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

Percentage Accurate: 95.6% → 96.1%

Time: 9.2s

Alternatives: 12

Speedup: 1.4×

• 27.3% 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: 96.1% 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]

Derivation

1. Initial program 96.5%

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

   1. associate-/r* 97.1%

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

3. Simplified 97.1%

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

4. Final simplification 97.1%

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

Alternative 2: 88.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -1.56 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{t}{3 \cdot \left(y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (/ t y) (/ 0.3333333333333333 z)))))
   (if (<= y -3.2e+50)
     (+ x (/ y (* z -3.0)))
     (if (<= y -2.15e-19)
       t_1
       (if (<= y -2e-60)
         (+ x (/ -0.3333333333333333 (/ z y)))
         (if (<= y -1.56e-254)
           t_1
           (if (<= y 6.6e-20)
             (+ x (/ t (* 3.0 (* y z))))
             (+ x (* y (/ -0.3333333333333333 z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((t / y) * (0.3333333333333333 / z));
	double tmp;
	if (y <= -3.2e+50) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= -2.15e-19) {
		tmp = t_1;
	} else if (y <= -2e-60) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else if (y <= -1.56e-254) {
		tmp = t_1;
	} else if (y <= 6.6e-20) {
		tmp = x + (t / (3.0 * (y * z)));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t / y) * (0.3333333333333333d0 / z))
    if (y <= (-3.2d+50)) then
        tmp = x + (y / (z * (-3.0d0)))
    else if (y <= (-2.15d-19)) then
        tmp = t_1
    else if (y <= (-2d-60)) then
        tmp = x + ((-0.3333333333333333d0) / (z / y))
    else if (y <= (-1.56d-254)) then
        tmp = t_1
    else if (y <= 6.6d-20) then
        tmp = x + (t / (3.0d0 * (y * z)))
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((t / y) * (0.3333333333333333 / z));
	double tmp;
	if (y <= -3.2e+50) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= -2.15e-19) {
		tmp = t_1;
	} else if (y <= -2e-60) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else if (y <= -1.56e-254) {
		tmp = t_1;
	} else if (y <= 6.6e-20) {
		tmp = x + (t / (3.0 * (y * z)));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((t / y) * (0.3333333333333333 / z))
	tmp = 0
	if y <= -3.2e+50:
		tmp = x + (y / (z * -3.0))
	elif y <= -2.15e-19:
		tmp = t_1
	elif y <= -2e-60:
		tmp = x + (-0.3333333333333333 / (z / y))
	elif y <= -1.56e-254:
		tmp = t_1
	elif y <= 6.6e-20:
		tmp = x + (t / (3.0 * (y * z)))
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(t / y) * Float64(0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -3.2e+50)
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	elseif (y <= -2.15e-19)
		tmp = t_1;
	elseif (y <= -2e-60)
		tmp = Float64(x + Float64(-0.3333333333333333 / Float64(z / y)));
	elseif (y <= -1.56e-254)
		tmp = t_1;
	elseif (y <= 6.6e-20)
		tmp = Float64(x + Float64(t / Float64(3.0 * Float64(y * z))));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((t / y) * (0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -3.2e+50)
		tmp = x + (y / (z * -3.0));
	elseif (y <= -2.15e-19)
		tmp = t_1;
	elseif (y <= -2e-60)
		tmp = x + (-0.3333333333333333 / (z / y));
	elseif (y <= -1.56e-254)
		tmp = t_1;
	elseif (y <= 6.6e-20)
		tmp = x + (t / (3.0 * (y * z)));
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+50], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.15e-19], t$95$1, If[LessEqual[y, -2e-60], N[(x + N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.56e-254], t$95$1, If[LessEqual[y, 6.6e-20], N[(x + N[(t / N[(3.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.19999999999999983e50

   1. Initial program 98.1%

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

      1. associate-+l- 98.1%

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

      2. sub-neg 98.1%

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

      3. sub-neg 98.1%

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

      4. distribute-neg-in 98.1%

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

      5. unsub-neg 98.1%

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

      6. neg-mul-1 98.1%

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

      7. associate-*r/ 98.1%

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

      8. associate-*l/ 98.0%

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

      9. distribute-neg-frac 98.0%

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

      10. neg-mul-1 98.0%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.6%

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

      15. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 96.2%

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

      1. *-commutative 96.2%

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

      2. clear-num 96.1%

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

      3. un-div-inv 96.2%

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

      4. div-inv 96.3%

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

      5. metadata-eval 96.3%

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

   6. Applied egg-rr 96.3%

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

   if -3.19999999999999983e50 < y < -2.15e-19 or -1.9999999999999999e-60 < y < -1.56e-254

   1. Initial program 93.1%

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

      1. associate-+l- 93.1%

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

      2. sub-neg 93.1%

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

      3. sub-neg 93.1%

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

      4. distribute-neg-in 93.1%

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

      5. unsub-neg 93.1%

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

      6. neg-mul-1 93.1%

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

      7. associate-*r/ 93.1%

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

      8. associate-*l/ 93.1%

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

      9. distribute-neg-frac 93.1%

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

      10. neg-mul-1 93.1%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      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%

