Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, H

Percentage Accurate: 95.9% → 99.2%

Time: 12.1s

Alternatives: 19

Speedup: 0.9×

• 27.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

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 * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 95.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

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 * 3.0d0))) + (t / ((z * 3.0d0) * y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;t \leq -1 \cdot 10^{-49}:\\ \;\;\;\;t_1 + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \mathbf{elif}\;t \leq 10^{-22}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= t -1e-49)
     (+ t_1 (/ t (* z (* y 3.0))))
     (if (<= t 1e-22)
       (+ x (/ (- (/ t y) y) (* z 3.0)))
       (+ t_1 (/ t (* y (* z 3.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if (t <= -1e-49) {
		tmp = t_1 + (t / (z * (y * 3.0)));
	} else if (t <= 1e-22) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = t_1 + (t / (y * (z * 3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (z * 3.0d0))
    if (t <= (-1d-49)) then
        tmp = t_1 + (t / (z * (y * 3.0d0)))
    else if (t <= 1d-22) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = t_1 + (t / (y * (z * 3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if (t <= -1e-49) {
		tmp = t_1 + (t / (z * (y * 3.0)));
	} else if (t <= 1e-22) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = t_1 + (t / (y * (z * 3.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if t <= -1e-49:
		tmp = t_1 + (t / (z * (y * 3.0)))
	elif t <= 1e-22:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = t_1 + (t / (y * (z * 3.0)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (t <= -1e-49)
		tmp = Float64(t_1 + Float64(t / Float64(z * Float64(y * 3.0))));
	elseif (t <= 1e-22)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(t_1 + Float64(t / Float64(y * Float64(z * 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if (t <= -1e-49)
		tmp = t_1 + (t / (z * (y * 3.0)));
	elseif (t <= 1e-22)
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = t_1 + (t / (y * (z * 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1e-49], N[(t$95$1 + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1e-22], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if t < -9.99999999999999936e-50

   1. Initial program 98.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 98.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 98.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 98.9%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]

   if -9.99999999999999936e-50 < t < 1e-22

   1. Initial program 90.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 90.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 90.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 90.6%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 90.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 90.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 90.5%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 90.5%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 99.8%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 99.8%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   if 1e-22 < t

   1. Initial program 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-49}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \mathbf{elif}\;t \leq 10^{-22}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]

Alternative 2: 89.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0024:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-65}:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{y \cdot z}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-72}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-251}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+30}:\\ \;\;\;\;x + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.0024)
   (+ x (/ (* y -0.3333333333333333) z))
   (if (<= y -1.6e-65)
     (+ x (* t (/ 0.3333333333333333 (* y z))))
     (if (<= y -2.4e-72)
       (- x (* 0.3333333333333333 (/ y z)))
       (if (<= y -9e-251)
         (+ x (/ (* 0.3333333333333333 (/ t y)) z))
         (if (<= y 9.5e+30)
           (+ x (* t (/ (/ 0.3333333333333333 z) y)))
           (- x (/ y (* z 3.0)))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.0024) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= -1.6e-65) {
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	} else if (y <= -2.4e-72) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= -9e-251) {
		tmp = x + ((0.3333333333333333 * (t / y)) / z);
	} else if (y <= 9.5e+30) {
		tmp = x + (t * ((0.3333333333333333 / z) / y));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	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 (y <= (-0.0024d0)) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else if (y <= (-1.6d-65)) then
        tmp = x + (t * (0.3333333333333333d0 / (y * z)))
    else if (y <= (-2.4d-72)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= (-9d-251)) then
        tmp = x + ((0.3333333333333333d0 * (t / y)) / z)
    else if (y <= 9.5d+30) then
        tmp = x + (t * ((0.3333333333333333d0 / z) / y))
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.0024) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= -1.6e-65) {
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	} else if (y <= -2.4e-72) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= -9e-251) {
		tmp = x + ((0.3333333333333333 * (t / y)) / z);
	} else if (y <= 9.5e+30) {
		tmp = x + (t * ((0.3333333333333333 / z) / y));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.0024:
		tmp = x + ((y * -0.3333333333333333) / z)
	elif y <= -1.6e-65:
		tmp = x + (t * (0.3333333333333333 / (y * z)))
	elif y <= -2.4e-72:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= -9e-251:
		tmp = x + ((0.3333333333333333 * (t / y)) / z)
	elif y <= 9.5e+30:
		tmp = x + (t * ((0.3333333333333333 / z) / y))
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.0024)
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	elseif (y <= -1.6e-65)
		tmp = Float64(x + Float64(t * Float64(0.3333333333333333 / Float64(y * z))));
	elseif (y <= -2.4e-72)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= -9e-251)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 * Float64(t / y)) / z));
	elseif (y <= 9.5e+30)
		tmp = Float64(x + Float64(t * Float64(Float64(0.3333333333333333 / z) / y)));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.0024)
		tmp = x + ((y * -0.3333333333333333) / z);
	elseif (y <= -1.6e-65)
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	elseif (y <= -2.4e-72)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= -9e-251)
		tmp = x + ((0.3333333333333333 * (t / y)) / z);
	elseif (y <= 9.5e+30)
		tmp = x + (t * ((0.3333333333333333 / z) / y));
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.0024], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e-65], N[(x + N[(t * N[(0.3333333333333333 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.4e-72], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9e-251], N[(x + N[(N[(0.3333333333333333 * N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e+30], N[(x + N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if y < -0.00239999999999999979

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around 0 94.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. *-commutative 94.2%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-*l/ 94.3%

         \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

      3. associate-*r/ 94.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   6. Simplified 94.2%

      \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   7. Taylor expanded in y around 0 94.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 94.3%

         \[\leadsto x + \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 94.3%

         \[\leadsto x + \frac{\color{blue}{y \cdot -0.3333333333333333}}{z} \]

   9. Simplified 94.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

   if -0.00239999999999999979 < y < -1.6e-65

   1. Initial program 99.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 80.9%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around inf 87.1%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 87.1%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. metadata-eval 87.1%

         \[\leadsto x + \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      3. times-frac 87.1%

         \[\leadsto x + \color{blue}{\frac{t \cdot 1}{\left(y \cdot z\right) \cdot 3}} \]

      4. *-commutative 87.1%

         \[\leadsto x + \frac{t \cdot 1}{\color{blue}{3 \cdot \left(y \cdot z\right)}} \]

      5. times-frac 87.2%

         \[\leadsto x + \color{blue}{\frac{t}{3} \cdot \frac{1}{y \cdot z}} \]

      6. associate-/r* 87.2%

         \[\leadsto x + \frac{t}{3} \cdot \color{blue}{\frac{\frac{1}{y}}{z}} \]

      7. associate-*l/ 87.1%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{\frac{1}{y}}{z}}{3}} \]

      8. associate-*r/ 87.1%

         \[\leadsto x + \color{blue}{t \cdot \frac{\frac{\frac{1}{y}}{z}}{3}} \]

      9. associate-/r* 87.1%

         \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{y}}{z \cdot 3}} \]

      10. associate-/l/ 87.1%

          \[\leadsto x + t \cdot \color{blue}{\frac{1}{\left(z \cdot 3\right) \cdot y}} \]

      11. associate-/r* 87.1%

          \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{z \cdot 3}}{y}} \]

      12. *-commutative 87.1%

          \[\leadsto x + t \cdot \frac{\frac{1}{\color{blue}{3 \cdot z}}}{y} \]

      13. associate-/r* 87.1%

          \[\leadsto x + t \cdot \frac{\color{blue}{\frac{\frac{1}{3}}{z}}}{y} \]

      14. metadata-eval 87.1%

          \[\leadsto x + t \cdot \frac{\frac{\color{blue}{0.3333333333333333}}{z}}{y} \]

   6. Simplified 87.1%

      \[\leadsto x + \color{blue}{t \cdot \frac{\frac{0.3333333333333333}{z}}{y}} \]

   7. Taylor expanded in z around 0 87.1%

      \[\leadsto x + t \cdot \color{blue}{\frac{0.3333333333333333}{y \cdot z}} \]

   if -1.6e-65 < y < -2.4e-72

   1. Initial program 100.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 100.0%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 100.0%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]

   4. Taylor expanded in t around 0 100.0%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]

   if -2.4e-72 < y < -8.99999999999999956e-251

   1. Initial program 83.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
   4. Step-by-step derivation

      1. *-commutative 95.9%

         \[\leadsto x + \color{blue}{\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}} \]

