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

Percentage Accurate: 95.6% → 99.5%

Time: 10.2s

Alternatives: 16

Speedup: 1.4×

• 28.4% 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: 95.6% 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: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-22} \lor \neg \left(z \cdot 3 \leq 5 \cdot 10^{-49}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -1e-22) (not (<= (* z 3.0) 5e-49)))
   (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))
   (+ x (* (/ -0.3333333333333333 z) (- y (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -1e-22) || !((z * 3.0) <= 5e-49)) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} 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 (((z * 3.0d0) <= (-1d-22)) .or. (.not. ((z * 3.0d0) <= 5d-49))) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    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 (((z * 3.0) <= -1e-22) || !((z * 3.0) <= 5e-49)) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} else {
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -1e-22) or not ((z * 3.0) <= 5e-49):
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))
	else:
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -1e-22) || !(Float64(z * 3.0) <= 5e-49))
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))));
	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 (((z * 3.0) <= -1e-22) || ~(((z * 3.0) <= 5e-49)))
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	else
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -1e-22], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 5e-49]], $MachinePrecision]], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $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 (*.f64 z 3) < -1e-22 or 4.9999999999999999e-49 < (*.f64 z 3)

   1. Initial program 99.8%

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

   if -1e-22 < (*.f64 z 3) < 4.9999999999999999e-49

   1. Initial program 86.3%

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

      1. associate-+l- 86.3%

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

      2. sub-neg 86.3%

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

      3. sub-neg 86.3%

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

      4. distribute-neg-in 86.3%

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

      5. unsub-neg 86.3%

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

      6. neg-mul-1 86.3%

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

      7. associate-*r/ 86.3%

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

      8. associate-*l/ 86.3%

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

      9. distribute-neg-frac 86.3%

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

      10. neg-mul-1 86.3%

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

      11. times-frac 97.9%

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

      12. distribute-lft-out-- 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-/r* 99.8%

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

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{-22} \lor \neg \left(z \cdot 3 \leq 5 \cdot 10^{-49}\right):\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \end{array} \]

Alternative 2: 97.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;t_1 + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 5 \cdot 10^{+283}:\\ \;\;\;\;t_1 + \frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= (+ t_1 (/ t (* y (* z 3.0)))) 5e+283)
     (+ t_1 (/ (* 0.3333333333333333 (/ t z)) y))
     (+ x (* (/ -0.3333333333333333 z) (- y (/ t y)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((t_1 + (t / (y * (z * 3.0)))) <= 5e+283) {
		tmp = t_1 + ((0.3333333333333333 * (t / 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) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (z * 3.0d0))
    if ((t_1 + (t / (y * (z * 3.0d0)))) <= 5d+283) then
        tmp = t_1 + ((0.3333333333333333d0 * (t / 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 t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((t_1 + (t / (y * (z * 3.0)))) <= 5e+283) {
		tmp = t_1 + ((0.3333333333333333 * (t / z)) / y);
	} else {
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if (t_1 + (t / (y * (z * 3.0)))) <= 5e+283:
		tmp = t_1 + ((0.3333333333333333 * (t / z)) / y)
	else:
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (Float64(t_1 + Float64(t / Float64(y * Float64(z * 3.0)))) <= 5e+283)
		tmp = Float64(t_1 + Float64(Float64(0.3333333333333333 * Float64(t / 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)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if ((t_1 + (t / (y * (z * 3.0)))) <= 5e+283)
		tmp = t_1 + ((0.3333333333333333 * (t / z)) / y);
	else
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	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[N[(t$95$1 + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 5e+283], N[(t$95$1 + N[(N[(0.3333333333333333 * N[(t / z), $MachinePrecision]), $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 (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y))) < 5.0000000000000004e283

   1. Initial program 97.2%

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

      1. associate-/r* 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in t around 0 98.9%

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

   if 5.0000000000000004e283 < (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))

   1. Initial program 82.7%

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

      1. associate-+l- 82.7%

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

      2. sub-neg 82.7%

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

      3. sub-neg 82.7%

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

      4. distribute-neg-in 82.7%

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

      5. unsub-neg 82.7%

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

      6. neg-mul-1 82.7%

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

      7. associate-*r/ 82.7%

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

      8. associate-*l/ 82.7%

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

      9. distribute-neg-frac 82.7%

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

      10. neg-mul-1 82.7%

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

      11. times-frac 96.4%

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

      12. distribute-lft-out-- 99.9%

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

      13. *-commutative 99.9%

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

      14. associate-/r* 99.9%

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

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 5 \cdot 10^{+283}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \end{array} \]

