Numeric.SpecFunctions:choose from math-functions-0.1.5.2

Percentage Accurate: 84.8% → 96.0%

Time: 6.0s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 84.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-182}:\\ \;\;\;\;x + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4e-182)
   (+ x (* x (/ y z)))
   (if (<= z 2.05e-38) (* (+ y z) (/ x z)) (* x (- (/ y z) -1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4e-182) {
		tmp = x + (x * (y / z));
	} else if (z <= 2.05e-38) {
		tmp = (y + z) * (x / z);
	} else {
		tmp = x * ((y / z) - -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.4d-182)) then
        tmp = x + (x * (y / z))
    else if (z <= 2.05d-38) then
        tmp = (y + z) * (x / z)
    else
        tmp = x * ((y / z) - (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4e-182) {
		tmp = x + (x * (y / z));
	} else if (z <= 2.05e-38) {
		tmp = (y + z) * (x / z);
	} else {
		tmp = x * ((y / z) - -1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.4e-182:
		tmp = x + (x * (y / z))
	elif z <= 2.05e-38:
		tmp = (y + z) * (x / z)
	else:
		tmp = x * ((y / z) - -1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4e-182)
		tmp = Float64(x + Float64(x * Float64(y / z)));
	elseif (z <= 2.05e-38)
		tmp = Float64(Float64(y + z) * Float64(x / z));
	else
		tmp = Float64(x * Float64(Float64(y / z) - -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.4e-182)
		tmp = x + (x * (y / z));
	elseif (z <= 2.05e-38)
		tmp = (y + z) * (x / z);
	else
		tmp = x * ((y / z) - -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4e-182], N[(x + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.05e-38], N[(N[(y + z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.39999999999999999e-182

   1. Initial program 85.1%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.1%

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

      2. remove-double-neg 99.1%

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

      3. unsub-neg 99.1%

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

      4. div-sub 99.1%

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

      5. remove-double-neg 99.1%

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

      6. distribute-frac-neg2 99.1%

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

      7. *-inverses 99.1%

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

      8. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

      1. sub-neg 99.1%

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

      2. metadata-eval 99.1%

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

      3. distribute-rgt-in 99.1%

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

      4. *-commutative 99.1%

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

      5. *-un-lft-identity 99.1%

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

   6. Applied egg-rr 99.1%

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

   if -5.39999999999999999e-182 < z < 2.0499999999999999e-38

   1. Initial program 94.3%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. *-commutative 94.3%

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

      2. associate-/l* 94.6%

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

   3. Simplified 94.6%

      \[\leadsto \color{blue}{\left(y + z\right) \cdot \frac{x}{z}} \]
   4. Add Preprocessing

   if 2.0499999999999999e-38 < z

   1. Initial program 81.5%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. div-sub 99.9%

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

      5. remove-double-neg 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-182}:\\ \;\;\;\;x + x \cdot \frac{y}{z}\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-38}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{z} - -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 6.6e+59) (fma x (/ y z) x) (/ (* x (+ y z)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 6.6e+59) {
		tmp = fma(x, (y / z), x);
	} else {
		tmp = (x * (y + z)) / z;
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 6.6e+59)
		tmp = fma(x, Float64(y / z), x);
	else
		tmp = Float64(Float64(x * Float64(y + z)) / z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 6.6e+59], N[(x * N[(y / z), $MachinePrecision] + x), $MachinePrecision], N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.5999999999999999e59