      2. associate-*r/ 95.8%

         \[\leadsto x + \color{blue}{\frac{\left(\frac{t}{y} - y\right) \cdot 0.3333333333333333}{z}} \]

   5. Applied egg-rr 95.8%

      \[\leadsto x + \color{blue}{\frac{\left(\frac{t}{y} - y\right) \cdot 0.3333333333333333}{z}} \]

   6. Taylor expanded in t around inf 95.8%

      \[\leadsto x + \frac{\color{blue}{0.3333333333333333 \cdot \frac{t}{y}}}{z} \]

   if -8.99999999999999956e-251 < y < 9.5000000000000003e30

   1. Initial program 96.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 88.0%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around inf 92.0%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 92.0%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. metadata-eval 92.0%

         \[\leadsto x + \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      3. times-frac 92.0%

         \[\leadsto x + \color{blue}{\frac{t \cdot 1}{\left(y \cdot z\right) \cdot 3}} \]

      4. *-commutative 92.0%

         \[\leadsto x + \frac{t \cdot 1}{\color{blue}{3 \cdot \left(y \cdot z\right)}} \]

      5. times-frac 92.1%

         \[\leadsto x + \color{blue}{\frac{t}{3} \cdot \frac{1}{y \cdot z}} \]

      6. associate-/r* 92.0%

         \[\leadsto x + \frac{t}{3} \cdot \color{blue}{\frac{\frac{1}{y}}{z}} \]

      7. associate-*l/ 92.0%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{\frac{1}{y}}{z}}{3}} \]

      8. associate-*r/ 92.0%

         \[\leadsto x + \color{blue}{t \cdot \frac{\frac{\frac{1}{y}}{z}}{3}} \]

      9. associate-/r* 92.1%

         \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{y}}{z \cdot 3}} \]

      10. associate-/l/ 92.0%

          \[\leadsto x + t \cdot \color{blue}{\frac{1}{\left(z \cdot 3\right) \cdot y}} \]

      11. associate-/r* 92.1%

          \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{z \cdot 3}}{y}} \]

      12. *-commutative 92.1%

          \[\leadsto x + t \cdot \frac{\frac{1}{\color{blue}{3 \cdot z}}}{y} \]

      13. associate-/r* 92.0%

          \[\leadsto x + t \cdot \frac{\color{blue}{\frac{\frac{1}{3}}{z}}}{y} \]

      14. metadata-eval 92.0%

          \[\leadsto x + t \cdot \frac{\frac{\color{blue}{0.3333333333333333}}{z}}{y} \]

   6. Simplified 92.0%

      \[\leadsto x + \color{blue}{t \cdot \frac{\frac{0.3333333333333333}{z}}{y}} \]

   if 9.5000000000000003e30 < y

   1. Initial program 99.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]

   4. Taylor expanded in t around 0 94.1%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. metadata-eval 94.1%

         \[\leadsto x - \color{blue}{\frac{1}{3}} \cdot \frac{y}{z} \]

      2. times-frac 94.2%

         \[\leadsto x - \color{blue}{\frac{1 \cdot y}{3 \cdot z}} \]

      3. *-un-lft-identity 94.2%

         \[\leadsto x - \frac{\color{blue}{y}}{3 \cdot z} \]

      4. *-commutative 94.2%

         \[\leadsto x - \frac{y}{\color{blue}{z \cdot 3}} \]

   6. Applied egg-rr 94.2%

      \[\leadsto x - \color{blue}{\frac{y}{z \cdot 3}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0024:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-65}:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{y \cdot z}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-72}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-251}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+30}:\\ \;\;\;\;x + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 3: 99.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-50} \lor \neg \left(t \leq 6 \cdot 10^{-43}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2e-50) (not (<= t 6e-43)))
   (+ (- x (/ y (* z 3.0))) (/ t (* z (* y 3.0))))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2e-50) || !(t <= 6e-43)) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	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 <= (-2d-50)) .or. (.not. (t <= 6d-43))) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (z * (y * 3.0d0)))
    else
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2e-50) || !(t <= 6e-43)) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2e-50) or not (t <= 6e-43):
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)))
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2e-50) || !(t <= 6e-43))
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(z * Float64(y * 3.0))));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2e-50) || ~((t <= 6e-43)))
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2e-50], N[Not[LessEqual[t, 6e-43]], $MachinePrecision]], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.00000000000000002e-50 or 6.00000000000000007e-43 < t

   1. Initial program 99.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 99.3%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 99.3%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]

   if -2.00000000000000002e-50 < t < 6.00000000000000007e-43

   1. Initial program 90.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 90.2%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 90.2%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 90.2%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 90.2%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 90.2%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 90.2%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 90.2%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 99.8%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 99.8%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 99.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{-50} \lor \neg \left(t \leq 6 \cdot 10^{-43}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]

Alternative 4: 96.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.8 \cdot 10^{-180}:\\ \;\;\;\;\left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y 7.8e-180)
   (- (+ (/ (/ t z) (* y 3.0)) x) (* y (/ 0.3333333333333333 z)))
   (+ (- x (/ y (* z 3.0))) (/ t (* z (* y 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.8e-180) {
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z));
	} else {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	}
	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 (y <= 7.8d-180) then
        tmp = (((t / z) / (y * 3.0d0)) + x) - (y * (0.3333333333333333d0 / z))
    else
        tmp = (x - (y / (z * 3.0d0))) + (t / (z * (y * 3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= 7.8e-180) {
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z));
	} else {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= 7.8e-180:
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z))
	else:
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= 7.8e-180)
		tmp = Float64(Float64(Float64(Float64(t / z) / Float64(y * 3.0)) + x) - Float64(y * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(z * Float64(y * 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= 7.8e-180)
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z));
	else
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, 7.8e-180], N[(N[(N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.8000000000000005e-180

   1. Initial program 93.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 93.0%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 93.0%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 93.0%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. +-commutative 93.0%

         \[\leadsto \color{blue}{\frac{t}{z \cdot \left(y \cdot 3\right)} + \left(x - \frac{y}{z \cdot 3}\right)} \]

      2. *-commutative 93.0%

         \[\leadsto \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} + \left(x - \frac{y}{z \cdot 3}\right) \]

      3. associate-*l* 93.0%

         \[\leadsto \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} + \left(x - \frac{y}{z \cdot 3}\right) \]

      4. associate-+r- 93.0%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

      5. associate-*l* 93.0%

         \[\leadsto \left(\frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} + x\right) - \frac{y}{z \cdot 3} \]

      6. *-commutative 93.0%

         \[\leadsto \left(\frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} + x\right) - \frac{y}{z \cdot 3} \]

      7. associate-/r* 98.2%

         \[\leadsto \left(\color{blue}{\frac{\frac{t}{z}}{y \cdot 3}} + x\right) - \frac{y}{z \cdot 3} \]

      8. div-inv 98.2%

         \[\leadsto \left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - \color{blue}{y \cdot \frac{1}{z \cdot 3}} \]

      9. metadata-eval 98.2%

         \[\leadsto \left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{0.3333333333333333}}} \]

      10. div-inv 98.2%

          \[\leadsto \left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{1}{\color{blue}{\frac{z}{0.3333333333333333}}} \]

      11. clear-num 98.2%

          \[\leadsto \left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \color{blue}{\frac{0.3333333333333333}{z}} \]

   5. Applied egg-rr 98.2%

      \[\leadsto \color{blue}{\left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{0.3333333333333333}{z}} \]

   if 7.8000000000000005e-180 < y

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 99.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.8 \cdot 10^{-180}:\\ \;\;\;\;\left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \end{array} \]

Alternative 5: 60.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+31}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.6e-13)
   (/ (* y -0.3333333333333333) z)
   (if (<= y -7.2e-130)
     x
     (if (<= y 3.6e+31)
       (* 0.3333333333333333 (/ t (* y z)))
       (* -0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-13) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -7.2e-130) {
		tmp = x;
	} else if (y <= 3.6e+31) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = -0.3333333333333333 * (y / z);
	}
	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 (y <= (-1.6d-13)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= (-7.2d-130)) then
        tmp = x
    else if (y <= 3.6d+31) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else
        tmp = (-0.3333333333333333d0) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.6e-13) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -7.2e-130) {
		tmp = x;
	} else if (y <= 3.6e+31) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = -0.3333333333333333 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.6e-13:
		tmp = (y * -0.3333333333333333) / z
	elif y <= -7.2e-130:
		tmp = x
	elif y <= 3.6e+31:
		tmp = 0.3333333333333333 * (t / (y * z))
	else:
		tmp = -0.3333333333333333 * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.6e-13)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= -7.2e-130)
		tmp = x;
	elseif (y <= 3.6e+31)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	else
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.6e-13)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= -7.2e-130)
		tmp = x;
	elseif (y <= 3.6e+31)
		tmp = 0.3333333333333333 * (t / (y * z));
	else
		tmp = -0.3333333333333333 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.6e-13], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -7.2e-130], x, If[LessEqual[y, 3.6e+31], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.6e-13

