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

Percentage Accurate: 89.3% → 96.4%

Time: 9.8s

Alternatives: 11

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: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ t_2 := \frac{x + \frac{y \cdot z - x}{t_1}}{x + 1}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{t_1}\\ \mathbf{elif}\;t_2 \leq 10^{+239}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

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 (+ x 1.0)) (/ z t_1))
     (if (<= t_2 1e+239) 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 / (x + 1.0)) * (z / t_1);
	} else if (t_2 <= 1e+239) {
		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 / (x + 1.0)) * (z / t_1);
	} else if (t_2 <= 1e+239) {
		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 / (x + 1.0)) * (z / t_1)
	elif t_2 <= 1e+239:
		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 / Float64(x + 1.0)) * Float64(z / t_1));
	elseif (t_2 <= 1e+239)
		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 / (x + 1.0)) * (z / t_1);
	elseif (t_2 <= 1e+239)
		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 / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, 1e+239], 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 23.0%

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

      1. *-commutative 23.0%

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

   3. Simplified 23.0%

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

   4. Taylor expanded in y around inf 22.6%

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

      1. times-frac 90.7%

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

      2. +-commutative 90.7%

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

   6. Simplified 90.7%

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

   if -inf.0 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1)) < 9.99999999999999991e238

   1. Initial program 98.1%

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

   if 9.99999999999999991e238 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x 1))

   1. Initial program 22.6%

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

      1. *-commutative 22.6%

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

   3. Simplified 22.6%

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

   4. Taylor expanded in z around inf 92.0%

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

4. Final simplification 97.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq -\infty:\\ \;\;\;\;\frac{y}{x + 1} \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 10^{+239}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]

Alternative 2: 68.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{if}\;x \leq -3.5 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-203}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z (- (* z t) x)))))
   (if (<= x -3.5e-21)
     1.0
     (if (<= x -2.5e-103)
       t_1
       (if (<= x 2.3e-203)
         (/ y t)
         (if (<= x 1.3e-157) t_1 (/ x (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -3.5e-21) {
		tmp = 1.0;
	} else if (x <= -2.5e-103) {
		tmp = t_1;
	} else if (x <= 2.3e-203) {
		tmp = y / t;
	} else if (x <= 1.3e-157) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / ((z * t) - x))
    if (x <= (-3.5d-21)) then
        tmp = 1.0d0
    else if (x <= (-2.5d-103)) then
        tmp = t_1
    else if (x <= 2.3d-203) then
        tmp = y / t
    else if (x <= 1.3d-157) then
        tmp = t_1
    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 t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -3.5e-21) {
		tmp = 1.0;
	} else if (x <= -2.5e-103) {
		tmp = t_1;
	} else if (x <= 2.3e-203) {
		tmp = y / t;
	} else if (x <= 1.3e-157) {
		tmp = t_1;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / ((z * t) - x))
	tmp = 0
	if x <= -3.5e-21:
		tmp = 1.0
	elif x <= -2.5e-103:
		tmp = t_1
	elif x <= 2.3e-203:
		tmp = y / t
	elif x <= 1.3e-157:
		tmp = t_1
	else:
		tmp = x / (x + 1.0)
	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 <= -3.5e-21)
		tmp = 1.0;
	elseif (x <= -2.5e-103)
		tmp = t_1;
	elseif (x <= 2.3e-203)
		tmp = Float64(y / t);
	elseif (x <= 1.3e-157)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + 1.0));
	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 <= -3.5e-21)
		tmp = 1.0;
	elseif (x <= -2.5e-103)
		tmp = t_1;
	elseif (x <= 2.3e-203)
		tmp = y / t;
	elseif (x <= 1.3e-157)
		tmp = t_1;
	else
		tmp = x / (x + 1.0);
	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, -3.5e-21], 1.0, If[LessEqual[x, -2.5e-103], t$95$1, If[LessEqual[x, 2.3e-203], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.3e-157], t$95$1, N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.5000000000000003e-21

