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

Percentage Accurate: 95.6% → 98.1%

Time: 13.4s

Alternatives: 16

Speedup: 0.7×

• 27.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{y} - y\\ \mathbf{if}\;y \leq -2.35 \cdot 10^{-80}:\\ \;\;\;\;x + t\_1 \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{z \cdot 3} \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ t y) y)))
   (if (<= y -2.35e-80)
     (+ x (* t_1 (/ 0.3333333333333333 z)))
     (if (<= y 2e-128)
       (+ x (/ (* t (/ 0.3333333333333333 z)) y))
       (+ x (* (/ 1.0 (* z 3.0)) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t / y) - y;
	double tmp;
	if (y <= -2.35e-80) {
		tmp = x + (t_1 * (0.3333333333333333 / z));
	} else if (y <= 2e-128) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x + ((1.0 / (z * 3.0)) * t_1);
	}
	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 = (t / y) - y
    if (y <= (-2.35d-80)) then
        tmp = x + (t_1 * (0.3333333333333333d0 / z))
    else if (y <= 2d-128) then
        tmp = x + ((t * (0.3333333333333333d0 / z)) / y)
    else
        tmp = x + ((1.0d0 / (z * 3.0d0)) * t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t / y) - y;
	double tmp;
	if (y <= -2.35e-80) {
		tmp = x + (t_1 * (0.3333333333333333 / z));
	} else if (y <= 2e-128) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x + ((1.0 / (z * 3.0)) * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t / y) - y
	tmp = 0
	if y <= -2.35e-80:
		tmp = x + (t_1 * (0.3333333333333333 / z))
	elif y <= 2e-128:
		tmp = x + ((t * (0.3333333333333333 / z)) / y)
	else:
		tmp = x + ((1.0 / (z * 3.0)) * t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t / y) - y)
	tmp = 0.0
	if (y <= -2.35e-80)
		tmp = Float64(x + Float64(t_1 * Float64(0.3333333333333333 / z)));
	elseif (y <= 2e-128)
		tmp = Float64(x + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	else
		tmp = Float64(x + Float64(Float64(1.0 / Float64(z * 3.0)) * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t / y) - y;
	tmp = 0.0;
	if (y <= -2.35e-80)
		tmp = x + (t_1 * (0.3333333333333333 / z));
	elseif (y <= 2e-128)
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	else
		tmp = x + ((1.0 / (z * 3.0)) * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[y, -2.35e-80], N[(x + N[(t$95$1 * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-128], N[(x + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] * t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.34999999999999986e-80

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. associate-+l+ 96.1%

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

      3. +-commutative 96.1%

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

      4. remove-double-neg 96.1%

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

      5. distribute-frac-neg 96.1%

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

      6. distribute-neg-in 96.1%

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

      7. remove-double-neg 96.1%

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

      8. sub-neg 96.1%

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

      9. neg-mul-1 96.1%

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

      10. times-frac 96.1%

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

      11. distribute-frac-neg 96.1%

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

      12. neg-mul-1 96.1%

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

      13. *-commutative 96.1%

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

      14. associate-/l* 96.1%

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

      15. *-commutative 96.1%

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

   3. Simplified 99.7%

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

   if -2.34999999999999986e-80 < y < 2.00000000000000011e-128

   1. Initial program 86.5%

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

      1. sub-neg 86.5%

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

      2. associate-+l+ 86.5%

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

      3. +-commutative 86.5%

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

      4. remove-double-neg 86.5%

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

      5. distribute-frac-neg 86.5%

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

      6. distribute-neg-in 86.5%

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

      7. remove-double-neg 86.5%

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

      8. sub-neg 86.5%

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

      9. neg-mul-1 86.5%

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

      10. times-frac 85.5%

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

      11. distribute-frac-neg 85.5%

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

      12. neg-mul-1 85.5%

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

      13. *-commutative 85.5%

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

      14. associate-/l* 85.5%

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

      15. *-commutative 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in y around 0 86.3%

