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

Percentage Accurate: 95.3% → 99.5%

Time: 8.2s

Alternatives: 9

Speedup: 1.0×

• 27.8% 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: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+15}:\\ \;\;\;\;x + \left(\frac{-0.3333333333333333}{\frac{z}{y}} + \frac{t}{z \cdot y} \cdot 0.3333333333333333\right)\\ \mathbf{elif}\;z \cdot 3 \leq 4 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -5e+15)
   (+
    x
    (+ (/ -0.3333333333333333 (/ z y)) (* (/ t (* z y)) 0.3333333333333333)))
   (if (<= (* z 3.0) 4e-7)
     (+ x (/ (- y (/ t y)) (* z -3.0)))
     (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -5e+15) {
		tmp = x + ((-0.3333333333333333 / (z / y)) + ((t / (z * y)) * 0.3333333333333333));
	} else if ((z * 3.0) <= 4e-7) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-5d+15)) then
        tmp = x + (((-0.3333333333333333d0) / (z / y)) + ((t / (z * y)) * 0.3333333333333333d0))
    else if ((z * 3.0d0) <= 4d-7) then
        tmp = x + ((y - (t / y)) / (z * (-3.0d0)))
    else
        tmp = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -5e+15) {
		tmp = x + ((-0.3333333333333333 / (z / y)) + ((t / (z * y)) * 0.3333333333333333));
	} else if ((z * 3.0) <= 4e-7) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -5e+15:
		tmp = x + ((-0.3333333333333333 / (z / y)) + ((t / (z * y)) * 0.3333333333333333))
	elif (z * 3.0) <= 4e-7:
		tmp = x + ((y - (t / y)) / (z * -3.0))
	else:
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -5e+15)
		tmp = Float64(x + Float64(Float64(-0.3333333333333333 / Float64(z / y)) + Float64(Float64(t / Float64(z * y)) * 0.3333333333333333)));
	elseif (Float64(z * 3.0) <= 4e-7)
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	else
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -5e+15)
		tmp = x + ((-0.3333333333333333 / (z / y)) + ((t / (z * y)) * 0.3333333333333333));
	elseif ((z * 3.0) <= 4e-7)
		tmp = x + ((y - (t / y)) / (z * -3.0));
	else
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -5e+15], N[(x + N[(N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 4e-7], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -5e15

   1. Initial program 99.6%

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

      1. associate-+l- 99.6%

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

      2. sub-neg 99.6%

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

      3. sub-neg 99.6%

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

      4. distribute-neg-in 99.6%

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

      5. distribute-neg-frac 99.6%

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

      6. neg-mul-1 99.6%

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

      7. *-commutative 99.6%

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

      8. times-frac 99.6%

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

      9. remove-double-neg 99.6%

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

      10. fma-def 99.6%

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

      11. metadata-eval 99.6%

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

      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* 95.9%

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

      14. associate-/l/ 95.9%

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

   3. Simplified 95.9%

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

      1. fma-udef 95.9%

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

      2. clear-num 95.9%

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

      3. un-div-inv 95.9%

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

      4. div-inv 95.8%

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

      5. associate-/l/ 99.7%

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

      6. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   if -5e15 < (*.f64 z 3) < 3.9999999999999998e-7

   1. Initial program 93.6%

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

      1. associate-+l- 93.6%

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

      2. sub-neg 93.6%

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

      3. sub-neg 93.6%

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

      4. distribute-neg-in 93.6%

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

      5. unsub-neg 93.6%

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

      6. neg-mul-1 93.6%

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

      7. associate-*r/ 93.6%

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

      8. associate-*l/ 93.6%

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

      9. distribute-neg-frac 93.6%

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

      10. neg-mul-1 93.6%

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

      11. times-frac 97.7%

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

      12. distribute-lft-out-- 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-/r* 99.8%

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

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.9%

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

      4. div-inv 99.9%

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

      5. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

   if 3.9999999999999998e-7 < (*.f64 z 3)

   1. Initial program 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+15}:\\ \;\;\;\;x + \left(\frac{-0.3333333333333333}{\frac{z}{y}} + \frac{t}{z \cdot y} \cdot 0.3333333333333333\right)\\ \mathbf{elif}\;z \cdot 3 \leq 4 \cdot 10^{-7}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \]