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around inf 85.5%

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

      1. +-commutative 85.5%

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

   6. Simplified 85.5%

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

      1. clear-num 85.5%

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

      2. inv-pow 85.5%

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

      3. +-commutative 85.5%

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

   8. Applied egg-rr 85.5%

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

      1. unpow-1 85.5%

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

   10. Simplified 85.5%

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

   11. Taylor expanded in x around inf 89.5%

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

   if -3.5000000000000003e-21 < x < -2.49999999999999983e-103 or 2.29999999999999991e-203 < x < 1.29999999999999994e-157

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in y around inf 59.4%

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

      1. times-frac 67.7%

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

      2. +-commutative 67.7%

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

   6. Simplified 67.7%

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

   7. Taylor expanded in x around 0 67.7%

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

   if -2.49999999999999983e-103 < x < 2.29999999999999991e-203

   1. Initial program 75.6%

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

      1. *-commutative 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in y around inf 45.5%

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

      1. times-frac 58.7%

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

      2. +-commutative 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in x around 0 58.7%

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

   8. Taylor expanded in z around inf 67.3%

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

   if 1.29999999999999994e-157 < x

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in t around inf 73.7%

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

      1. +-commutative 73.7%

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

   6. Simplified 73.7%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-21}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-203}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 3: 67.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{if}\;x \leq -4.2 \cdot 10^{-22}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-202}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-157}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ z (- (* z t) x)))))
   (if (<= x -4.2e-22)
     (- 1.0 (* (/ y x) (/ z x)))
     (if (<= x -7.6e-103)
       t_1
       (if (<= x 3.1e-202)
         (/ y t)
         (if (<= x 1.3e-157) t_1 (/ x (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -4.2e-22) {
		tmp = 1.0 - ((y / x) * (z / x));
	} else if (x <= -7.6e-103) {
		tmp = t_1;
	} else if (x <= 3.1e-202) {
		tmp = y / t;
	} else if (x <= 1.3e-157) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = y * (z / ((z * t) - x))
    if (x <= (-4.2d-22)) then
        tmp = 1.0d0 - ((y / x) * (z / x))
    else if (x <= (-7.6d-103)) then
        tmp = t_1
    else if (x <= 3.1d-202) then
        tmp = y / t
    else if (x <= 1.3d-157) then
        tmp = t_1
    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 t_1 = y * (z / ((z * t) - x));
	double tmp;
	if (x <= -4.2e-22) {
		tmp = 1.0 - ((y / x) * (z / x));
	} else if (x <= -7.6e-103) {
		tmp = t_1;
	} else if (x <= 3.1e-202) {
		tmp = y / t;
	} else if (x <= 1.3e-157) {
		tmp = t_1;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (z / ((z * t) - x))
	tmp = 0
	if x <= -4.2e-22:
		tmp = 1.0 - ((y / x) * (z / x))
	elif x <= -7.6e-103:
		tmp = t_1
	elif x <= 3.1e-202:
		tmp = y / t
	elif x <= 1.3e-157:
		tmp = t_1
	else:
		tmp = x / (x + 1.0)
	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 <= -4.2e-22)
		tmp = Float64(1.0 - Float64(Float64(y / x) * Float64(z / x)));
	elseif (x <= -7.6e-103)
		tmp = t_1;
	elseif (x <= 3.1e-202)
		tmp = Float64(y / t);
	elseif (x <= 1.3e-157)
		tmp = t_1;
	else
		tmp = Float64(x / Float64(x + 1.0));
	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 <= -4.2e-22)
		tmp = 1.0 - ((y / x) * (z / x));
	elseif (x <= -7.6e-103)
		tmp = t_1;
	elseif (x <= 3.1e-202)
		tmp = y / t;
	elseif (x <= 1.3e-157)
		tmp = t_1;
	else
		tmp = x / (x + 1.0);
	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, -4.2e-22], N[(1.0 - N[(N[(y / x), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -7.6e-103], t$95$1, If[LessEqual[x, 3.1e-202], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.3e-157], t$95$1, N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -4.20000000000000016e-22

