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

Percentage Accurate: 89.8% → 98.7%

Time: 12.1s

Alternatives: 13

Speedup: 0.2×

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: 89.8% 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: 98.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y}{\frac{t_1}{z}}}{x + 1}\\ t_3 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_3 \leq -5 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_3 \leq 2:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t_3 \leq \infty:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x))
        (t_2 (/ (+ x (/ y (/ t_1 z))) (+ x 1.0)))
        (t_3 (/ (+ x (/ (- (* y z) x) t_1)) (+ x 1.0))))
   (if (<= t_3 -5e+24)
     t_2
     (if (<= t_3 2.0)
       t_3
       (if (<= t_3 INFINITY) t_2 (/ (+ x (/ y t)) (+ x 1.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (y / (t_1 / z))) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -5e+24) {
		tmp = t_2;
	} else if (t_3 <= 2.0) {
		tmp = t_3;
	} else if (t_3 <= ((double) INFINITY)) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double t_2 = (x + (y / (t_1 / z))) / (x + 1.0);
	double t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	double tmp;
	if (t_3 <= -5e+24) {
		tmp = t_2;
	} else if (t_3 <= 2.0) {
		tmp = t_3;
	} else if (t_3 <= Double.POSITIVE_INFINITY) {
		tmp = t_2;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	t_2 = (x + (y / (t_1 / z))) / (x + 1.0)
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0)
	tmp = 0
	if t_3 <= -5e+24:
		tmp = t_2
	elif t_3 <= 2.0:
		tmp = t_3
	elif t_3 <= math.inf:
		tmp = t_2
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	t_2 = Float64(Float64(x + Float64(y / Float64(t_1 / z))) / Float64(x + 1.0))
	t_3 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / t_1)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_3 <= -5e+24)
		tmp = t_2;
	elseif (t_3 <= 2.0)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	t_2 = (x + (y / (t_1 / z))) / (x + 1.0);
	t_3 = (x + (((y * z) - x) / t_1)) / (x + 1.0);
	tmp = 0.0;
	if (t_3 <= -5e+24)
		tmp = t_2;
	elseif (t_3 <= 2.0)
		tmp = t_3;
	elseif (t_3 <= Inf)
		tmp = t_2;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x + N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -5e+24], t$95$2, If[LessEqual[t$95$3, 2.0], t$95$3, If[LessEqual[t$95$3, Infinity], t$95$2, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < -5.00000000000000045e24 or 2 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < +inf.0

   1. Initial program 66.8%

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

      1. *-commutative 66.8%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in y around inf 66.8%

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

      1. associate-/l* 98.3%

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

   6. Simplified 98.3%

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

   if -5.00000000000000045e24 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 2