Alternative 3: 82.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+57}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{+71}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -1e+57)
   (- x (/ y (* z 3.0)))
   (if (<= (* z 3.0) 5e+71)
     (* (/ 0.3333333333333333 z) (- (/ t y) y))
     (- x (/ (/ y z) 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -1e+57) {
		tmp = x - (y / (z * 3.0));
	} else if ((z * 3.0) <= 5e+71) {
		tmp = (0.3333333333333333 / z) * ((t / y) - 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 ((z * 3.0d0) <= (-1d+57)) then
        tmp = x - (y / (z * 3.0d0))
    else if ((z * 3.0d0) <= 5d+71) then
        tmp = (0.3333333333333333d0 / z) * ((t / y) - 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 ((z * 3.0) <= -1e+57) {
		tmp = x - (y / (z * 3.0));
	} else if ((z * 3.0) <= 5e+71) {
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	} else {
		tmp = x - ((y / z) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -1e+57:
		tmp = x - (y / (z * 3.0))
	elif (z * 3.0) <= 5e+71:
		tmp = (0.3333333333333333 / z) * ((t / y) - y)
	else:
		tmp = x - ((y / z) / 3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -1e+57)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (Float64(z * 3.0) <= 5e+71)
		tmp = Float64(Float64(0.3333333333333333 / z) * Float64(Float64(t / y) - y));
	else
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -1e+57)
		tmp = x - (y / (z * 3.0));
	elseif ((z * 3.0) <= 5e+71)
		tmp = (0.3333333333333333 / z) * ((t / y) - y);
	else
		tmp = x - ((y / z) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -1e+57], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 5e+71], N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -1.00000000000000005e57

   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-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 83.8%

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

      1. metadata-eval 83.8%

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

      2. times-frac 83.9%

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

      3. *-un-lft-identity 83.9%

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

      4. *-commutative 83.9%

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

   6. Applied egg-rr 83.9%

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

   if -1.00000000000000005e57 < (*.f64 z 3) < 4.99999999999999972e71

   1. Initial program 90.7%

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

      1. associate-/r* 95.6%

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

   3. Simplified 95.6%

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

   4. Taylor expanded in t around 0 95.6%

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

   5. Taylor expanded in x around 0 79.7%

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

      1. distribute-lft-out-- 79.7%

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

      2. associate-/r* 85.3%

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

      3. div-sub 86.6%

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

      4. associate-*r/ 87.2%

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

      5. *-commutative 87.2%

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

      6. associate-*r/ 87.1%

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

   7. Simplified 87.1%

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

   if 4.99999999999999972e71 < (*.f64 z 3)

   1. Initial program 99.7%

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

      1. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 79.5%

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

      1. metadata-eval 79.5%

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

      2. times-frac 79.5%

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

      3. *-un-lft-identity 79.5%

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

      4. *-commutative 79.5%

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

      5. associate-/r* 79.5%

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

   6. Applied egg-rr 79.5%

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

4. Final simplification 85.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+57}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \leq 5 \cdot 10^{+71}:\\ \;\;\;\;\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \]

Alternative 4: 60.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+121}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-73}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6e+121)
   (/ (* y -0.3333333333333333) z)
   (if (<= y -8.8e-19)
     x
     (if (<= y 9e-73)
       (* (/ t y) (/ 0.3333333333333333 z))
       (if (<= y 2.2e+63) x (* y (/ -0.3333333333333333 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e+121) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -8.8e-19) {
		tmp = x;
	} else if (y <= 9e-73) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else if (y <= 2.2e+63) {
		tmp = x;
	} else {
		tmp = 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 <= (-6d+121)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= (-8.8d-19)) then
        tmp = x
    else if (y <= 9d-73) then
        tmp = (t / y) * (0.3333333333333333d0 / z)
    else if (y <= 2.2d+63) then
        tmp = x
    else
        tmp = 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 <= -6e+121) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -8.8e-19) {
		tmp = x;
	} else if (y <= 9e-73) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else if (y <= 2.2e+63) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6e+121:
		tmp = (y * -0.3333333333333333) / z
	elif y <= -8.8e-19:
		tmp = x
	elif y <= 9e-73:
		tmp = (t / y) * (0.3333333333333333 / z)
	elif y <= 2.2e+63:
		tmp = x
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6e+121)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= -8.8e-19)
		tmp = x;
	elseif (y <= 9e-73)
		tmp = Float64(Float64(t / y) * Float64(0.3333333333333333 / z));
	elseif (y <= 2.2e+63)
		tmp = x;
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6e+121)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= -8.8e-19)
		tmp = x;
	elseif (y <= 9e-73)
		tmp = (t / y) * (0.3333333333333333 / z);
	elseif (y <= 2.2e+63)
		tmp = x;
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6e+121], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -8.8e-19], x, If[LessEqual[y, 9e-73], N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e+63], x, N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.0000000000000005e121

