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

Percentage Accurate: 89.3% → 94.7%

Time: 10.2s

Alternatives: 9

Speedup: 0.4×

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: 94.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+247}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ x (/ (- (* y z) x) (- (* z t) x))) (+ x 1.0))))
   (if (<= t_1 2e+247) t_1 (/ (+ x (/ y t)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 2e+247) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0d0)
    if (t_1 <= 2d+247) then
        tmp = t_1
    else
        tmp = (x + (y / t)) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	double tmp;
	if (t_1 <= 2e+247) {
		tmp = t_1;
	} else {
		tmp = (x + (y / t)) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0)
	tmp = 0
	if t_1 <= 2e+247:
		tmp = t_1
	else:
		tmp = (x + (y / t)) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x + Float64(Float64(Float64(y * z) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_1 <= 2e+247)
		tmp = t_1;
	else
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x + (((y * z) - x) / ((z * t) - x))) / (x + 1.0);
	tmp = 0.0;
	if (t_1 <= 2e+247)
		tmp = t_1;
	else
		tmp = (x + (y / t)) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x + N[(N[(N[(y * z), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+247], t$95$1, N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64))) < 1.9999999999999999e247

   1. Initial program 96.8%

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

   if 1.9999999999999999e247 < (/.f64 (+.f64 x (/.f64 (-.f64 (*.f64 y z) x) (-.f64 (*.f64 t z) x))) (+.f64 x #s(literal 1 binary64)))

   1. Initial program 31.3%

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

      1. *-commutative 31.3%

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

   3. Simplified 31.3%

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

   5. Taylor expanded in z around inf 90.3%

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

4. Final simplification 96.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1} \leq 2 \cdot 10^{+247}:\\ \;\;\;\;\frac{x + \frac{y \cdot z - x}{z \cdot t - x}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 67.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -1.04 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-58}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= x -1.04e-29)
     t_1
     (if (<= x 1.35e-148)
       (/ y t)
       (if (<= x 1.8e-58)
         (- 1.0 (/ (* y z) x))
         (if (<= x 1.8e-31) (/ y (* t (+ x 1.0))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -1.04e-29) {
		tmp = t_1;
	} else if (x <= 1.35e-148) {
		tmp = y / t;
	} else if (x <= 1.8e-58) {
		tmp = 1.0 - ((y * z) / x);
	} else if (x <= 1.8e-31) {
		tmp = y / (t * (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 / (x + 1.0d0)
    if (x <= (-1.04d-29)) then
        tmp = t_1
    else if (x <= 1.35d-148) then
        tmp = y / t
    else if (x <= 1.8d-58) then
        tmp = 1.0d0 - ((y * z) / x)
    else if (x <= 1.8d-31) then
        tmp = y / (t * (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 / (x + 1.0);
	double tmp;
	if (x <= -1.04e-29) {
		tmp = t_1;
	} else if (x <= 1.35e-148) {
		tmp = y / t;
	} else if (x <= 1.8e-58) {
		tmp = 1.0 - ((y * z) / x);
	} else if (x <= 1.8e-31) {
		tmp = y / (t * (x + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -1.04e-29:
		tmp = t_1
	elif x <= 1.35e-148:
		tmp = y / t
	elif x <= 1.8e-58:
		tmp = 1.0 - ((y * z) / x)
	elif x <= 1.8e-31:
		tmp = y / (t * (x + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -1.04e-29)
		tmp = t_1;
	elseif (x <= 1.35e-148)
		tmp = Float64(y / t);
	elseif (x <= 1.8e-58)
		tmp = Float64(1.0 - Float64(Float64(y * z) / x));
	elseif (x <= 1.8e-31)
		tmp = Float64(y / Float64(t * Float64(x + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -1.04e-29)
		tmp = t_1;
	elseif (x <= 1.35e-148)
		tmp = y / t;
	elseif (x <= 1.8e-58)
		tmp = 1.0 - ((y * z) / x);
	elseif (x <= 1.8e-31)
		tmp = y / (t * (x + 1.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.04e-29], t$95$1, If[LessEqual[x, 1.35e-148], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.8e-58], N[(1.0 - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e-31], N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.03999999999999995e-29 or 1.80000000000000002e-31 < x