   1. Initial program 97.5%

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

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

   1. Initial program 0.0%

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

      1. *-commutative 0.0%

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

   3. Simplified 0.0%

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

   4. Taylor expanded in z around inf 100.0%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -5 \cdot 10^{+24}:\\ \;\;\;\;\frac{x + \frac{y}{\frac{z \cdot t - x}{z}}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq \infty:\\ \;\;\;\;\frac{x + \frac{y}{\frac{z \cdot t - x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 2: 79.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-153}:\\ \;\;\;\;1 - \frac{z \cdot \frac{y}{x}}{x + 1}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+39}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -1.05e-47)
     t_1
     (if (<= t 7.5e-153)
       (- 1.0 (/ (* z (/ y x)) (+ x 1.0)))
       (if (<= t 1.56e+39) (/ (- x (/ x (- (* z t) x))) (+ 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 tmp;
	if (t <= -1.05e-47) {
		tmp = t_1;
	} else if (t <= 7.5e-153) {
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0));
	} else if (t <= 1.56e+39) {
		tmp = (x - (x / ((z * t) - x))) / (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) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-1.05d-47)) then
        tmp = t_1
    else if (t <= 7.5d-153) then
        tmp = 1.0d0 - ((z * (y / x)) / (x + 1.0d0))
    else if (t <= 1.56d+39) then
        tmp = (x - (x / ((z * t) - x))) / (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 tmp;
	if (t <= -1.05e-47) {
		tmp = t_1;
	} else if (t <= 7.5e-153) {
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0));
	} else if (t <= 1.56e+39) {
		tmp = (x - (x / ((z * t) - x))) / (x + 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 <= -1.05e-47:
		tmp = t_1
	elif t <= 7.5e-153:
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0))
	elif t <= 1.56e+39:
		tmp = (x - (x / ((z * t) - x))) / (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))
	tmp = 0.0
	if (t <= -1.05e-47)
		tmp = t_1;
	elseif (t <= 7.5e-153)
		tmp = Float64(1.0 - Float64(Float64(z * Float64(y / x)) / Float64(x + 1.0)));
	elseif (t <= 1.56e+39)
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / 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);
	tmp = 0.0;
	if (t <= -1.05e-47)
		tmp = t_1;
	elseif (t <= 7.5e-153)
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0));
	elseif (t <= 1.56e+39)
		tmp = (x - (x / ((z * t) - x))) / (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]}, If[LessEqual[t, -1.05e-47], t$95$1, If[LessEqual[t, 7.5e-153], N[(1.0 - N[(N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.56e+39], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.05e-47 or 1.56000000000000009e39 < t

   1. Initial program 82.2%

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

      1. *-commutative 82.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in z around inf 93.4%

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

   if -1.05e-47 < t < 7.5e-153

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around 0 75.0%

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

      1. associate-+r+ 75.0%

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

      2. mul-1-neg 75.0%

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

      3. unsub-neg 75.0%

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

      4. +-commutative 75.0%

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

      5. associate-/l* 81.5%

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

      6. +-commutative 81.5%

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

   6. Simplified 81.5%

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

      1. div-sub 81.5%

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

      2. pow1 81.5%

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

      3. pow1 81.5%

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

      4. pow-div 81.5%

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

      5. metadata-eval 81.5%

         \[\leadsto {\left(x + 1\right)}^{\color{blue}{0}} - \frac{\frac{y}{\frac{x}{z}}}{x + 1} \]

      6. metadata-eval 81.5%

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

      7. associate-/r/ 77.8%

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

   8. Applied egg-rr 77.8%

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

   if 7.5e-153 < t < 1.56000000000000009e39

   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 y around 0 77.3%

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

      1. +-commutative 77.3%

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

   6. Simplified 77.3%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{-47}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 7.5 \cdot 10^{-153}:\\ \;\;\;\;1 - \frac{z \cdot \frac{y}{x}}{x + 1}\\ \mathbf{elif}\;t \leq 1.56 \cdot 10^{+39}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 3: 80.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{if}\;t \leq -1.6 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 10^{-160}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ y t)) (+ x 1.0))))
   (if (<= t -1.6e-46)
     t_1
     (if (<= t 1e-160)
       (/ (- (+ x 1.0) (/ y (/ x z))) (+ x 1.0))
       (if (<= t 1.4e+39) (/ (- x (/ x (- (* z t) x))) (+ 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 tmp;
	if (t <= -1.6e-46) {
		tmp = t_1;
	} else if (t <= 1e-160) {
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	} else if (t <= 1.4e+39) {
		tmp = (x - (x / ((z * t) - x))) / (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) :: tmp
    t_1 = (x + (y / t)) / (x + 1.0d0)
    if (t <= (-1.6d-46)) then
        tmp = t_1
    else if (t <= 1d-160) then
        tmp = ((x + 1.0d0) - (y / (x / z))) / (x + 1.0d0)
    else if (t <= 1.4d+39) then
        tmp = (x - (x / ((z * t) - x))) / (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 tmp;
	if (t <= -1.6e-46) {
		tmp = t_1;
	} else if (t <= 1e-160) {
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	} else if (t <= 1.4e+39) {
		tmp = (x - (x / ((z * t) - x))) / (x + 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 <= -1.6e-46:
		tmp = t_1
	elif t <= 1e-160:
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0)
	elif t <= 1.4e+39:
		tmp = (x - (x / ((z * t) - x))) / (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))
	tmp = 0.0
	if (t <= -1.6e-46)
		tmp = t_1;
	elseif (t <= 1e-160)
		tmp = Float64(Float64(Float64(x + 1.0) - Float64(y / Float64(x / z))) / Float64(x + 1.0));
	elseif (t <= 1.4e+39)
		tmp = Float64(Float64(x - Float64(x / Float64(Float64(z * t) - x))) / 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);
	tmp = 0.0;
	if (t <= -1.6e-46)
		tmp = t_1;
	elseif (t <= 1e-160)
		tmp = ((x + 1.0) - (y / (x / z))) / (x + 1.0);
	elseif (t <= 1.4e+39)
		tmp = (x - (x / ((z * t) - x))) / (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]}, If[LessEqual[t, -1.6e-46], t$95$1, If[LessEqual[t, 1e-160], N[(N[(N[(x + 1.0), $MachinePrecision] - N[(y / N[(x / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.4e+39], N[(N[(x - N[(x / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.6e-46 or 1.40000000000000001e39 < t

