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

Percentage Accurate: 95.5% → 99.1%

Time: 10.9s

Alternatives: 16

Speedup: 1.4×

• 28.8% 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: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+149} \lor \neg \left(z \cdot 3 \leq 5 \cdot 10^{-22}\right):\\ \;\;\;\;x + \left(\frac{-0.3333333333333333}{\frac{z}{y}} + \frac{t}{y \cdot z} \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{-3}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -5e+149) (not (<= (* z 3.0) 5e-22)))
   (+
    x
    (+ (/ -0.3333333333333333 (/ z y)) (* (/ t (* y z)) 0.3333333333333333)))
   (+ x (/ (/ (- y (/ t y)) -3.0) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -5e+149) || !((z * 3.0) <= 5e-22)) {
		tmp = x + ((-0.3333333333333333 / (z / y)) + ((t / (y * z)) * 0.3333333333333333));
	} else {
		tmp = x + (((y - (t / y)) / -3.0) / 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 (((z * 3.0d0) <= (-5d+149)) .or. (.not. ((z * 3.0d0) <= 5d-22))) then
        tmp = x + (((-0.3333333333333333d0) / (z / y)) + ((t / (y * z)) * 0.3333333333333333d0))
    else
        tmp = x + (((y - (t / y)) / (-3.0d0)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -5e+149) || !((z * 3.0) <= 5e-22)) {
		tmp = x + ((-0.3333333333333333 / (z / y)) + ((t / (y * z)) * 0.3333333333333333));
	} else {
		tmp = x + (((y - (t / y)) / -3.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -5e+149) or not ((z * 3.0) <= 5e-22):
		tmp = x + ((-0.3333333333333333 / (z / y)) + ((t / (y * z)) * 0.3333333333333333))
	else:
		tmp = x + (((y - (t / y)) / -3.0) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -5e+149) || !(Float64(z * 3.0) <= 5e-22))
		tmp = Float64(x + Float64(Float64(-0.3333333333333333 / Float64(z / y)) + Float64(Float64(t / Float64(y * z)) * 0.3333333333333333)));
	else
		tmp = Float64(x + Float64(Float64(Float64(y - Float64(t / y)) / -3.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -5e+149) || ~(((z * 3.0) <= 5e-22)))
		tmp = x + ((-0.3333333333333333 / (z / y)) + ((t / (y * z)) * 0.3333333333333333));
	else
		tmp = x + (((y - (t / y)) / -3.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -5e+149], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 5e-22]], $MachinePrecision]], N[(x + N[(N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / -3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -4.9999999999999999e149 or 4.99999999999999954e-22 < (*.f64 z 3)

   1. Initial program 99.8%

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

      1. associate-+l- 99.8%

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

      2. sub-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. distribute-neg-in 99.8%

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

      5. distribute-neg-frac 99.8%

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

      6. neg-mul-1 99.8%

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

      7. *-commutative 99.8%

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

      8. times-frac 99.8%

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

      9. remove-double-neg 99.8%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. associate-*l* 99.7%

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

      13. associate-/r* 97.0%

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

      14. associate-/l/ 97.0%

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

   3. Simplified 97.0%

      \[\leadsto \color{blue}{x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \frac{\frac{\frac{t}{z}}{y}}{3}\right)} \]
   4. Step-by-step derivation

      1. fma-udef 97.0%

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

      2. clear-num 96.9%

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

      3. un-div-inv 97.0%

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

      4. div-inv 96.9%

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

      5. associate-/l/ 99.6%

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

      6. metadata-eval 99.6%

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

   5. Applied egg-rr 99.6%

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

   if -4.9999999999999999e149 < (*.f64 z 3) < 4.99999999999999954e-22

   1. Initial program 94.3%

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

      1. associate-+l- 94.3%

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

      2. sub-neg 94.3%

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

      3. sub-neg 94.3%

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

      4. distribute-neg-in 94.3%

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

      5. unsub-neg 94.3%

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

      6. neg-mul-1 94.3%

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

      7. associate-*r/ 94.3%

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

      8. associate-*l/ 94.2%

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

      9. distribute-neg-frac 94.2%

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

      10. neg-mul-1 94.2%

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

      11. times-frac 99.2%

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

      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* 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. associate-*l/ 99.7%

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

      2. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. associate-/r/ 99.7%

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

   7. Simplified 99.7%

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

      1. *-commutative 99.7%

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

      2. associate-*l* 99.6%

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

      3. metadata-eval 99.6%

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

      4. div-inv 99.7%

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

      5. times-frac 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. associate-/r* 99.8%

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

   9. Applied egg-rr 99.8%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+149} \lor \neg \left(z \cdot 3 \leq 5 \cdot 10^{-22}\right):\\ \;\;\;\;x + \left(\frac{-0.3333333333333333}{\frac{z}{y}} + \frac{t}{y \cdot z} \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{-3}}{z}\\ \end{array} \]

Alternative 2: 97.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{if}\;t_1 \leq 2.2 \cdot 10^{+278}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{z}}{-3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))))
   (if (<= t_1 2.2e+278) t_1 (+ x (/ (/ (- y (/ t y)) z) -3.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	double tmp;
	if (t_1 <= 2.2e+278) {
		tmp = t_1;
	} else {
		tmp = x + (((y - (t / y)) / z) / -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    if (t_1 <= 2.2d+278) then
        tmp = t_1
    else
        tmp = x + (((y - (t / y)) / z) / (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	double tmp;
	if (t_1 <= 2.2e+278) {
		tmp = t_1;
	} else {
		tmp = x + (((y - (t / y)) / z) / -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))
	tmp = 0
	if t_1 <= 2.2e+278:
		tmp = t_1
	else:
		tmp = x + (((y - (t / y)) / z) / -3.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))))
	tmp = 0.0
	if (t_1 <= 2.2e+278)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(Float64(Float64(y - Float64(t / y)) / z) / -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	tmp = 0.0;
	if (t_1 <= 2.2e+278)
		tmp = t_1;
	else
		tmp = x + (((y - (t / y)) / z) / -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2.2e+278], t$95$1, N[(x + N[(N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y))) < 2.19999999999999989e278

