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

Percentage Accurate: 89.0% → 94.1%

Time: 9.4s

Alternatives: 8

Speedup: 0.8×

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: 89.0% 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: 94.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+151}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{z \cdot y - x}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\right) - \frac{x}{t \cdot \left(z \cdot \left(x + 1\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.8e+151)
   (/ (+ x (/ y t)) (+ x 1.0))
   (if (<= z 4.2e+58)
     (/ (+ x (/ 1.0 (/ (- (* z t) x) (- (* z y) x)))) (+ x 1.0))
     (-
      (+ (/ x (+ x 1.0)) (/ y (* t (+ x 1.0))))
      (/ x (* t (* z (+ x 1.0))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.8e+151) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 4.2e+58) {
		tmp = (x + (1.0 / (((z * t) - x) / ((z * y) - x)))) / (x + 1.0);
	} else {
		tmp = ((x / (x + 1.0)) + (y / (t * (x + 1.0)))) - (x / (t * (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 (z <= (-2.8d+151)) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else if (z <= 4.2d+58) then
        tmp = (x + (1.0d0 / (((z * t) - x) / ((z * y) - x)))) / (x + 1.0d0)
    else
        tmp = ((x / (x + 1.0d0)) + (y / (t * (x + 1.0d0)))) - (x / (t * (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 (z <= -2.8e+151) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else if (z <= 4.2e+58) {
		tmp = (x + (1.0 / (((z * t) - x) / ((z * y) - x)))) / (x + 1.0);
	} else {
		tmp = ((x / (x + 1.0)) + (y / (t * (x + 1.0)))) - (x / (t * (z * (x + 1.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.8e+151:
		tmp = (x + (y / t)) / (x + 1.0)
	elif z <= 4.2e+58:
		tmp = (x + (1.0 / (((z * t) - x) / ((z * y) - x)))) / (x + 1.0)
	else:
		tmp = ((x / (x + 1.0)) + (y / (t * (x + 1.0)))) - (x / (t * (z * (x + 1.0))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.8e+151)
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	elseif (z <= 4.2e+58)
		tmp = Float64(Float64(x + Float64(1.0 / Float64(Float64(Float64(z * t) - x) / Float64(Float64(z * y) - x)))) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(Float64(x / Float64(x + 1.0)) + Float64(y / Float64(t * Float64(x + 1.0)))) - Float64(x / Float64(t * Float64(z * Float64(x + 1.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.8e+151)
		tmp = (x + (y / t)) / (x + 1.0);
	elseif (z <= 4.2e+58)
		tmp = (x + (1.0 / (((z * t) - x) / ((z * y) - x)))) / (x + 1.0);
	else
		tmp = ((x / (x + 1.0)) + (y / (t * (x + 1.0)))) - (x / (t * (z * (x + 1.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.8e+151], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.2e+58], N[(N[(x + N[(1.0 / N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(y / N[(t * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x / N[(t * N[(z * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.79999999999999987e151

   1. Initial program 69.7%

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

      1. *-commutative 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in z around inf 92.0%

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

   if -2.79999999999999987e151 < z < 4.20000000000000024e58

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

   3. Simplified 99.2%

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

      1. clear-num 99.2%

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

      2. inv-pow 99.2%

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

      3. fma-neg 99.2%

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

   5. Applied egg-rr 99.2%

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

      1. unpow-1 99.2%

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

      2. *-commutative 99.2%

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

      3. fma-neg 99.2%

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

      4. *-commutative 99.2%

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

   7. Simplified 99.2%

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

   if 4.20000000000000024e58 < z

   1. Initial program 86.1%

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

      1. *-commutative 86.1%

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

   3. Simplified 86.1%

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

   4. Taylor expanded in t around inf 94.8%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+151}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+58}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{z \cdot y - x}}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{x}{x + 1} + \frac{y}{t \cdot \left(x + 1\right)}\right) - \frac{x}{t \cdot \left(z \cdot \left(x + 1\right)\right)}\\ \end{array} \]