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

   4. Taylor expanded in y around 0 93.1%

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

      1. neg-mul-1 93.1%

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

      2. distribute-neg-frac 93.1%

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

   6. Simplified 93.1%

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

   7. Taylor expanded in z around 0 86.4%

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

      1. associate-/r* 91.5%

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

      2. metadata-eval 91.5%

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

      3. times-frac 93.0%

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

      4. neg-mul-1 93.0%

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

      5. associate-*l/ 93.1%

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

      6. associate-*r/ 89.3%

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

      7. neg-mul-1 89.3%

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

      8. associate-/r* 89.3%

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

      9. metadata-eval 89.3%

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

   9. Simplified 89.3%

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

       1. div-inv 89.3%

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

       2. associate-*l* 93.0%

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

       3. div-inv 93.1%

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

   11. Applied egg-rr 93.1%

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

   if -2.15e-19 < y < -1.9999999999999999e-60

   1. Initial program 99.3%

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

      1. associate-+l- 99.3%

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

      2. sub-neg 99.3%

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

      3. sub-neg 99.3%

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

      4. distribute-neg-in 99.3%

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

      5. unsub-neg 99.3%

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

      6. neg-mul-1 99.3%

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

      7. associate-*r/ 99.3%

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

      8. associate-*l/ 99.8%

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

      9. distribute-neg-frac 99.8%

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

      10. neg-mul-1 99.8%

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

      11. times-frac 86.6%

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

      12. distribute-lft-out-- 86.6%

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

      13. *-commutative 86.6%

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

      14. associate-/r* 86.3%

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

      15. metadata-eval 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in y around inf 97.0%

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

      1. associate-*l/ 97.0%

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

      2. associate-/l* 97.4%

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

   6. Applied egg-rr 97.4%

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

   if -1.56e-254 < y < 6.6e-20

   1. Initial program 94.4%

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

      1. associate-+l- 94.4%

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

      2. sub-neg 94.4%

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

      3. sub-neg 94.4%

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

      4. distribute-neg-in 94.4%

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

      5. unsub-neg 94.4%

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

      6. neg-mul-1 94.4%

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

      7. associate-*r/ 94.4%

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

      8. associate-*l/ 94.4%

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

      9. distribute-neg-frac 94.4%

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

      10. neg-mul-1 94.4%

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

      11. times-frac 87.1%

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

      12. distribute-lft-out-- 87.1%

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

      13. *-commutative 87.1%

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

      14. associate-/r* 87.1%

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

      15. metadata-eval 87.1%

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

   3. Simplified 87.1%

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

   4. Taylor expanded in y around 0 85.8%

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

      1. neg-mul-1 85.8%

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

      2. distribute-neg-frac 85.8%

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

   6. Simplified 85.8%

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

      1. clear-num 85.7%

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

      2. frac-2neg 85.7%

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

      3. frac-times 93.0%

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

      4. *-un-lft-identity 93.0%

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

      5. remove-double-neg 93.0%

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

      6. div-inv 93.1%

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

      7. metadata-eval 93.1%

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

   8. Applied egg-rr 93.1%

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

      1. *-commutative 93.1%

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

      2. metadata-eval 93.1%

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

      3. distribute-lft-neg-in 93.1%

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

      4. distribute-rgt-neg-in 93.1%

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

      5. associate-*l* 93.0%

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

      6. distribute-rgt-neg-out 93.0%

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

      7. distribute-lft-neg-in 93.0%

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

      8. remove-double-neg 93.0%

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

      9. *-commutative 93.0%

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

   10. Simplified 93.0%

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

   if 6.6e-20 < y

   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-+l- 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. distribute-neg-in 99.7%

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

      5. unsub-neg 99.7%

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

      6. neg-mul-1 99.7%

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

      7. associate-*r/ 99.7%

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

      8. associate-*l/ 99.6%

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

      9. distribute-neg-frac 99.6%

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

      10. neg-mul-1 99.6%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      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%