   1. Initial program 82.2%

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

      1. *-commutative 82.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in z around inf 93.4%

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

   if -1.6e-46 < t < 9.9999999999999999e-161

   1. Initial program 90.8%

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

      1. *-commutative 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around 0 75.0%

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

      1. associate-+r+ 75.0%

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

      2. mul-1-neg 75.0%

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

      3. unsub-neg 75.0%

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

      4. +-commutative 75.0%

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

      5. associate-/l* 81.5%

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

      6. +-commutative 81.5%

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

   6. Simplified 81.5%

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

   if 9.9999999999999999e-161 < t < 1.40000000000000001e39

   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 y around 0 77.3%

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

      1. +-commutative 77.3%

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

   6. Simplified 77.3%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-46}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;t \leq 10^{-160}:\\ \;\;\;\;\frac{\left(x + 1\right) - \frac{y}{\frac{x}{z}}}{x + 1}\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+39}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 4: 88.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{-23} \lor \neg \left(y \leq 2.95 \cdot 10^{-167}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{t_1}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{t_1}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)))
   (if (or (<= y -1.35e-23) (not (<= y 2.95e-167)))
     (/ (+ x (/ y (/ t_1 z))) (+ x 1.0))
     (/ (- x (/ x t_1)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if ((y <= -1.35e-23) || !(y <= 2.95e-167)) {
		tmp = (x + (y / (t_1 / z))) / (x + 1.0);
	} else {
		tmp = (x - (x / t_1)) / (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 = (z * t) - x
    if ((y <= (-1.35d-23)) .or. (.not. (y <= 2.95d-167))) then
        tmp = (x + (y / (t_1 / z))) / (x + 1.0d0)
    else
        tmp = (x - (x / t_1)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if ((y <= -1.35e-23) || !(y <= 2.95e-167)) {
		tmp = (x + (y / (t_1 / z))) / (x + 1.0);
	} else {
		tmp = (x - (x / t_1)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	tmp = 0
	if (y <= -1.35e-23) or not (y <= 2.95e-167):
		tmp = (x + (y / (t_1 / z))) / (x + 1.0)
	else:
		tmp = (x - (x / t_1)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if ((y <= -1.35e-23) || !(y <= 2.95e-167))
		tmp = Float64(Float64(x + Float64(y / Float64(t_1 / z))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x - Float64(x / t_1)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (z * t) - x;
	tmp = 0.0;
	if ((y <= -1.35e-23) || ~((y <= 2.95e-167)))
		tmp = (x + (y / (t_1 / z))) / (x + 1.0);
	else
		tmp = (x - (x / t_1)) / (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]}, If[Or[LessEqual[y, -1.35e-23], N[Not[LessEqual[y, 2.95e-167]], $MachinePrecision]], N[(N[(x + N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(x / t$95$1), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.34999999999999992e-23 or 2.95000000000000011e-167 < y