   1. Initial program 98.3%

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

   if 2.19999999999999989e278 < (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))

   1. Initial program 88.7%

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

      1. associate-+l- 88.7%

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

      2. sub-neg 88.7%

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

      3. sub-neg 88.7%

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

      4. distribute-neg-in 88.7%

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

      5. unsub-neg 88.7%

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

      6. neg-mul-1 88.7%

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

      7. associate-*r/ 88.7%

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

      8. associate-*l/ 88.7%

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

      9. distribute-neg-frac 88.7%

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

      10. neg-mul-1 88.7%

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

      11. times-frac 98.1%

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

      12. distribute-lft-out-- 99.9%

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

      13. *-commutative 99.9%

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

      14. associate-/r* 99.9%

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

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. associate-*l/ 99.9%

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

      2. clear-num 99.9%

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

   5. Applied egg-rr 99.9%

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

      1. associate-/r/ 99.9%

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

   7. Simplified 99.9%

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

      1. *-commutative 99.9%

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

      2. associate-*l* 99.8%

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

      3. metadata-eval 99.8%

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

      4. div-inv 99.9%

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

      5. times-frac 99.9%

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

      6. *-un-lft-identity 99.9%

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

      7. associate-/l/ 99.9%

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

   9. Applied egg-rr 99.9%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 2.2 \cdot 10^{+278}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{z}}{-3}\\ \end{array} \]

Alternative 3: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-80} \lor \neg \left(y \leq 2.45 \cdot 10^{-231}\right):\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{-3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \left(\frac{1}{y} \cdot \frac{t}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1e-80) (not (<= y 2.45e-231)))
   (+ x (/ (/ (- y (/ t y)) -3.0) z))
   (+ x (* 0.3333333333333333 (* (/ 1.0 y) (/ t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1e-80) || !(y <= 2.45e-231)) {
		tmp = x + (((y - (t / y)) / -3.0) / z);
	} else {
		tmp = x + (0.3333333333333333 * ((1.0 / y) * (t / 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 <= (-1d-80)) .or. (.not. (y <= 2.45d-231))) then
        tmp = x + (((y - (t / y)) / (-3.0d0)) / z)
    else
        tmp = x + (0.3333333333333333d0 * ((1.0d0 / y) * (t / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1e-80) || !(y <= 2.45e-231)) {
		tmp = x + (((y - (t / y)) / -3.0) / z);
	} else {
		tmp = x + (0.3333333333333333 * ((1.0 / y) * (t / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1e-80) or not (y <= 2.45e-231):
		tmp = x + (((y - (t / y)) / -3.0) / z)
	else:
		tmp = x + (0.3333333333333333 * ((1.0 / y) * (t / z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1e-80) || !(y <= 2.45e-231))
		tmp = Float64(x + Float64(Float64(Float64(y - Float64(t / y)) / -3.0) / z));
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(Float64(1.0 / y) * Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1e-80) || ~((y <= 2.45e-231)))
		tmp = x + (((y - (t / y)) / -3.0) / z);
	else
		tmp = x + (0.3333333333333333 * ((1.0 / y) * (t / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1e-80], N[Not[LessEqual[y, 2.45e-231]], $MachinePrecision]], N[(x + N[(N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / -3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 * N[(N[(1.0 / y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.99999999999999961e-81 or 2.45000000000000002e-231 < y

   1. Initial program 98.4%

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

      1. associate-+l- 98.4%

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

      2. sub-neg 98.4%

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

      3. sub-neg 98.4%

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

      4. distribute-neg-in 98.4%

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

      5. unsub-neg 98.4%

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

      6. neg-mul-1 98.4%

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

      7. associate-*r/ 98.4%

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

      8. associate-*l/ 98.4%

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

      9. distribute-neg-frac 98.4%

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

      10. neg-mul-1 98.4%

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

      11. times-frac 98.7%

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

      12. distribute-lft-out-- 99.2%

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

      13. *-commutative 99.2%

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

      14. associate-/r* 99.2%

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

      15. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. associate-*l/ 99.2%

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

      2. clear-num 99.2%

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

   5. Applied egg-rr 99.2%

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

      1. associate-/r/ 99.2%

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

   7. Simplified 99.2%

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

      1. *-commutative 99.2%

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

      2. associate-*l* 99.1%

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

      3. metadata-eval 99.1%

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

      4. div-inv 99.2%

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

      5. times-frac 99.3%

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

      6. *-un-lft-identity 99.3%

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

      7. associate-/r* 99.3%

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

   9. Applied egg-rr 99.3%

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

   if -9.99999999999999961e-81 < y < 2.45000000000000002e-231

   1. Initial program 89.2%

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

   2. Taylor expanded in y around 0 89.0%

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

      1. *-un-lft-identity 89.0%

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

      2. times-frac 96.2%

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

   4. Applied egg-rr 96.2%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(\frac{1}{y} \cdot \frac{t}{z}\right)} + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-80} \lor \neg \left(y \leq 2.45 \cdot 10^{-231}\right):\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{-3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \left(\frac{1}{y} \cdot \frac{t}{z}\right)\\ \end{array} \]