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around 0 91.7%

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

      1. associate-+r+ 91.7%

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

      2. +-commutative 91.7%

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

      3. associate-+l+ 91.7%

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

      4. mul-1-neg 91.7%

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

      5. unsub-neg 91.7%

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

      6. associate-/l* 94.4%

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

      7. +-commutative 94.4%

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

   6. Simplified 94.4%

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

   7. Taylor expanded in y around 0 91.7%

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

      1. mul-1-neg 91.7%

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

      2. unsub-neg 91.7%

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

      3. associate-/r* 91.7%

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

      4. associate-*l/ 94.4%

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

      5. *-commutative 94.4%

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

   9. Simplified 94.4%

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

   10. Taylor expanded in x around inf 91.4%

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

       1. unpow2 91.4%

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

       2. times-frac 94.2%

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

   12. Simplified 94.2%

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

   if -4.20000000000000016e-22 < x < -7.6000000000000001e-103 or 3.1e-202 < x < 1.29999999999999994e-157

   1. Initial program 91.3%

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

      1. *-commutative 91.3%

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

   3. Simplified 91.3%

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

   4. Taylor expanded in y around inf 59.4%

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

      1. times-frac 67.7%

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

      2. +-commutative 67.7%

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

   6. Simplified 67.7%

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

   7. Taylor expanded in x around 0 67.7%

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

   if -7.6000000000000001e-103 < x < 3.1e-202

   1. Initial program 75.6%

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

      1. *-commutative 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in y around inf 45.5%

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

      1. times-frac 58.7%

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

      2. +-commutative 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in x around 0 58.7%

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

   8. Taylor expanded in z around inf 67.3%

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

   if 1.29999999999999994e-157 < x

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in t around inf 73.7%

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

      1. +-commutative 73.7%

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

   6. Simplified 73.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-22}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq -7.6 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-202}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-157}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 4: 67.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := z \cdot t - x\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{-21}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \frac{z}{t_1}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-201}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-157}:\\ \;\;\;\;\frac{y}{\frac{t_1}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (* z t) x)))
   (if (<= x -2.2e-21)
     (- 1.0 (* (/ y x) (/ z x)))
     (if (<= x -2.5e-103)
       (* y (/ z t_1))
       (if (<= x 1.9e-201)
         (/ y t)
         (if (<= x 1.3e-157) (/ y (/ t_1 z)) (/ x (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (z * t) - x;
	double tmp;
	if (x <= -2.2e-21) {
		tmp = 1.0 - ((y / x) * (z / x));
	} else if (x <= -2.5e-103) {
		tmp = y * (z / t_1);
	} else if (x <= 1.9e-201) {
		tmp = y / t;
	} else if (x <= 1.3e-157) {
		tmp = y / (t_1 / z);
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (z * t) - x
    if (x <= (-2.2d-21)) then
        tmp = 1.0d0 - ((y / x) * (z / x))
    else if (x <= (-2.5d-103)) then
        tmp = y * (z / t_1)
    else if (x <= 1.9d-201) then
        tmp = y / t
    else if (x <= 1.3d-157) then
        tmp = y / (t_1 / z)
    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 t_1 = (z * t) - x;
	double tmp;
	if (x <= -2.2e-21) {
		tmp = 1.0 - ((y / x) * (z / x));
	} else if (x <= -2.5e-103) {
		tmp = y * (z / t_1);
	} else if (x <= 1.9e-201) {
		tmp = y / t;
	} else if (x <= 1.3e-157) {
		tmp = y / (t_1 / z);
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (z * t) - x
	tmp = 0
	if x <= -2.2e-21:
		tmp = 1.0 - ((y / x) * (z / x))
	elif x <= -2.5e-103:
		tmp = y * (z / t_1)
	elif x <= 1.9e-201:
		tmp = y / t
	elif x <= 1.3e-157:
		tmp = y / (t_1 / z)
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(z * t) - x)
	tmp = 0.0
	if (x <= -2.2e-21)
		tmp = Float64(1.0 - Float64(Float64(y / x) * Float64(z / x)));
	elseif (x <= -2.5e-103)
		tmp = Float64(y * Float64(z / t_1));
	elseif (x <= 1.9e-201)
		tmp = Float64(y / t);
	elseif (x <= 1.3e-157)
		tmp = Float64(y / Float64(t_1 / z));
	else
		tmp = Float64(x / 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 (x <= -2.2e-21)
		tmp = 1.0 - ((y / x) * (z / x));
	elseif (x <= -2.5e-103)
		tmp = y * (z / t_1);
	elseif (x <= 1.9e-201)
		tmp = y / t;
	elseif (x <= 1.3e-157)
		tmp = y / (t_1 / z);
	else
		tmp = x / (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[LessEqual[x, -2.2e-21], N[(1.0 - N[(N[(y / x), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.5e-103], N[(y * N[(z / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.9e-201], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.3e-157], N[(y / N[(t$95$1 / z), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < -2.2000000000000001e-21