   1. Initial program 78.4%

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

      1. *-commutative 78.4%

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

   3. Simplified 78.4%

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

   4. Taylor expanded in y around inf 72.4%

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

      1. associate-/l* 87.3%

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

   6. Simplified 87.3%

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

   if -1.34999999999999992e-23 < y < 2.95000000000000011e-167

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. 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 2 regimes into one program.

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-23} \lor \neg \left(y \leq 2.95 \cdot 10^{-167}\right):\\ \;\;\;\;\frac{x + \frac{y}{\frac{z \cdot t - x}{z}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x - \frac{x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 5: 67.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-38}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{-z}{x}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-126}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8e-38)
   (/ 1.0 (/ (+ x 1.0) x))
   (if (<= x -8e-74)
     (* y (/ (- z) x))
     (if (<= x -1.9e-126)
       1.0
       (if (<= x 1.15e-27) (/ y (* t (+ x 1.0))) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8e-38) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= -8e-74) {
		tmp = y * (-z / x);
	} else if (x <= -1.9e-126) {
		tmp = 1.0;
	} else if (x <= 1.15e-27) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-8d-38)) then
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    else if (x <= (-8d-74)) then
        tmp = y * (-z / x)
    else if (x <= (-1.9d-126)) then
        tmp = 1.0d0
    else if (x <= 1.15d-27) then
        tmp = y / (t * (x + 1.0d0))
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8e-38) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= -8e-74) {
		tmp = y * (-z / x);
	} else if (x <= -1.9e-126) {
		tmp = 1.0;
	} else if (x <= 1.15e-27) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8e-38:
		tmp = 1.0 / ((x + 1.0) / x)
	elif x <= -8e-74:
		tmp = y * (-z / x)
	elif x <= -1.9e-126:
		tmp = 1.0
	elif x <= 1.15e-27:
		tmp = y / (t * (x + 1.0))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8e-38)
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	elseif (x <= -8e-74)
		tmp = Float64(y * Float64(Float64(-z) / x));
	elseif (x <= -1.9e-126)
		tmp = 1.0;
	elseif (x <= 1.15e-27)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8e-38)
		tmp = 1.0 / ((x + 1.0) / x);
	elseif (x <= -8e-74)
		tmp = y * (-z / x);
	elseif (x <= -1.9e-126)
		tmp = 1.0;
	elseif (x <= 1.15e-27)
		tmp = y / (t * (x + 1.0));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8e-38], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8e-74], N[(y * N[((-z) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e-126], 1.0, If[LessEqual[x, 1.15e-27], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.9999999999999997e-38

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

      1. clear-num 85.4%

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

      2. inv-pow 85.4%

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

      3. fma-neg 85.4%

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

   5. Applied egg-rr 85.4%

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

      1. unpow-1 85.4%

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

      2. fma-neg 85.4%

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

      3. *-commutative 85.4%

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

      4. *-commutative 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in t around inf 84.1%