Alternative 4: 88.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+84}:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e+49)
   (+ x (/ y (* z -3.0)))
   (if (<= y 7.2e+84)
     (+ x (* t (/ 0.3333333333333333 (* y z))))
     (+ x (/ (/ y z) -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e+49) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= 7.2e+84) {
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	} else {
		tmp = x + ((y / z) / -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.45d+49)) then
        tmp = x + (y / (z * (-3.0d0)))
    else if (y <= 7.2d+84) then
        tmp = x + (t * (0.3333333333333333d0 / (y * z)))
    else
        tmp = x + ((y / z) / (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e+49) {
		tmp = x + (y / (z * -3.0));
	} else if (y <= 7.2e+84) {
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	} else {
		tmp = x + ((y / z) / -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e+49:
		tmp = x + (y / (z * -3.0))
	elif y <= 7.2e+84:
		tmp = x + (t * (0.3333333333333333 / (y * z)))
	else:
		tmp = x + ((y / z) / -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e+49)
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	elseif (y <= 7.2e+84)
		tmp = Float64(x + Float64(t * Float64(0.3333333333333333 / Float64(y * z))));
	else
		tmp = Float64(x + Float64(Float64(y / z) / -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45e+49)
		tmp = x + (y / (z * -3.0));
	elseif (y <= 7.2e+84)
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	else
		tmp = x + ((y / z) / -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e+49], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+84], N[(x + N[(t * N[(0.3333333333333333 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45e49

   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 99.7%

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

      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* 99.6%

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

      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. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. associate-/r/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around inf 96.4%

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

      1. *-commutative 96.4%

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

      2. metadata-eval 96.4%

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

      3. div-inv 96.5%

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

      4. frac-times 96.5%

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

      5. *-un-lft-identity 96.5%

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

   10. Applied egg-rr 96.5%

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

   if -1.45e49 < y < 7.1999999999999999e84

   1. Initial program 94.5%

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

      1. associate-+l- 94.5%

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

      2. sub-neg 94.5%

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

      3. sub-neg 94.5%

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

      4. distribute-neg-in 94.5%

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

      5. unsub-neg 94.5%

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

      6. neg-mul-1 94.5%

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

      7. associate-*r/ 94.5%

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

      8. associate-*l/ 94.5%

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

      9. distribute-neg-frac 94.5%

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

      10. neg-mul-1 94.5%

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

      11. times-frac 92.4%

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

      12. distribute-lft-out-- 92.4%

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

      13. *-commutative 92.4%

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

      14. associate-/r* 92.5%

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

      15. metadata-eval 92.5%

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

   3. Simplified 92.5%

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

      1. associate-*l/ 92.5%

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

      2. clear-num 92.5%

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

   5. Applied egg-rr 92.5%

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

      1. associate-/r/ 92.4%

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

   7. Simplified 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l* 92.4%

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

      3. metadata-eval 92.4%

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

      4. div-inv 92.4%

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

      5. times-frac 92.5%

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

      6. *-un-lft-identity 92.5%

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

      7. associate-/r* 92.5%

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

   9. Applied egg-rr 92.5%

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

   10. Taylor expanded in y around 0 90.1%

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

       1. associate-*r/ 90.0%

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

       2. associate-/l* 90.0%

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

       3. associate-/r/ 90.0%

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

       4. associate-/l/ 90.0%

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

       5. *-commutative 90.0%

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

       6. associate-/l/ 90.0%

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

   12. Simplified 90.0%

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

   if 7.1999999999999999e84 < y

   1. Initial program 97.4%

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

      1. associate-+l- 97.4%

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

      2. sub-neg 97.4%

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

      3. sub-neg 97.4%

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

      4. distribute-neg-in 97.4%

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

      5. unsub-neg 97.4%

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

      6. neg-mul-1 97.4%

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

      7. associate-*r/ 97.4%

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

      8. associate-*l/ 97.4%

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

      9. distribute-neg-frac 97.4%

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

      10. neg-mul-1 97.4%

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

      11. times-frac 97.4%

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

      12. distribute-lft-out-- 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/r* 99.6%

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

      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. Step-by-step derivation

      1. associate-*l/ 99.6%

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

      2. clear-num 99.6%

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

   5. Applied egg-rr 99.6%

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

      1. associate-/r/ 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around inf 97.0%

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

      1. *-commutative 97.0%

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

      2. *-commutative 97.0%

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

      3. metadata-eval 97.0%

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

      4. div-inv 96.9%

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

      5. associate-*l/ 97.1%

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

      6. div-inv 97.2%

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

   10. Applied egg-rr 97.2%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+84}:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]

Alternative 5: 88.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{1}{z} \cdot \frac{y}{-3}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+84}:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.25e+54)
   (+ x (* (/ 1.0 z) (/ y -3.0)))
   (if (<= y 7.2e+84)
     (+ x (* t (/ 0.3333333333333333 (* y z))))
     (+ x (/ (/ y z) -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e+54) {
		tmp = x + ((1.0 / z) * (y / -3.0));
	} else if (y <= 7.2e+84) {
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	} else {
		tmp = x + ((y / z) / -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.25d+54)) then
        tmp = x + ((1.0d0 / z) * (y / (-3.0d0)))
    else if (y <= 7.2d+84) then
        tmp = x + (t * (0.3333333333333333d0 / (y * z)))
    else
        tmp = x + ((y / z) / (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e+54) {
		tmp = x + ((1.0 / z) * (y / -3.0));
	} else if (y <= 7.2e+84) {
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	} else {
		tmp = x + ((y / z) / -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.25e+54:
		tmp = x + ((1.0 / z) * (y / -3.0))
	elif y <= 7.2e+84:
		tmp = x + (t * (0.3333333333333333 / (y * z)))
	else:
		tmp = x + ((y / z) / -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.25e+54)
		tmp = Float64(x + Float64(Float64(1.0 / z) * Float64(y / -3.0)));
	elseif (y <= 7.2e+84)
		tmp = Float64(x + Float64(t * Float64(0.3333333333333333 / Float64(y * z))));
	else
		tmp = Float64(x + Float64(Float64(y / z) / -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.25e+54)
		tmp = x + ((1.0 / z) * (y / -3.0));
	elseif (y <= 7.2e+84)
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	else
		tmp = x + ((y / z) / -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.25e+54], N[(x + N[(N[(1.0 / z), $MachinePrecision] * N[(y / -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+84], N[(x + N[(t * N[(0.3333333333333333 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25000000000000001e54

   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 99.7%

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

      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* 99.6%

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

      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. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. associate-/r/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around inf 96.4%