   1. Initial program 84.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-*l/ 84.4%

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

      2. distribute-lft-in 82.2%

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

      3. remove-double-neg 82.2%

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

      4. distribute-lft-neg-out 82.2%

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

      5. distribute-frac-neg 82.2%

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

      6. distribute-rgt-neg-out 82.2%

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

      7. distribute-frac-neg 82.2%

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

      8. distribute-lft-neg-out 82.2%

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

      9. distribute-rgt-neg-out 82.2%

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

      10. remove-double-neg 82.2%

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

      11. associate-*l/ 80.3%

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

      12. associate-*r/ 82.0%

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

      13. fma-undefine 82.0%

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

      14. remove-double-neg 82.0%

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

      15. distribute-rgt-neg-out 82.0%

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

      16. distribute-lft-neg-out 82.0%

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

      17. distribute-frac-neg2 82.0%

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

      18. associate-*l/ 84.0%

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

      19. associate-/l* 98.0%

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

      20. *-inverses 98.0%

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

      21. *-rgt-identity 98.0%

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

   3. Simplified 98.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{y}{z}, x\right)} \]
   4. Add Preprocessing

   if 6.5999999999999999e59 < y

   1. Initial program 93.2%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{+59}:\\ \;\;\;\;\mathsf{fma}\left(x, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-13} \lor \neg \left(y \leq 2.5 \cdot 10^{-141}\right) \land \left(y \leq 2.65 \cdot 10^{-105} \lor \neg \left(y \leq 4.6 \cdot 10^{+51}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e-13)
         (and (not (<= y 2.5e-141))
              (or (<= y 2.65e-105) (not (<= y 4.6e+51)))))
   (* x (/ y z))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e-13) || (!(y <= 2.5e-141) && ((y <= 2.65e-105) || !(y <= 4.6e+51)))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.8d-13)) .or. (.not. (y <= 2.5d-141)) .and. (y <= 2.65d-105) .or. (.not. (y <= 4.6d+51))) then
        tmp = x * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e-13) || (!(y <= 2.5e-141) && ((y <= 2.65e-105) || !(y <= 4.6e+51)))) {
		tmp = x * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.8e-13) or (not (y <= 2.5e-141) and ((y <= 2.65e-105) or not (y <= 4.6e+51))):
		tmp = x * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e-13) || (!(y <= 2.5e-141) && ((y <= 2.65e-105) || !(y <= 4.6e+51))))
		tmp = Float64(x * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.8e-13) || (~((y <= 2.5e-141)) && ((y <= 2.65e-105) || ~((y <= 4.6e+51)))))
		tmp = x * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.8e-13], And[N[Not[LessEqual[y, 2.5e-141]], $MachinePrecision], Or[LessEqual[y, 2.65e-105], N[Not[LessEqual[y, 4.6e+51]], $MachinePrecision]]]], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.7999999999999999e-13 or 2.5e-141 < y < 2.6500000000000001e-105 or 4.6000000000000001e51 < y

   1. Initial program 92.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 90.4%

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

      2. remove-double-neg 90.4%

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

      3. unsub-neg 90.4%

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

      4. div-sub 90.4%

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

      5. remove-double-neg 90.4%

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

      6. distribute-frac-neg2 90.4%

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

      7. *-inverses 90.4%

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

      8. metadata-eval 90.4%

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

   3. Simplified 90.4%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 78.6%

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

      1. associate-*r/ 72.0%

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

   7. Simplified 72.0%

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

   if -1.7999999999999999e-13 < y < 2.5e-141 or 2.6500000000000001e-105 < y < 4.6000000000000001e51