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 98.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 98.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 98.5%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 98.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 98.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 98.5%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 98.5%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 99.8%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 99.8%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around inf 58.4%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 58.5%

         \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

   8. Simplified 58.5%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

   if -1.6e-13 < y < -7.2000000000000003e-130

   1. Initial program 96.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 85.4%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in x around inf 62.5%

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

   if -7.2000000000000003e-130 < y < 3.59999999999999996e31

   1. Initial program 92.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 92.4%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 92.4%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 92.4%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 92.4%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 92.3%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 92.3%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 92.3%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 90.1%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 90.1%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 90.1%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around 0 68.4%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]

   if 3.59999999999999996e31 < y

   1. Initial program 99.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 99.9%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 99.9%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 99.9%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 99.9%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around inf 66.4%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-130}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+31}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 6: 61.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+31}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.5e-14)
   (/ (* y -0.3333333333333333) z)
   (if (<= y -1.25e-129)
     x
     (if (<= y 4.6e+31)
       (* 0.3333333333333333 (/ (/ t z) y))
       (* -0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e-14) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -1.25e-129) {
		tmp = x;
	} else if (y <= 4.6e+31) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = -0.3333333333333333 * (y / z);
	}
	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 (y <= (-6.5d-14)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= (-1.25d-129)) then
        tmp = x
    else if (y <= 4.6d+31) then
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    else
        tmp = (-0.3333333333333333d0) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.5e-14) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -1.25e-129) {
		tmp = x;
	} else if (y <= 4.6e+31) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = -0.3333333333333333 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.5e-14:
		tmp = (y * -0.3333333333333333) / z
	elif y <= -1.25e-129:
		tmp = x
	elif y <= 4.6e+31:
		tmp = 0.3333333333333333 * ((t / z) / y)
	else:
		tmp = -0.3333333333333333 * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.5e-14)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= -1.25e-129)
		tmp = x;
	elseif (y <= 4.6e+31)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	else
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.5e-14)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= -1.25e-129)
		tmp = x;
	elseif (y <= 4.6e+31)
		tmp = 0.3333333333333333 * ((t / z) / y);
	else
		tmp = -0.3333333333333333 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e-14], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -1.25e-129], x, If[LessEqual[y, 4.6e+31], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.5000000000000001e-14

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 98.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 98.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 98.5%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 98.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 98.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 98.5%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 98.5%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 99.8%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 99.8%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around inf 58.4%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   7. Step-by-step derivation

      1. associate-*r/ 58.5%

         \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

   8. Simplified 58.5%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

   if -6.5000000000000001e-14 < y < -1.25000000000000007e-129

   1. Initial program 96.4%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 85.4%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in x around inf 62.5%

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

   if -1.25000000000000007e-129 < y < 4.5999999999999999e31

   1. Initial program 92.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 92.4%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 92.4%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 92.4%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 92.4%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 92.3%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 92.3%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 92.3%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 90.1%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 90.1%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 90.1%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around 0 68.4%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   7. Step-by-step derivation

      1. expm1-log1p-u 37.2%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{y \cdot z}\right)\right)} \]

      2. expm1-udef 29.5%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{t}{y \cdot z}\right)} - 1\right)} \]

      3. *-commutative 29.5%

         \[\leadsto 0.3333333333333333 \cdot \left(e^{\mathsf{log1p}\left(\frac{t}{\color{blue}{z \cdot y}}\right)} - 1\right) \]

   8. Applied egg-rr 29.5%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{t}{z \cdot y}\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 37.2%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{z \cdot y}\right)\right)} \]

      2. expm1-log1p 68.4%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{t}{z \cdot y}} \]

      3. associate-/r* 72.4%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{z}}{y}} \]

   10. Simplified 72.4%

       \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{z}}{y}} \]

   if 4.5999999999999999e31 < y

   1. Initial program 99.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 99.9%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 99.9%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 99.9%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 99.9%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around inf 66.4%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1.25 \cdot 10^{-129}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+31}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 7: 89.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00037:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+30}:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.00037)
   (+ x (/ (* y -0.3333333333333333) z))
   (if (<= y 6.6e+30)
     (+ x (* t (/ 0.3333333333333333 (* y z))))
     (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.00037) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 6.6e+30) {
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	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 (y <= (-0.00037d0)) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else if (y <= 6.6d+30) then
        tmp = x + (t * (0.3333333333333333d0 / (y * z)))
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.00037) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 6.6e+30) {
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.00037:
		tmp = x + ((y * -0.3333333333333333) / z)
	elif y <= 6.6e+30:
		tmp = x + (t * (0.3333333333333333 / (y * z)))
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.00037)
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	elseif (y <= 6.6e+30)
		tmp = Float64(x + Float64(t * Float64(0.3333333333333333 / Float64(y * z))));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.00037)
		tmp = x + ((y * -0.3333333333333333) / z);
	elseif (y <= 6.6e+30)
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.00037], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+30], N[(x + N[(t * N[(0.3333333333333333 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.6999999999999999e-4

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around 0 94.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. *-commutative 94.2%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-*l/ 94.3%

         \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

      3. associate-*r/ 94.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   6. Simplified 94.2%

      \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   7. Taylor expanded in y around 0 94.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 94.3%

         \[\leadsto x + \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 94.3%

         \[\leadsto x + \frac{\color{blue}{y \cdot -0.3333333333333333}}{z} \]

   9. Simplified 94.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

   if -3.6999999999999999e-4 < y < 6.60000000000000053e30

   1. Initial program 93.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around inf 88.5%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 88.5%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. metadata-eval 88.5%

         \[\leadsto x + \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      3. times-frac 88.5%

         \[\leadsto x + \color{blue}{\frac{t \cdot 1}{\left(y \cdot z\right) \cdot 3}} \]

      4. *-commutative 88.5%

         \[\leadsto x + \frac{t \cdot 1}{\color{blue}{3 \cdot \left(y \cdot z\right)}} \]

      5. times-frac 88.6%

         \[\leadsto x + \color{blue}{\frac{t}{3} \cdot \frac{1}{y \cdot z}} \]

      6. associate-/r* 88.6%

         \[\leadsto x + \frac{t}{3} \cdot \color{blue}{\frac{\frac{1}{y}}{z}} \]

      7. associate-*l/ 88.6%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{\frac{1}{y}}{z}}{3}} \]

      8. associate-*r/ 88.6%

         \[\leadsto x + \color{blue}{t \cdot \frac{\frac{\frac{1}{y}}{z}}{3}} \]

      9. associate-/r* 88.6%

         \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{y}}{z \cdot 3}} \]

      10. associate-/l/ 88.6%

          \[\leadsto x + t \cdot \color{blue}{\frac{1}{\left(z \cdot 3\right) \cdot y}} \]

      11. associate-/r* 88.6%

          \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{z \cdot 3}}{y}} \]

      12. *-commutative 88.6%

          \[\leadsto x + t \cdot \frac{\frac{1}{\color{blue}{3 \cdot z}}}{y} \]

      13. associate-/r* 88.6%

          \[\leadsto x + t \cdot \frac{\color{blue}{\frac{\frac{1}{3}}{z}}}{y} \]

      14. metadata-eval 88.6%

          \[\leadsto x + t \cdot \frac{\frac{\color{blue}{0.3333333333333333}}{z}}{y} \]

   6. Simplified 88.6%

      \[\leadsto x + \color{blue}{t \cdot \frac{\frac{0.3333333333333333}{z}}{y}} \]

   7. Taylor expanded in z around 0 88.5%

      \[\leadsto x + t \cdot \color{blue}{\frac{0.3333333333333333}{y \cdot z}} \]

   if 6.60000000000000053e30 < y

   1. Initial program 99.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]

   4. Taylor expanded in t around 0 94.1%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. metadata-eval 94.1%

         \[\leadsto x - \color{blue}{\frac{1}{3}} \cdot \frac{y}{z} \]