   1. Initial program 94.3%

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

      1. associate-/r* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around 0 74.2%

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

      1. associate-/r* 74.2%

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

      2. associate-*r/ 74.2%

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

      3. associate-*r/ 74.3%

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

      4. div-sub 79.9%

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

      5. distribute-lft-out-- 79.9%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in t around 0 79.9%

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

      1. *-commutative 79.9%

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

   9. Simplified 79.9%

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

   if -6.0000000000000005e121 < y < -8.7999999999999994e-19 or 9e-73 < y < 2.1999999999999999e63

   1. Initial program 98.0%

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

      1. associate-/r* 94.8%

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

   3. Simplified 94.8%

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

   4. Taylor expanded in x around inf 51.9%

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

   if -8.7999999999999994e-19 < y < 9e-73

   1. Initial program 89.9%

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

      1. associate-/r* 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 64.0%

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

      1. associate-/r* 66.2%

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

      2. associate-*r/ 66.9%

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

      3. associate-*r/ 67.0%

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

      4. div-sub 67.0%

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

      5. distribute-lft-out-- 67.0%

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

   6. Simplified 67.0%

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

   7. Taylor expanded in t around inf 64.8%

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

      1. associate-*r/ 64.7%

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

      2. associate-/l* 64.7%

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

   9. Simplified 64.7%

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

       1. associate-/l/ 64.7%

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

       2. metadata-eval 64.7%

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

       3. frac-times 64.7%

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

       4. clear-num 64.7%

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

   11. Applied egg-rr 64.7%

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

   if 2.1999999999999999e63 < 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-/r* 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around 0 77.9%

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

      1. associate-/r* 77.9%

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

      2. associate-*r/ 77.9%

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

      3. associate-*r/ 77.9%

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

      4. div-sub 77.9%

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

      5. distribute-lft-out-- 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in t around 0 77.9%

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

      1. *-commutative 77.9%

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

   9. Simplified 77.9%

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

   10. Taylor expanded in y around 0 77.9%

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

       1. associate-*r/ 77.9%

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

       2. associate-*l/ 77.9%

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

       3. *-commutative 77.9%

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

   12. Simplified 77.9%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+121}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -8.8 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-73}:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 5: 62.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-113}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.5e+123)
   (/ (* y -0.3333333333333333) z)
   (if (<= y -6.6e-18)
     x
     (if (<= y 3e-113)
       (* (/ t z) (/ 0.3333333333333333 y))
       (if (<= y 4.9e+53) x (* y (/ -0.3333333333333333 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.5e+123) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -6.6e-18) {
		tmp = x;
	} else if (y <= 3e-113) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else if (y <= 4.9e+53) {
		tmp = x;
	} else {
		tmp = 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 <= (-8.5d+123)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= (-6.6d-18)) then
        tmp = x
    else if (y <= 3d-113) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else if (y <= 4.9d+53) then
        tmp = x
    else
        tmp = 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 <= -8.5e+123) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -6.6e-18) {
		tmp = x;
	} else if (y <= 3e-113) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else if (y <= 4.9e+53) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.5e+123:
		tmp = (y * -0.3333333333333333) / z
	elif y <= -6.6e-18:
		tmp = x
	elif y <= 3e-113:
		tmp = (t / z) * (0.3333333333333333 / y)
	elif y <= 4.9e+53:
		tmp = x
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.5e+123)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= -6.6e-18)
		tmp = x;
	elseif (y <= 3e-113)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	elseif (y <= 4.9e+53)
		tmp = x;
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.5e+123)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= -6.6e-18)
		tmp = x;
	elseif (y <= 3e-113)
		tmp = (t / z) * (0.3333333333333333 / y);
	elseif (y <= 4.9e+53)
		tmp = x;
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.5e+123], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -6.6e-18], x, If[LessEqual[y, 3e-113], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.9e+53], x, N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.5e123