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around inf 89.5%

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

      1. +-commutative 89.5%

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

   7. Simplified 89.5%

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

   if -1.03999999999999995e-29 < x < 1.34999999999999994e-148

   1. Initial program 90.3%

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

      1. *-commutative 90.3%

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

   3. Simplified 90.3%

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

   5. Taylor expanded in x around 0 62.9%

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

   if 1.34999999999999994e-148 < x < 1.80000000000000005e-58

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. *-un-lft-identity 99.7%

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

      3. associate-/r* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t around 0 51.4%

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

      1. associate-+r+ 51.4%

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

      2. +-commutative 51.4%

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

      3. mul-1-neg 51.4%

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

      4. associate-*r/ 51.4%

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

      5. sub-neg 51.4%

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

      6. +-commutative 51.4%

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

      7. div-sub 51.4%

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

      8. *-inverses 51.4%

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

      9. associate-/l* 51.4%

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

      10. +-commutative 51.4%

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

   9. Simplified 51.4%

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

   10. Taylor expanded in x around 0 51.4%

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

   if 1.80000000000000005e-58 < x < 1.80000000000000002e-31

   1. Initial program 77.8%

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

      1. *-commutative 77.8%

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

   3. Simplified 77.8%

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

   5. Taylor expanded in z around inf 75.0%

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

   6. Taylor expanded in y around inf 63.8%

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

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{-29}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-58}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{t \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 67.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -1.14 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-148}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-58}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ x (+ x 1.0))))
   (if (<= x -1.14e-29)
     t_1
     (if (<= x 1.1e-148)
       (/ y t)
       (if (<= x 1.3e-58)
         (- 1.0 (/ (* y z) x))
         (if (<= x 2.5e-31) (/ y t) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -1.14e-29) {
		tmp = t_1;
	} else if (x <= 1.1e-148) {
		tmp = y / t;
	} else if (x <= 1.3e-58) {
		tmp = 1.0 - ((y * z) / x);
	} else if (x <= 2.5e-31) {
		tmp = y / t;
	} 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 / (x + 1.0d0)
    if (x <= (-1.14d-29)) then
        tmp = t_1
    else if (x <= 1.1d-148) then
        tmp = y / t
    else if (x <= 1.3d-58) then
        tmp = 1.0d0 - ((y * z) / x)
    else if (x <= 2.5d-31) then
        tmp = y / t
    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 / (x + 1.0);
	double tmp;
	if (x <= -1.14e-29) {
		tmp = t_1;
	} else if (x <= 1.1e-148) {
		tmp = y / t;
	} else if (x <= 1.3e-58) {
		tmp = 1.0 - ((y * z) / x);
	} else if (x <= 2.5e-31) {
		tmp = y / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -1.14e-29:
		tmp = t_1
	elif x <= 1.1e-148:
		tmp = y / t
	elif x <= 1.3e-58:
		tmp = 1.0 - ((y * z) / x)
	elif x <= 2.5e-31:
		tmp = y / t
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -1.14e-29)
		tmp = t_1;
	elseif (x <= 1.1e-148)
		tmp = Float64(y / t);
	elseif (x <= 1.3e-58)
		tmp = Float64(1.0 - Float64(Float64(y * z) / x));
	elseif (x <= 2.5e-31)
		tmp = Float64(y / t);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -1.14e-29)
		tmp = t_1;
	elseif (x <= 1.1e-148)
		tmp = y / t;
	elseif (x <= 1.3e-58)
		tmp = 1.0 - ((y * z) / x);
	elseif (x <= 2.5e-31)
		tmp = y / t;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.14e-29], t$95$1, If[LessEqual[x, 1.1e-148], N[(y / t), $MachinePrecision], If[LessEqual[x, 1.3e-58], N[(1.0 - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.5e-31], N[(y / t), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.13999999999999995e-29 or 2.5e-31 < x

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around inf 89.5%

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

      1. +-commutative 89.5%

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

   7. Simplified 89.5%

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

   if -1.13999999999999995e-29 < x < 1.10000000000000009e-148 or 1.30000000000000003e-58 < x < 2.5e-31

   1. Initial program 89.2%

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

      1. *-commutative 89.2%

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

   3. Simplified 89.2%

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

   5. Taylor expanded in x around 0 63.0%

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

   if 1.10000000000000009e-148 < x < 1.30000000000000003e-58

   1. Initial program 99.7%

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

      1. *-commutative 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. *-un-lft-identity 99.7%