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around 0 91.7%

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

      1. associate-+r+ 91.7%

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

      2. +-commutative 91.7%

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

      3. associate-+l+ 91.7%

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

      4. mul-1-neg 91.7%

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

      5. unsub-neg 91.7%

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

      6. associate-/l* 94.4%

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

      7. +-commutative 94.4%

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

   6. Simplified 94.4%

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

   7. Taylor expanded in y around 0 91.7%

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

      1. mul-1-neg 91.7%

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

      2. unsub-neg 91.7%

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

      3. associate-/r* 91.7%

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

      4. associate-*l/ 94.4%

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

      5. *-commutative 94.4%

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

   9. Simplified 94.4%

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

   10. Taylor expanded in x around inf 91.4%

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

       1. unpow2 91.4%

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

       2. times-frac 94.2%

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

   12. Simplified 94.2%

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

   if -2.2000000000000001e-21 < x < -2.49999999999999983e-103

   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 inf 43.7%

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

      1. times-frac 51.9%

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

      2. +-commutative 51.9%

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

   6. Simplified 51.9%

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

   7. Taylor expanded in x around 0 51.9%

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

   if -2.49999999999999983e-103 < x < 1.9e-201

   1. Initial program 75.6%

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

      1. *-commutative 75.6%

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

   3. Simplified 75.6%

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

   4. Taylor expanded in y around inf 45.5%

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

      1. times-frac 58.7%

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

      2. +-commutative 58.7%

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

   6. Simplified 58.7%

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

   7. Taylor expanded in x around 0 58.7%

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

   8. Taylor expanded in z around inf 67.3%

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

   if 1.9e-201 < x < 1.29999999999999994e-157

   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 inf 90.9%

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

      1. times-frac 99.1%

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

      2. +-commutative 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in x around 0 99.1%

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

      1. clear-num 99.3%

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

      2. un-div-inv 99.6%

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

      3. *-commutative 99.6%

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

   9. Applied egg-rr 99.6%

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

   if 1.29999999999999994e-157 < x

   1. Initial program 87.9%

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

      1. *-commutative 87.9%

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

   3. Simplified 87.9%

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

   4. Taylor expanded in t around inf 73.7%

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

      1. +-commutative 73.7%

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

   6. Simplified 73.7%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-21}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-103}:\\ \;\;\;\;y \cdot \frac{z}{z \cdot t - x}\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-201}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-157}:\\ \;\;\;\;\frac{y}{\frac{z \cdot t - x}{z}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 5: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-25} \lor \neg \left(t \leq 3.5 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.55e-25) (not (<= t 3.5e-105)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (- 1.0 (/ y (/ x z)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.55e-25) || !(t <= 3.5e-105)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.55d-25)) .or. (.not. (t <= 3.5d-105))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + (1.0d0 - (y / (x / z)))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.55e-25) || !(t <= 3.5e-105)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.55e-25) or not (t <= 3.5e-105):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.55e-25) || !(t <= 3.5e-105))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(1.0 - Float64(y / Float64(x / z)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.55e-25) || ~((t <= 3.5e-105)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + (1.0 - (y / (x / z)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.55e-25], N[Not[LessEqual[t, 3.5e-105]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(1.0 - 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 < -1.54999999999999997e-25 or 3.5e-105 < t

   1. Initial program 83.9%

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

      1. *-commutative 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in z around inf 89.9%

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

   if -1.54999999999999997e-25 < t < 3.5e-105

   1. Initial program 93.1%

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

      1. *-commutative 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around 0 79.1%