      2. times-frac 94.2%

         \[\leadsto x - \color{blue}{\frac{1 \cdot y}{3 \cdot z}} \]

      3. *-un-lft-identity 94.2%

         \[\leadsto x - \frac{\color{blue}{y}}{3 \cdot z} \]

      4. *-commutative 94.2%

         \[\leadsto x - \frac{y}{\color{blue}{z \cdot 3}} \]

   6. Applied egg-rr 94.2%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00037:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+30}:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 8: 89.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.011:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+31}:\\ \;\;\;\;x + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.011)
   (+ x (/ (* y -0.3333333333333333) z))
   (if (<= y 1.05e+31)
     (+ x (* t (/ (/ 0.3333333333333333 z) y)))
     (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.011) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 1.05e+31) {
		tmp = x + (t * ((0.3333333333333333 / z) / y));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	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 (y <= (-0.011d0)) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else if (y <= 1.05d+31) then
        tmp = x + (t * ((0.3333333333333333d0 / z) / y))
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.011) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 1.05e+31) {
		tmp = x + (t * ((0.3333333333333333 / z) / y));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.011:
		tmp = x + ((y * -0.3333333333333333) / z)
	elif y <= 1.05e+31:
		tmp = x + (t * ((0.3333333333333333 / z) / y))
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.011)
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	elseif (y <= 1.05e+31)
		tmp = Float64(x + Float64(t * Float64(Float64(0.3333333333333333 / z) / y)));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.011)
		tmp = x + ((y * -0.3333333333333333) / z);
	elseif (y <= 1.05e+31)
		tmp = x + (t * ((0.3333333333333333 / z) / y));
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.011], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+31], N[(x + N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.010999999999999999

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around 0 94.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. *-commutative 94.2%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-*l/ 94.3%

         \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

      3. associate-*r/ 94.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   6. Simplified 94.2%

      \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   7. Taylor expanded in y around 0 94.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 94.3%

         \[\leadsto x + \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 94.3%

         \[\leadsto x + \frac{\color{blue}{y \cdot -0.3333333333333333}}{z} \]

   9. Simplified 94.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

   if -0.010999999999999999 < y < 1.04999999999999989e31

   1. Initial program 93.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around inf 88.5%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 88.5%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. metadata-eval 88.5%

         \[\leadsto x + \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      3. times-frac 88.5%

         \[\leadsto x + \color{blue}{\frac{t \cdot 1}{\left(y \cdot z\right) \cdot 3}} \]

      4. *-commutative 88.5%

         \[\leadsto x + \frac{t \cdot 1}{\color{blue}{3 \cdot \left(y \cdot z\right)}} \]

      5. times-frac 88.6%

         \[\leadsto x + \color{blue}{\frac{t}{3} \cdot \frac{1}{y \cdot z}} \]

      6. associate-/r* 88.6%

         \[\leadsto x + \frac{t}{3} \cdot \color{blue}{\frac{\frac{1}{y}}{z}} \]

      7. associate-*l/ 88.6%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{\frac{1}{y}}{z}}{3}} \]

      8. associate-*r/ 88.6%

         \[\leadsto x + \color{blue}{t \cdot \frac{\frac{\frac{1}{y}}{z}}{3}} \]

      9. associate-/r* 88.6%

         \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{y}}{z \cdot 3}} \]

      10. associate-/l/ 88.6%

          \[\leadsto x + t \cdot \color{blue}{\frac{1}{\left(z \cdot 3\right) \cdot y}} \]

      11. associate-/r* 88.6%

          \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{z \cdot 3}}{y}} \]

      12. *-commutative 88.6%

          \[\leadsto x + t \cdot \frac{\frac{1}{\color{blue}{3 \cdot z}}}{y} \]

      13. associate-/r* 88.6%

          \[\leadsto x + t \cdot \frac{\color{blue}{\frac{\frac{1}{3}}{z}}}{y} \]

      14. metadata-eval 88.6%

          \[\leadsto x + t \cdot \frac{\frac{\color{blue}{0.3333333333333333}}{z}}{y} \]

   6. Simplified 88.6%

      \[\leadsto x + \color{blue}{t \cdot \frac{\frac{0.3333333333333333}{z}}{y}} \]

   if 1.04999999999999989e31 < y

   1. Initial program 99.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]

   4. Taylor expanded in t around 0 94.1%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. metadata-eval 94.1%

         \[\leadsto x - \color{blue}{\frac{1}{3}} \cdot \frac{y}{z} \]

      2. times-frac 94.2%

         \[\leadsto x - \color{blue}{\frac{1 \cdot y}{3 \cdot z}} \]

      3. *-un-lft-identity 94.2%

         \[\leadsto x - \frac{\color{blue}{y}}{3 \cdot z} \]

      4. *-commutative 94.2%

         \[\leadsto x - \frac{y}{\color{blue}{z \cdot 3}} \]

   6. Applied egg-rr 94.2%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.011:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+31}:\\ \;\;\;\;x + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 9: 91.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.006:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.006)
   (+ x (/ (* y -0.3333333333333333) z))
   (if (<= y 9.8e+30)
     (+ x (/ (* t (/ 0.3333333333333333 z)) y))
     (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.006) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 9.8e+30) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	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 (y <= (-0.006d0)) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else if (y <= 9.8d+30) then
        tmp = x + ((t * (0.3333333333333333d0 / z)) / y)
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.006) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 9.8e+30) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.006:
		tmp = x + ((y * -0.3333333333333333) / z)
	elif y <= 9.8e+30:
		tmp = x + ((t * (0.3333333333333333 / z)) / y)
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.006)
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	elseif (y <= 9.8e+30)
		tmp = Float64(x + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.006)
		tmp = x + ((y * -0.3333333333333333) / z);
	elseif (y <= 9.8e+30)
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.006], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+30], N[(x + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0060000000000000001

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around 0 94.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. *-commutative 94.2%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-*l/ 94.3%

         \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

      3. associate-*r/ 94.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   6. Simplified 94.2%

      \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   7. Taylor expanded in y around 0 94.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 94.3%

         \[\leadsto x + \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 94.3%

         \[\leadsto x + \frac{\color{blue}{y \cdot -0.3333333333333333}}{z} \]

   9. Simplified 94.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

   if -0.0060000000000000001 < y < 9.79999999999999969e30

   1. Initial program 93.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around inf 88.5%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 88.5%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. metadata-eval 88.5%

         \[\leadsto x + \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      3. times-frac 88.5%

         \[\leadsto x + \color{blue}{\frac{t \cdot 1}{\left(y \cdot z\right) \cdot 3}} \]

      4. *-commutative 88.5%

         \[\leadsto x + \frac{t \cdot 1}{\color{blue}{3 \cdot \left(y \cdot z\right)}} \]

      5. times-frac 88.6%

         \[\leadsto x + \color{blue}{\frac{t}{3} \cdot \frac{1}{y \cdot z}} \]

      6. associate-/r* 88.6%

         \[\leadsto x + \frac{t}{3} \cdot \color{blue}{\frac{\frac{1}{y}}{z}} \]

      7. associate-*l/ 88.6%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{\frac{1}{y}}{z}}{3}} \]

      8. associate-*r/ 88.6%

         \[\leadsto x + \color{blue}{t \cdot \frac{\frac{\frac{1}{y}}{z}}{3}} \]

      9. associate-/r* 88.6%

         \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{y}}{z \cdot 3}} \]

      10. associate-/l/ 88.6%

          \[\leadsto x + t \cdot \color{blue}{\frac{1}{\left(z \cdot 3\right) \cdot y}} \]

      11. associate-/r* 88.6%

          \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{z \cdot 3}}{y}} \]

      12. *-commutative 88.6%

          \[\leadsto x + t \cdot \frac{\frac{1}{\color{blue}{3 \cdot z}}}{y} \]

      13. associate-/r* 88.6%

          \[\leadsto x + t \cdot \frac{\color{blue}{\frac{\frac{1}{3}}{z}}}{y} \]

      14. metadata-eval 88.6%

          \[\leadsto x + t \cdot \frac{\frac{\color{blue}{0.3333333333333333}}{z}}{y} \]

   6. Simplified 88.6%

      \[\leadsto x + \color{blue}{t \cdot \frac{\frac{0.3333333333333333}{z}}{y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 93.6%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   8. Applied egg-rr 93.6%

      \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   if 9.79999999999999969e30 < y