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

      3. associate-/r* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t around 0 51.4%

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

      1. associate-+r+ 51.4%

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

      2. +-commutative 51.4%

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

      3. mul-1-neg 51.4%

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

      4. associate-*r/ 51.4%

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

      5. sub-neg 51.4%

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

      6. +-commutative 51.4%

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

      7. div-sub 51.4%

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

      8. *-inverses 51.4%

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

      9. associate-/l* 51.4%

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

      10. +-commutative 51.4%

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

   9. Simplified 51.4%

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

   10. Taylor expanded in x around 0 51.4%

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

Alternative 4: 83.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-105} \lor \neg \left(t \leq 5.2 \cdot 10^{-76}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{\frac{z}{x}}{-1 - x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.5e-105) (not (<= t 5.2e-76)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (+ 1.0 (* y (/ (/ z x) (- -1.0 x))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.5e-105) || !(t <= 5.2e-76)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-1.5d-105)) .or. (.not. (t <= 5.2d-76))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 + (y * ((z / x) / ((-1.0d0) - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.5e-105) || !(t <= 5.2e-76)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.5e-105) or not (t <= 5.2e-76):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.5e-105) || !(t <= 5.2e-76))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 + Float64(y * Float64(Float64(z / x) / Float64(-1.0 - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.5e-105) || ~((t <= 5.2e-76)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 + (y * ((z / x) / (-1.0 - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.5e-105], N[Not[LessEqual[t, 5.2e-76]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * N[(N[(z / x), $MachinePrecision] / N[(-1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.5e-105 or 5.1999999999999999e-76 < t

   1. Initial program 90.2%

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

      1. *-commutative 90.2%

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

   3. Simplified 90.2%

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

   5. Taylor expanded in z around inf 91.7%

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

   if -1.5e-105 < t < 5.1999999999999999e-76

   1. Initial program 94.1%

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

      1. *-commutative 94.1%

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

   3. Simplified 94.1%

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

      1. clear-num 94.1%

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

      2. *-un-lft-identity 94.1%

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

      3. associate-/r* 94.1%

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

   6. Applied egg-rr 94.1%

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

   7. Taylor expanded in t around 0 74.2%

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

      1. associate-+r+ 74.2%

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

      2. +-commutative 74.2%

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

      3. mul-1-neg 74.2%

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

      4. associate-*r/ 77.1%

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

      5. sub-neg 77.1%

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

      6. +-commutative 77.1%

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

      7. div-sub 77.1%

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

      8. *-inverses 77.1%

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

      9. associate-/l* 77.6%

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

      10. +-commutative 77.6%

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

   9. Simplified 77.6%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{-105} \lor \neg \left(t \leq 5.2 \cdot 10^{-76}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{\frac{z}{x}}{-1 - x}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 78.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-177} \lor \neg \left(z \leq 9 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.2e-177) (not (<= z 9e-87)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (/ (* y z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e-177) || !(z <= 9e-87)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y * z) / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-3.2d-177)) .or. (.not. (z <= 9d-87))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y * z) / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e-177) || !(z <= 9e-87)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y * z) / x);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.2e-177) or not (z <= 9e-87):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((y * z) / x)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.2e-177) || !(z <= 9e-87))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y * z) / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.2e-177) || ~((z <= 9e-87)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((y * z) / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.2e-177], N[Not[LessEqual[z, 9e-87]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.1999999999999998e-177 or 8.99999999999999915e-87 < z

   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. Add Preprocessing

   5. Taylor expanded in z around inf 87.0%

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

   if -3.1999999999999998e-177 < z < 8.99999999999999915e-87

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. *-un-lft-identity 99.7%

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

      3. associate-/r* 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in t around 0 81.3%