Alternative 2: 99.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+15} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{+40}\right):\\ \;\;\;\;x + \left(\frac{-0.3333333333333333}{\frac{z}{y}} + \frac{t}{z \cdot y} \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -5e+15) (not (<= (* z 3.0) 2e+40)))
   (+
    x
    (+ (/ -0.3333333333333333 (/ z y)) (* (/ t (* z y)) 0.3333333333333333)))
   (+ x (/ (- y (/ t y)) (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -5e+15) || !((z * 3.0) <= 2e+40)) {
		tmp = x + ((-0.3333333333333333 / (z / y)) + ((t / (z * y)) * 0.3333333333333333));
	} 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) :: tmp
    if (((z * 3.0d0) <= (-5d+15)) .or. (.not. ((z * 3.0d0) <= 2d+40))) then
        tmp = x + (((-0.3333333333333333d0) / (z / y)) + ((t / (z * y)) * 0.3333333333333333d0))
    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 tmp;
	if (((z * 3.0) <= -5e+15) || !((z * 3.0) <= 2e+40)) {
		tmp = x + ((-0.3333333333333333 / (z / y)) + ((t / (z * y)) * 0.3333333333333333));
	} else {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -5e+15) or not ((z * 3.0) <= 2e+40):
		tmp = x + ((-0.3333333333333333 / (z / y)) + ((t / (z * y)) * 0.3333333333333333))
	else:
		tmp = x + ((y - (t / y)) / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -5e+15) || !(Float64(z * 3.0) <= 2e+40))
		tmp = Float64(x + Float64(Float64(-0.3333333333333333 / Float64(z / y)) + Float64(Float64(t / Float64(z * y)) * 0.3333333333333333)));
	else
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -5e+15) || ~(((z * 3.0) <= 2e+40)))
		tmp = x + ((-0.3333333333333333 / (z / y)) + ((t / (z * y)) * 0.3333333333333333));
	else
		tmp = x + ((y - (t / y)) / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -5e+15], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 2e+40]], $MachinePrecision]], N[(x + N[(N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -5e15 or 2.00000000000000006e40 < (*.f64 z 3)

   1. Initial program 99.7%

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

      1. associate-+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. distribute-neg-frac 99.7%

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

      6. neg-mul-1 99.7%

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

      7. *-commutative 99.7%

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

      8. times-frac 99.6%

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

      9. remove-double-neg 99.6%

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

      10. fma-def 99.6%

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

      11. metadata-eval 99.6%

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

      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* 96.8%

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

      14. associate-/l/ 96.8%

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

   3. Simplified 96.8%

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

      1. fma-udef 96.8%

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

      2. clear-num 96.8%

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

      3. un-div-inv 96.8%

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

      4. div-inv 96.7%

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

      5. associate-/l/ 99.7%

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

      6. metadata-eval 99.7%

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

   5. Applied egg-rr 99.7%

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

   if -5e15 < (*.f64 z 3) < 2.00000000000000006e40

   1. Initial program 94.2%

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

      1. associate-+l- 94.2%

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

      2. sub-neg 94.2%

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

      3. sub-neg 94.2%

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

      4. distribute-neg-in 94.2%

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

      5. unsub-neg 94.2%

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

      6. neg-mul-1 94.2%

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

      7. associate-*r/ 94.2%

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

      8. associate-*l/ 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 97.9%

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

      12. distribute-lft-out-- 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-/r* 99.8%

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

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

      4. div-inv 99.9%

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

      5. metadata-eval 99.9%

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

   5. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+15} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{+40}\right):\\ \;\;\;\;x + \left(\frac{-0.3333333333333333}{\frac{z}{y}} + \frac{t}{z \cdot y} \cdot 0.3333333333333333\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \]

Alternative 3: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-186} \lor \neg \left(y \leq 3 \cdot 10^{-137}\right):\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.8e-186) (not (<= y 3e-137)))
   (+ x (* (- y (/ t y)) (/ -0.3333333333333333 z)))
   (+ x (* (/ t z) (/ 0.3333333333333333 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.8e-186) || !(y <= 3e-137)) {
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.8d-186)) .or. (.not. (y <= 3d-137))) then
        tmp = x + ((y - (t / y)) * ((-0.3333333333333333d0) / z))
    else
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.8e-186) || !(y <= 3e-137)) {
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.8e-186) or not (y <= 3e-137):
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z))
	else:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.8e-186) || !(y <= 3e-137))
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.8e-186) || ~((y <= 3e-137)))
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	else
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.8e-186], N[Not[LessEqual[y, 3e-137]], $MachinePrecision]], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.80000000000000006e-186 or 2.9999999999999998e-137 < y