   1. Initial program 99.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]

   4. Taylor expanded in t around 0 94.1%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. metadata-eval 94.1%

         \[\leadsto x - \color{blue}{\frac{1}{3}} \cdot \frac{y}{z} \]

      2. times-frac 94.2%

         \[\leadsto x - \color{blue}{\frac{1 \cdot y}{3 \cdot z}} \]

      3. *-un-lft-identity 94.2%

         \[\leadsto x - \frac{\color{blue}{y}}{3 \cdot z} \]

      4. *-commutative 94.2%

         \[\leadsto x - \frac{y}{\color{blue}{z \cdot 3}} \]

   6. Applied egg-rr 94.2%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.006:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 10: 92.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0027:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{3}}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.0027)
   (+ x (/ (* y -0.3333333333333333) z))
   (if (<= y 6.6e+30) (+ x (/ (/ (/ t 3.0) z) y)) (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.0027) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 6.6e+30) {
		tmp = x + (((t / 3.0) / z) / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	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 (y <= (-0.0027d0)) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else if (y <= 6.6d+30) then
        tmp = x + (((t / 3.0d0) / z) / y)
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.0027) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 6.6e+30) {
		tmp = x + (((t / 3.0) / z) / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.0027:
		tmp = x + ((y * -0.3333333333333333) / z)
	elif y <= 6.6e+30:
		tmp = x + (((t / 3.0) / z) / y)
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.0027)
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	elseif (y <= 6.6e+30)
		tmp = Float64(x + Float64(Float64(Float64(t / 3.0) / z) / y));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.0027)
		tmp = x + ((y * -0.3333333333333333) / z);
	elseif (y <= 6.6e+30)
		tmp = x + (((t / 3.0) / z) / y);
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.0027], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e+30], N[(x + N[(N[(N[(t / 3.0), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.0027000000000000001

   1. Initial program 98.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around 0 94.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. *-commutative 94.2%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-*l/ 94.3%

         \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

      3. associate-*r/ 94.2%

         \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   6. Simplified 94.2%

      \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   7. Taylor expanded in y around 0 94.2%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 94.3%

         \[\leadsto x + \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 94.3%

         \[\leadsto x + \frac{\color{blue}{y \cdot -0.3333333333333333}}{z} \]

   9. Simplified 94.3%

      \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

   if -0.0027000000000000001 < y < 6.60000000000000053e30

   1. Initial program 93.0%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around inf 88.5%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 88.5%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. metadata-eval 88.5%

         \[\leadsto x + \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      3. times-frac 88.5%

         \[\leadsto x + \color{blue}{\frac{t \cdot 1}{\left(y \cdot z\right) \cdot 3}} \]

      4. *-commutative 88.5%

         \[\leadsto x + \frac{t \cdot 1}{\color{blue}{3 \cdot \left(y \cdot z\right)}} \]

      5. times-frac 88.6%

         \[\leadsto x + \color{blue}{\frac{t}{3} \cdot \frac{1}{y \cdot z}} \]

      6. associate-/r* 88.6%

         \[\leadsto x + \frac{t}{3} \cdot \color{blue}{\frac{\frac{1}{y}}{z}} \]

      7. associate-*l/ 88.6%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{\frac{1}{y}}{z}}{3}} \]

      8. associate-*r/ 88.6%

         \[\leadsto x + \color{blue}{t \cdot \frac{\frac{\frac{1}{y}}{z}}{3}} \]

      9. associate-/r* 88.6%

         \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{y}}{z \cdot 3}} \]

      10. associate-/l/ 88.6%

          \[\leadsto x + t \cdot \color{blue}{\frac{1}{\left(z \cdot 3\right) \cdot y}} \]

      11. associate-/r* 88.6%

          \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{z \cdot 3}}{y}} \]

      12. *-commutative 88.6%

          \[\leadsto x + t \cdot \frac{\frac{1}{\color{blue}{3 \cdot z}}}{y} \]

      13. associate-/r* 88.6%

          \[\leadsto x + t \cdot \frac{\color{blue}{\frac{\frac{1}{3}}{z}}}{y} \]

      14. metadata-eval 88.6%

          \[\leadsto x + t \cdot \frac{\frac{\color{blue}{0.3333333333333333}}{z}}{y} \]

   6. Simplified 88.6%

      \[\leadsto x + \color{blue}{t \cdot \frac{\frac{0.3333333333333333}{z}}{y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 93.6%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   8. Applied egg-rr 93.6%

      \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]
   9. Step-by-step derivation

      1. clear-num 93.5%

         \[\leadsto x + \frac{t \cdot \color{blue}{\frac{1}{\frac{z}{0.3333333333333333}}}}{y} \]

      2. div-inv 93.6%

         \[\leadsto x + \frac{t \cdot \frac{1}{\color{blue}{z \cdot \frac{1}{0.3333333333333333}}}}{y} \]

      3. metadata-eval 93.6%

         \[\leadsto x + \frac{t \cdot \frac{1}{z \cdot \color{blue}{3}}}{y} \]

      4. un-div-inv 93.5%

         \[\leadsto x + \frac{\color{blue}{\frac{t}{z \cdot 3}}}{y} \]

   10. Applied egg-rr 93.5%

       \[\leadsto x + \frac{\color{blue}{\frac{t}{z \cdot 3}}}{y} \]
   11. Step-by-step derivation

       1. *-commutative 93.5%

          \[\leadsto x + \frac{\frac{t}{\color{blue}{3 \cdot z}}}{y} \]

       2. associate-/r* 93.6%

          \[\leadsto x + \frac{\color{blue}{\frac{\frac{t}{3}}{z}}}{y} \]

   12. Simplified 93.6%

       \[\leadsto x + \frac{\color{blue}{\frac{\frac{t}{3}}{z}}}{y} \]

   if 6.60000000000000053e30 < y

   1. Initial program 99.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]

   4. Taylor expanded in t around 0 94.1%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. metadata-eval 94.1%

         \[\leadsto x - \color{blue}{\frac{1}{3}} \cdot \frac{y}{z} \]

      2. times-frac 94.2%

         \[\leadsto x - \color{blue}{\frac{1 \cdot y}{3 \cdot z}} \]

      3. *-un-lft-identity 94.2%

         \[\leadsto x - \frac{\color{blue}{y}}{3 \cdot z} \]

      4. *-commutative 94.2%

         \[\leadsto x - \frac{y}{\color{blue}{z \cdot 3}} \]

   6. Applied egg-rr 94.2%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0027:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{3}}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 11: 95.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+164}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{3}}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.7e+164)
   (+ x (/ (/ (/ t 3.0) z) y))
   (- x (* (/ 0.3333333333333333 z) (- y (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.7e+164) {
		tmp = x + (((t / 3.0) / z) / y);
	} else {
		tmp = x - ((0.3333333333333333 / z) * (y - (t / y)));
	}
	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 <= (-2.7d+164)) then
        tmp = x + (((t / 3.0d0) / z) / y)
    else
        tmp = x - ((0.3333333333333333d0 / z) * (y - (t / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.7e+164) {
		tmp = x + (((t / 3.0) / z) / y);
	} else {
		tmp = x - ((0.3333333333333333 / z) * (y - (t / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.7e+164:
		tmp = x + (((t / 3.0) / z) / y)
	else:
		tmp = x - ((0.3333333333333333 / z) * (y - (t / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.7e+164)
		tmp = Float64(x + Float64(Float64(Float64(t / 3.0) / z) / y));
	else
		tmp = Float64(x - Float64(Float64(0.3333333333333333 / z) * Float64(y - Float64(t / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.7e+164)
		tmp = x + (((t / 3.0) / z) / y);
	else
		tmp = x - ((0.3333333333333333 / z) * (y - (t / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.7e+164], N[(x + N[(N[(N[(t / 3.0), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.70000000000000006e164

   1. Initial program 97.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 73.2%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around inf 90.5%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 90.5%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. metadata-eval 90.5%

         \[\leadsto x + \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      3. times-frac 90.3%

         \[\leadsto x + \color{blue}{\frac{t \cdot 1}{\left(y \cdot z\right) \cdot 3}} \]

      4. *-commutative 90.3%

         \[\leadsto x + \frac{t \cdot 1}{\color{blue}{3 \cdot \left(y \cdot z\right)}} \]

      5. times-frac 90.4%

         \[\leadsto x + \color{blue}{\frac{t}{3} \cdot \frac{1}{y \cdot z}} \]