   1. Initial program 79.3%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. div-sub 99.9%

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

      5. remove-double-neg 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.1%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{-13} \lor \neg \left(y \leq 2.5 \cdot 10^{-141}\right) \land \left(y \leq 2.65 \cdot 10^{-105} \lor \neg \left(y \leq 4.6 \cdot 10^{+51}\right)\right):\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 71.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= y -1.9e-13)
     t_0
     (if (<= y 2.5e-141)
       x
       (if (<= y 2.65e-105) (* x (/ y z)) (if (<= y 7e+52) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -1.9e-13) {
		tmp = t_0;
	} else if (y <= 2.5e-141) {
		tmp = x;
	} else if (y <= 2.65e-105) {
		tmp = x * (y / z);
	} else if (y <= 7e+52) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x / z)
    if (y <= (-1.9d-13)) then
        tmp = t_0
    else if (y <= 2.5d-141) then
        tmp = x
    else if (y <= 2.65d-105) then
        tmp = x * (y / z)
    else if (y <= 7d+52) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -1.9e-13) {
		tmp = t_0;
	} else if (y <= 2.5e-141) {
		tmp = x;
	} else if (y <= 2.65e-105) {
		tmp = x * (y / z);
	} else if (y <= 7e+52) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if y <= -1.9e-13:
		tmp = t_0
	elif y <= 2.5e-141:
		tmp = x
	elif y <= 2.65e-105:
		tmp = x * (y / z)
	elif y <= 7e+52:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -1.9e-13)
		tmp = t_0;
	elseif (y <= 2.5e-141)
		tmp = x;
	elseif (y <= 2.65e-105)
		tmp = Float64(x * Float64(y / z));
	elseif (y <= 7e+52)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (y <= -1.9e-13)
		tmp = t_0;
	elseif (y <= 2.5e-141)
		tmp = x;
	elseif (y <= 2.65e-105)
		tmp = x * (y / z);
	elseif (y <= 7e+52)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.9e-13], t$95$0, If[LessEqual[y, 2.5e-141], x, If[LessEqual[y, 2.65e-105], N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+52], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9e-13 or 7e52 < y

   1. Initial program 92.7%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.9%

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

      2. remove-double-neg 89.9%

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

      3. unsub-neg 89.9%

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

      4. div-sub 89.9%

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

      5. remove-double-neg 89.9%

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

      6. distribute-frac-neg2 89.9%

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

      7. *-inverses 89.9%

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

      8. metadata-eval 89.9%

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

   3. Simplified 89.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-/l* 77.0%

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

   7. Applied egg-rr 77.0%

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

   if -1.9e-13 < y < 2.5e-141 or 2.6500000000000001e-105 < y < 7e52

   1. Initial program 79.3%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. div-sub 99.9%

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

      5. remove-double-neg 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.1%

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

   if 2.5e-141 < y < 2.6500000000000001e-105

   1. Initial program 94.7%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.3%

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

      2. remove-double-neg 99.3%

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

      3. unsub-neg 99.3%

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

      4. div-sub 99.3%

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

      5. remove-double-neg 99.3%

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

      6. distribute-frac-neg2 99.3%

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

      7. *-inverses 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 73.3%

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

      1. associate-*r/ 78.1%

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

   7. Simplified 78.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-105}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \frac{x}{z}\\ \mathbf{if}\;y \leq -5 \cdot 10^{-12}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (/ x z))))
   (if (<= y -5e-12)
     t_0
     (if (<= y 2.5e-141)
       x
       (if (<= y 2.65e-105) (/ x (/ z y)) (if (<= y 2.3e+52) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -5e-12) {
		tmp = t_0;
	} else if (y <= 2.5e-141) {
		tmp = x;
	} else if (y <= 2.65e-105) {
		tmp = x / (z / y);
	} else if (y <= 2.3e+52) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x / z)
    if (y <= (-5d-12)) then
        tmp = t_0
    else if (y <= 2.5d-141) then
        tmp = x
    else if (y <= 2.65d-105) then
        tmp = x / (z / y)
    else if (y <= 2.3d+52) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (x / z);
	double tmp;
	if (y <= -5e-12) {
		tmp = t_0;
	} else if (y <= 2.5e-141) {
		tmp = x;
	} else if (y <= 2.65e-105) {
		tmp = x / (z / y);
	} else if (y <= 2.3e+52) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (x / z)
	tmp = 0
	if y <= -5e-12:
		tmp = t_0
	elif y <= 2.5e-141:
		tmp = x
	elif y <= 2.65e-105:
		tmp = x / (z / y)
	elif y <= 2.3e+52:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(x / z))
	tmp = 0.0
	if (y <= -5e-12)
		tmp = t_0;
	elseif (y <= 2.5e-141)
		tmp = x;
	elseif (y <= 2.65e-105)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= 2.3e+52)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (x / z);
	tmp = 0.0;
	if (y <= -5e-12)
		tmp = t_0;
	elseif (y <= 2.5e-141)
		tmp = x;
	elseif (y <= 2.65e-105)
		tmp = x / (z / y);
	elseif (y <= 2.3e+52)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e-12], t$95$0, If[LessEqual[y, 2.5e-141], x, If[LessEqual[y, 2.65e-105], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+52], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9999999999999997e-12 or 2.3e52 < y