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

   4. Taylor expanded in y around inf 90.0%

      \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -2.15 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -1.56 \cdot 10^{-254}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{t}{3 \cdot \left(y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 3: 88.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -1.05 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (/ t y) (/ 0.3333333333333333 z)))))
   (if (<= y -1.05e+47)
     (+ x (/ y (* z -3.0)))
     (if (<= y -1.35e-19)
       t_1
       (if (<= y -2e-60)
         (+ x (/ -0.3333333333333333 (/ z y)))
         (if (<= y -4.9e-254)
           t_1
           (if (<= y 4.5e-20)
             (+ x (/ t (* y (* z 3.0))))
             (+ x (* y (/ -0.3333333333333333 z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((t / y) * (0.3333333333333333 / z));
	double tmp;
	if (y <= -1.05e+47) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= -1.35e-19) {
		tmp = t_1;
	} else if (y <= -2e-60) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else if (y <= -4.9e-254) {
		tmp = t_1;
	} else if (y <= 4.5e-20) {
		tmp = x + (t / (y * (z * 3.0)));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t / y) * (0.3333333333333333d0 / z))
    if (y <= (-1.05d+47)) then
        tmp = x + (y / (z * (-3.0d0)))
    else if (y <= (-1.35d-19)) then
        tmp = t_1
    else if (y <= (-2d-60)) then
        tmp = x + ((-0.3333333333333333d0) / (z / y))
    else if (y <= (-4.9d-254)) then
        tmp = t_1
    else if (y <= 4.5d-20) then
        tmp = x + (t / (y * (z * 3.0d0)))
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((t / y) * (0.3333333333333333 / z));
	double tmp;
	if (y <= -1.05e+47) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= -1.35e-19) {
		tmp = t_1;
	} else if (y <= -2e-60) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else if (y <= -4.9e-254) {
		tmp = t_1;
	} else if (y <= 4.5e-20) {
		tmp = x + (t / (y * (z * 3.0)));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((t / y) * (0.3333333333333333 / z))
	tmp = 0
	if y <= -1.05e+47:
		tmp = x + (y / (z * -3.0))
	elif y <= -1.35e-19:
		tmp = t_1
	elif y <= -2e-60:
		tmp = x + (-0.3333333333333333 / (z / y))
	elif y <= -4.9e-254:
		tmp = t_1
	elif y <= 4.5e-20:
		tmp = x + (t / (y * (z * 3.0)))
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(t / y) * Float64(0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -1.05e+47)
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	elseif (y <= -1.35e-19)
		tmp = t_1;
	elseif (y <= -2e-60)
		tmp = Float64(x + Float64(-0.3333333333333333 / Float64(z / y)));
	elseif (y <= -4.9e-254)
		tmp = t_1;
	elseif (y <= 4.5e-20)
		tmp = Float64(x + Float64(t / Float64(y * Float64(z * 3.0))));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((t / y) * (0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -1.05e+47)
		tmp = x + (y / (z * -3.0));
	elseif (y <= -1.35e-19)
		tmp = t_1;
	elseif (y <= -2e-60)
		tmp = x + (-0.3333333333333333 / (z / y));
	elseif (y <= -4.9e-254)
		tmp = t_1;
	elseif (y <= 4.5e-20)
		tmp = x + (t / (y * (z * 3.0)));
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.05e+47], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-19], t$95$1, If[LessEqual[y, -2e-60], N[(x + N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.9e-254], t$95$1, If[LessEqual[y, 4.5e-20], N[(x + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.05e47

   1. Initial program 98.1%

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

      1. associate-+l- 98.1%

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

      2. sub-neg 98.1%

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

      3. sub-neg 98.1%

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

      4. distribute-neg-in 98.1%

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

      5. unsub-neg 98.1%

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

      6. neg-mul-1 98.1%

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

      7. associate-*r/ 98.1%

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

      8. associate-*l/ 98.0%

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

      9. distribute-neg-frac 98.0%

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

      10. neg-mul-1 98.0%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.6%

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

      15. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 96.2%

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

      1. *-commutative 96.2%

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

      2. clear-num 96.1%

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

      3. un-div-inv 96.2%

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

      4. div-inv 96.3%

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

      5. metadata-eval 96.3%

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

   6. Applied egg-rr 96.3%

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

   if -1.05e47 < y < -1.35e-19 or -1.9999999999999999e-60 < y < -4.8999999999999998e-254

   1. Initial program 93.1%

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

      1. associate-+l- 93.1%

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

      2. sub-neg 93.1%

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

      3. sub-neg 93.1%

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

      4. distribute-neg-in 93.1%

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

      5. unsub-neg 93.1%

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

      6. neg-mul-1 93.1%

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

      7. associate-*r/ 93.1%

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

      8. associate-*l/ 93.1%

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

      9. distribute-neg-frac 93.1%

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

      10. neg-mul-1 93.1%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      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%

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

   4. Taylor expanded in y around 0 93.1%

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

      1. neg-mul-1 93.1%

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

      2. distribute-neg-frac 93.1%

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

   6. Simplified 93.1%

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

   7. Taylor expanded in z around 0 86.4%

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

      1. associate-/r* 91.5%

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

      2. metadata-eval 91.5%

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

      3. times-frac 93.0%

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

      4. neg-mul-1 93.0%

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

      5. associate-*l/ 93.1%

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

      6. associate-*r/ 89.3%

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

      7. neg-mul-1 89.3%

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

      8. associate-/r* 89.3%

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

      9. metadata-eval 89.3%

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

   9. Simplified 89.3%

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

       1. div-inv 89.3%

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

       2. associate-*l* 93.0%

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

       3. div-inv 93.1%

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

   11. Applied egg-rr 93.1%

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

   if -1.35e-19 < y < -1.9999999999999999e-60

   1. Initial program 99.3%

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

      1. associate-+l- 99.3%

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

      2. sub-neg 99.3%

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

      3. sub-neg 99.3%

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

      4. distribute-neg-in 99.3%

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

      5. unsub-neg 99.3%

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

      6. neg-mul-1 99.3%

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

      7. associate-*r/ 99.3%

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

      8. associate-*l/ 99.8%

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

      9. distribute-neg-frac 99.8%

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

      10. neg-mul-1 99.8%

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

      11. times-frac 86.6%

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

      12. distribute-lft-out-- 86.6%

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

      13. *-commutative 86.6%

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

      14. associate-/r* 86.3%

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

      15. metadata-eval 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in y around inf 97.0%