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

      1. associate-+r+ 79.1%

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

      2. +-commutative 79.1%

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

      3. associate-+l+ 79.1%

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

      4. mul-1-neg 79.1%

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

      5. unsub-neg 79.1%

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

      6. associate-/l* 82.0%

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

      7. +-commutative 82.0%

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

   6. Simplified 82.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.55 \cdot 10^{-25} \lor \neg \left(t \leq 3.5 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \left(1 - \frac{y}{\frac{x}{z}}\right)}{x + 1}\\ \end{array} \]

Alternative 6: 81.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-29} \lor \neg \left(t \leq 2 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z \cdot \frac{y}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3e-29) (not (<= t 2e-105)))
   (/ (+ 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 <= -3e-29) || !(t <= 2e-105)) {
		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 <= (-3d-29)) .or. (.not. (t <= 2d-105))) 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 <= -3e-29) || !(t <= 2e-105)) {
		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 <= -3e-29) or not (t <= 2e-105):
		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 <= -3e-29) || !(t <= 2e-105))
		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 <= -3e-29) || ~((t <= 2e-105)))
		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, -3e-29], N[Not[LessEqual[t, 2e-105]], $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 < -3.0000000000000003e-29 or 1.99999999999999993e-105 < t

   1. Initial program 83.5%

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

      1. *-commutative 83.5%

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

   3. Simplified 83.5%

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

   4. Taylor expanded in z around inf 88.9%

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

   if -3.0000000000000003e-29 < t < 1.99999999999999993e-105

   1. Initial program 93.9%

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

      1. *-commutative 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in t around 0 79.5%

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

      1. associate-+r+ 79.5%

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

      2. +-commutative 79.5%

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

      3. associate-+l+ 79.5%

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

      4. mul-1-neg 79.5%

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

      5. unsub-neg 79.5%

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

      6. associate-/l* 82.4%

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

      7. +-commutative 82.4%

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

   6. Simplified 82.4%

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

   7. Taylor expanded in y around 0 79.5%

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

      1. mul-1-neg 79.5%

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

      2. unsub-neg 79.5%

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

      3. associate-/r* 79.5%

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

      4. associate-*l/ 79.5%

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

      5. *-commutative 79.5%

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

   9. Simplified 79.5%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3 \cdot 10^{-29} \lor \neg \left(t \leq 2 \cdot 10^{-105}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{z \cdot \frac{y}{x}}{x + 1}\\ \end{array} \]

Alternative 7: 76.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-19}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-17}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.65e-19)
   (- 1.0 (* (/ y x) (/ z x)))
   (if (<= x 7e-17) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.65e-19) {
		tmp = 1.0 - ((y / x) * (z / x));
	} else if (x <= 7e-17) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.65d-19)) then
        tmp = 1.0d0 - ((y / x) * (z / x))
    else if (x <= 7d-17) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.65e-19) {
		tmp = 1.0 - ((y / x) * (z / x));
	} else if (x <= 7e-17) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.65e-19:
		tmp = 1.0 - ((y / x) * (z / x))
	elif x <= 7e-17:
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.65e-19)
		tmp = Float64(1.0 - Float64(Float64(y / x) * Float64(z / x)));
	elseif (x <= 7e-17)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.65e-19)
		tmp = 1.0 - ((y / x) * (z / x));
	elseif (x <= 7e-17)
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.65e-19], N[(1.0 - N[(N[(y / x), $MachinePrecision] * N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7e-17], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -1.6499999999999999e-19