   1. Initial program 92.7%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.9%

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

      2. remove-double-neg 89.9%

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

      3. unsub-neg 89.9%

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

      4. div-sub 89.9%

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

      5. remove-double-neg 89.9%

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

      6. distribute-frac-neg2 89.9%

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

      7. *-inverses 89.9%

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

      8. metadata-eval 89.9%

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

   3. Simplified 89.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-/l* 77.0%

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

   7. Applied egg-rr 77.0%

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

   if -4.9999999999999997e-12 < y < 2.5e-141 or 2.6500000000000001e-105 < y < 2.3e52

   1. Initial program 79.3%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. div-sub 99.9%

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

      5. remove-double-neg 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.1%

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

   if 2.5e-141 < y < 2.6500000000000001e-105

   1. Initial program 94.7%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.3%

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

      2. remove-double-neg 99.3%

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

      3. unsub-neg 99.3%

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

      4. div-sub 99.3%

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

      5. remove-double-neg 99.3%

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

      6. distribute-frac-neg2 99.3%

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

      7. *-inverses 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 73.3%

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

      1. associate-*r/ 78.1%

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

   7. Simplified 78.1%

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

      1. clear-num 78.6%

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

      2. un-div-inv 78.6%

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

   9. Applied egg-rr 78.6%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+52}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 71.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e-15)
   (* y (/ x z))
   (if (<= y 2.5e-141)
     x
     (if (<= y 2.65e-105) (/ x (/ z y)) (if (<= y 3.3e+50) x (/ y (/ z x)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e-15) {
		tmp = y * (x / z);
	} else if (y <= 2.5e-141) {
		tmp = x;
	} else if (y <= 2.65e-105) {
		tmp = x / (z / y);
	} else if (y <= 3.3e+50) {
		tmp = x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.4d-15)) then
        tmp = y * (x / z)
    else if (y <= 2.5d-141) then
        tmp = x
    else if (y <= 2.65d-105) then
        tmp = x / (z / y)
    else if (y <= 3.3d+50) then
        tmp = x
    else
        tmp = y / (z / x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e-15) {
		tmp = y * (x / z);
	} else if (y <= 2.5e-141) {
		tmp = x;
	} else if (y <= 2.65e-105) {
		tmp = x / (z / y);
	} else if (y <= 3.3e+50) {
		tmp = x;
	} else {
		tmp = y / (z / x);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.4e-15:
		tmp = y * (x / z)
	elif y <= 2.5e-141:
		tmp = x
	elif y <= 2.65e-105:
		tmp = x / (z / y)
	elif y <= 3.3e+50:
		tmp = x
	else:
		tmp = y / (z / x)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e-15)
		tmp = Float64(y * Float64(x / z));
	elseif (y <= 2.5e-141)
		tmp = x;
	elseif (y <= 2.65e-105)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= 3.3e+50)
		tmp = x;
	else
		tmp = Float64(y / Float64(z / x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.4e-15)
		tmp = y * (x / z);
	elseif (y <= 2.5e-141)
		tmp = x;
	elseif (y <= 2.65e-105)
		tmp = x / (z / y);
	elseif (y <= 3.3e+50)
		tmp = x;
	else
		tmp = y / (z / x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.4e-15], N[(y * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-141], x, If[LessEqual[y, 2.65e-105], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+50], x, N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.40000000000000007e-15