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

      1. associate-*l/ 97.0%

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

      2. associate-/l* 97.4%

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

   6. Applied egg-rr 97.4%

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

   if -4.8999999999999998e-254 < y < 4.5000000000000001e-20

   1. Initial program 94.4%

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

   2. Taylor expanded in x around inf 93.1%

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

   if 4.5000000000000001e-20 < y

   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-+l- 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. distribute-neg-in 99.7%

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

      5. unsub-neg 99.7%

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

      6. neg-mul-1 99.7%

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

      7. associate-*r/ 99.7%

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

      8. associate-*l/ 99.6%

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

      9. distribute-neg-frac 99.6%

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

      10. neg-mul-1 99.6%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      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%

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

   4. Taylor expanded in y around inf 90.0%

      \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 93.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+47}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -4.9 \cdot 10^{-254}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 4: 87.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (/ t y) (/ 0.3333333333333333 z)))))
   (if (<= y -3.2e+50)
     (+ x (/ y (* z -3.0)))
     (if (<= y -1.35e-19)
       t_1
       (if (<= y -2e-60)
         (+ x (/ -0.3333333333333333 (/ z y)))
         (if (<= y 6.6e-20) t_1 (+ x (* y (/ -0.3333333333333333 z)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((t / y) * (0.3333333333333333 / z));
	double tmp;
	if (y <= -3.2e+50) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= -1.35e-19) {
		tmp = t_1;
	} else if (y <= -2e-60) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else if (y <= 6.6e-20) {
		tmp = t_1;
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + ((t / y) * (0.3333333333333333d0 / z))
    if (y <= (-3.2d+50)) then
        tmp = x + (y / (z * (-3.0d0)))
    else if (y <= (-1.35d-19)) then
        tmp = t_1
    else if (y <= (-2d-60)) then
        tmp = x + ((-0.3333333333333333d0) / (z / y))
    else if (y <= 6.6d-20) then
        tmp = t_1
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((t / y) * (0.3333333333333333 / z));
	double tmp;
	if (y <= -3.2e+50) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= -1.35e-19) {
		tmp = t_1;
	} else if (y <= -2e-60) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else if (y <= 6.6e-20) {
		tmp = t_1;
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((t / y) * (0.3333333333333333 / z))
	tmp = 0
	if y <= -3.2e+50:
		tmp = x + (y / (z * -3.0))
	elif y <= -1.35e-19:
		tmp = t_1
	elif y <= -2e-60:
		tmp = x + (-0.3333333333333333 / (z / y))
	elif y <= 6.6e-20:
		tmp = t_1
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(t / y) * Float64(0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -3.2e+50)
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	elseif (y <= -1.35e-19)
		tmp = t_1;
	elseif (y <= -2e-60)
		tmp = Float64(x + Float64(-0.3333333333333333 / Float64(z / y)));
	elseif (y <= 6.6e-20)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((t / y) * (0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -3.2e+50)
		tmp = x + (y / (z * -3.0));
	elseif (y <= -1.35e-19)
		tmp = t_1;
	elseif (y <= -2e-60)
		tmp = x + (-0.3333333333333333 / (z / y));
	elseif (y <= 6.6e-20)
		tmp = t_1;
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+50], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.35e-19], t$95$1, If[LessEqual[y, -2e-60], N[(x + N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.6e-20], t$95$1, N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.19999999999999983e50

   1. Initial program 98.1%

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

      1. associate-+l- 98.1%

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

      2. sub-neg 98.1%

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

      3. sub-neg 98.1%

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

      4. distribute-neg-in 98.1%

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

      5. unsub-neg 98.1%

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

      6. neg-mul-1 98.1%

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

      7. associate-*r/ 98.1%

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

      8. associate-*l/ 98.0%

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

      9. distribute-neg-frac 98.0%

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

      10. neg-mul-1 98.0%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.6%

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

      15. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 96.2%

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

      1. *-commutative 96.2%

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

      2. clear-num 96.1%

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

      3. un-div-inv 96.2%

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

      4. div-inv 96.3%

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

      5. metadata-eval 96.3%

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

   6. Applied egg-rr 96.3%

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

   if -3.19999999999999983e50 < y < -1.35e-19 or -1.9999999999999999e-60 < y < 6.6e-20