      6. associate-/r* 90.4%

         \[\leadsto x + \frac{t}{3} \cdot \color{blue}{\frac{\frac{1}{y}}{z}} \]

      7. associate-*l/ 90.5%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{\frac{1}{y}}{z}}{3}} \]

      8. associate-*r/ 90.4%

         \[\leadsto x + \color{blue}{t \cdot \frac{\frac{\frac{1}{y}}{z}}{3}} \]

      9. associate-/r* 90.3%

         \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{y}}{z \cdot 3}} \]

      10. associate-/l/ 90.3%

          \[\leadsto x + t \cdot \color{blue}{\frac{1}{\left(z \cdot 3\right) \cdot y}} \]

      11. associate-/r* 90.3%

          \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{z \cdot 3}}{y}} \]

      12. *-commutative 90.3%

          \[\leadsto x + t \cdot \frac{\frac{1}{\color{blue}{3 \cdot z}}}{y} \]

      13. associate-/r* 90.4%

          \[\leadsto x + t \cdot \frac{\color{blue}{\frac{\frac{1}{3}}{z}}}{y} \]

      14. metadata-eval 90.4%

          \[\leadsto x + t \cdot \frac{\frac{\color{blue}{0.3333333333333333}}{z}}{y} \]

   6. Simplified 90.4%

      \[\leadsto x + \color{blue}{t \cdot \frac{\frac{0.3333333333333333}{z}}{y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 92.4%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   8. Applied egg-rr 92.4%

      \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]
   9. Step-by-step derivation

      1. clear-num 92.3%

         \[\leadsto x + \frac{t \cdot \color{blue}{\frac{1}{\frac{z}{0.3333333333333333}}}}{y} \]

      2. div-inv 92.4%

         \[\leadsto x + \frac{t \cdot \frac{1}{\color{blue}{z \cdot \frac{1}{0.3333333333333333}}}}{y} \]

      3. metadata-eval 92.4%

         \[\leadsto x + \frac{t \cdot \frac{1}{z \cdot \color{blue}{3}}}{y} \]

      4. un-div-inv 92.4%

         \[\leadsto x + \frac{\color{blue}{\frac{t}{z \cdot 3}}}{y} \]

   10. Applied egg-rr 92.4%

       \[\leadsto x + \frac{\color{blue}{\frac{t}{z \cdot 3}}}{y} \]
   11. Step-by-step derivation

       1. *-commutative 92.4%

          \[\leadsto x + \frac{\frac{t}{\color{blue}{3 \cdot z}}}{y} \]

       2. associate-/r* 92.5%

          \[\leadsto x + \frac{\color{blue}{\frac{\frac{t}{3}}{z}}}{y} \]

   12. Simplified 92.5%

       \[\leadsto x + \frac{\color{blue}{\frac{\frac{t}{3}}{z}}}{y} \]

   if -2.70000000000000006e164 < t

   1. Initial program 95.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.7 \cdot 10^{+164}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{3}}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \end{array} \]

Alternative 12: 95.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+164}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{3}}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.7e+164)
   (+ x (/ (/ (/ t 3.0) z) y))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.7e+164) {
		tmp = x + (((t / 3.0) / z) / y);
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	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 <= (-3.7d+164)) then
        tmp = x + (((t / 3.0d0) / z) / y)
    else
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.7e+164) {
		tmp = x + (((t / 3.0) / z) / y);
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.7e+164:
		tmp = x + (((t / 3.0) / z) / y)
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.7e+164)
		tmp = Float64(x + Float64(Float64(Float64(t / 3.0) / z) / y));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.7e+164)
		tmp = x + (((t / 3.0) / z) / y);
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.7e+164], N[(x + N[(N[(N[(t / 3.0), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.7000000000000001e164

   1. Initial program 97.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 73.2%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around inf 90.5%

      \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 90.5%

         \[\leadsto x + \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. metadata-eval 90.5%

         \[\leadsto x + \frac{t}{y \cdot z} \cdot \color{blue}{\frac{1}{3}} \]

      3. times-frac 90.3%

         \[\leadsto x + \color{blue}{\frac{t \cdot 1}{\left(y \cdot z\right) \cdot 3}} \]

      4. *-commutative 90.3%

         \[\leadsto x + \frac{t \cdot 1}{\color{blue}{3 \cdot \left(y \cdot z\right)}} \]

      5. times-frac 90.4%

         \[\leadsto x + \color{blue}{\frac{t}{3} \cdot \frac{1}{y \cdot z}} \]

      6. associate-/r* 90.4%

         \[\leadsto x + \frac{t}{3} \cdot \color{blue}{\frac{\frac{1}{y}}{z}} \]

      7. associate-*l/ 90.5%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{\frac{1}{y}}{z}}{3}} \]

      8. associate-*r/ 90.4%

         \[\leadsto x + \color{blue}{t \cdot \frac{\frac{\frac{1}{y}}{z}}{3}} \]

      9. associate-/r* 90.3%

         \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{y}}{z \cdot 3}} \]

      10. associate-/l/ 90.3%

          \[\leadsto x + t \cdot \color{blue}{\frac{1}{\left(z \cdot 3\right) \cdot y}} \]

      11. associate-/r* 90.3%

          \[\leadsto x + t \cdot \color{blue}{\frac{\frac{1}{z \cdot 3}}{y}} \]

      12. *-commutative 90.3%

          \[\leadsto x + t \cdot \frac{\frac{1}{\color{blue}{3 \cdot z}}}{y} \]

      13. associate-/r* 90.4%

          \[\leadsto x + t \cdot \frac{\color{blue}{\frac{\frac{1}{3}}{z}}}{y} \]

      14. metadata-eval 90.4%

          \[\leadsto x + t \cdot \frac{\frac{\color{blue}{0.3333333333333333}}{z}}{y} \]

   6. Simplified 90.4%

      \[\leadsto x + \color{blue}{t \cdot \frac{\frac{0.3333333333333333}{z}}{y}} \]
   7. Step-by-step derivation

      1. associate-*r/ 92.4%

         \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   8. Applied egg-rr 92.4%

      \[\leadsto x + \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]
   9. Step-by-step derivation

      1. clear-num 92.3%

         \[\leadsto x + \frac{t \cdot \color{blue}{\frac{1}{\frac{z}{0.3333333333333333}}}}{y} \]

      2. div-inv 92.4%

         \[\leadsto x + \frac{t \cdot \frac{1}{\color{blue}{z \cdot \frac{1}{0.3333333333333333}}}}{y} \]

      3. metadata-eval 92.4%

         \[\leadsto x + \frac{t \cdot \frac{1}{z \cdot \color{blue}{3}}}{y} \]

      4. un-div-inv 92.4%

         \[\leadsto x + \frac{\color{blue}{\frac{t}{z \cdot 3}}}{y} \]

   10. Applied egg-rr 92.4%

       \[\leadsto x + \frac{\color{blue}{\frac{t}{z \cdot 3}}}{y} \]
   11. Step-by-step derivation

       1. *-commutative 92.4%

          \[\leadsto x + \frac{\frac{t}{\color{blue}{3 \cdot z}}}{y} \]

       2. associate-/r* 92.5%

          \[\leadsto x + \frac{\color{blue}{\frac{\frac{t}{3}}{z}}}{y} \]

   12. Simplified 92.5%

       \[\leadsto x + \frac{\color{blue}{\frac{\frac{t}{3}}{z}}}{y} \]

   if -3.7000000000000001e164 < t

   1. Initial program 95.2%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 95.2%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 95.2%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 95.2%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 95.2%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 95.2%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 95.2%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 95.2%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 96.8%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 96.8%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 96.8%

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

4. Final simplification 96.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.7 \cdot 10^{+164}:\\ \;\;\;\;x + \frac{\frac{\frac{t}{3}}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]

Alternative 13: 77.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-129} \lor \neg \left(y \leq 2.4 \cdot 10^{-19}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.25e-129) (not (<= y 2.4e-19)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* 0.3333333333333333 (/ (/ t z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.25e-129) || !(y <= 2.4e-19)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * ((t / z) / y);
	}
	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 ((y <= (-1.25d-129)) .or. (.not. (y <= 2.4d-19))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.25e-129) || !(y <= 2.4e-19)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * ((t / z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.25e-129) or not (y <= 2.4e-19):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * ((t / z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.25e-129) || !(y <= 2.4e-19))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.25e-129) || ~((y <= 2.4e-19)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * ((t / z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.25e-129], N[Not[LessEqual[y, 2.4e-19]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25000000000000007e-129 or 2.40000000000000023e-19 < y