   1. Initial program 94.3%

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

      1. associate-/r* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around 0 74.2%

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

      1. associate-/r* 74.2%

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

      2. associate-*r/ 74.2%

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

      3. associate-*r/ 74.3%

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

      4. div-sub 79.9%

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

      5. distribute-lft-out-- 79.9%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in t around 0 79.9%

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

      1. *-commutative 79.9%

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

   9. Simplified 79.9%

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

   if -8.5e123 < y < -6.6000000000000003e-18 or 3.0000000000000001e-113 < y < 4.90000000000000018e53

   1. Initial program 96.6%

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

      1. associate-/r* 95.3%

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

   3. Simplified 95.3%

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

   4. Taylor expanded in x around inf 51.0%

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

   if -6.6000000000000003e-18 < y < 3.0000000000000001e-113

   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-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 65.2%

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

      1. associate-/r* 66.7%

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

      2. associate-*r/ 67.5%

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

      3. associate-*r/ 67.5%

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

      4. div-sub 67.5%

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

      5. distribute-lft-out-- 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in t around inf 66.0%

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

      1. associate-*r/ 66.0%

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

      2. associate-/l* 66.0%

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

   9. Simplified 66.0%

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

       1. associate-/l/ 65.9%

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

       2. metadata-eval 65.9%

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

       3. frac-times 66.0%

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

       4. clear-num 66.0%

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

       5. times-frac 63.8%

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

       6. *-commutative 63.8%

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

       7. times-frac 70.8%

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

   11. Applied egg-rr 70.8%

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

   if 4.90000000000000018e53 < 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-/r* 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around 0 77.9%

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

      1. associate-/r* 77.9%

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

      2. associate-*r/ 77.9%

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

      3. associate-*r/ 77.9%

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

      4. div-sub 77.9%

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

      5. distribute-lft-out-- 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in t around 0 77.9%

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

      1. *-commutative 77.9%

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

   9. Simplified 77.9%

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

   10. Taylor expanded in y around 0 77.9%

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

       1. associate-*r/ 77.9%

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

       2. associate-*l/ 77.9%

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

       3. *-commutative 77.9%

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

   12. Simplified 77.9%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-18}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-113}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{+53}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 6: 87.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+117}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+39}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+117)
   (- x (/ y (* z 3.0)))
   (if (<= y 9e+39)
     (+ x (* 0.3333333333333333 (/ t (* y z))))
     (- x (/ (/ y z) 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+117) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 9e+39) {
		tmp = x + (0.3333333333333333 * (t / (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 <= (-1.7d+117)) then
        tmp = x - (y / (z * 3.0d0))
    else if (y <= 9d+39) then
        tmp = x + (0.3333333333333333d0 * (t / (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 <= -1.7e+117) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 9e+39) {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	} else {
		tmp = x - ((y / z) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e+117:
		tmp = x - (y / (z * 3.0))
	elif y <= 9e+39:
		tmp = x + (0.3333333333333333 * (t / (y * z)))
	else:
		tmp = x - ((y / z) / 3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+117)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (y <= 9e+39)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(y * z))));
	else
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e+117)
		tmp = x - (y / (z * 3.0));
	elseif (y <= 9e+39)
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	else
		tmp = x - ((y / z) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e+117], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+39], N[(x + N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e117

   1. Initial program 94.3%

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

      1. associate-/r* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in t around 0 99.7%

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

      1. metadata-eval 99.7%

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

      2. times-frac 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. *-commutative 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -1.7e117 < y < 8.99999999999999991e39

   1. Initial program 92.4%

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

      1. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around 0 86.3%

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

   if 8.99999999999999991e39 < 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-/r* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in t around 0 99.7%

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

      1. metadata-eval 99.7%

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

      2. times-frac 99.8%

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

      3. *-un-lft-identity 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+117}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+39}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \]

Alternative 7: 87.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+117}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{t \cdot 0.3333333333333333}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+117)
   (- x (/ y (* z 3.0)))
   (if (<= y 7e+39)
     (+ 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 <= -1.7e+117) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 7e+39) {
		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 <= (-1.7d+117)) then
        tmp = x - (y / (z * 3.0d0))
    else if (y <= 7d+39) 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 <= -1.7e+117) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 7e+39) {
		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 <= -1.7e+117:
		tmp = x - (y / (z * 3.0))
	elif y <= 7e+39:
		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 <= -1.7e+117)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (y <= 7e+39)
		tmp = Float64(x + Float64(Float64(t * 0.3333333333333333) / Float64(y * z)));
	else
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e+117)
		tmp = x - (y / (z * 3.0));
	elseif (y <= 7e+39)
		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, -1.7e+117], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e+39], N[(x + N[(N[(t * 0.3333333333333333), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e117