   1. Initial program 93.9%

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

      1. associate-+l- 93.9%

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

      2. sub-neg 93.9%

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

      3. sub-neg 93.9%

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

      4. distribute-neg-in 93.9%

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

      5. unsub-neg 93.9%

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

      6. neg-mul-1 93.9%

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

      7. associate-*r/ 93.9%

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

      8. associate-*l/ 93.9%

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

      9. distribute-neg-frac 93.9%

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

      10. neg-mul-1 93.9%

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

      11. times-frac 92.3%

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

      12. distribute-lft-out-- 92.3%

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

      13. *-commutative 92.3%

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

      14. associate-/r* 92.3%

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

      15. metadata-eval 92.3%

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

   3. Simplified 92.3%

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

   4. Taylor expanded in y around 0 88.8%

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

      1. neg-mul-1 88.8%

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

      2. distribute-neg-frac 88.8%

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

   6. Simplified 88.8%

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

   7. Taylor expanded in z around 0 90.2%

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

      1. associate-/r* 88.2%

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

      2. metadata-eval 88.2%

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

      3. times-frac 88.7%

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

      4. neg-mul-1 88.7%

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

      5. associate-*l/ 88.8%

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

      6. associate-*r/ 94.0%

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

      7. neg-mul-1 94.0%

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

      8. associate-/r* 94.0%

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

      9. metadata-eval 94.0%

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

   9. Simplified 94.0%

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

       1. div-inv 94.0%

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

       2. associate-*l* 88.7%

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

       3. div-inv 88.8%

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

   11. Applied egg-rr 88.8%

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

   if -1.35e-19 < y < -1.9999999999999999e-60

   1. Initial program 99.3%

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

      1. associate-+l- 99.3%

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

      2. sub-neg 99.3%

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

      3. sub-neg 99.3%

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

      4. distribute-neg-in 99.3%

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

      5. unsub-neg 99.3%

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

      6. neg-mul-1 99.3%

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

      7. associate-*r/ 99.3%

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

      8. associate-*l/ 99.8%

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

      9. distribute-neg-frac 99.8%

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

      10. neg-mul-1 99.8%

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

      11. times-frac 86.6%

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

      12. distribute-lft-out-- 86.6%

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

      13. *-commutative 86.6%

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

      14. associate-/r* 86.3%

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

      15. metadata-eval 86.3%

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

   3. Simplified 86.3%

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

   4. Taylor expanded in y around inf 97.0%

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

      1. associate-*l/ 97.0%

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

      2. associate-/l* 97.4%

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

   6. Applied egg-rr 97.4%

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

   if 6.6e-20 < y

   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-+l- 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. distribute-neg-in 99.7%

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

      5. unsub-neg 99.7%

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

      6. neg-mul-1 99.7%

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

      7. associate-*r/ 99.7%

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

      8. associate-*l/ 99.6%

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

      9. distribute-neg-frac 99.6%

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

      10. neg-mul-1 99.6%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      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%

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

   4. Taylor expanded in y around inf 90.0%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 5: 91.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7e+45)
   (+ x (/ y (* z -3.0)))
   (if (<= y -1.4e-19)
     (+ x (* (/ t y) (/ 0.3333333333333333 z)))
     (if (<= y -3.7e-57)
       (+ x (/ -0.3333333333333333 (/ z y)))
       (if (<= y 2.9e-20)
         (+ x (/ (* t (/ 0.3333333333333333 z)) y))
         (+ x (* y (/ -0.3333333333333333 z))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e+45) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= -1.4e-19) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} else if (y <= -3.7e-57) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else if (y <= 2.9e-20) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7d+45)) then
        tmp = x + (y / (z * (-3.0d0)))
    else if (y <= (-1.4d-19)) then
        tmp = x + ((t / y) * (0.3333333333333333d0 / z))
    else if (y <= (-3.7d-57)) then
        tmp = x + ((-0.3333333333333333d0) / (z / y))
    else if (y <= 2.9d-20) then
        tmp = x + ((t * (0.3333333333333333d0 / z)) / y)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e+45) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= -1.4e-19) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} else if (y <= -3.7e-57) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else if (y <= 2.9e-20) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7e+45:
		tmp = x + (y / (z * -3.0))
	elif y <= -1.4e-19:
		tmp = x + ((t / y) * (0.3333333333333333 / z))
	elif y <= -3.7e-57:
		tmp = x + (-0.3333333333333333 / (z / y))
	elif y <= 2.9e-20:
		tmp = x + ((t * (0.3333333333333333 / z)) / y)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7e+45)
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	elseif (y <= -1.4e-19)
		tmp = Float64(x + Float64(Float64(t / y) * Float64(0.3333333333333333 / z)));
	elseif (y <= -3.7e-57)
		tmp = Float64(x + Float64(-0.3333333333333333 / Float64(z / y)));
	elseif (y <= 2.9e-20)
		tmp = Float64(x + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7e+45)
		tmp = x + (y / (z * -3.0));
	elseif (y <= -1.4e-19)
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	elseif (y <= -3.7e-57)
		tmp = x + (-0.3333333333333333 / (z / y));
	elseif (y <= 2.9e-20)
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7e+45], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.4e-19], N[(x + N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.7e-57], N[(x + N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e-20], N[(x + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -7.00000000000000046e45

   1. Initial program 98.1%

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

      1. associate-+l- 98.1%

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

      2. sub-neg 98.1%

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

      3. sub-neg 98.1%

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

      4. distribute-neg-in 98.1%

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

      5. unsub-neg 98.1%

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

      6. neg-mul-1 98.1%

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

      7. associate-*r/ 98.1%

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

      8. associate-*l/ 98.0%

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

      9. distribute-neg-frac 98.0%

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

      10. neg-mul-1 98.0%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.6%

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

      15. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 96.2%

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

      1. *-commutative 96.2%

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

      2. clear-num 96.1%

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

      3. un-div-inv 96.2%

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

      4. div-inv 96.3%

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

      5. metadata-eval 96.3%

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

   6. Applied egg-rr 96.3%

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

   if -7.00000000000000046e45 < y < -1.40000000000000001e-19

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. sub-neg 99.4%

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

      3. sub-neg 99.4%

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

      4. distribute-neg-in 99.4%

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

      5. unsub-neg 99.4%

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

      6. neg-mul-1 99.4%

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

      7. associate-*r/ 99.4%

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

      8. associate-*l/ 99.5%

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

      9. distribute-neg-frac 99.5%

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

      10. neg-mul-1 99.5%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      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%