Alternative 2: 94.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+153} \lor \neg \left(z \leq 6.2 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{z \cdot y - x}}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.7e+153) (not (<= z 6.2e+55)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ 1.0 (/ (- (* z t) x) (- (* z y) x)))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.7e+153) || !(z <= 6.2e+55)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (1.0 / (((z * t) - x) / ((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 ((z <= (-1.7d+153)) .or. (.not. (z <= 6.2d+55))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + (1.0d0 / (((z * t) - x) / ((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 ((z <= -1.7e+153) || !(z <= 6.2e+55)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (1.0 / (((z * t) - x) / ((z * y) - x)))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.7e+153) or not (z <= 6.2e+55):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + (1.0 / (((z * t) - x) / ((z * y) - x)))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.7e+153) || !(z <= 6.2e+55))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(1.0 / Float64(Float64(Float64(z * t) - x) / Float64(Float64(z * y) - x)))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.7e+153) || ~((z <= 6.2e+55)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + (1.0 / (((z * t) - x) / ((z * y) - x)))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.7e+153], N[Not[LessEqual[z, 6.2e+55]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(1.0 / N[(N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6999999999999999e153 or 6.19999999999999987e55 < z

   1. Initial program 78.6%

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

      1. *-commutative 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in z around inf 93.4%

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

   if -1.6999999999999999e153 < z < 6.19999999999999987e55

   1. Initial program 99.2%

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

      1. *-commutative 99.2%

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

   3. Simplified 99.2%

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

      1. clear-num 99.2%

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

      2. inv-pow 99.2%

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

      3. fma-neg 99.2%

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

   5. Applied egg-rr 99.2%

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

      1. unpow-1 99.2%

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

      2. *-commutative 99.2%

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

      3. fma-neg 99.2%

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

      4. *-commutative 99.2%

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

   7. Simplified 99.2%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.7 \cdot 10^{+153} \lor \neg \left(z \leq 6.2 \cdot 10^{+55}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{1}{\frac{z \cdot t - x}{z \cdot y - x}}}{x + 1}\\ \end{array} \]

Alternative 3: 94.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+151} \lor \neg \left(z \leq 3.6 \cdot 10^{+58}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.18e+151) (not (<= z 3.6e+58)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (/ (+ x (/ (- (* z y) x) (- (* z t) x))) (+ x 1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.18e+151) || !(z <= 3.6e+58)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.18d+151)) .or. (.not. (z <= 3.6d+58))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.18e+151) || !(z <= 3.6e+58)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.18e+151) or not (z <= 3.6e+58):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.18e+151) || !(z <= 3.6e+58))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(Float64(x + Float64(Float64(Float64(z * y) - x) / Float64(Float64(z * t) - x))) / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.18e+151) || ~((z <= 3.6e+58)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = (x + (((z * y) - x) / ((z * t) - x))) / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.18e+151], N[Not[LessEqual[z, 3.6e+58]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(N[(z * y), $MachinePrecision] - x), $MachinePrecision] / N[(N[(z * t), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.18000000000000005e151 or 3.59999999999999996e58 < z

   1. Initial program 78.6%

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

      1. *-commutative 78.6%

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

   3. Simplified 78.6%

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

   4. Taylor expanded in z around inf 93.4%

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

   if -1.18000000000000005e151 < z < 3.59999999999999996e58

   1. Initial program 99.2%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.18 \cdot 10^{+151} \lor \neg \left(z \leq 3.6 \cdot 10^{+58}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + \frac{z \cdot y - x}{z \cdot t - x}}{x + 1}\\ \end{array} \]