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

      1. *-commutative 96.4%

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

      2. metadata-eval 96.4%

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

      3. div-inv 96.5%

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

   10. Applied egg-rr 96.5%

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

   if -1.25000000000000001e54 < y < 7.1999999999999999e84

   1. Initial program 94.5%

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

      1. associate-+l- 94.5%

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

      2. sub-neg 94.5%

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

      3. sub-neg 94.5%

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

      4. distribute-neg-in 94.5%

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

      5. unsub-neg 94.5%

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

      6. neg-mul-1 94.5%

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

      7. associate-*r/ 94.5%

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

      8. associate-*l/ 94.5%

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

      9. distribute-neg-frac 94.5%

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

      10. neg-mul-1 94.5%

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

      11. times-frac 92.4%

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

      12. distribute-lft-out-- 92.4%

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

      13. *-commutative 92.4%

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

      14. associate-/r* 92.5%

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

      15. metadata-eval 92.5%

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

   3. Simplified 92.5%

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

      1. associate-*l/ 92.5%

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

      2. clear-num 92.5%

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

   5. Applied egg-rr 92.5%

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

      1. associate-/r/ 92.4%

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

   7. Simplified 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l* 92.4%

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

      3. metadata-eval 92.4%

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

      4. div-inv 92.4%

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

      5. times-frac 92.5%

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

      6. *-un-lft-identity 92.5%

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

      7. associate-/r* 92.5%

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

   9. Applied egg-rr 92.5%

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

   10. Taylor expanded in y around 0 90.1%

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

       1. associate-*r/ 90.0%

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

       2. associate-/l* 90.0%

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

       3. associate-/r/ 90.0%

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

       4. associate-/l/ 90.0%

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

       5. *-commutative 90.0%

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

       6. associate-/l/ 90.0%

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

   12. Simplified 90.0%

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

   if 7.1999999999999999e84 < y

   1. Initial program 97.4%

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

      1. associate-+l- 97.4%

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

      2. sub-neg 97.4%

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

      3. sub-neg 97.4%

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

      4. distribute-neg-in 97.4%

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

      5. unsub-neg 97.4%

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

      6. neg-mul-1 97.4%

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

      7. associate-*r/ 97.4%

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

      8. associate-*l/ 97.4%

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

      9. distribute-neg-frac 97.4%

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

      10. neg-mul-1 97.4%

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

      11. times-frac 97.4%

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

      12. distribute-lft-out-- 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/r* 99.6%

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

      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. Step-by-step derivation

      1. associate-*l/ 99.6%

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

      2. clear-num 99.6%

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

   5. Applied egg-rr 99.6%

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

      1. associate-/r/ 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around inf 97.0%

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

      1. *-commutative 97.0%

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

      2. *-commutative 97.0%

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

      3. metadata-eval 97.0%

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

      4. div-inv 96.9%

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

      5. associate-*l/ 97.1%

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

      6. div-inv 97.2%

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

   10. Applied egg-rr 97.2%

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

4. Final simplification 92.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+54}:\\ \;\;\;\;x + \frac{1}{z} \cdot \frac{y}{-3}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+84}:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]

Alternative 6: 89.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{1}{z} \cdot \frac{y}{-3}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+84}:\\ \;\;\;\;x + \frac{t}{3 \cdot \left(y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e+50)
   (+ x (* (/ 1.0 z) (/ y -3.0)))
   (if (<= y 7.2e+84) (+ x (/ t (* 3.0 (* y z)))) (+ x (/ (/ y z) -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e+50) {
		tmp = x + ((1.0 / z) * (y / -3.0));
	} else if (y <= 7.2e+84) {
		tmp = x + (t / (3.0 * (y * z)));
	} else {
		tmp = x + ((y / z) / -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.5d+50)) then
        tmp = x + ((1.0d0 / z) * (y / (-3.0d0)))
    else if (y <= 7.2d+84) then
        tmp = x + (t / (3.0d0 * (y * z)))
    else
        tmp = x + ((y / z) / (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e+50) {
		tmp = x + ((1.0 / z) * (y / -3.0));
	} else if (y <= 7.2e+84) {
		tmp = x + (t / (3.0 * (y * z)));
	} else {
		tmp = x + ((y / z) / -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e+50:
		tmp = x + ((1.0 / z) * (y / -3.0))
	elif y <= 7.2e+84:
		tmp = x + (t / (3.0 * (y * z)))
	else:
		tmp = x + ((y / z) / -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e+50)
		tmp = Float64(x + Float64(Float64(1.0 / z) * Float64(y / -3.0)));
	elseif (y <= 7.2e+84)
		tmp = Float64(x + Float64(t / Float64(3.0 * Float64(y * z))));
	else
		tmp = Float64(x + Float64(Float64(y / z) / -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.5e+50)
		tmp = x + ((1.0 / z) * (y / -3.0));
	elseif (y <= 7.2e+84)
		tmp = x + (t / (3.0 * (y * z)));
	else
		tmp = x + ((y / z) / -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e+50], N[(x + N[(N[(1.0 / z), $MachinePrecision] * N[(y / -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e+84], N[(x + N[(t / N[(3.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4999999999999998e50

   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 99.7%

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

      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* 99.6%

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

      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. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. associate-/r/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around inf 96.4%