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

   4. Taylor expanded in y around 0 82.8%

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

      1. neg-mul-1 82.8%

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

      2. distribute-neg-frac 82.8%

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

   6. Simplified 82.8%

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

   7. Taylor expanded in z around 0 77.8%

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

      1. associate-/r* 77.8%

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

      2. metadata-eval 77.8%

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

      3. times-frac 82.8%

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

      4. neg-mul-1 82.8%

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

      5. associate-*l/ 82.8%

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

      6. associate-*r/ 71.9%

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

      7. neg-mul-1 71.9%

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

      8. associate-/r* 71.9%

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

      9. metadata-eval 71.9%

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

   9. Simplified 71.9%

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

       1. div-inv 71.9%

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

       2. associate-*l* 82.7%

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

       3. div-inv 82.8%

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

   11. Applied egg-rr 82.8%

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

   if -1.40000000000000001e-19 < y < -3.7e-57

   1. Initial program 99.2%

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

      1. associate-+l- 99.2%

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

      2. sub-neg 99.2%

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

      3. sub-neg 99.2%

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

      4. distribute-neg-in 99.2%

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

      5. unsub-neg 99.2%

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

      6. neg-mul-1 99.2%

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

      7. associate-*r/ 99.2%

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

      8. associate-*l/ 99.7%

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

      9. distribute-neg-frac 99.7%

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

      10. neg-mul-1 99.7%

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

      11. times-frac 99.7%

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

      12. distribute-lft-out-- 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/r* 99.5%

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

      15. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 99.5%

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

      1. associate-*l/ 99.5%

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

      2. associate-/l* 100.0%

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

   6. Applied egg-rr 100.0%

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

   if -3.7e-57 < y < 2.9e-20

   1. Initial program 93.1%

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

      1. associate-+l- 93.1%

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

      2. sub-neg 93.1%

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

      3. sub-neg 93.1%

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

      4. distribute-neg-in 93.1%

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

      5. unsub-neg 93.1%

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

      6. neg-mul-1 93.1%

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

      7. associate-*r/ 93.1%

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

      8. associate-*l/ 93.1%

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

      9. distribute-neg-frac 93.1%

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

      10. neg-mul-1 93.1%

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

      11. times-frac 90.5%

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

      12. distribute-lft-out-- 90.5%

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

      13. *-commutative 90.5%

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

      14. associate-/r* 90.5%

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

      15. metadata-eval 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in y around 0 88.9%

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

      1. neg-mul-1 88.9%

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

      2. distribute-neg-frac 88.9%

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

   6. Simplified 88.9%

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

   7. Taylor expanded in z around 0 92.1%

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

      1. associate-/r* 88.9%

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

      2. metadata-eval 88.9%

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

      3. times-frac 88.8%

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

      4. neg-mul-1 88.8%

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

      5. associate-*l/ 88.9%

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

      6. associate-*r/ 97.3%

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

      7. neg-mul-1 97.3%

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

      8. associate-/r* 97.3%

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

      9. metadata-eval 97.3%

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

   9. Simplified 97.3%

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

   if 2.9e-20 < y

   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-+l- 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. distribute-neg-in 99.7%

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

      5. unsub-neg 99.7%

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

      6. neg-mul-1 99.7%

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

      7. associate-*r/ 99.7%

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

      8. associate-*l/ 99.6%

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

      9. distribute-neg-frac 99.6%

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

      10. neg-mul-1 99.6%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      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%

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

   4. Taylor expanded in y around inf 90.0%

      \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+45}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{-20}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 6: 91.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.65e+46)
   (+ x (/ y (* z -3.0)))
   (if (<= y -1.45e-19)
     (+ x (* (/ t y) (/ 0.3333333333333333 z)))
     (if (<= y -3.7e-57)
       (+ x (/ -0.3333333333333333 (/ z y)))
       (if (<= y 1.5e-19)
         (+ x (/ (/ t (* z 3.0)) y))
         (+ x (* y (/ -0.3333333333333333 z))))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e+46) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= -1.45e-19) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} else if (y <= -3.7e-57) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else if (y <= 1.5e-19) {
		tmp = x + ((t / (z * 3.0)) / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.65d+46)) then
        tmp = x + (y / (z * (-3.0d0)))
    else if (y <= (-1.45d-19)) then
        tmp = x + ((t / y) * (0.3333333333333333d0 / z))
    else if (y <= (-3.7d-57)) then
        tmp = x + ((-0.3333333333333333d0) / (z / y))
    else if (y <= 1.5d-19) then
        tmp = x + ((t / (z * 3.0d0)) / y)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.65e+46) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= -1.45e-19) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} else if (y <= -3.7e-57) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else if (y <= 1.5e-19) {
		tmp = x + ((t / (z * 3.0)) / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.65e+46:
		tmp = x + (y / (z * -3.0))
	elif y <= -1.45e-19:
		tmp = x + ((t / y) * (0.3333333333333333 / z))
	elif y <= -3.7e-57:
		tmp = x + (-0.3333333333333333 / (z / y))
	elif y <= 1.5e-19:
		tmp = x + ((t / (z * 3.0)) / y)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.65e+46)
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	elseif (y <= -1.45e-19)
		tmp = Float64(x + Float64(Float64(t / y) * Float64(0.3333333333333333 / z)));
	elseif (y <= -3.7e-57)
		tmp = Float64(x + Float64(-0.3333333333333333 / Float64(z / y)));
	elseif (y <= 1.5e-19)
		tmp = Float64(x + Float64(Float64(t / Float64(z * 3.0)) / y));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.65e+46)
		tmp = x + (y / (z * -3.0));
	elseif (y <= -1.45e-19)
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	elseif (y <= -3.7e-57)
		tmp = x + (-0.3333333333333333 / (z / y));
	elseif (y <= 1.5e-19)
		tmp = x + ((t / (z * 3.0)) / y);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.65e+46], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.45e-19], N[(x + N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.7e-57], N[(x + N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-19], N[(x + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -1.6499999999999999e46