Alternative 4: 81.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-129} \lor \neg \left(t \leq 3.1 \cdot 10^{-142}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -7.6e-129) (not (<= t 3.1e-142)))
   (/ (+ x (/ y t)) (+ x 1.0))
   (- 1.0 (/ (* y (/ z x)) (+ x 1.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -7.6e-129) || !(t <= 3.1e-142)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y * (z / 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 <= (-7.6d-129)) .or. (.not. (t <= 3.1d-142))) then
        tmp = (x + (y / t)) / (x + 1.0d0)
    else
        tmp = 1.0d0 - ((y * (z / 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 <= -7.6e-129) || !(t <= 3.1e-142)) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0 - ((y * (z / x)) / (x + 1.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -7.6e-129) or not (t <= 3.1e-142):
		tmp = (x + (y / t)) / (x + 1.0)
	else:
		tmp = 1.0 - ((y * (z / x)) / (x + 1.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -7.6e-129) || !(t <= 3.1e-142))
		tmp = Float64(Float64(x + Float64(y / t)) / Float64(x + 1.0));
	else
		tmp = Float64(1.0 - Float64(Float64(y * Float64(z / x)) / Float64(x + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -7.6e-129) || ~((t <= 3.1e-142)))
		tmp = (x + (y / t)) / (x + 1.0);
	else
		tmp = 1.0 - ((y * (z / x)) / (x + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -7.6e-129], N[Not[LessEqual[t, 3.1e-142]], $MachinePrecision]], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(y * N[(z / x), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.59999999999999969e-129 or 3.1e-142 < t

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

   3. Simplified 89.0%

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

   4. Taylor expanded in z around inf 88.6%

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

   if -7.59999999999999969e-129 < t < 3.1e-142

   1. Initial program 94.9%

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

      1. *-commutative 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in t around 0 74.2%

      \[\leadsto \color{blue}{\frac{1 + \left(x + -1 \cdot \frac{y \cdot z}{x}\right)}{1 + x}} \]
   5. 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. mul-1-neg 74.2%

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

      3. unsub-neg 74.2%

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

      4. +-commutative 74.2%

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

      5. associate-/l* 77.9%

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

      6. +-commutative 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in y around 0 73.8%

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

      1. mul-1-neg 73.8%

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

      2. associate-/r* 74.2%

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

      3. associate-*r/ 78.0%

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

      4. +-commutative 78.0%

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

      5. sub-neg 78.0%

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

   9. Simplified 78.0%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.6 \cdot 10^{-129} \lor \neg \left(t \leq 3.1 \cdot 10^{-142}\right):\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{y \cdot \frac{z}{x}}{x + 1}\\ \end{array} \]

Alternative 5: 77.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.3e-10) 1.0 (if (<= x 2.3e+58) (/ (+ x (/ y t)) (+ x 1.0)) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.3e-10) {
		tmp = 1.0;
	} else if (x <= 2.3e+58) {
		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 <= (-2.3d-10)) then
        tmp = 1.0d0
    else if (x <= 2.3d+58) 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 <= -2.3e-10) {
		tmp = 1.0;
	} else if (x <= 2.3e+58) {
		tmp = (x + (y / t)) / (x + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.3e-10:
		tmp = 1.0
	elif x <= 2.3e+58:
		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 <= -2.3e-10)
		tmp = 1.0;
	elseif (x <= 2.3e+58)
		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 <= -2.3e-10)
		tmp = 1.0;
	elseif (x <= 2.3e+58)
		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, -2.3e-10], 1.0, If[LessEqual[x, 2.3e+58], N[(N[(x + N[(y / t), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.30000000000000007e-10 or 2.30000000000000002e58 < x

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

   3. Simplified 89.4%

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

      1. clear-num 89.4%

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

      2. inv-pow 89.4%

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

      3. fma-neg 89.4%

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

   5. Applied egg-rr 89.4%

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

      1. unpow-1 89.4%

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

      2. *-commutative 89.4%

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

      3. fma-neg 89.4%

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

      4. *-commutative 89.4%

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

   7. Simplified 89.4%

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

   8. Taylor expanded in z around inf 76.5%

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

   9. Taylor expanded in x around inf 93.8%

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

   if -2.30000000000000007e-10 < x < 2.30000000000000002e58

   1. Initial program 92.0%

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

      1. *-commutative 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in z around inf 76.8%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{-10}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+58}:\\ \;\;\;\;\frac{x + \frac{y}{t}}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 67.7% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-76}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.4e-13) 1.0 (if (<= x 6.6e-76) (/ y t) 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.4e-13) {
		tmp = 1.0;
	} else if (x <= 6.6e-76) {
		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 <= (-1.4d-13)) then
        tmp = 1.0d0
    else if (x <= 6.6d-76) 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 <= -1.4e-13) {
		tmp = 1.0;
	} else if (x <= 6.6e-76) {
		tmp = y / t;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.4e-13:
		tmp = 1.0
	elif x <= 6.6e-76:
		tmp = y / t
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.4e-13)
		tmp = 1.0;
	elseif (x <= 6.6e-76)
		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 <= -1.4e-13)
		tmp = 1.0;
	elseif (x <= 6.6e-76)
		tmp = y / t;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.4e-13], 1.0, If[LessEqual[x, 6.6e-76], N[(y / t), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4000000000000001e-13 or 6.59999999999999967e-76 < x