   1. Initial program 94.3%

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

      1. associate-/r* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in t around 0 99.7%

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

      1. metadata-eval 99.7%

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

      2. times-frac 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. *-commutative 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -1.7e117 < y < 7.0000000000000003e39

   1. Initial program 92.4%

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

      1. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around 0 86.3%

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

      1. associate-*r/ 86.3%

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

      2. *-commutative 86.3%

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

   6. Applied egg-rr 86.3%

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

   if 7.0000000000000003e39 < 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-/r* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in t around 0 99.7%

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

      1. metadata-eval 99.7%

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

      2. times-frac 99.8%

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

      3. *-un-lft-identity 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+117}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+39}:\\ \;\;\;\;x + \frac{t \cdot 0.3333333333333333}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \]

Alternative 8: 87.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+117}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{\frac{0.3333333333333333}{z}}{\frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+117)
   (- x (/ y (* z 3.0)))
   (if (<= y 1.22e+41)
     (+ x (/ (/ 0.3333333333333333 z) (/ y t)))
     (- x (/ (/ y z) 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+117) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 1.22e+41) {
		tmp = x + ((0.3333333333333333 / z) / (y / t));
	} 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 <= (-1.7d+117)) then
        tmp = x - (y / (z * 3.0d0))
    else if (y <= 1.22d+41) then
        tmp = x + ((0.3333333333333333d0 / z) / (y / t))
    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 <= -1.7e+117) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 1.22e+41) {
		tmp = x + ((0.3333333333333333 / z) / (y / t));
	} else {
		tmp = x - ((y / z) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e+117:
		tmp = x - (y / (z * 3.0))
	elif y <= 1.22e+41:
		tmp = x + ((0.3333333333333333 / z) / (y / t))
	else:
		tmp = x - ((y / z) / 3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+117)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (y <= 1.22e+41)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / z) / Float64(y / t)));
	else
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e+117)
		tmp = x - (y / (z * 3.0));
	elseif (y <= 1.22e+41)
		tmp = x + ((0.3333333333333333 / z) / (y / t));
	else
		tmp = x - ((y / z) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e+117], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.22e+41], N[(x + N[(N[(0.3333333333333333 / z), $MachinePrecision] / N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e117

   1. Initial program 94.3%

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

      1. associate-/r* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in t around 0 99.7%

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

      1. metadata-eval 99.7%

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

      2. times-frac 99.9%

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

      3. *-un-lft-identity 99.9%

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

      4. *-commutative 99.9%

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

   6. Applied egg-rr 99.9%

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

   if -1.7e117 < y < 1.22e41

   1. Initial program 92.4%

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

      1. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around 0 86.3%

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

      1. *-un-lft-identity 86.3%

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

      2. *-commutative 86.3%

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

      3. times-frac 86.7%

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

   6. Applied egg-rr 86.7%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(\frac{1}{z} \cdot \frac{t}{y}\right)} + x \]
   7. Step-by-step derivation

      1. associate-*r* 87.2%

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

      2. div-inv 87.2%

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

      3. clear-num 87.2%

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

      4. un-div-inv 87.7%

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

   8. Applied egg-rr 87.7%

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

   if 1.22e41 < 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-/r* 97.7%

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

   3. Simplified 97.7%

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

   4. Taylor expanded in t around 0 99.7%

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

      1. metadata-eval 99.7%

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

      2. times-frac 99.8%

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

      3. *-un-lft-identity 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+117}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{+41}:\\ \;\;\;\;x + \frac{\frac{0.3333333333333333}{z}}{\frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \end{array} \]

Alternative 9: 78.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-17} \lor \neg \left(y \leq 3.4 \cdot 10^{-113}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.55e-17) (not (<= y 3.4e-113)))
   (- x (* 0.3333333333333333 (/ y z)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.55e-17) || !(y <= 3.4e-113)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / 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 <= (-1.55d-17)) .or. (.not. (y <= 3.4d-113))) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.55e-17) || !(y <= 3.4e-113)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.55e-17) or not (y <= 3.4e-113):
		tmp = x - (0.3333333333333333 * (y / z))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.55e-17) || !(y <= 3.4e-113))
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.55e-17) || ~((y <= 3.4e-113)))
		tmp = x - (0.3333333333333333 * (y / z));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.55e-17], N[Not[LessEqual[y, 3.4e-113]], $MachinePrecision]], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5499999999999999e-17 or 3.4000000000000002e-113 < y