   1. Initial program 98.1%

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

      1. associate-+l- 98.1%

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

      2. sub-neg 98.1%

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

      3. sub-neg 98.1%

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

      4. distribute-neg-in 98.1%

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

      5. unsub-neg 98.1%

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

      6. neg-mul-1 98.1%

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

      7. associate-*r/ 98.1%

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

      8. associate-*l/ 98.0%

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

      9. distribute-neg-frac 98.0%

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

      10. neg-mul-1 98.0%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.6%

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

      15. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 96.2%

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

      1. *-commutative 96.2%

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

      2. clear-num 96.1%

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

      3. un-div-inv 96.2%

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

      4. div-inv 96.3%

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

      5. metadata-eval 96.3%

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

   6. Applied egg-rr 96.3%

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

   if -1.6499999999999999e46 < y < -1.45e-19

   1. Initial program 99.4%

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

      1. associate-+l- 99.4%

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

      2. sub-neg 99.4%

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

      3. sub-neg 99.4%

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

      4. distribute-neg-in 99.4%

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

      5. unsub-neg 99.4%

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

      6. neg-mul-1 99.4%

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

      7. associate-*r/ 99.4%

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

      8. associate-*l/ 99.5%

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

      9. distribute-neg-frac 99.5%

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

      10. neg-mul-1 99.5%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      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%

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

   4. Taylor expanded in y around 0 82.8%

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

      1. neg-mul-1 82.8%

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

      2. distribute-neg-frac 82.8%

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

   6. Simplified 82.8%

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

   7. Taylor expanded in z around 0 77.8%

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

      1. associate-/r* 77.8%

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

      2. metadata-eval 77.8%

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

      3. times-frac 82.8%

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

      4. neg-mul-1 82.8%

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

      5. associate-*l/ 82.8%

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

      6. associate-*r/ 71.9%

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

      7. neg-mul-1 71.9%

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

      8. associate-/r* 71.9%

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

      9. metadata-eval 71.9%

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

   9. Simplified 71.9%

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

       1. div-inv 71.9%

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

       2. associate-*l* 82.7%

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

       3. div-inv 82.8%

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

   11. Applied egg-rr 82.8%

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

   if -1.45e-19 < y < -3.7e-57

   1. Initial program 99.2%

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

      1. associate-+l- 99.2%

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

      2. sub-neg 99.2%

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

      3. sub-neg 99.2%

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

      4. distribute-neg-in 99.2%

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

      5. unsub-neg 99.2%

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

      6. neg-mul-1 99.2%

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

      7. associate-*r/ 99.2%

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

      8. associate-*l/ 99.7%

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

      9. distribute-neg-frac 99.7%

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

      10. neg-mul-1 99.7%

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

      11. times-frac 99.7%

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

      12. distribute-lft-out-- 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/r* 99.5%

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

      15. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 99.5%

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

      1. associate-*l/ 99.5%

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

      2. associate-/l* 100.0%

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

   6. Applied egg-rr 100.0%

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

   if -3.7e-57 < y < 1.49999999999999996e-19

   1. Initial program 93.1%

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

      1. associate-/r* 99.0%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in x around inf 97.4%

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

   if 1.49999999999999996e-19 < y

   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-+l- 99.7%

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

      2. sub-neg 99.7%

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

      3. sub-neg 99.7%

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

      4. distribute-neg-in 99.7%

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

      5. unsub-neg 99.7%

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

      6. neg-mul-1 99.7%

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

      7. associate-*r/ 99.7%

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

      8. associate-*l/ 99.6%

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

      9. distribute-neg-frac 99.6%

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

      10. neg-mul-1 99.6%

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

      11. times-frac 99.6%

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

      12. distribute-lft-out-- 99.6%

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

      13. *-commutative 99.6%

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

      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%

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

   4. Taylor expanded in y around inf 90.0%

      \[\leadsto x + \frac{-0.3333333333333333}{z} \cdot \color{blue}{y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+46}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -1.45 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-19}:\\ \;\;\;\;x + \frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 7: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x - (y / (z * 3.0d0))) + (t / (z * (y * 3.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