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

      1. *-commutative 96.4%

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

      2. metadata-eval 96.4%

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

      3. div-inv 96.5%

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

   10. Applied egg-rr 96.5%

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

   if -5.4999999999999998e50 < y < 7.1999999999999999e84

   1. Initial program 94.5%

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

      1. associate-+l- 94.5%

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

      2. sub-neg 94.5%

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

      3. sub-neg 94.5%

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

      4. distribute-neg-in 94.5%

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

      5. unsub-neg 94.5%

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

      6. neg-mul-1 94.5%

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

      7. associate-*r/ 94.5%

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

      8. associate-*l/ 94.5%

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

      9. distribute-neg-frac 94.5%

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

      10. neg-mul-1 94.5%

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

      11. times-frac 92.4%

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

      12. distribute-lft-out-- 92.4%

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

      13. *-commutative 92.4%

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

      14. associate-/r* 92.5%

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

      15. metadata-eval 92.5%

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

   3. Simplified 92.5%

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

      1. associate-*l/ 92.5%

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

      2. clear-num 92.5%

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

   5. Applied egg-rr 92.5%

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

      1. associate-/r/ 92.4%

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

   7. Simplified 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l* 92.4%

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

      3. metadata-eval 92.4%

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

      4. div-inv 92.4%

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

      5. times-frac 92.5%

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

      6. *-un-lft-identity 92.5%

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

      7. associate-/r* 92.5%

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

   9. Applied egg-rr 92.5%

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

   10. Taylor expanded in y around 0 90.1%

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

       1. *-commutative 90.1%

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

       2. associate-/r* 87.7%

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

       3. associate-/r/ 87.7%

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

       4. associate-/l/ 90.1%

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

   12. Simplified 90.1%

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

   13. Taylor expanded in z around 0 90.1%

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

   if 7.1999999999999999e84 < y

   1. Initial program 97.4%

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

      1. associate-+l- 97.4%

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

      2. sub-neg 97.4%

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

      3. sub-neg 97.4%

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

      4. distribute-neg-in 97.4%

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

      5. unsub-neg 97.4%

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

      6. neg-mul-1 97.4%

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

      7. associate-*r/ 97.4%

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

      8. associate-*l/ 97.4%

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

      9. distribute-neg-frac 97.4%

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

      10. neg-mul-1 97.4%

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

      11. times-frac 97.4%

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

      12. distribute-lft-out-- 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/r* 99.6%

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

      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. Step-by-step derivation

      1. associate-*l/ 99.6%

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

      2. clear-num 99.6%

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

   5. Applied egg-rr 99.6%

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

      1. associate-/r/ 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around inf 97.0%

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

      1. *-commutative 97.0%

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

      2. *-commutative 97.0%

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

      3. metadata-eval 97.0%

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

      4. div-inv 96.9%

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

      5. associate-*l/ 97.1%

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

      6. div-inv 97.2%

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

   10. Applied egg-rr 97.2%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{1}{z} \cdot \frac{y}{-3}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{+84}:\\ \;\;\;\;x + \frac{t}{3 \cdot \left(y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]

Alternative 7: 89.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{1}{z} \cdot \frac{y}{-3}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+84}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.35e+49)
   (+ x (* (/ 1.0 z) (/ y -3.0)))
   (if (<= y 7.5e+84) (+ x (/ t (* y (* z 3.0)))) (+ x (/ (/ y z) -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.35e+49) {
		tmp = x + ((1.0 / z) * (y / -3.0));
	} else if (y <= 7.5e+84) {
		tmp = x + (t / (y * (z * 3.0)));
	} else {
		tmp = x + ((y / z) / -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.35d+49)) then
        tmp = x + ((1.0d0 / z) * (y / (-3.0d0)))
    else if (y <= 7.5d+84) then
        tmp = x + (t / (y * (z * 3.0d0)))
    else
        tmp = x + ((y / z) / (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.35e+49) {
		tmp = x + ((1.0 / z) * (y / -3.0));
	} else if (y <= 7.5e+84) {
		tmp = x + (t / (y * (z * 3.0)));
	} else {
		tmp = x + ((y / z) / -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.35e+49:
		tmp = x + ((1.0 / z) * (y / -3.0))
	elif y <= 7.5e+84:
		tmp = x + (t / (y * (z * 3.0)))
	else:
		tmp = x + ((y / z) / -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.35e+49)
		tmp = Float64(x + Float64(Float64(1.0 / z) * Float64(y / -3.0)));
	elseif (y <= 7.5e+84)
		tmp = Float64(x + Float64(t / Float64(y * Float64(z * 3.0))));
	else
		tmp = Float64(x + Float64(Float64(y / z) / -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.35e+49)
		tmp = x + ((1.0 / z) * (y / -3.0));
	elseif (y <= 7.5e+84)
		tmp = x + (t / (y * (z * 3.0)));
	else
		tmp = x + ((y / z) / -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.35e+49], N[(x + N[(N[(1.0 / z), $MachinePrecision] * N[(y / -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+84], N[(x + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y / z), $MachinePrecision] / -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3499999999999999e49

   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 99.7%

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

      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* 99.6%

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

      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. Step-by-step derivation

      1. associate-*l/ 99.7%

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

      2. clear-num 99.7%

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

   5. Applied egg-rr 99.7%

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

      1. associate-/r/ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around inf 96.4%