   1. Initial program 89.0%

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

      1. *-commutative 89.0%

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

   3. Simplified 89.0%

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

      1. clear-num 89.0%

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

      2. inv-pow 89.0%

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

      3. fma-neg 89.0%

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

   5. Applied egg-rr 89.0%

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

      1. unpow-1 89.0%

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

      2. *-commutative 89.0%

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

      3. fma-neg 89.0%

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

      4. *-commutative 89.0%

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

   7. Simplified 89.0%

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

   8. Taylor expanded in z around inf 74.3%

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

   9. Taylor expanded in x around inf 86.1%

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

   if -1.4000000000000001e-13 < x < 6.59999999999999967e-76

   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. Step-by-step derivation

      1. clear-num 93.0%

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

      2. inv-pow 93.0%

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

      3. fma-neg 93.0%

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

   5. Applied egg-rr 93.0%

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

      1. unpow-1 93.0%

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

      2. *-commutative 93.0%

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

      3. fma-neg 93.0%

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

      4. *-commutative 93.0%

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

   7. Simplified 93.0%

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

   8. Taylor expanded in x around 0 65.9%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-13}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-76}:\\ \;\;\;\;\frac{y}{t}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 55.8% accurate, 3.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-72}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.8e-72) 1.0 (if (<= x 1.9e-99) x 1.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.8e-72) {
		tmp = 1.0;
	} else if (x <= 1.9e-99) {
		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 <= (-7.8d-72)) then
        tmp = 1.0d0
    else if (x <= 1.9d-99) 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 <= -7.8e-72) {
		tmp = 1.0;
	} else if (x <= 1.9e-99) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.8e-72:
		tmp = 1.0
	elif x <= 1.9e-99:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.8e-72)
		tmp = 1.0;
	elseif (x <= 1.9e-99)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.8e-72)
		tmp = 1.0;
	elseif (x <= 1.9e-99)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.8e-72], 1.0, If[LessEqual[x, 1.9e-99], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -7.8e-72 or 1.8999999999999998e-99 < x

   1. Initial program 89.9%

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

      1. *-commutative 89.9%

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

   3. Simplified 89.9%

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

      1. clear-num 89.9%

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

      2. inv-pow 89.9%

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

      3. fma-neg 89.9%

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

   5. Applied egg-rr 89.9%

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

      1. unpow-1 89.9%

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

      2. *-commutative 89.9%

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

      3. fma-neg 89.9%

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

      4. *-commutative 89.9%

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

   7. Simplified 89.9%

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

   8. Taylor expanded in z around inf 72.7%

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

   9. Taylor expanded in x around inf 81.6%

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

   if -7.8e-72 < x < 1.8999999999999998e-99

   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. Taylor expanded in t around inf 17.5%

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

      1. +-commutative 17.5%

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

   6. Simplified 17.5%

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

   7. Taylor expanded in x around 0 17.5%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-72}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{-99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 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 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. Step-by-step derivation

   1. clear-num 90.8%

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

   2. inv-pow 90.8%

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

   3. fma-neg 90.8%

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

5. Applied egg-rr 90.8%

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

   1. unpow-1 90.8%

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

   2. *-commutative 90.8%

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

   3. fma-neg 90.8%

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

   4. *-commutative 90.8%

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

7. Simplified 90.8%

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

8. Taylor expanded in z around inf 76.6%

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

9. Taylor expanded in x around inf 52.8%

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

10. Final simplification 52.8%

    \[\leadsto 1 \]

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 2023306 
(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)))