   1. Initial program 97.0%

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

      1. associate-/r* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in t around 0 87.3%

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

   if -1.5499999999999999e-17 < y < 3.4000000000000002e-113

   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-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 65.2%

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

      1. associate-/r* 66.7%

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

      2. associate-*r/ 67.5%

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

      3. associate-*r/ 67.5%

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

      4. div-sub 67.5%

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

      5. distribute-lft-out-- 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in t around inf 66.0%

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

      1. associate-*r/ 66.0%

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

      2. associate-/l* 66.0%

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

   9. Simplified 66.0%

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

       1. associate-/l/ 65.9%

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

       2. metadata-eval 65.9%

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

       3. frac-times 66.0%

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

       4. clear-num 66.0%

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

       5. times-frac 63.8%

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

       6. *-commutative 63.8%

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

       7. times-frac 70.8%

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

   11. Applied egg-rr 70.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-17} \lor \neg \left(y \leq 3.4 \cdot 10^{-113}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]

Alternative 10: 78.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-18} \lor \neg \left(y \leq 2.8 \cdot 10^{-113}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.02e-18) (not (<= y 2.8e-113)))
   (- x (/ y (* z 3.0)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e-18) || !(y <= 2.8e-113)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (t / z) * (0.3333333333333333 / 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 <= (-1.02d-18)) .or. (.not. (y <= 2.8d-113))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.02e-18) || !(y <= 2.8e-113)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.02e-18) or not (y <= 2.8e-113):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.02e-18) || !(y <= 2.8e-113))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.02e-18) || ~((y <= 2.8e-113)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.02e-18], N[Not[LessEqual[y, 2.8e-113]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.02e-18 or 2.8e-113 < y

   1. Initial program 97.0%

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

      1. associate-/r* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in t around 0 87.3%

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

      1. metadata-eval 87.3%

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

      2. times-frac 87.4%

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

      3. *-un-lft-identity 87.4%

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

      4. *-commutative 87.4%

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

   6. Applied egg-rr 87.4%

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

   if -1.02e-18 < y < 2.8e-113

   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-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 65.2%

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

      1. associate-/r* 66.7%

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

      2. associate-*r/ 67.5%

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

      3. associate-*r/ 67.5%

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

      4. div-sub 67.5%

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

      5. distribute-lft-out-- 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in t around inf 66.0%

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

      1. associate-*r/ 66.0%

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

      2. associate-/l* 66.0%

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

   9. Simplified 66.0%

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

       1. associate-/l/ 65.9%

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

       2. metadata-eval 65.9%

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

       3. frac-times 66.0%

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

       4. clear-num 66.0%

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

       5. times-frac 63.8%

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

       6. *-commutative 63.8%

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

       7. times-frac 70.8%

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

   11. Applied egg-rr 70.8%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{-18} \lor \neg \left(y \leq 2.8 \cdot 10^{-113}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]

Alternative 11: 78.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-19} \lor \neg \left(y \leq 1.6 \cdot 10^{-113}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.4e-19) (not (<= y 1.6e-113)))
   (- 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 <= -8.4e-19) || !(y <= 1.6e-113)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (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 <= (-8.4d-19)) .or. (.not. (y <= 1.6d-113))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (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 <= -8.4e-19) || !(y <= 1.6e-113)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (t / z) / (y * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8.4e-19) or not (y <= 1.6e-113):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = (t / z) / (y * 3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.4e-19) || !(y <= 1.6e-113))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(t / z) / Float64(y * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8.4e-19) || ~((y <= 1.6e-113)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = (t / z) / (y * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.4e-19], N[Not[LessEqual[y, 1.6e-113]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.3999999999999996e-19 or 1.6000000000000001e-113 < y

   1. Initial program 97.0%

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

      1. associate-/r* 95.1%

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

   3. Simplified 95.1%

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

   4. Taylor expanded in t around 0 87.3%

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

      1. metadata-eval 87.3%

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

      2. times-frac 87.4%

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

      3. *-un-lft-identity 87.4%

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

      4. *-commutative 87.4%

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

   6. Applied egg-rr 87.4%

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

   if -8.3999999999999996e-19 < y < 1.6000000000000001e-113

   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-/r* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 65.2%