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

      1. *-commutative 96.4%

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

      2. metadata-eval 96.4%

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

      3. div-inv 96.5%

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

   10. Applied egg-rr 96.5%

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

   if -2.3499999999999999e49 < y < 7.5000000000000001e84

   1. Initial program 94.5%

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

      1. associate-+l- 94.5%

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

      2. sub-neg 94.5%

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

      3. sub-neg 94.5%

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

      4. distribute-neg-in 94.5%

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

      5. unsub-neg 94.5%

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

      6. neg-mul-1 94.5%

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

      7. associate-*r/ 94.5%

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

      8. associate-*l/ 94.5%

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

      9. distribute-neg-frac 94.5%

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

      10. neg-mul-1 94.5%

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

      11. times-frac 92.4%

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

      12. distribute-lft-out-- 92.4%

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

      13. *-commutative 92.4%

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

      14. associate-/r* 92.5%

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

      15. metadata-eval 92.5%

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

   3. Simplified 92.5%

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

      1. associate-*l/ 92.5%

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

      2. clear-num 92.5%

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

   5. Applied egg-rr 92.5%

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

      1. associate-/r/ 92.4%

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

   7. Simplified 92.4%

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

      1. *-commutative 92.4%

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

      2. associate-*l* 92.4%

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

      3. metadata-eval 92.4%

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

      4. div-inv 92.4%

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

      5. times-frac 92.5%

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

      6. *-un-lft-identity 92.5%

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

      7. associate-/r* 92.5%

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

   9. Applied egg-rr 92.5%

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

   10. Taylor expanded in y around 0 90.1%

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

       1. *-commutative 90.1%

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

       2. associate-/r* 87.7%

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

       3. associate-/r/ 87.7%

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

       4. associate-/l/ 90.1%

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

   12. Simplified 90.1%

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

   13. Taylor expanded in z around 0 90.2%

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

       1. *-commutative 90.2%

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

   15. Simplified 90.2%

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

   if 7.5000000000000001e84 < y

   1. Initial program 97.4%

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

      1. associate-+l- 97.4%

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

      2. sub-neg 97.4%

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

      3. sub-neg 97.4%

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

      4. distribute-neg-in 97.4%

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

      5. unsub-neg 97.4%

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

      6. neg-mul-1 97.4%

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

      7. associate-*r/ 97.4%

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

      8. associate-*l/ 97.4%

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

      9. distribute-neg-frac 97.4%

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

      10. neg-mul-1 97.4%

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

      11. times-frac 97.4%

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

      12. distribute-lft-out-- 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/r* 99.6%

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

      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. Step-by-step derivation

      1. associate-*l/ 99.6%

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

      2. clear-num 99.6%

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

   5. Applied egg-rr 99.6%

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

      1. associate-/r/ 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around inf 97.0%

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

      1. *-commutative 97.0%

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

      2. *-commutative 97.0%

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

      3. metadata-eval 97.0%

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

      4. div-inv 96.9%

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

      5. associate-*l/ 97.1%

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

      6. div-inv 97.2%

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

   10. Applied egg-rr 97.2%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{1}{z} \cdot \frac{y}{-3}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+84}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{y}{z}}{-3}\\ \end{array} \]

Alternative 8: 96.0% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. associate-+l- 96.2%

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

   2. sub-neg 96.2%

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

   3. sub-neg 96.2%

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

   4. distribute-neg-in 96.2%

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

   5. unsub-neg 96.2%

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

   6. neg-mul-1 96.2%

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

   7. associate-*r/ 96.2%

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

   8. associate-*l/ 96.2%

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

   9. distribute-neg-frac 96.2%

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

   10. neg-mul-1 96.2%

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

   11. times-frac 94.9%

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

   12. distribute-lft-out-- 95.3%

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

   13. *-commutative 95.3%

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

   14. associate-/r* 95.3%

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

   15. metadata-eval 95.3%

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

3. Simplified 95.3%

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

4. Final simplification 95.3%

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

Alternative 9: 96.1% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. associate-+l- 96.2%

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

   2. sub-neg 96.2%

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

   3. sub-neg 96.2%

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

   4. distribute-neg-in 96.2%

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

   5. unsub-neg 96.2%

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

   6. neg-mul-1 96.2%

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

   7. associate-*r/ 96.2%

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

   8. associate-*l/ 96.2%

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

   9. distribute-neg-frac 96.2%

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

   10. neg-mul-1 96.2%

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

   11. times-frac 94.9%

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

   12. distribute-lft-out-- 95.3%

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

   13. *-commutative 95.3%

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

   14. associate-/r* 95.3%

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

   15. metadata-eval 95.3%

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

3. Simplified 95.3%

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

4. Taylor expanded in y around 0 96.1%

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

   1. +-commutative 96.1%

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

   2. metadata-eval 96.1%

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

   3. cancel-sign-sub-inv 96.1%

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

   4. associate-/r* 94.9%

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

   5. associate-*r/ 94.9%

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

   6. associate-*r/ 94.9%

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

   7. div-sub 95.3%

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

   8. distribute-lft-out-- 95.3%

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

6. Simplified 95.3%

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

7. Final simplification 95.3%

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

Alternative 10: 96.1% accurate, 1.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((y - (t / y)) / (z * -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 - (t / y)) / (z * (-3.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. associate-+l- 96.2%

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

   2. sub-neg 96.2%

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

   3. sub-neg 96.2%

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

   4. distribute-neg-in 96.2%

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

   5. unsub-neg 96.2%

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

   6. neg-mul-1 96.2%

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

   7. associate-*r/ 96.2%

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

   8. associate-*l/ 96.2%

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

   9. distribute-neg-frac 96.2%

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

   10. neg-mul-1 96.2%

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

   11. times-frac 94.9%

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

   12. distribute-lft-out-- 95.3%

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

   13. *-commutative 95.3%

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

   14. associate-/r* 95.3%

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

   15. metadata-eval 95.3%

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

3. Simplified 95.3%

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

   1. *-commutative 95.3%

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

   2. clear-num 95.3%

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

   3. un-div-inv 95.3%

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

   4. div-inv 95.3%

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

   5. metadata-eval 95.3%

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

5. Applied egg-rr 95.3%

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

6. Final simplification 95.3%

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

Alternative 11: 96.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + \frac{\frac{y - \frac{t}{y}}{-3}}{z} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + (((y - (t / y)) / -3.0) / 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 - (t / y)) / (-3.0d0)) / z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. associate-+l- 96.2%