   1. Initial program 97.1%

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

      1. *-commutative 97.1%

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

   3. Simplified 97.1%

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

   4. Taylor expanded in t around 0 92.9%

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

      1. associate-+r+ 92.9%

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

      2. +-commutative 92.9%

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

      3. associate-+l+ 92.9%

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

      4. mul-1-neg 92.9%

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

      5. unsub-neg 92.9%

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

      6. associate-/l* 95.7%

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

      7. +-commutative 95.7%

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

   6. Simplified 95.7%

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

   7. Taylor expanded in y around 0 92.9%

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

      1. mul-1-neg 92.9%

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

      2. unsub-neg 92.9%

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

      3. associate-/r* 92.9%

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

      4. associate-*l/ 95.6%

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

      5. *-commutative 95.6%

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

   9. Simplified 95.6%

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

   10. Taylor expanded in x around inf 92.5%

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

       1. unpow2 92.5%

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

       2. times-frac 95.4%

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

   12. Simplified 95.4%

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

   if -1.6499999999999999e-19 < x < 7.0000000000000003e-17

   1. Initial program 82.3%

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

      1. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in z around inf 75.3%

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

   if 7.0000000000000003e-17 < x

   1. Initial program 87.8%

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

      1. *-commutative 87.8%

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

   3. Simplified 87.8%

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

   4. Taylor expanded in t around inf 88.2%

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

      1. +-commutative 88.2%

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

   6. Simplified 88.2%

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

      1. clear-num 88.1%

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

      2. inv-pow 88.1%

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

      3. +-commutative 88.1%

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

   8. Applied egg-rr 88.1%

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

      1. unpow-1 88.1%

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

   10. Simplified 88.1%

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

   11. Taylor expanded in x around inf 90.6%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-19}:\\ \;\;\;\;1 - \frac{y}{x} \cdot \frac{z}{x}\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-17}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 67.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-161}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.4e-22)
   1.0
   (if (<= x 2.6e-161)
     (/ y t)
     (if (<= x 3e-40) x (if (<= x 3.6e-17) (/ y t) 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.4e-22) {
		tmp = 1.0;
	} else if (x <= 2.6e-161) {
		tmp = y / t;
	} else if (x <= 3e-40) {
		tmp = x;
	} else if (x <= 3.6e-17) {
		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 <= (-2.4d-22)) then
        tmp = 1.0d0
    else if (x <= 2.6d-161) then
        tmp = y / t
    else if (x <= 3d-40) then
        tmp = x
    else if (x <= 3.6d-17) 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 <= -2.4e-22) {
		tmp = 1.0;
	} else if (x <= 2.6e-161) {
		tmp = y / t;
	} else if (x <= 3e-40) {
		tmp = x;
	} else if (x <= 3.6e-17) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.4e-22:
		tmp = 1.0
	elif x <= 2.6e-161:
		tmp = y / t
	elif x <= 3e-40:
		tmp = x
	elif x <= 3.6e-17:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.4e-22)
		tmp = 1.0;
	elseif (x <= 2.6e-161)
		tmp = Float64(y / t);
	elseif (x <= 3e-40)
		tmp = x;
	elseif (x <= 3.6e-17)
		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 <= -2.4e-22)
		tmp = 1.0;
	elseif (x <= 2.6e-161)
		tmp = y / t;
	elseif (x <= 3e-40)
		tmp = x;
	elseif (x <= 3.6e-17)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.4e-22], 1.0, If[LessEqual[x, 2.6e-161], N[(y / t), $MachinePrecision], If[LessEqual[x, 3e-40], x, If[LessEqual[x, 3.6e-17], N[(y / t), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.40000000000000002e-22 or 3.59999999999999995e-17 < x

   1. Initial program 93.1%

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

      1. *-commutative 93.1%

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

   3. Simplified 93.1%

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

   4. Taylor expanded in t around inf 86.7%

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

      1. +-commutative 86.7%

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

   6. Simplified 86.7%

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

      1. clear-num 86.7%

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

      2. inv-pow 86.7%

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

      3. +-commutative 86.7%

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

   8. Applied egg-rr 86.7%

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

      1. unpow-1 86.7%

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

   10. Simplified 86.7%

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

   11. Taylor expanded in x around inf 90.0%

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

   if -2.40000000000000002e-22 < x < 2.59999999999999995e-161 or 3.0000000000000002e-40 < x < 3.59999999999999995e-17