   1. Initial program 98.1%

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

      1. associate-+l- 98.1%

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

      2. sub-neg 98.1%

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

      3. sub-neg 98.1%

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

      4. distribute-neg-in 98.1%

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

      5. unsub-neg 98.1%

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

      6. neg-mul-1 98.1%

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

      7. associate-*r/ 98.1%

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

      8. associate-*l/ 98.1%

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

      9. distribute-neg-frac 98.1%

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

      10. neg-mul-1 98.1%

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

      11. times-frac 97.6%

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

      12. distribute-lft-out-- 99.2%

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

      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%

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

   if -4.80000000000000006e-186 < y < 2.9999999999999998e-137

   1. Initial program 91.9%

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

      1. associate-+l- 91.9%

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

      2. sub-neg 91.9%

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

      3. sub-neg 91.9%

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

      4. distribute-neg-in 91.9%

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

      5. unsub-neg 91.9%

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

      6. neg-mul-1 91.9%

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

      7. associate-*r/ 91.9%

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

      8. associate-*l/ 91.9%

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

      9. distribute-neg-frac 91.9%

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

      10. neg-mul-1 91.9%

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

      11. times-frac 84.0%

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

      12. distribute-lft-out-- 84.0%

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

      13. *-commutative 84.0%

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

      14. associate-/r* 83.9%

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

      15. metadata-eval 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in y around 0 91.8%

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

      1. associate-*r/ 91.9%

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

   6. Simplified 91.9%

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

      1. times-frac 97.2%

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

      2. *-commutative 97.2%

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

   8. Applied egg-rr 97.2%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-186} \lor \neg \left(y \leq 3 \cdot 10^{-137}\right):\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]

Alternative 4: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-186} \lor \neg \left(y \leq 1.5 \cdot 10^{-131}\right):\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4e-186) (not (<= y 1.5e-131)))
   (+ x (/ (- y (/ t y)) (* z -3.0)))
   (+ x (* (/ t z) (/ 0.3333333333333333 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4e-186) || !(y <= 1.5e-131)) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4d-186)) .or. (.not. (y <= 1.5d-131))) then
        tmp = x + ((y - (t / y)) / (z * (-3.0d0)))
    else
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4e-186) || !(y <= 1.5e-131)) {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4e-186) or not (y <= 1.5e-131):
		tmp = x + ((y - (t / y)) / (z * -3.0))
	else:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4e-186) || !(y <= 1.5e-131))
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	else
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4e-186) || ~((y <= 1.5e-131)))
		tmp = x + ((y - (t / y)) / (z * -3.0));
	else
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4e-186], N[Not[LessEqual[y, 1.5e-131]], $MachinePrecision]], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9999999999999996e-186 or 1.49999999999999998e-131 < y

   1. Initial program 98.1%

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

      1. associate-+l- 98.1%

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

      2. sub-neg 98.1%

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

      3. sub-neg 98.1%

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

      4. distribute-neg-in 98.1%

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

      5. unsub-neg 98.1%

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

      6. neg-mul-1 98.1%

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

      7. associate-*r/ 98.1%

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

      8. associate-*l/ 98.1%

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

      9. distribute-neg-frac 98.1%

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

      10. neg-mul-1 98.1%

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

      11. times-frac 97.6%

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

      12. distribute-lft-out-- 99.2%

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

      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. *-commutative 99.2%

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

      2. clear-num 99.2%

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

      3. un-div-inv 99.3%

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

      4. div-inv 99.3%

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

      5. metadata-eval 99.3%

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

   5. Applied egg-rr 99.3%

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

   if -3.9999999999999996e-186 < y < 1.49999999999999998e-131

   1. Initial program 91.9%

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

      1. associate-+l- 91.9%

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

      2. sub-neg 91.9%

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

      3. sub-neg 91.9%

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

      4. distribute-neg-in 91.9%

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

      5. unsub-neg 91.9%

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

      6. neg-mul-1 91.9%

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

      7. associate-*r/ 91.9%

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

      8. associate-*l/ 91.9%

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

      9. distribute-neg-frac 91.9%

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

      10. neg-mul-1 91.9%

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

      11. times-frac 84.0%

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

      12. distribute-lft-out-- 84.0%

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

      13. *-commutative 84.0%

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

      14. associate-/r* 83.9%

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

      15. metadata-eval 83.9%

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

   3. Simplified 83.9%

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

   4. Taylor expanded in y around 0 91.8%

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

      1. associate-*r/ 91.9%

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

   6. Simplified 91.9%

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

      1. times-frac 97.2%

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

      2. *-commutative 97.2%

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

   8. Applied egg-rr 97.2%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-186} \lor \neg \left(y \leq 1.5 \cdot 10^{-131}\right):\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]