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

   2. sub-neg 96.2%

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

   3. sub-neg 96.2%

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

   4. distribute-neg-in 96.2%

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

   5. unsub-neg 96.2%

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

   6. neg-mul-1 96.2%

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

   7. associate-*r/ 96.2%

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

   8. associate-*l/ 96.2%

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

   9. distribute-neg-frac 96.2%

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

   10. neg-mul-1 96.2%

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

   11. times-frac 94.9%

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

   12. distribute-lft-out-- 95.3%

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

   13. *-commutative 95.3%

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

   14. associate-/r* 95.3%

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

   15. metadata-eval 95.3%

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

3. Simplified 95.3%

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

   1. associate-*l/ 95.3%

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

   2. clear-num 95.3%

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

5. Applied egg-rr 95.3%

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

   1. associate-/r/ 95.3%

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

7. Simplified 95.3%

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

   1. *-commutative 95.3%

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

   2. associate-*l* 95.2%

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

   3. metadata-eval 95.2%

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

   4. div-inv 95.3%

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

   5. times-frac 95.3%

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

   6. *-un-lft-identity 95.3%

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

   7. associate-/r* 95.4%

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

9. Applied egg-rr 95.4%

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

10. Final simplification 95.4%

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

Alternative 12: 48.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+79} \lor \neg \left(y \leq 4.7 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.2e+79) (not (<= y 4.7e+86)))
   (/ -0.3333333333333333 (/ z y))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e+79) || !(y <= 4.7e+86)) {
		tmp = -0.3333333333333333 / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.2d+79)) .or. (.not. (y <= 4.7d+86))) then
        tmp = (-0.3333333333333333d0) / (z / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e+79) || !(y <= 4.7e+86)) {
		tmp = -0.3333333333333333 / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.2e+79) or not (y <= 4.7e+86):
		tmp = -0.3333333333333333 / (z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.2e+79) || !(y <= 4.7e+86))
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.2e+79) || ~((y <= 4.7e+86)))
		tmp = -0.3333333333333333 / (z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.2e+79], N[Not[LessEqual[y, 4.7e+86]], $MachinePrecision]], N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000016e79 or 4.7000000000000002e86 < y

   1. Initial program 98.7%

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

   2. Taylor expanded in t around 0 97.3%

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

      1. add-sqr-sqrt 52.5%

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

      2. sqrt-unprod 47.9%

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

      3. swap-sqr 47.9%

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

      4. metadata-eval 47.9%

         \[\leadsto x - \sqrt{\color{blue}{0.1111111111111111} \cdot \left(\frac{y}{z} \cdot \frac{y}{z}\right)} \]

      5. metadata-eval 47.9%

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

      6. swap-sqr 47.9%

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

      7. clear-num 47.9%

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

      8. div-inv 47.9%

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

      9. clear-num 47.9%

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

      10. div-inv 47.9%

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

      11. sqrt-unprod 8.9%

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

      12. add-sqr-sqrt 18.3%

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

   4. Applied egg-rr 18.3%

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

   5. Taylor expanded in x around 0 1.4%

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

      1. add-sqr-sqrt 52.5%

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

      2. sqrt-unprod 47.9%

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

      3. swap-sqr 47.9%

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

      4. metadata-eval 47.9%

         \[\leadsto x - \sqrt{\color{blue}{0.1111111111111111} \cdot \left(\frac{y}{z} \cdot \frac{y}{z}\right)} \]

      5. metadata-eval 47.9%

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

      6. swap-sqr 47.9%

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

      7. clear-num 47.9%

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

      8. div-inv 47.9%

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

      9. clear-num 47.9%

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

      10. div-inv 47.9%

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

      11. sqrt-unprod 8.9%

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

      12. add-sqr-sqrt 18.3%

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

   7. Applied egg-rr 79.0%

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

   if -4.20000000000000016e79 < y < 4.7000000000000002e86

   1. Initial program 94.8%

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

   2. Taylor expanded in x around inf 32.8%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+79} \lor \neg \left(y \leq 4.7 \cdot 10^{+86}\right):\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 48.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+80} \lor \neg \left(y \leq 5.1 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3e+80) (not (<= y 5.1e+89))) (/ (/ y -3.0) z) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e+80) || !(y <= 5.1e+89)) {
		tmp = (y / -3.0) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3d+80)) .or. (.not. (y <= 5.1d+89))) then
        tmp = (y / (-3.0d0)) / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3e+80) || !(y <= 5.1e+89)) {
		tmp = (y / -3.0) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3e+80) or not (y <= 5.1e+89):
		tmp = (y / -3.0) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3e+80) || !(y <= 5.1e+89))
		tmp = Float64(Float64(y / -3.0) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3e+80) || ~((y <= 5.1e+89)))
		tmp = (y / -3.0) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3e+80], N[Not[LessEqual[y, 5.1e+89]], $MachinePrecision]], N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999987e80 or 5.10000000000000027e89 < y

   1. Initial program 98.7%

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

   2. Taylor expanded in t around 0 97.3%

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

      1. add-sqr-sqrt 52.5%

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

      2. sqrt-unprod 47.9%

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

      3. swap-sqr 47.9%

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

      4. metadata-eval 47.9%

         \[\leadsto x - \sqrt{\color{blue}{0.1111111111111111} \cdot \left(\frac{y}{z} \cdot \frac{y}{z}\right)} \]

      5. metadata-eval 47.9%

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

      6. swap-sqr 47.9%

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

      7. clear-num 47.9%

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

      8. div-inv 47.9%

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

      9. clear-num 47.9%

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

      10. div-inv 47.9%

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

      11. sqrt-unprod 8.9%

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

      12. add-sqr-sqrt 18.3%

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

   4. Applied egg-rr 18.3%

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

   5. Taylor expanded in x around 0 1.4%

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

      1. add-sqr-sqrt 0.9%

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

      2. sqrt-unprod 25.0%

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

      3. swap-sqr 25.0%

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

      4. metadata-eval 25.0%

         \[\leadsto \sqrt{\color{blue}{0.1111111111111111} \cdot \left(\frac{y}{z} \cdot \frac{y}{z}\right)} \]