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

   if -7.9999999999999997e-38 < x < -7.99999999999999966e-74

   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 y around inf 48.4%

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

      1. times-frac 55.8%

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

      2. +-commutative 55.8%

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

   6. Simplified 55.8%

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

   7. Taylor expanded in x around 0 55.8%

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

   8. Taylor expanded in z around 0 41.7%

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

      1. associate-*r/ 41.7%

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

      2. neg-mul-1 41.7%

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

   10. Simplified 41.7%

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

   if -7.99999999999999966e-74 < x < -1.8999999999999999e-126 or 1.15e-27 < x

   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 68.4%

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

   5. Taylor expanded in x around inf 85.1%

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

   if -1.8999999999999999e-126 < x < 1.15e-27

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in y around inf 52.5%

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

      1. times-frac 57.8%

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

      2. +-commutative 57.8%

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

   6. Simplified 57.8%

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

   7. Taylor expanded in z around inf 54.8%

      \[\leadsto \color{blue}{\frac{y}{t \cdot \left(1 + x\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8 \cdot 10^{-38}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{-z}{x}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-126}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 79.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-46} \lor \neg \left(t \leq 1.4 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z \cdot \frac{y}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.6e-46) (not (<= t 1.4e+39)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (/ (* z (/ y x)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e-46) || !(t <= 1.4e+39)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.6d-46)) .or. (.not. (t <= 1.4d+39))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((z * (y / x)) / (x + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.6e-46) || !(t <= 1.4e+39)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.6e-46) or not (t <= 1.4e+39):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.6e-46) || !(t <= 1.4e+39))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(z * Float64(y / x)) / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.6e-46) || ~((t <= 1.4e+39)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((z * (y / x)) / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.6e-46], N[Not[LessEqual[t, 1.4e+39]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(z * N[(y / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.6e-46 or 1.40000000000000001e39 < t

   1. Initial program 82.2%

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

      1. *-commutative 82.2%

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

   3. Simplified 82.2%

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

   4. Taylor expanded in z around inf 93.4%

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

   if -1.6e-46 < t < 1.40000000000000001e39

   1. Initial program 91.4%

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

      1. *-commutative 91.4%

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

   3. Simplified 91.4%

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

   4. Taylor expanded in t around 0 71.0%

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

      1. associate-+r+ 71.0%

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

      2. mul-1-neg 71.0%

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

      3. unsub-neg 71.0%

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

      4. +-commutative 71.0%

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

      5. associate-/l* 75.7%

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

      6. +-commutative 75.7%

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

   6. Simplified 75.7%

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

      1. div-sub 75.7%

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

      2. pow1 75.7%

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

      3. pow1 75.7%

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

      4. pow-div 75.7%

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

      5. metadata-eval 75.7%

         \[\leadsto {\left(x + 1\right)}^{\color{blue}{0}} - \frac{\frac{y}{\frac{x}{z}}}{x + 1} \]

      6. metadata-eval 75.7%

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

      7. associate-/r/ 72.7%

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

   8. Applied egg-rr 72.7%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.6 \cdot 10^{-46} \lor \neg \left(t \leq 1.4 \cdot 10^{+39}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z \cdot \frac{y}{x}}{x + 1}\\ \end{array} \]

Alternative 7: 76.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-176} \lor \neg \left(z \leq 3.8 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.9e-176) (not (<= z 3.8e-73)))
   (/ (+ x (/ y t)) (+ x 1.0))
   1.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.9e-176) || !(z <= 3.8e-73)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.9d-176)) .or. (.not. (z <= 3.8d-73))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.9e-176) || !(z <= 3.8e-73)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.9e-176) or not (z <= 3.8e-73):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.9e-176) || !(z <= 3.8e-73))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.9e-176) || ~((z <= 3.8e-73)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.9e-176], N[Not[LessEqual[z, 3.8e-73]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]