Alternative 5: 87.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-39} \lor \neg \left(y \leq 2.6 \cdot 10^{+86}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e-39) (not (<= y 2.6e+86)))
   (+ x (/ y (* z -3.0)))
   (+ x (* (/ t y) (/ 0.3333333333333333 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e-39) || !(y <= 2.6e+86)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.8d-39)) .or. (.not. (y <= 2.6d+86))) then
        tmp = x + (y / (z * (-3.0d0)))
    else
        tmp = x + ((t / y) * (0.3333333333333333d0 / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e-39) || !(y <= 2.6e+86)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.8e-39) or not (y <= 2.6e+86):
		tmp = x + (y / (z * -3.0))
	else:
		tmp = x + ((t / y) * (0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e-39) || !(y <= 2.6e+86))
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	else
		tmp = Float64(x + Float64(Float64(t / y) * Float64(0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.8e-39) || ~((y <= 2.6e+86)))
		tmp = x + (y / (z * -3.0));
	else
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.8e-39], N[Not[LessEqual[y, 2.6e+86]], $MachinePrecision]], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.8000000000000002e-39 or 2.5999999999999998e86 < y

   1. Initial program 97.2%

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

      1. associate-+l- 97.2%

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

      2. sub-neg 97.2%

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

      3. sub-neg 97.2%

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

      4. distribute-neg-in 97.2%

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

      5. unsub-neg 97.2%

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

      6. neg-mul-1 97.2%

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

      7. associate-*r/ 97.2%

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

      8. associate-*l/ 97.1%

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

      9. distribute-neg-frac 97.1%

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

      10. neg-mul-1 97.1%

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

      11. times-frac 97.1%

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

      12. distribute-lft-out-- 99.7%

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

      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. *-commutative 99.7%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.8%

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

      4. div-inv 99.8%

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

      5. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 92.5%

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

      1. associate-*r/ 92.5%

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

      2. associate-*l/ 92.6%

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

      3. metadata-eval 92.6%

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

      4. associate-/r* 92.6%

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

      5. *-commutative 92.6%

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

      6. associate-*l/ 92.6%

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

      7. *-lft-identity 92.6%

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

   8. Simplified 92.6%

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

   if -3.8000000000000002e-39 < y < 2.5999999999999998e86

   1. Initial program 95.6%

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

      1. associate-+l- 95.6%

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

      2. sub-neg 95.6%

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

      3. sub-neg 95.6%

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

      4. distribute-neg-in 95.6%

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

      5. unsub-neg 95.6%

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

      6. neg-mul-1 95.6%

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

      7. associate-*r/ 95.6%

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

      8. associate-*l/ 95.6%

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

      9. distribute-neg-frac 95.6%

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

      10. neg-mul-1 95.6%

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

      11. times-frac 90.8%

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

      12. distribute-lft-out-- 90.8%

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

      13. *-commutative 90.8%

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

      14. associate-/r* 90.8%

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

      15. metadata-eval 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in y around 0 93.8%

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

      1. *-commutative 93.8%

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

      2. associate-*l/ 93.8%

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

      3. times-frac 88.9%

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

   6. Simplified 88.9%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-39} \lor \neg \left(y \leq 2.6 \cdot 10^{+86}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \end{array} \]

Alternative 6: 90.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-39} \lor \neg \left(y \leq 2.6 \cdot 10^{+86}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.5e-39) (not (<= y 2.6e+86)))
   (+ x (/ y (* z -3.0)))
   (+ x (* (/ t z) (/ 0.3333333333333333 y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.5e-39) || !(y <= 2.6e+86)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.5d-39)) .or. (.not. (y <= 2.6d+86))) then
        tmp = x + (y / (z * (-3.0d0)))
    else
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.5e-39) || !(y <= 2.6e+86)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.5e-39) or not (y <= 2.6e+86):
		tmp = x + (y / (z * -3.0))
	else:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.5e-39) || !(y <= 2.6e+86))
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	else
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.5e-39) || ~((y <= 2.6e+86)))
		tmp = x + (y / (z * -3.0));
	else
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.5e-39], N[Not[LessEqual[y, 2.6e+86]], $MachinePrecision]], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.50000000000000014e-39 or 2.5999999999999998e86 < y