2. Taylor expanded in z around 0 96.4%

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

   1. associate-*r* 96.5%

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

   2. *-commutative 96.5%

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

   3. *-commutative 96.5%

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

4. Simplified 96.5%

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

5. Final simplification 96.5%

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

Alternative 8: 95.7% 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 96.5%

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

   1. associate-+l- 96.5%

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

   2. sub-neg 96.5%

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

   3. sub-neg 96.5%

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

   4. distribute-neg-in 96.5%

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

   5. unsub-neg 96.5%

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

   6. neg-mul-1 96.5%

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

   7. associate-*r/ 96.5%

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

   8. associate-*l/ 96.4%

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

   9. distribute-neg-frac 96.4%

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

   10. neg-mul-1 96.4%

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

   11. times-frac 95.6%

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

   12. distribute-lft-out-- 95.6%

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

   13. *-commutative 95.6%

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

   14. associate-/r* 95.7%

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

   15. metadata-eval 95.7%

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

3. Simplified 95.7%

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

4. Final simplification 95.7%

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

Alternative 9: 64.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{-0.3333333333333333}{z} \end{array} \]

FPCore

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

C

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

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 * ((-0.3333333333333333d0) / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l- 96.5%

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

   2. sub-neg 96.5%

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

   3. sub-neg 96.5%

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

   4. distribute-neg-in 96.5%

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

   5. unsub-neg 96.5%

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

   6. neg-mul-1 96.5%

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

   7. associate-*r/ 96.5%

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

   8. associate-*l/ 96.4%

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

   9. distribute-neg-frac 96.4%

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

   10. neg-mul-1 96.4%

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

   11. times-frac 95.6%

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

   12. distribute-lft-out-- 95.6%

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

   13. *-commutative 95.6%

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

   14. associate-/r* 95.7%

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

   15. metadata-eval 95.7%

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

3. Simplified 95.7%

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

4. Taylor expanded in y around inf 65.3%

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

5. Final simplification 65.3%

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

Alternative 10: 64.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x + \frac{-0.3333333333333333}{\frac{z}{y}} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l- 96.5%

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

   2. sub-neg 96.5%

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

   3. sub-neg 96.5%

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

   4. distribute-neg-in 96.5%

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

   5. unsub-neg 96.5%

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

   6. neg-mul-1 96.5%

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

   7. associate-*r/ 96.5%

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

   8. associate-*l/ 96.4%

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

   9. distribute-neg-frac 96.4%

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

   10. neg-mul-1 96.4%

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

   11. times-frac 95.6%

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

   12. distribute-lft-out-- 95.6%

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

   13. *-commutative 95.6%

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

   14. associate-/r* 95.7%

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

   15. metadata-eval 95.7%

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

3. Simplified 95.7%

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

4. Taylor expanded in y around inf 65.3%

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

   1. associate-*l/ 65.4%

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

   2. associate-/l* 65.3%

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

6. Applied egg-rr 65.3%

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

7. Final simplification 65.3%

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

Alternative 11: 64.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x + \frac{y \cdot -0.3333333333333333}{z} \end{array} \]

FPCore

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

C

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

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 * (-0.3333333333333333d0)) / z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. associate-+l- 96.5%

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

   2. sub-neg 96.5%

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

   3. sub-neg 96.5%

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

   4. distribute-neg-in 96.5%

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

   5. unsub-neg 96.5%

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

   6. neg-mul-1 96.5%

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

   7. associate-*r/ 96.5%

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

   8. associate-*l/ 96.4%

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

   9. distribute-neg-frac 96.4%

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

   10. neg-mul-1 96.4%

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

   11. times-frac 95.6%

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

   12. distribute-lft-out-- 95.6%

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

   13. *-commutative 95.6%

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

   14. associate-/r* 95.7%

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

   15. metadata-eval 95.7%

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

3. Simplified 95.7%

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

4. Taylor expanded in y around inf 65.3%

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

5. Taylor expanded in z around 0 65.3%

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

   1. associate-*r/ 65.4%

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

   2. *-commutative 65.4%

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

7. Simplified 65.4%

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

8. Final simplification 65.4%

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

Alternative 12: 30.7% 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 96.5%

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

   1. associate-+l- 96.5%

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

   2. sub-neg 96.5%

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

   3. sub-neg 96.5%

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

   4. distribute-neg-in 96.5%

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

   5. unsub-neg 96.5%

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

   6. neg-mul-1 96.5%

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

   7. associate-*r/ 96.5%

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

   8. associate-*l/ 96.4%

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

   9. distribute-neg-frac 96.4%

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

   10. neg-mul-1 96.4%

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

   11. times-frac 95.6%

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

   12. distribute-lft-out-- 95.6%

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

   13. *-commutative 95.6%

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

   14. associate-/r* 95.7%

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

   15. metadata-eval 95.7%

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

3. Simplified 95.7%

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

4. Taylor expanded in y around inf 65.3%

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

5. Taylor expanded in x around inf 28.3%

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

6. Final simplification 28.3%

   \[\leadsto x \]

Developer target: 96.1% 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 2023174 
(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))))