   1. Initial program 92.4%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 94.8%

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

      2. remove-double-neg 94.8%

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

      3. unsub-neg 94.8%

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

      4. div-sub 94.8%

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

      5. remove-double-neg 94.8%

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

      6. distribute-frac-neg2 94.8%

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

      7. *-inverses 94.8%

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

      8. metadata-eval 94.8%

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

   3. Simplified 94.8%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 79.0%

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

      1. *-commutative 79.0%

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

      2. associate-/l* 77.2%

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

   7. Applied egg-rr 77.2%

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

   if -1.40000000000000007e-15 < y < 2.5e-141 or 2.6500000000000001e-105 < y < 3.3e50

   1. Initial program 79.3%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. div-sub 99.9%

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

      5. remove-double-neg 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.1%

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

   if 2.5e-141 < y < 2.6500000000000001e-105

   1. Initial program 94.7%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.3%

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

      2. remove-double-neg 99.3%

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

      3. unsub-neg 99.3%

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

      4. div-sub 99.3%

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

      5. remove-double-neg 99.3%

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

      6. distribute-frac-neg2 99.3%

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

      7. *-inverses 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 73.3%

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

      1. associate-*r/ 78.1%

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

   7. Simplified 78.1%

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

      1. clear-num 78.6%

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

      2. un-div-inv 78.6%

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

   9. Applied egg-rr 78.6%

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

   if 3.3e50 < y

   1. Initial program 93.2%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 83.5%

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

      2. remove-double-neg 83.5%

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

      3. unsub-neg 83.5%

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

      4. div-sub 83.5%

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

      5. remove-double-neg 83.5%

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

      6. distribute-frac-neg2 83.5%

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

      7. *-inverses 83.5%

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

      8. metadata-eval 83.5%

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

   3. Simplified 83.5%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-/l* 76.9%

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

   7. Applied egg-rr 76.9%

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

      1. clear-num 76.9%

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

      2. un-div-inv 77.0%

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

   9. Applied egg-rr 77.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+50}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot x}{z}\\ \mathbf{if}\;y \leq -9.8 \cdot 10^{-14}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* y x) z)))
   (if (<= y -9.8e-14)
     t_0
     (if (<= y 2.5e-141)
       x
       (if (<= y 2.65e-105) (/ x (/ z y)) (if (<= y 1.35e+54) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = (y * x) / z;
	double tmp;
	if (y <= -9.8e-14) {
		tmp = t_0;
	} else if (y <= 2.5e-141) {
		tmp = x;
	} else if (y <= 2.65e-105) {
		tmp = x / (z / y);
	} else if (y <= 1.35e+54) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y * x) / z
    if (y <= (-9.8d-14)) then
        tmp = t_0
    else if (y <= 2.5d-141) then
        tmp = x
    else if (y <= 2.65d-105) then
        tmp = x / (z / y)
    else if (y <= 1.35d+54) then
        tmp = x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (y * x) / z;
	double tmp;
	if (y <= -9.8e-14) {
		tmp = t_0;
	} else if (y <= 2.5e-141) {
		tmp = x;
	} else if (y <= 2.65e-105) {
		tmp = x / (z / y);
	} else if (y <= 1.35e+54) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (y * x) / z
	tmp = 0
	if y <= -9.8e-14:
		tmp = t_0
	elif y <= 2.5e-141:
		tmp = x
	elif y <= 2.65e-105:
		tmp = x / (z / y)
	elif y <= 1.35e+54:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(y * x) / z)
	tmp = 0.0
	if (y <= -9.8e-14)
		tmp = t_0;
	elseif (y <= 2.5e-141)
		tmp = x;
	elseif (y <= 2.65e-105)
		tmp = Float64(x / Float64(z / y));
	elseif (y <= 1.35e+54)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (y * x) / z;
	tmp = 0.0;
	if (y <= -9.8e-14)
		tmp = t_0;
	elseif (y <= 2.5e-141)
		tmp = x;
	elseif (y <= 2.65e-105)
		tmp = x / (z / y);
	elseif (y <= 1.35e+54)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]}, If[LessEqual[y, -9.8e-14], t$95$0, If[LessEqual[y, 2.5e-141], x, If[LessEqual[y, 2.65e-105], N[(x / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+54], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.79999999999999989e-14 or 1.35000000000000005e54 < y