   1. Initial program 97.2%

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

      1. associate-+l- 97.2%

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

      2. sub-neg 97.2%

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

      3. sub-neg 97.2%

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

      4. distribute-neg-in 97.2%

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

      5. unsub-neg 97.2%

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

      6. neg-mul-1 97.2%

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

      7. associate-*r/ 97.2%

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

      8. associate-*l/ 97.1%

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

      9. distribute-neg-frac 97.1%

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

      10. neg-mul-1 97.1%

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

      11. times-frac 97.1%

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

      12. distribute-lft-out-- 99.7%

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

      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. *-commutative 99.7%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.8%

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

      4. div-inv 99.8%

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

      5. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 92.5%

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

      1. associate-*r/ 92.5%

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

      2. associate-*l/ 92.6%

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

      3. metadata-eval 92.6%

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

      4. associate-/r* 92.6%

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

      5. *-commutative 92.6%

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

      6. associate-*l/ 92.6%

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

      7. *-lft-identity 92.6%

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

   8. Simplified 92.6%

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

   if -1.50000000000000014e-39 < y < 2.5999999999999998e86

   1. Initial program 95.6%

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

      1. associate-+l- 95.6%

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

      2. sub-neg 95.6%

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

      3. sub-neg 95.6%

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

      4. distribute-neg-in 95.6%

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

      5. unsub-neg 95.6%

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

      6. neg-mul-1 95.6%

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

      7. associate-*r/ 95.6%

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

      8. associate-*l/ 95.6%

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

      9. distribute-neg-frac 95.6%

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

      10. neg-mul-1 95.6%

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

      11. times-frac 90.8%

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

      12. distribute-lft-out-- 90.8%

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

      13. *-commutative 90.8%

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

      14. associate-/r* 90.8%

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

      15. metadata-eval 90.8%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in y around 0 93.8%

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

      1. associate-*r/ 93.8%

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

   6. Simplified 93.8%

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

      1. times-frac 95.9%

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

      2. *-commutative 95.9%

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

   8. Applied egg-rr 95.9%

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

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-39} \lor \neg \left(y \leq 2.6 \cdot 10^{+86}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]

Alternative 7: 64.1% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (y * ((-0.3333333333333333d0) / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.3%

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

   1. associate-+l- 96.3%

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

   2. sub-neg 96.3%

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

   3. sub-neg 96.3%

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

   4. distribute-neg-in 96.3%

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

   5. unsub-neg 96.3%

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

   6. neg-mul-1 96.3%

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

   7. associate-*r/ 96.3%

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

   8. associate-*l/ 96.3%

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

   9. distribute-neg-frac 96.3%

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

   10. neg-mul-1 96.3%

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

   11. times-frac 93.6%

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

   12. distribute-lft-out-- 94.8%

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

   13. *-commutative 94.8%

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

   14. associate-/r* 94.7%

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

   15. metadata-eval 94.7%

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

3. Simplified 94.7%

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

4. Taylor expanded in y around inf 58.5%

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

5. Final simplification 58.5%

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

Alternative 8: 64.1% 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 96.3%

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

   1. associate-+l- 96.3%

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

   2. sub-neg 96.3%

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

   3. sub-neg 96.3%

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

   4. distribute-neg-in 96.3%

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

   5. unsub-neg 96.3%

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

   6. neg-mul-1 96.3%

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

   7. associate-*r/ 96.3%

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

   8. associate-*l/ 96.3%

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

   9. distribute-neg-frac 96.3%

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

   10. neg-mul-1 96.3%

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

   11. times-frac 93.6%

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

   12. distribute-lft-out-- 94.8%

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

   13. *-commutative 94.8%

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

   14. associate-/r* 94.7%

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

   15. metadata-eval 94.7%

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

3. Simplified 94.7%

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

   1. *-commutative 94.7%

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

   2. clear-num 94.7%

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

   3. un-div-inv 94.8%

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

   4. div-inv 94.8%

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

   5. metadata-eval 94.8%

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

5. Applied egg-rr 94.8%

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

6. Taylor expanded in y around inf 58.5%

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

   1. associate-*r/ 58.5%

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

   2. associate-*l/ 58.5%

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

   3. metadata-eval 58.5%

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

   4. associate-/r* 58.5%

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

   5. *-commutative 58.5%

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

   6. associate-*l/ 58.6%

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

   7. *-lft-identity 58.6%

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

8. Simplified 58.6%

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

9. Final simplification 58.6%

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

Alternative 9: 30.9% 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 96.3%

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

2. Taylor expanded in x around inf 25.9%

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

3. Final simplification 25.9%

   \[\leadsto x \]

Developer target: 96.0% 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 2023199 
(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))))