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

      1. associate-+r+ 81.3%

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

      2. +-commutative 81.3%

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

      3. mul-1-neg 81.3%

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

      4. associate-*r/ 81.4%

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

      5. sub-neg 81.4%

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

      6. +-commutative 81.4%

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

      7. div-sub 81.4%

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

      8. *-inverses 81.4%

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

      9. associate-/l* 81.4%

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

      10. +-commutative 81.4%

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

   9. Simplified 81.4%

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

   10. Taylor expanded in x around 0 79.7%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-177} \lor \neg \left(z \leq 9 \cdot 10^{-87}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot z}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 68.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-29} \lor \neg \left(x \leq 1.6 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= x -4.2e-29) (not (<= x 1.6e-31))) (/ x (+ x 1.0)) (/ y t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.2e-29) || !(x <= 1.6e-31)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x <= (-4.2d-29)) .or. (.not. (x <= 1.6d-31))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = y / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x <= -4.2e-29) || !(x <= 1.6e-31)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = y / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x <= -4.2e-29) or not (x <= 1.6e-31):
		tmp = x / (x + 1.0)
	else:
		tmp = y / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((x <= -4.2e-29) || !(x <= 1.6e-31))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(y / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x <= -4.2e-29) || ~((x <= 1.6e-31)))
		tmp = x / (x + 1.0);
	else
		tmp = y / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[x, -4.2e-29], N[Not[LessEqual[x, 1.6e-31]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.19999999999999979e-29 or 1.60000000000000009e-31 < x

   1. Initial program 92.6%

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

      1. *-commutative 92.6%

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

   3. Simplified 92.6%

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

   5. Taylor expanded in t around inf 89.5%

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

      1. +-commutative 89.5%

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

   7. Simplified 89.5%

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

   if -4.19999999999999979e-29 < x < 1.60000000000000009e-31

   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. Add Preprocessing

   5. Taylor expanded in x around 0 56.8%

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

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-29} \lor \neg \left(x \leq 1.6 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.35 \cdot 10^{-18}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-31}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -3.35e-18) 1.0 (if (<= x 1.65e-31) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.35e-18) {
		tmp = 1.0;
	} else if (x <= 1.65e-31) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-3.35d-18)) then
        tmp = 1.0d0
    else if (x <= 1.65d-31) then
        tmp = y / t
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -3.35e-18) {
		tmp = 1.0;
	} else if (x <= 1.65e-31) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -3.35e-18:
		tmp = 1.0
	elif x <= 1.65e-31:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -3.35e-18)
		tmp = 1.0;
	elseif (x <= 1.65e-31)
		tmp = Float64(y / t);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -3.35e-18)
		tmp = 1.0;
	elseif (x <= 1.65e-31)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -3.35e-18], 1.0, If[LessEqual[x, 1.65e-31], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3499999999999999e-18 or 1.65e-31 < x

   1. Initial program 92.5%

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

      1. *-commutative 92.5%

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

   3. Simplified 92.5%

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

   5. Taylor expanded in x around inf 87.7%

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

   if -3.3499999999999999e-18 < x < 1.65e-31

   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. Add Preprocessing

   5. Taylor expanded in x around 0 55.9%

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

Alternative 8: 55.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-14}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.4 \cdot 10^{-10}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.15e-14) 1.0 (if (<= x 7.4e-10) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.15e-14) {
		tmp = 1.0;
	} else if (x <= 7.4e-10) {
		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 <= (-1.15d-14)) then
        tmp = 1.0d0
    else if (x <= 7.4d-10) 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 <= -1.15e-14) {
		tmp = 1.0;
	} else if (x <= 7.4e-10) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.15e-14:
		tmp = 1.0
	elif x <= 7.4e-10:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.15e-14)
		tmp = 1.0;
	elseif (x <= 7.4e-10)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.15e-14)
		tmp = 1.0;
	elseif (x <= 7.4e-10)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.15e-14], 1.0, If[LessEqual[x, 7.4e-10], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.14999999999999999e-14 or 7.4000000000000003e-10 < x

   1. Initial program 92.2%

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

      1. *-commutative 92.2%

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

   3. Simplified 92.2%

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

   5. Taylor expanded in x around inf 90.9%

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

   if -1.14999999999999999e-14 < x < 7.4000000000000003e-10

   1. Initial program 91.2%

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

      1. *-commutative 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in t around inf 25.8%

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

      1. +-commutative 25.8%

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

   7. Simplified 25.8%

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

   8. Taylor expanded in x around 0 25.8%

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

Alternative 9: 53.3% 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 91.7%

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

   1. *-commutative 91.7%

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

3. Simplified 91.7%

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

5. Taylor expanded in x around inf 49.5%

   \[\leadsto \color{blue}{1} \]
6. Add Preprocessing

Developer target: 99.5% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024097 
(FPCore (x y z t)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :alt
  (/ (+ x (- (/ y (- t (/ x z))) (/ x (- (* t z) x)))) (+ x 1.0))

  (/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0)))