x <= 1.48e-139) {
		tmp = y / (t + (x * t));
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8e-68:
		tmp = 1.0
	elif x <= 1.48e-139:
		tmp = y / (t + (x * t))
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8e-68)
		tmp = 1.0;
	elseif (x <= 1.48e-139)
		tmp = Float64(y / Float64(t + Float64(x * 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 <= -8e-68)
		tmp = 1.0;
	elseif (x <= 1.48e-139)
		tmp = y / (t + (x * t));
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8e-68], 1.0, If[LessEqual[x, 1.48e-139], N[(y / N[(t + N[(x * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.00000000000000053e-68

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in z around inf 68.8%

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

   5. Taylor expanded in x around inf 79.5%

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

   if -8.00000000000000053e-68 < x < 1.47999999999999991e-139

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in y around inf 56.3%

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

      1. *-commutative 56.3%

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

      2. *-commutative 56.3%

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

      3. times-frac 58.2%

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

      4. *-commutative 58.2%

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

      5. +-commutative 58.2%

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

   6. Simplified 58.2%

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

   7. Taylor expanded in t around inf 57.1%

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

      1. distribute-lft-in 57.1%

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

      2. *-rgt-identity 57.1%

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

   9. Simplified 57.1%

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

   if 1.47999999999999991e-139 < x

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in t around inf 72.3%

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

      1. +-commutative 72.3%

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

   6. Simplified 72.3%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-68}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.48 \cdot 10^{-139}:\\ \;\;\;\;\frac{y}{t + x \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 10: 66.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-68}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-139}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.8e-68) 1.0 (if (<= x 6.1e-139) (/ y t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.8e-68) {
		tmp = 1.0;
	} else if (x <= 6.1e-139) {
		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 <= (-6.8d-68)) then
        tmp = 1.0d0
    else if (x <= 6.1d-139) 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 <= -6.8e-68) {
		tmp = 1.0;
	} else if (x <= 6.1e-139) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.8e-68:
		tmp = 1.0
	elif x <= 6.1e-139:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.8e-68)
		tmp = 1.0;
	elseif (x <= 6.1e-139)
		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 <= -6.8e-68)
		tmp = 1.0;
	elseif (x <= 6.1e-139)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.8e-68], 1.0, If[LessEqual[x, 6.1e-139], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.80000000000000037e-68

   1. Initial program 92.7%

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

      1. *-commutative 92.7%

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

   3. Simplified 92.7%

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

   4. Taylor expanded in z around inf 68.8%

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

   5. Taylor expanded in x around inf 79.5%

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

   if -6.80000000000000037e-68 < x < 6.0999999999999998e-139

   1. Initial program 86.7%

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

      1. *-commutative 86.7%

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

   3. Simplified 86.7%

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

   4. Taylor expanded in z around inf 70.9%

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

   5. Taylor expanded in x around 0 57.1%

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

   if 6.0999999999999998e-139 < x

   1. Initial program 87.2%

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

      1. *-commutative 87.2%

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

   3. Simplified 87.2%

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

   4. Taylor expanded in t around inf 72.3%

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

      1. +-commutative 72.3%

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

   6. Simplified 72.3%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-68}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.1 \cdot 10^{-139}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 11: 65.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-67}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.8e-67) 1.0 (if (<= x 9.8e-148) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.8e-67) {
		tmp = 1.0;
	} else if (x <= 9.8e-148) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.8d-67)) then
        tmp = 1.0d0
    else if (x <= 9.8d-148) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.8e-67) {
		tmp = 1.0;
	} else if (x <= 9.8e-148) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.8e-67:
		tmp = 1.0
	elif x <= 9.8e-148:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.8e-67)
		tmp = 1.0;
	elseif (x <= 9.8e-148)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.8e-67)
		tmp = 1.0;
	elseif (x <= 9.8e-148)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.8e-67], 1.0, If[LessEqual[x, 9.8e-148], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.79999999999999988e-67 or 9.8000000000000001e-148 < x

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

   3. Simplified 90.0%

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

   4. Taylor expanded in z around inf 68.2%

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

   5. Taylor expanded in x around inf 74.6%

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

   if -3.79999999999999988e-67 < x < 9.8000000000000001e-148

   1. Initial program 86.4%

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

      1. *-commutative 86.4%

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

   3. Simplified 86.4%

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

   4. Taylor expanded in z around inf 72.4%

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

   5. Taylor expanded in x around 0 58.3%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-67}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12: 53.9% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-108}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.8e-108) 1.0 (if (<= x 1.22e-291) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e-108) {
		tmp = 1.0;
	} else if (x <= 1.22e-291) {
		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 <= (-1.8d-108)) then
        tmp = 1.0d0
    else if (x <= 1.22d-291) 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 <= -1.8e-108) {
		tmp = 1.0;
	} else if (x <= 1.22e-291) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.8e-108:
		tmp = 1.0
	elif x <= 1.22e-291:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.8e-108)
		tmp = 1.0;
	elseif (x <= 1.22e-291)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.8e-108)
		tmp = 1.0;
	elseif (x <= 1.22e-291)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.8e-108], 1.0, If[LessEqual[x, 1.22e-291], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8e-108 or 1.21999999999999993e-291 < x

   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. Taylor expanded in z around inf 67.9%

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

   5. Taylor expanded in x around inf 62.6%

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

   if -1.8e-108 < x < 1.21999999999999993e-291

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   4. Taylor expanded in t around inf 25.3%

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

      1. +-commutative 25.3%

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

   6. Simplified 25.3%

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

   7. Taylor expanded in x around 0 25.3%

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

4. Final simplification 55.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-108}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-291}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

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 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 z around inf 69.7%

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

5. Taylor expanded in x around inf 52.1%

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

6. Final simplification 52.1%

   \[\leadsto 1 \]

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 2023292 
(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)))