Derivation

1. Split input into 2 regimes

2. if z < -4.8999999999999997e-176 or 3.8000000000000003e-73 < z

   1. Initial program 81.1%

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

      1. *-commutative 81.1%

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

   3. Simplified 81.1%

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

   4. Taylor expanded in z around inf 77.4%

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

   if -4.8999999999999997e-176 < z < 3.8000000000000003e-73

   1. Initial program 99.9%

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

      1. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in z around inf 50.9%

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

   5. Taylor expanded in x around inf 72.5%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.9 \cdot 10^{-176} \lor \neg \left(z \leq 3.8 \cdot 10^{-73}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 71.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-37}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.6e-37)
   (/ 1.0 (/ (+ x 1.0) x))
   (if (<= x 3.7e-27) (* y (/ z (- (* z t) x))) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.6e-37) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= 3.7e-27) {
		tmp = y * (z / ((z * t) - 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 <= (-2.6d-37)) then
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    else if (x <= 3.7d-27) then
        tmp = y * (z / ((z * t) - 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 <= -2.6e-37) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= 3.7e-27) {
		tmp = y * (z / ((z * t) - x));
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.6e-37:
		tmp = 1.0 / ((x + 1.0) / x)
	elif x <= 3.7e-27:
		tmp = y * (z / ((z * t) - x))
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.6e-37)
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	elseif (x <= 3.7e-27)
		tmp = Float64(y * Float64(z / Float64(Float64(z * t) - x)));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.6e-37)
		tmp = 1.0 / ((x + 1.0) / x);
	elseif (x <= 3.7e-27)
		tmp = y * (z / ((z * t) - x));
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.6e-37], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.7e-27], N[(y * N[(z / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -2.5999999999999998e-37

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

      1. clear-num 85.4%

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

      2. inv-pow 85.4%

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

      3. fma-neg 85.4%

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

   5. Applied egg-rr 85.4%

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

      1. unpow-1 85.4%

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

      2. fma-neg 85.4%

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

      3. *-commutative 85.4%

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

      4. *-commutative 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in t around inf 84.1%

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

   if -2.5999999999999998e-37 < x < 3.70000000000000029e-27

   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 49.0%

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

      1. times-frac 54.9%

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

      2. +-commutative 54.9%

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

   6. Simplified 54.9%

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

   7. Taylor expanded in x around 0 54.9%

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

   if 3.70000000000000029e-27 < x

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in z around inf 73.1%

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

   5. Taylor expanded in x around inf 91.6%

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

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{-37}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-27}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 71.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq 1.36 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{\frac{z \cdot t - x}{z}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -5.8e-37)
   (/ 1.0 (/ (+ x 1.0) x))
   (if (<= x 1.36e-27) (/ y (/ (- (* z t) x) z)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -5.8e-37) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= 1.36e-27) {
		tmp = y / (((z * t) - x) / z);
	} 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 <= (-5.8d-37)) then
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    else if (x <= 1.36d-27) then
        tmp = y / (((z * t) - x) / z)
    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 <= -5.8e-37) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= 1.36e-27) {
		tmp = y / (((z * t) - x) / z);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -5.8e-37:
		tmp = 1.0 / ((x + 1.0) / x)
	elif x <= 1.36e-27:
		tmp = y / (((z * t) - x) / z)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -5.8e-37)
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	elseif (x <= 1.36e-27)
		tmp = Float64(y / Float64(Float64(Float64(z * t) - x) / z));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -5.8e-37)
		tmp = 1.0 / ((x + 1.0) / x);
	elseif (x <= 1.36e-27)
		tmp = y / (((z * t) - x) / z);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -5.8e-37], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.36e-27], N[(y / N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -5.80000000000000009e-37

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

      1. clear-num 85.4%

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

      2. inv-pow 85.4%

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

      3. fma-neg 85.4%

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

   5. Applied egg-rr 85.4%

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

      1. unpow-1 85.4%

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

      2. fma-neg 85.4%

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

      3. *-commutative 85.4%

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

      4. *-commutative 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in t around inf 84.1%

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

   if -5.80000000000000009e-37 < x < 1.36e-27

   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 49.0%

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

      1. times-frac 54.9%

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

      2. +-commutative 54.9%

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

   6. Simplified 54.9%

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

   7. Taylor expanded in x around 0 54.9%

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

   8. Taylor expanded in y around 0 49.0%

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

      1. associate-/l* 55.0%

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

   10. Simplified 55.0%

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

   if 1.36e-27 < x

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   4. Taylor expanded in z around inf 73.1%