   1. Initial program 92.7%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 89.9%

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

      2. remove-double-neg 89.9%

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

      3. unsub-neg 89.9%

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

      4. div-sub 89.9%

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

      5. remove-double-neg 89.9%

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

      6. distribute-frac-neg2 89.9%

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

      7. *-inverses 89.9%

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

      8. metadata-eval 89.9%

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

   3. Simplified 89.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 78.9%

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

   if -9.79999999999999989e-14 < y < 2.5e-141 or 2.6500000000000001e-105 < y < 1.35000000000000005e54

   1. Initial program 79.3%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. unsub-neg 99.9%

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

      4. div-sub 99.9%

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

      5. remove-double-neg 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. *-inverses 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 84.1%

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

   if 2.5e-141 < y < 2.6500000000000001e-105

   1. Initial program 94.7%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.3%

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

      2. remove-double-neg 99.3%

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

      3. unsub-neg 99.3%

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

      4. div-sub 99.3%

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

      5. remove-double-neg 99.3%

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

      6. distribute-frac-neg2 99.3%

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

      7. *-inverses 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 73.3%

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

      1. associate-*r/ 78.1%

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

   7. Simplified 78.1%

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

      1. clear-num 78.6%

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

      2. un-div-inv 78.6%

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

   9. Applied egg-rr 78.6%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-14}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-141}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{-105}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+54}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 96.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-182} \lor \neg \left(z \leq 2 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} - -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -5.2e-182) (not (<= z 2e-38)))
   (* x (- (/ y z) -1.0))
   (* (+ y z) (/ x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2e-182) || !(z <= 2e-38)) {
		tmp = x * ((y / z) - -1.0);
	} else {
		tmp = (y + z) * (x / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-5.2d-182)) .or. (.not. (z <= 2d-38))) then
        tmp = x * ((y / z) - (-1.0d0))
    else
        tmp = (y + z) * (x / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -5.2e-182) || !(z <= 2e-38)) {
		tmp = x * ((y / z) - -1.0);
	} else {
		tmp = (y + z) * (x / z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -5.2e-182) or not (z <= 2e-38):
		tmp = x * ((y / z) - -1.0)
	else:
		tmp = (y + z) * (x / z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -5.2e-182) || !(z <= 2e-38))
		tmp = Float64(x * Float64(Float64(y / z) - -1.0));
	else
		tmp = Float64(Float64(y + z) * Float64(x / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -5.2e-182) || ~((z <= 2e-38)))
		tmp = x * ((y / z) - -1.0);
	else
		tmp = (y + z) * (x / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -5.2e-182], N[Not[LessEqual[z, 2e-38]], $MachinePrecision]], N[(x * N[(N[(y / z), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(y + z), $MachinePrecision] * N[(x / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000011e-182 or 1.9999999999999999e-38 < z

   1. Initial program 83.6%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 99.4%

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

      2. remove-double-neg 99.4%

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

      3. unsub-neg 99.4%

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

      4. div-sub 99.4%

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

      5. remove-double-neg 99.4%

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

      6. distribute-frac-neg2 99.4%

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

      7. *-inverses 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
   4. Add Preprocessing