   1. Initial program 98.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 97.1%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around 0 86.6%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. *-commutative 86.6%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-*l/ 86.5%

         \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

      3. associate-*r/ 86.5%

         \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   6. Simplified 86.5%

      \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   if -1.25000000000000007e-129 < y < 2.40000000000000023e-19

   1. Initial program 91.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 91.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 91.5%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 91.5%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 89.1%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 89.1%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 89.1%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around 0 71.9%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   7. Step-by-step derivation

      1. expm1-log1p-u 39.2%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{y \cdot z}\right)\right)} \]

      2. expm1-udef 31.6%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{t}{y \cdot z}\right)} - 1\right)} \]

      3. *-commutative 31.6%

         \[\leadsto 0.3333333333333333 \cdot \left(e^{\mathsf{log1p}\left(\frac{t}{\color{blue}{z \cdot y}}\right)} - 1\right) \]

   8. Applied egg-rr 31.6%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{t}{z \cdot y}\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 39.2%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{z \cdot y}\right)\right)} \]

      2. expm1-log1p 71.9%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{t}{z \cdot y}} \]

      3. associate-/r* 76.4%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{z}}{y}} \]

   10. Simplified 76.4%

       \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{z}}{y}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-129} \lor \neg \left(y \leq 2.4 \cdot 10^{-19}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \]

Alternative 14: 77.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e-129)
   (+ x (/ (* y -0.3333333333333333) z))
   (if (<= y 4.2e-20)
     (* 0.3333333333333333 (/ (/ t z) y))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-129) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 4.2e-20) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	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 (y <= (-1.05d-129)) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else if (y <= 4.2d-20) then
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e-129) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 4.2e-20) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e-129:
		tmp = x + ((y * -0.3333333333333333) / z)
	elif y <= 4.2e-20:
		tmp = 0.3333333333333333 * ((t / z) / y)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e-129)
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	elseif (y <= 4.2e-20)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.05e-129)
		tmp = x + ((y * -0.3333333333333333) / z);
	elseif (y <= 4.2e-20)
		tmp = 0.3333333333333333 * ((t / z) / y);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e-129], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-20], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e-129

   1. Initial program 97.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around 0 84.7%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. *-commutative 84.7%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-*l/ 84.8%

         \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

      3. associate-*r/ 84.7%

         \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   6. Simplified 84.7%

      \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   7. Taylor expanded in y around 0 84.7%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 84.8%

         \[\leadsto x + \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 84.8%

         \[\leadsto x + \frac{\color{blue}{y \cdot -0.3333333333333333}}{z} \]

   9. Simplified 84.8%

      \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

   if -1.05e-129 < y < 4.1999999999999998e-20

   1. Initial program 91.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 91.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 91.5%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 91.5%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 89.1%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 89.1%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 89.1%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around 0 71.9%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   7. Step-by-step derivation

      1. expm1-log1p-u 39.2%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{y \cdot z}\right)\right)} \]

      2. expm1-udef 31.6%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{t}{y \cdot z}\right)} - 1\right)} \]

      3. *-commutative 31.6%

         \[\leadsto 0.3333333333333333 \cdot \left(e^{\mathsf{log1p}\left(\frac{t}{\color{blue}{z \cdot y}}\right)} - 1\right) \]

   8. Applied egg-rr 31.6%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{t}{z \cdot y}\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 39.2%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{z \cdot y}\right)\right)} \]

      2. expm1-log1p 71.9%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{t}{z \cdot y}} \]

      3. associate-/r* 76.4%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{z}}{y}} \]

   10. Simplified 76.4%

       \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{z}}{y}} \]

   if 4.1999999999999998e-20 < y

   1. Initial program 99.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around 0 89.0%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. *-commutative 89.0%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-*l/ 88.8%

         \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

      3. associate-*r/ 88.8%

         \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   6. Simplified 88.8%

      \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 15: 77.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-130}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.4e-130)
   (+ x (/ (* y -0.3333333333333333) z))
   (if (<= y 4.2e-20)
     (* 0.3333333333333333 (/ (/ t z) y))
     (- x (* 0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.4e-130) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 4.2e-20) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	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 (y <= (-5.4d-130)) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else if (y <= 4.2d-20) then
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    else
        tmp = x - (0.3333333333333333d0 * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.4e-130) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 4.2e-20) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.4e-130:
		tmp = x + ((y * -0.3333333333333333) / z)
	elif y <= 4.2e-20:
		tmp = 0.3333333333333333 * ((t / z) / y)
	else:
		tmp = x - (0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.4e-130)
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	elseif (y <= 4.2e-20)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	else
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.4e-130)
		tmp = x + ((y * -0.3333333333333333) / z);
	elseif (y <= 4.2e-20)
		tmp = 0.3333333333333333 * ((t / z) / y);
	else
		tmp = x - (0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.4e-130], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.2e-20], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.39999999999999982e-130

   1. Initial program 97.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around 0 84.7%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. *-commutative 84.7%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-*l/ 84.8%

         \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

      3. associate-*r/ 84.7%

         \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   6. Simplified 84.7%

      \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   7. Taylor expanded in y around 0 84.7%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 84.8%

         \[\leadsto x + \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 84.8%

         \[\leadsto x + \frac{\color{blue}{y \cdot -0.3333333333333333}}{z} \]

   9. Simplified 84.8%

      \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

   if -5.39999999999999982e-130 < y < 4.1999999999999998e-20

   1. Initial program 91.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 91.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 91.5%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 91.5%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 89.1%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 89.1%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 89.1%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around 0 71.9%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   7. Step-by-step derivation

      1. expm1-log1p-u 39.2%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{y \cdot z}\right)\right)} \]

      2. expm1-udef 31.6%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{t}{y \cdot z}\right)} - 1\right)} \]

      3. *-commutative 31.6%

         \[\leadsto 0.3333333333333333 \cdot \left(e^{\mathsf{log1p}\left(\frac{t}{\color{blue}{z \cdot y}}\right)} - 1\right) \]

   8. Applied egg-rr 31.6%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{t}{z \cdot y}\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 39.2%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{z \cdot y}\right)\right)} \]

      2. expm1-log1p 71.9%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{t}{z \cdot y}} \]

      3. associate-/r* 76.4%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{z}}{y}} \]

   10. Simplified 76.4%

       \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{z}}{y}} \]

   if 4.1999999999999998e-20 < y

   1. Initial program 99.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]

   4. Taylor expanded in t around 0 89.0%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.4 \cdot 10^{-130}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-20}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]

Alternative 16: 77.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-19}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.25e-129)
   (+ x (/ (* y -0.3333333333333333) z))
   (if (<= y 2.4e-19)
     (* 0.3333333333333333 (/ (/ t z) y))
     (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e-129) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 2.4e-19) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	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 (y <= (-1.25d-129)) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else if (y <= 2.4d-19) then
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e-129) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 2.4e-19) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.25e-129:
		tmp = x + ((y * -0.3333333333333333) / z)
	elif y <= 2.4e-19:
		tmp = 0.3333333333333333 * ((t / z) / y)
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.25e-129)
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	elseif (y <= 2.4e-19)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.25e-129)
		tmp = x + ((y * -0.3333333333333333) / z);
	elseif (y <= 2.4e-19)
		tmp = 0.3333333333333333 * ((t / z) / y);
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.25e-129], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-19], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25000000000000007e-129

   1. Initial program 97.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around 0 84.7%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. *-commutative 84.7%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-*l/ 84.8%

         \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

      3. associate-*r/ 84.7%

         \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   6. Simplified 84.7%

      \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   7. Taylor expanded in y around 0 84.7%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 84.8%

         \[\leadsto x + \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 84.8%

         \[\leadsto x + \frac{\color{blue}{y \cdot -0.3333333333333333}}{z} \]

   9. Simplified 84.8%

      \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

   if -1.25000000000000007e-129 < y < 2.40000000000000023e-19

   1. Initial program 91.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 91.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 91.5%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 91.5%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 89.1%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 89.1%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 89.1%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around 0 71.9%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   7. Step-by-step derivation

      1. expm1-log1p-u 39.2%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{y \cdot z}\right)\right)} \]

      2. expm1-udef 31.6%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{t}{y \cdot z}\right)} - 1\right)} \]