      5. metadata-eval 25.0%

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

      6. swap-sqr 25.0%

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

      7. clear-num 25.0%

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

      8. div-inv 25.0%

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

      9. clear-num 25.0%

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

      10. div-inv 25.0%

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

      11. sqrt-unprod 36.1%

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

      12. add-sqr-sqrt 79.0%

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

      13. div-inv 79.1%

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

      14. metadata-eval 79.1%

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

      15. clear-num 79.0%

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

      16. times-frac 79.2%

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

      17. *-un-lft-identity 79.2%

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

      18. associate-/r* 79.2%

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

   7. Applied egg-rr 79.2%

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

   if -2.99999999999999987e80 < y < 5.10000000000000027e89

   1. Initial program 94.8%

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

   2. Taylor expanded in x around inf 32.8%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+80} \lor \neg \left(y \leq 5.1 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 48.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+80}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3e+80)
   (/ (* y -0.3333333333333333) z)
   (if (<= y 4.7e+86) x (/ -0.3333333333333333 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e+80) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 4.7e+86) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3d+80)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= 4.7d+86) then
        tmp = x
    else
        tmp = (-0.3333333333333333d0) / (z / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3e+80) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 4.7e+86) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3e+80:
		tmp = (y * -0.3333333333333333) / z
	elif y <= 4.7e+86:
		tmp = x
	else:
		tmp = -0.3333333333333333 / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3e+80)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= 4.7e+86)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3e+80)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= 4.7e+86)
		tmp = x;
	else
		tmp = -0.3333333333333333 / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3e+80], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 4.7e+86], x, N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.99999999999999987e80

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 97.7%

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

      1. add-sqr-sqrt 63.7%

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

      2. sqrt-unprod 53.0%

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

      3. swap-sqr 53.1%

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

      4. metadata-eval 53.1%

         \[\leadsto x - \sqrt{\color{blue}{0.1111111111111111} \cdot \left(\frac{y}{z} \cdot \frac{y}{z}\right)} \]

      5. metadata-eval 53.1%

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

      6. swap-sqr 53.0%

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

      7. clear-num 53.0%

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

      8. div-inv 53.0%

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

      9. clear-num 53.0%

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

      10. div-inv 53.0%

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

      11. sqrt-unprod 10.1%

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

      12. add-sqr-sqrt 21.0%

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

   4. Applied egg-rr 21.0%

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

   5. Taylor expanded in x around 0 1.8%

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

      1. add-sqr-sqrt 1.2%

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

      2. sqrt-unprod 17.6%

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

      3. swap-sqr 17.6%

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

      4. metadata-eval 17.6%

         \[\leadsto \sqrt{\color{blue}{0.1111111111111111} \cdot \left(\frac{y}{z} \cdot \frac{y}{z}\right)} \]

      5. metadata-eval 17.6%

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

      6. swap-sqr 17.6%

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

      7. clear-num 17.7%

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

      8. div-inv 17.6%

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

      9. clear-num 17.7%

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

      10. div-inv 17.6%

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

      11. sqrt-unprod 24.0%

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

      12. add-sqr-sqrt 76.0%

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

      13. associate-/r/ 76.0%

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

      14. associate-*l/ 76.1%

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

   7. Applied egg-rr 76.1%

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

   if -2.99999999999999987e80 < y < 4.7000000000000002e86

   1. Initial program 94.8%

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

   2. Taylor expanded in x around inf 32.8%

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

   if 4.7000000000000002e86 < y

   1. Initial program 97.3%

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

   2. Taylor expanded in t around 0 96.9%

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

      1. add-sqr-sqrt 38.8%

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

      2. sqrt-unprod 41.7%

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

      3. swap-sqr 41.7%

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

      4. metadata-eval 41.7%

         \[\leadsto x - \sqrt{\color{blue}{0.1111111111111111} \cdot \left(\frac{y}{z} \cdot \frac{y}{z}\right)} \]

      5. metadata-eval 41.7%

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

      6. swap-sqr 41.7%

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

      7. clear-num 41.7%

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

      8. div-inv 41.7%

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

      9. clear-num 41.7%

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

      10. div-inv 41.7%

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

      11. sqrt-unprod 7.5%

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

      12. add-sqr-sqrt 15.0%

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

   4. Applied egg-rr 15.0%

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

   5. Taylor expanded in x around 0 0.9%

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

      1. add-sqr-sqrt 38.8%

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

      2. sqrt-unprod 41.7%

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

      3. swap-sqr 41.7%

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

      4. metadata-eval 41.7%

         \[\leadsto x - \sqrt{\color{blue}{0.1111111111111111} \cdot \left(\frac{y}{z} \cdot \frac{y}{z}\right)} \]

      5. metadata-eval 41.7%

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

      6. swap-sqr 41.7%

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

      7. clear-num 41.7%

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

      8. div-inv 41.7%

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

      9. clear-num 41.7%

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

      10. div-inv 41.7%

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

      11. sqrt-unprod 7.5%

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

      12. add-sqr-sqrt 15.0%

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

   7. Applied egg-rr 82.7%

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

4. Final simplification 49.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+80}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 4.7 \cdot 10^{+86}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]

Alternative 15: 63.7% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{z \cdot -3} \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. associate-+l- 96.2%

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

   2. sub-neg 96.2%

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

   3. sub-neg 96.2%

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

   4. distribute-neg-in 96.2%

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

   5. unsub-neg 96.2%

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

   6. neg-mul-1 96.2%

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

   7. associate-*r/ 96.2%

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

   8. associate-*l/ 96.2%

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

   9. distribute-neg-frac 96.2%

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

   10. neg-mul-1 96.2%

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

   11. times-frac 94.9%

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

   12. distribute-lft-out-- 95.3%

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

   13. *-commutative 95.3%

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

   14. associate-/r* 95.3%

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

   15. metadata-eval 95.3%

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

3. Simplified 95.3%

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

   1. associate-*l/ 95.3%

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

   2. clear-num 95.3%

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

5. Applied egg-rr 95.3%

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

   1. associate-/r/ 95.3%

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

7. Simplified 95.3%

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

8. Taylor expanded in y around inf 60.6%

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

   1. *-commutative 60.6%

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

   2. metadata-eval 60.6%

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

   3. div-inv 60.6%

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

   4. frac-times 60.6%

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

   5. *-un-lft-identity 60.6%

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

10. Applied egg-rr 60.6%

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

11. Final simplification 60.6%

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

Alternative 16: 30.4% 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 96.2%

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

2. Taylor expanded in x around inf 28.2%

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

3. Final simplification 28.2%

   \[\leadsto x \]

Developer target: 96.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023200 
(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))))