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

   5. Taylor expanded in x around inf 91.6%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-37}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq 1.36 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{\frac{z \cdot t - x}{z}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 67.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{-z}{x}\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-126}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.58 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.8e-38)
   (/ x (+ x 1.0))
   (if (<= x -4.5e-74)
     (* y (/ (- z) x))
     (if (<= x -2.2e-126) 1.0 (if (<= x 1.58e-27) (/ y t) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.8e-38) {
		tmp = x / (x + 1.0);
	} else if (x <= -4.5e-74) {
		tmp = y * (-z / x);
	} else if (x <= -2.2e-126) {
		tmp = 1.0;
	} else if (x <= 1.58e-27) {
		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 <= (-2.8d-38)) then
        tmp = x / (x + 1.0d0)
    else if (x <= (-4.5d-74)) then
        tmp = y * (-z / x)
    else if (x <= (-2.2d-126)) then
        tmp = 1.0d0
    else if (x <= 1.58d-27) 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 <= -2.8e-38) {
		tmp = x / (x + 1.0);
	} else if (x <= -4.5e-74) {
		tmp = y * (-z / x);
	} else if (x <= -2.2e-126) {
		tmp = 1.0;
	} else if (x <= 1.58e-27) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.8e-38:
		tmp = x / (x + 1.0)
	elif x <= -4.5e-74:
		tmp = y * (-z / x)
	elif x <= -2.2e-126:
		tmp = 1.0
	elif x <= 1.58e-27:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.8e-38)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= -4.5e-74)
		tmp = Float64(y * Float64(Float64(-z) / x));
	elseif (x <= -2.2e-126)
		tmp = 1.0;
	elseif (x <= 1.58e-27)
		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 <= -2.8e-38)
		tmp = x / (x + 1.0);
	elseif (x <= -4.5e-74)
		tmp = y * (-z / x);
	elseif (x <= -2.2e-126)
		tmp = 1.0;
	elseif (x <= 1.58e-27)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.8e-38], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.5e-74], N[(y * N[((-z) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.2e-126], 1.0, If[LessEqual[x, 1.58e-27], N[(y / t), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.8e-38

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in t around inf 84.1%

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

      1. +-commutative 84.1%

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

   6. Simplified 84.1%

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

   if -2.8e-38 < x < -4.4999999999999999e-74

   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 y around inf 48.4%

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

      1. times-frac 55.8%

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

      2. +-commutative 55.8%

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

   6. Simplified 55.8%

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

   7. Taylor expanded in x around 0 55.8%

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

   8. Taylor expanded in z around 0 41.7%

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

      1. associate-*r/ 41.7%

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

      2. neg-mul-1 41.7%

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

   10. Simplified 41.7%

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

   if -4.4999999999999999e-74 < x < -2.20000000000000014e-126 or 1.58e-27 < x

   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 68.4%

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

   5. Taylor expanded in x around inf 85.1%

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

   if -2.20000000000000014e-126 < x < 1.58e-27

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in z around inf 67.0%

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

   5. Taylor expanded in x around 0 54.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{-z}{x}\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{-126}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.58 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 67.2% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{-z}{x}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-126}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.8e-38)
   (/ 1.0 (/ (+ x 1.0) x))
   (if (<= x -1.45e-74)
     (* y (/ (- z) x))
     (if (<= x -1.9e-126) 1.0 (if (<= x 9e-28) (/ y t) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.8e-38) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= -1.45e-74) {
		tmp = y * (-z / x);
	} else if (x <= -1.9e-126) {
		tmp = 1.0;
	} else if (x <= 9e-28) {
		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 <= (-2.8d-38)) then
        tmp = 1.0d0 / ((x + 1.0d0) / x)
    else if (x <= (-1.45d-74)) then
        tmp = y * (-z / x)
    else if (x <= (-1.9d-126)) then
        tmp = 1.0d0
    else if (x <= 9d-28) 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 <= -2.8e-38) {
		tmp = 1.0 / ((x + 1.0) / x);
	} else if (x <= -1.45e-74) {
		tmp = y * (-z / x);
	} else if (x <= -1.9e-126) {
		tmp = 1.0;
	} else if (x <= 9e-28) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.8e-38:
		tmp = 1.0 / ((x + 1.0) / x)
	elif x <= -1.45e-74:
		tmp = y * (-z / x)
	elif x <= -1.9e-126:
		tmp = 1.0
	elif x <= 9e-28:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.8e-38)
		tmp = Float64(1.0 / Float64(Float64(x + 1.0) / x));
	elseif (x <= -1.45e-74)
		tmp = Float64(y * Float64(Float64(-z) / x));
	elseif (x <= -1.9e-126)
		tmp = 1.0;
	elseif (x <= 9e-28)
		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 <= -2.8e-38)
		tmp = 1.0 / ((x + 1.0) / x);
	elseif (x <= -1.45e-74)
		tmp = y * (-z / x);
	elseif (x <= -1.9e-126)
		tmp = 1.0;
	elseif (x <= 9e-28)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.8e-38], N[(1.0 / N[(N[(x + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.45e-74], N[(y * N[((-z) / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -1.9e-126], 1.0, If[LessEqual[x, 9e-28], N[(y / t), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.8e-38