      3. *-commutative 31.6%

         \[\leadsto 0.3333333333333333 \cdot \left(e^{\mathsf{log1p}\left(\frac{t}{\color{blue}{z \cdot y}}\right)} - 1\right) \]

   8. Applied egg-rr 31.6%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{t}{z \cdot y}\right)} - 1\right)} \]
   9. Step-by-step derivation

      1. expm1-def 39.2%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{t}{z \cdot y}\right)\right)} \]

      2. expm1-log1p 71.9%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{t}{z \cdot y}} \]

      3. associate-/r* 76.4%

         \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{z}}{y}} \]

   10. Simplified 76.4%

       \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{z}}{y}} \]

   if 2.40000000000000023e-19 < y

   1. Initial program 99.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]

   4. Taylor expanded in t around 0 89.0%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. metadata-eval 89.0%

         \[\leadsto x - \color{blue}{\frac{1}{3}} \cdot \frac{y}{z} \]

      2. times-frac 89.0%

         \[\leadsto x - \color{blue}{\frac{1 \cdot y}{3 \cdot z}} \]

      3. *-un-lft-identity 89.0%

         \[\leadsto x - \frac{\color{blue}{y}}{3 \cdot z} \]

      4. *-commutative 89.0%

         \[\leadsto x - \frac{y}{\color{blue}{z \cdot 3}} \]

   6. Applied egg-rr 89.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-19}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 17: 77.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.24 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-20}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.24e-129)
   (+ x (/ (* y -0.3333333333333333) z))
   (if (<= y 2.7e-20)
     (/ (* t (/ 0.3333333333333333 z)) y)
     (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.24e-129) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 2.7e-20) {
		tmp = (t * (0.3333333333333333 / z)) / y;
	} else {
		tmp = x - (y / (z * 3.0));
	}
	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 (y <= (-1.24d-129)) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else if (y <= 2.7d-20) then
        tmp = (t * (0.3333333333333333d0 / z)) / y
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.24e-129) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 2.7e-20) {
		tmp = (t * (0.3333333333333333 / z)) / y;
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.24e-129:
		tmp = x + ((y * -0.3333333333333333) / z)
	elif y <= 2.7e-20:
		tmp = (t * (0.3333333333333333 / z)) / y
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.24e-129)
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	elseif (y <= 2.7e-20)
		tmp = Float64(Float64(t * Float64(0.3333333333333333 / z)) / y);
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.24e-129)
		tmp = x + ((y * -0.3333333333333333) / z);
	elseif (y <= 2.7e-20)
		tmp = (t * (0.3333333333333333 / z)) / y;
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.24e-129], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-20], N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.24000000000000004e-129

   1. Initial program 97.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in t around 0 84.7%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. *-commutative 84.7%

         \[\leadsto x + \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} \]

      2. associate-*l/ 84.8%

         \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

      3. associate-*r/ 84.7%

         \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   6. Simplified 84.7%

      \[\leadsto x + \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]

   7. Taylor expanded in y around 0 84.7%

      \[\leadsto x + \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   8. Step-by-step derivation

      1. associate-*r/ 84.8%

         \[\leadsto x + \color{blue}{\frac{-0.3333333333333333 \cdot y}{z}} \]

      2. *-commutative 84.8%

         \[\leadsto x + \frac{\color{blue}{y \cdot -0.3333333333333333}}{z} \]

   9. Simplified 84.8%

      \[\leadsto x + \color{blue}{\frac{y \cdot -0.3333333333333333}{z}} \]

   if -1.24000000000000004e-129 < y < 2.7e-20

   1. Initial program 91.5%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 91.6%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 91.5%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 91.5%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 91.5%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 89.1%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 89.1%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 89.1%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around 0 71.9%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   7. Step-by-step derivation

      1. *-commutative 71.9%

         \[\leadsto \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

      2. associate-*l/ 71.9%

         \[\leadsto \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]

      3. metadata-eval 71.9%

         \[\leadsto \frac{t \cdot \color{blue}{\frac{1}{3}}}{y \cdot z} \]

      4. div-inv 72.0%

         \[\leadsto \frac{\color{blue}{\frac{t}{3}}}{y \cdot z} \]

      5. associate-/l/ 76.4%

         \[\leadsto \color{blue}{\frac{\frac{\frac{t}{3}}{z}}{y}} \]

      6. associate-/l/ 76.3%

         \[\leadsto \frac{\color{blue}{\frac{t}{z \cdot 3}}}{y} \]

      7. div-inv 76.4%

         \[\leadsto \frac{\color{blue}{t \cdot \frac{1}{z \cdot 3}}}{y} \]

      8. *-commutative 76.4%

         \[\leadsto \frac{t \cdot \frac{1}{\color{blue}{3 \cdot z}}}{y} \]

      9. associate-/r* 76.4%

         \[\leadsto \frac{t \cdot \color{blue}{\frac{\frac{1}{3}}{z}}}{y} \]

      10. metadata-eval 76.4%

          \[\leadsto \frac{t \cdot \frac{\color{blue}{0.3333333333333333}}{z}}{y} \]

   8. Applied egg-rr 76.4%

      \[\leadsto \color{blue}{\frac{t \cdot \frac{0.3333333333333333}{z}}{y}} \]

   if 2.7e-20 < y

   1. Initial program 99.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 99.9%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]

   4. Taylor expanded in t around 0 89.0%

      \[\leadsto \color{blue}{x - 0.3333333333333333 \cdot \frac{y}{z}} \]
   5. Step-by-step derivation

      1. metadata-eval 89.0%

         \[\leadsto x - \color{blue}{\frac{1}{3}} \cdot \frac{y}{z} \]

      2. times-frac 89.0%

         \[\leadsto x - \color{blue}{\frac{1 \cdot y}{3 \cdot z}} \]

      3. *-un-lft-identity 89.0%

         \[\leadsto x - \frac{\color{blue}{y}}{3 \cdot z} \]

      4. *-commutative 89.0%

         \[\leadsto x - \frac{y}{\color{blue}{z \cdot 3}} \]

   6. Applied egg-rr 89.0%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.24 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-20}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 18: 46.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+30}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.7e+56) x (if (<= x 6e+30) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.7e+56) {
		tmp = x;
	} else if (x <= 6e+30) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.7d+56)) then
        tmp = x
    else if (x <= 6d+30) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.7e+56) {
		tmp = x;
	} else if (x <= 6e+30) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.7e+56:
		tmp = x
	elif x <= 6e+30:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.7e+56)
		tmp = x;
	elseif (x <= 6e+30)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.7e+56)
		tmp = x;
	elseif (x <= 6e+30)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.7e+56], x, If[LessEqual[x, 6e+30], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.7e56 or 5.99999999999999956e30 < x

   1. Initial program 93.6%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   3. Simplified 97.2%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   4. Taylor expanded in x around inf 65.7%

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

   if -1.7e56 < x < 5.99999999999999956e30

   1. Initial program 96.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. associate-*l* 96.8%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} \]

      2. *-commutative 96.8%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} \]

   3. Simplified 96.8%

      \[\leadsto \color{blue}{\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}} \]
   4. Step-by-step derivation

      1. *-commutative 96.8%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \color{blue}{\left(3 \cdot y\right)}} \]

      2. associate-*l* 96.8%

         \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\color{blue}{\left(z \cdot 3\right) \cdot y}} \]

      3. associate-+l- 96.8%

         \[\leadsto \color{blue}{x - \left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

      4. *-commutative 96.8%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \frac{t}{\color{blue}{y \cdot \left(z \cdot 3\right)}}\right) \]

      5. associate-/r* 91.2%

         \[\leadsto x - \left(\frac{y}{z \cdot 3} - \color{blue}{\frac{\frac{t}{y}}{z \cdot 3}}\right) \]

      6. sub-div 91.2%

         \[\leadsto x - \color{blue}{\frac{y - \frac{t}{y}}{z \cdot 3}} \]

   5. Applied egg-rr 91.2%

      \[\leadsto \color{blue}{x - \frac{y - \frac{t}{y}}{z \cdot 3}} \]

   6. Taylor expanded in y around inf 39.3%

      \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+30}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 19: 30.5% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

3. Simplified 93.5%

   \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

4. Taylor expanded in x around inf 31.5%

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

5. Final simplification 31.5%

   \[\leadsto x \]

Developer target: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y)))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

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 * 3.0d0))) + ((t / (z * 3.0d0)) / y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y)

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(t / Float64(z * 3.0)) / y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023331 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))