   if -5.20000000000000011e-182 < z < 1.9999999999999999e-38

   1. Initial program 94.3%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. *-commutative 94.3%

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

      2. associate-/l* 94.6%

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

   3. Simplified 94.6%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-182} \lor \neg \left(z \leq 2 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(\frac{y}{z} - -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + z\right) \cdot \frac{x}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{+59}:\\ \;\;\;\;x + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 6.6e+59) (+ x (* x (/ y z))) (/ (* x (+ y z)) z)))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 6.6e+59) {
		tmp = x + (x * (y / z));
	} else {
		tmp = (x * (y + z)) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 6.6d+59) then
        tmp = x + (x * (y / z))
    else
        tmp = (x * (y + z)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 6.6e+59) {
		tmp = x + (x * (y / z));
	} else {
		tmp = (x * (y + z)) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 6.6e+59:
		tmp = x + (x * (y / z))
	else:
		tmp = (x * (y + z)) / z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 6.6e+59)
		tmp = Float64(x + Float64(x * Float64(y / z)));
	else
		tmp = Float64(Float64(x * Float64(y + z)) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 6.6e+59)
		tmp = x + (x * (y / z));
	else
		tmp = (x * (y + z)) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 6.6e+59], N[(x + N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.5999999999999999e59

   1. Initial program 84.8%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Step-by-step derivation

      1. associate-/l* 98.0%

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

      2. remove-double-neg 98.0%

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

      3. unsub-neg 98.0%

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

      4. div-sub 98.0%

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

      5. remove-double-neg 98.0%

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

      6. distribute-frac-neg2 98.0%

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

      7. *-inverses 98.0%

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

      8. metadata-eval 98.0%

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

   3. Simplified 98.0%

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

      1. sub-neg 98.0%

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

      2. metadata-eval 98.0%

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

      3. distribute-rgt-in 98.0%

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

      4. *-commutative 98.0%

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

      5. *-un-lft-identity 98.0%

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

   6. Applied egg-rr 98.0%

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

   if 6.5999999999999999e59 < y

   1. Initial program 93.2%

      \[\frac{x \cdot \left(y + z\right)}{z} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 6.6 \cdot 10^{+59}:\\ \;\;\;\;x + x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \left(y + z\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 86.6%

   \[\frac{x \cdot \left(y + z\right)}{z} \]
2. Step-by-step derivation

   1. associate-/l* 94.7%

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

   2. remove-double-neg 94.7%

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

   3. unsub-neg 94.7%

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

   4. div-sub 94.7%

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

   5. remove-double-neg 94.7%

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

   6. distribute-frac-neg2 94.7%

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

   7. *-inverses 94.7%

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

   8. metadata-eval 94.7%

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

3. Simplified 94.7%

   \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
4. Add Preprocessing

5. Final simplification 94.7%

   \[\leadsto x \cdot \left(\frac{y}{z} - -1\right) \]
6. Add Preprocessing

Alternative 11: 51.0% accurate, 7.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 86.6%

   \[\frac{x \cdot \left(y + z\right)}{z} \]
2. Step-by-step derivation

   1. associate-/l* 94.7%

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

   2. remove-double-neg 94.7%

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

   3. unsub-neg 94.7%

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

   4. div-sub 94.7%

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

   5. remove-double-neg 94.7%

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

   6. distribute-frac-neg2 94.7%

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

   7. *-inverses 94.7%

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

   8. metadata-eval 94.7%

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

3. Simplified 94.7%

   \[\leadsto \color{blue}{x \cdot \left(\frac{y}{z} - -1\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 49.0%

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

6. Final simplification 49.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{\frac{z}{y + z}} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ x (/ z (+ y z))))

C

double code(double x, double y, double z) {
	return x / (z / (y + z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x / (z / (y + z))
end function

Java

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

Python

def code(x, y, z):
	return x / (z / (y + z))

Julia

function code(x, y, z)
	return Float64(x / Float64(z / Float64(y + z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x / (z / (y + z));
end

Wolfram

code[x_, y_, z_] := N[(x / N[(z / N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024130 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"
  :precision binary64

  :alt
  (/ x (/ z (+ y z)))

  (/ (* x (+ y z)) z))