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

      1. associate-/r* 66.7%

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

      2. associate-*r/ 67.5%

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

      3. associate-*r/ 67.5%

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

      4. div-sub 67.5%

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

      5. distribute-lft-out-- 67.5%

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

   6. Simplified 67.5%

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

   7. Taylor expanded in t around inf 66.0%

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

      1. associate-*r/ 66.0%

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

      2. associate-/l* 66.0%

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

   9. Simplified 66.0%

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

       1. associate-/l/ 65.9%

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

       2. metadata-eval 65.9%

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

       3. frac-times 66.0%

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

       4. clear-num 66.0%

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

       5. times-frac 63.8%

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

       6. *-commutative 63.8%

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

       7. times-frac 70.8%

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

   11. Applied egg-rr 70.8%

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

       1. clear-num 70.7%

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

       2. un-div-inv 70.8%

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

       3. div-inv 70.9%

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

       4. metadata-eval 70.9%

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

   13. Applied egg-rr 70.9%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{-19} \lor \neg \left(y \leq 1.6 \cdot 10^{-113}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \]

Alternative 12: 96.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (* (/ -0.3333333333333333 z) (- y (/ t y)))))

C

double code(double x, double y, double z, double t) {
	return x + ((-0.3333333333333333 / z) * (y - (t / 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 + (((-0.3333333333333333d0) / z) * (y - (t / y)))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((-0.3333333333333333 / z) * (y - (t / y)));
}

Python

def code(x, y, z, t):
	return x + ((-0.3333333333333333 / z) * (y - (t / y)))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(-0.3333333333333333 / z) * Float64(y - Float64(t / y))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
end

Wolfram

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

Derivation

1. Initial program 94.1%

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

   1. associate-+l- 94.1%

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

   2. sub-neg 94.1%

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

   3. sub-neg 94.1%

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

   4. distribute-neg-in 94.1%

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

   5. unsub-neg 94.1%

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

   6. neg-mul-1 94.1%

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

   7. associate-*r/ 94.1%

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

   8. associate-*l/ 94.0%

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

   9. distribute-neg-frac 94.0%

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

   10. neg-mul-1 94.0%

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

   11. times-frac 95.3%

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

   12. distribute-lft-out-- 96.1%

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

   13. *-commutative 96.1%

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

   14. associate-/r* 96.1%

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

   15. metadata-eval 96.1%

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

3. Simplified 96.1%

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

4. Final simplification 96.1%

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

Alternative 13: 48.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+118} \lor \neg \left(y \leq 2.85 \cdot 10^{+62}\right):\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7.5e+118) (not (<= y 2.85e+62)))
   (* y (/ -0.3333333333333333 z))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7.5e+118) || !(y <= 2.85e+62)) {
		tmp = y * (-0.3333333333333333 / 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 ((y <= (-7.5d+118)) .or. (.not. (y <= 2.85d+62))) then
        tmp = y * ((-0.3333333333333333d0) / 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 ((y <= -7.5e+118) || !(y <= 2.85e+62)) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7.5e+118) or not (y <= 2.85e+62):
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7.5e+118) || !(y <= 2.85e+62))
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7.5e+118) || ~((y <= 2.85e+62)))
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7.5e+118], N[Not[LessEqual[y, 2.85e+62]], $MachinePrecision]], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -7.50000000000000003e118 or 2.84999999999999999e62 < y