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

      1. clear-num 85.4%

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

      2. inv-pow 85.4%

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

      3. fma-neg 85.4%

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

   5. Applied egg-rr 85.4%

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

      1. unpow-1 85.4%

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

      2. fma-neg 85.4%

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

      3. *-commutative 85.4%

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

      4. *-commutative 85.4%

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

   7. Simplified 85.4%

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

   8. Taylor expanded in t around inf 84.1%

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

   if -2.8e-38 < x < -1.45e-74

   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 y around inf 48.4%

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

      1. times-frac 55.8%

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

      2. +-commutative 55.8%

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

   6. Simplified 55.8%

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

   7. Taylor expanded in x around 0 55.8%

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

   8. Taylor expanded in z around 0 41.7%

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

      1. associate-*r/ 41.7%

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

      2. neg-mul-1 41.7%

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

   10. Simplified 41.7%

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

   if -1.45e-74 < x < -1.8999999999999999e-126 or 8.9999999999999996e-28 < x

   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 68.4%

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

   5. Taylor expanded in x around inf 85.1%

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

   if -1.8999999999999999e-126 < x < 8.9999999999999996e-28

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in z around inf 67.0%

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

   5. Taylor expanded in x around 0 54.8%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-38}:\\ \;\;\;\;\frac{1}{\frac{x + 1}{x}}\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-74}:\\ \;\;\;\;y \cdot \frac{-z}{x}\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-126}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-28}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 12: 67.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-126}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.2e-126) 1.0 (if (<= x 1.15e-27) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.2e-126) {
		tmp = 1.0;
	} else if (x <= 1.15e-27) {
		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 <= (-2.2d-126)) then
        tmp = 1.0d0
    else if (x <= 1.15d-27) 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 <= -2.2e-126) {
		tmp = 1.0;
	} else if (x <= 1.15e-27) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.2e-126:
		tmp = 1.0
	elif x <= 1.15e-27:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.2e-126)
		tmp = 1.0;
	elseif (x <= 1.15e-27)
		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 <= -2.2e-126)
		tmp = 1.0;
	elseif (x <= 1.15e-27)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.2e-126], 1.0, If[LessEqual[x, 1.15e-27], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.20000000000000014e-126 or 1.15e-27 < x

   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 z around inf 70.8%

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

   5. Taylor expanded in x around inf 78.5%

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

   if -2.20000000000000014e-126 < x < 1.15e-27

   1. Initial program 85.3%

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

      1. *-commutative 85.3%

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

   3. Simplified 85.3%

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

   4. Taylor expanded in z around inf 67.0%

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

   5. Taylor expanded in x around 0 54.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-126}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-27}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 13: 53.9% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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 69.4%

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

5. Taylor expanded in x around inf 53.5%

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

6. Final simplification 53.5%

   \[\leadsto 1 \]

Developer target: 99.6% 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 2023325 
(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)))