   1. Initial program 79.3%

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

      1. *-commutative 79.3%

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

   3. Simplified 79.3%

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

   4. Taylor expanded in y around inf 47.9%

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

      1. times-frac 60.1%

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

      2. +-commutative 60.1%

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

   6. Simplified 60.1%

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

   7. Taylor expanded in x around 0 60.1%

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

   8. Taylor expanded in z around inf 60.7%

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

   if 2.59999999999999995e-161 < x < 3.0000000000000002e-40

   1. Initial program 95.2%

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

      1. *-commutative 95.2%

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

   3. Simplified 95.2%

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

   4. Taylor expanded in t around inf 43.8%

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

      1. +-commutative 43.8%

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

   6. Simplified 43.8%

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

   7. Taylor expanded in x around 0 43.8%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-161}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-40}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-17}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 67.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-161}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6e-22) 1.0 (if (<= x 2.75e-161) (/ y t) (/ x (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6e-22) {
		tmp = 1.0;
	} else if (x <= 2.75e-161) {
		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 <= (-6d-22)) then
        tmp = 1.0d0
    else if (x <= 2.75d-161) 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 <= -6e-22) {
		tmp = 1.0;
	} else if (x <= 2.75e-161) {
		tmp = y / t;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6e-22:
		tmp = 1.0
	elif x <= 2.75e-161:
		tmp = y / t
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6e-22)
		tmp = 1.0;
	elseif (x <= 2.75e-161)
		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 <= -6e-22)
		tmp = 1.0;
	elseif (x <= 2.75e-161)
		tmp = y / t;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6e-22], 1.0, If[LessEqual[x, 2.75e-161], N[(y / t), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.9999999999999998e-22

   1. Initial program 97.2%

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

      1. *-commutative 97.2%

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

   3. Simplified 97.2%

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

   4. Taylor expanded in t around inf 85.5%

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

      1. +-commutative 85.5%

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

   6. Simplified 85.5%

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

      1. clear-num 85.5%

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

      2. inv-pow 85.5%

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

      3. +-commutative 85.5%

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

   8. Applied egg-rr 85.5%

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

      1. unpow-1 85.5%

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

   10. Simplified 85.5%

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

   11. Taylor expanded in x around inf 89.5%

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

   if -5.9999999999999998e-22 < x < 2.75e-161

   1. Initial program 80.4%

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

      1. *-commutative 80.4%

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

   3. Simplified 80.4%

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

   4. Taylor expanded in y around inf 49.4%

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

      1. times-frac 61.2%

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

      2. +-commutative 61.2%

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

   6. Simplified 61.2%

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

   7. Taylor expanded in x around 0 61.2%

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

   8. Taylor expanded in z around inf 60.9%

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

   if 2.75e-161 < x

   1. Initial program 88.0%

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

      1. *-commutative 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in t around inf 72.8%

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

      1. +-commutative 72.8%

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

   6. Simplified 72.8%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{-22}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-161}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 10: 55.6% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.55e-19) 1.0 (if (<= x 5.5e-18) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.55e-19) {
		tmp = 1.0;
	} else if (x <= 5.5e-18) {
		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 <= (-1.55d-19)) then
        tmp = 1.0d0
    else if (x <= 5.5d-18) 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 <= -1.55e-19) {
		tmp = 1.0;
	} else if (x <= 5.5e-18) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.55e-19:
		tmp = 1.0
	elif x <= 5.5e-18:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.55e-19)
		tmp = 1.0;
	elseif (x <= 5.5e-18)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.55e-19)
		tmp = 1.0;
	elseif (x <= 5.5e-18)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.55e-19], 1.0, If[LessEqual[x, 5.5e-18], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.5499999999999999e-19 or 5.5e-18 < x

   1. Initial program 93.0%

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

      1. *-commutative 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in 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%

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

   11. Taylor expanded in x around inf 90.6%

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

   if -1.5499999999999999e-19 < x < 5.5e-18

   1. Initial program 82.3%

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

      1. *-commutative 82.3%

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

   3. Simplified 82.3%

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

   4. Taylor expanded in t around inf 24.8%

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

      1. +-commutative 24.8%

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

   6. Simplified 24.8%

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

   7. Taylor expanded in x around 0 24.8%

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

4. Final simplification 57.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.55 \cdot 10^{-19}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 54.3% 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 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 t around inf 55.3%

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

   1. +-commutative 55.3%

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

6. Simplified 55.3%

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

   1. clear-num 55.3%

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

   2. inv-pow 55.3%

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

   3. +-commutative 55.3%

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

8. Applied egg-rr 55.3%

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

   1. unpow-1 55.3%

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

10. Simplified 55.3%

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

11. Taylor expanded in x around inf 50.5%

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

12. Final simplification 50.5%

    \[\leadsto 1 \]

Developer target: 99.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023293 
(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)))