   1. Initial program 97.4%

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

      1. associate-/r* 94.9%

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

   3. Simplified 94.9%

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

   4. Taylor expanded in x around 0 76.3%

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

      1. associate-/r* 76.3%

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

      2. associate-*r/ 76.3%

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

      3. associate-*r/ 76.3%

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

      4. div-sub 78.8%

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

      5. distribute-lft-out-- 78.8%

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

   6. Simplified 78.8%

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

   7. Taylor expanded in t around 0 78.8%

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

      1. *-commutative 78.8%

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

   9. Simplified 78.8%

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

   10. Taylor expanded in y around 0 78.7%

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

       1. associate-*r/ 78.8%

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

       2. associate-*l/ 78.7%

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

       3. *-commutative 78.7%

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

   12. Simplified 78.7%

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

   if -7.50000000000000003e118 < y < 2.84999999999999999e62

   1. Initial program 92.5%

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

      1. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around inf 36.7%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.5 \cdot 10^{+118} \lor \neg \left(y \leq 2.85 \cdot 10^{+62}\right):\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 48.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+117}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.7e+117)
   (* -0.3333333333333333 (/ y z))
   (if (<= y 1.65e+64) x (* y (/ -0.3333333333333333 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.7e+117) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 1.65e+64) {
		tmp = x;
	} else {
		tmp = 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 <= (-1.7d+117)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (y <= 1.65d+64) then
        tmp = x
    else
        tmp = 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 <= -1.7e+117) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 1.65e+64) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.7e+117:
		tmp = -0.3333333333333333 * (y / z)
	elif y <= 1.65e+64:
		tmp = x
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.7e+117)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (y <= 1.65e+64)
		tmp = x;
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.7e+117)
		tmp = -0.3333333333333333 * (y / z);
	elseif (y <= 1.65e+64)
		tmp = x;
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.7e+117], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+64], x, N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e117

   1. Initial program 94.3%

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

      1. associate-/r* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in y around inf 79.7%

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

      1. *-commutative 79.7%

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

   6. Simplified 79.7%

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

   if -1.7e117 < y < 1.64999999999999994e64

   1. Initial program 92.5%

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

      1. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around inf 36.7%

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

   if 1.64999999999999994e64 < 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-/r* 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around 0 77.9%

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

      1. associate-/r* 77.9%

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

      2. associate-*r/ 77.9%

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

      3. associate-*r/ 77.9%

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

      4. div-sub 77.9%

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

      5. distribute-lft-out-- 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in t around 0 77.9%

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

      1. *-commutative 77.9%

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

   9. Simplified 77.9%

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

   10. Taylor expanded in y around 0 77.9%

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

       1. associate-*r/ 77.9%

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

       2. associate-*l/ 77.9%

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

       3. *-commutative 77.9%

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

   12. Simplified 77.9%

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

4. Final simplification 50.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+117}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+64}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 15: 48.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+119}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8e+119)
   (/ (* y -0.3333333333333333) z)
   (if (<= y 2.85e+63) x (* y (/ -0.3333333333333333 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8e+119) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 2.85e+63) {
		tmp = x;
	} else {
		tmp = 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 <= (-8d+119)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= 2.85d+63) then
        tmp = x
    else
        tmp = 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 <= -8e+119) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 2.85e+63) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8e+119:
		tmp = (y * -0.3333333333333333) / z
	elif y <= 2.85e+63:
		tmp = x
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8e+119)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= 2.85e+63)
		tmp = x;
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8e+119)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= 2.85e+63)
		tmp = x;
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8e+119], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.85e+63], x, N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.99999999999999955e119

   1. Initial program 94.3%

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

      1. associate-/r* 91.5%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around 0 74.2%

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

      1. associate-/r* 74.2%

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

      2. associate-*r/ 74.2%

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

      3. associate-*r/ 74.3%

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

      4. div-sub 79.9%

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

      5. distribute-lft-out-- 79.9%

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

   6. Simplified 79.9%

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

   7. Taylor expanded in t around 0 79.9%

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

      1. *-commutative 79.9%

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

   9. Simplified 79.9%

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

   if -7.99999999999999955e119 < y < 2.8500000000000001e63

   1. Initial program 92.5%

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

      1. associate-/r* 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around inf 36.7%

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

   if 2.8500000000000001e63 < 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-/r* 97.6%

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

   3. Simplified 97.6%

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

   4. Taylor expanded in x around 0 77.9%

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

      1. associate-/r* 77.9%

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

      2. associate-*r/ 77.9%

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

      3. associate-*r/ 77.9%

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

      4. div-sub 77.9%

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

      5. distribute-lft-out-- 77.9%

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

   6. Simplified 77.9%

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

   7. Taylor expanded in t around 0 77.9%

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

      1. *-commutative 77.9%

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

   9. Simplified 77.9%

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

   10. Taylor expanded in y around 0 77.9%

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

       1. associate-*r/ 77.9%

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

       2. associate-*l/ 77.9%

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

       3. *-commutative 77.9%

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

   12. Simplified 77.9%

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

4. Final simplification 50.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+119}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{+63}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 16: 30.1% 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 94.1%

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

   1. associate-/r* 97.2%

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

3. Simplified 97.2%

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

4. Taylor expanded in x around inf 32.2%

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

5. Final simplification 32.2%

   \[\leadsto x \]

Developer target: 95.9% 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 2023228 
(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))))