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

      1. +-commutative 86.3%

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

   7. Simplified 86.3%

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

      1. metadata-eval 86.3%

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

      2. associate-/r* 85.6%

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

      3. times-frac 85.6%

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

      4. *-commutative 85.6%

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

      5. associate-*l/ 85.5%

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

      6. associate-*r/ 99.8%

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

      7. inv-pow 99.8%

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

      8. unpow-prod-down 99.7%

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

      9. inv-pow 99.7%

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

      10. metadata-eval 99.7%

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

      11. *-commutative 99.7%

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

      12. un-div-inv 99.7%

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

   9. Applied egg-rr 99.7%

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

   if 2.00000000000000011e-128 < y

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. associate-+l+ 96.1%

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

      3. +-commutative 96.1%

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

      4. remove-double-neg 96.1%

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

      5. distribute-frac-neg 96.1%

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

      6. distribute-neg-in 96.1%

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

      7. remove-double-neg 96.1%

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

      8. sub-neg 96.1%

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

      9. neg-mul-1 96.1%

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

      10. times-frac 97.3%

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

      11. distribute-frac-neg 97.3%

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

      12. neg-mul-1 97.3%

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

      13. *-commutative 97.3%

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

      14. associate-/l* 97.3%

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

      15. *-commutative 97.3%

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

   3. Simplified 99.8%

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

      1. div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

      1. *-commutative 99.7%

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

      2. inv-pow 99.7%

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

      3. metadata-eval 99.7%

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

      4. unpow-prod-down 99.8%

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

      5. inv-pow 99.8%

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

   8. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-80}:\\ \;\;\;\;x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-128}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{z \cdot 3} \cdot \left(\frac{t}{y} - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\left(\frac{t}{z \cdot \left(3 \cdot y\right)} + x\right) + \frac{1}{-3 \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{z \cdot 3} \cdot \left(\frac{t}{y} - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -2e-11)
   (+ (+ (/ t (* z (* 3.0 y))) x) (/ 1.0 (* -3.0 (/ z y))))
   (+ x (* (/ 1.0 (* z 3.0)) (- (/ t y) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -2e-11) {
		tmp = ((t / (z * (3.0 * y))) + x) + (1.0 / (-3.0 * (z / y)));
	} else {
		tmp = x + ((1.0 / (z * 3.0)) * ((t / y) - 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) <= (-2d-11)) then
        tmp = ((t / (z * (3.0d0 * y))) + x) + (1.0d0 / ((-3.0d0) * (z / y)))
    else
        tmp = x + ((1.0d0 / (z * 3.0d0)) * ((t / y) - 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) <= -2e-11) {
		tmp = ((t / (z * (3.0 * y))) + x) + (1.0 / (-3.0 * (z / y)));
	} else {
		tmp = x + ((1.0 / (z * 3.0)) * ((t / y) - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -2e-11:
		tmp = ((t / (z * (3.0 * y))) + x) + (1.0 / (-3.0 * (z / y)))
	else:
		tmp = x + ((1.0 / (z * 3.0)) * ((t / y) - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -2e-11)
		tmp = Float64(Float64(Float64(t / Float64(z * Float64(3.0 * y))) + x) + Float64(1.0 / Float64(-3.0 * Float64(z / y))));
	else
		tmp = Float64(x + Float64(Float64(1.0 / Float64(z * 3.0)) * Float64(Float64(t / y) - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -2e-11)
		tmp = ((t / (z * (3.0 * y))) + x) + (1.0 / (-3.0 * (z / y)));
	else
		tmp = x + ((1.0 / (z * 3.0)) * ((t / y) - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -2e-11], N[(N[(N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + N[(1.0 / N[(-3.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -1.99999999999999988e-11

   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. +-commutative 99.7%

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

      2. associate-+r- 99.7%

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

      3. sub-neg 99.7%

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

      4. associate-*l* 99.7%

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

      5. *-commutative 99.7%

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

      6. distribute-frac-neg2 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

      8. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. *-commutative 99.8%

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

      4. *-un-lft-identity 99.8%

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

      5. times-frac 99.8%

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

      6. metadata-eval 99.8%

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

   6. Applied egg-rr 99.8%

      \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \color{blue}{{\left(-3 \cdot \frac{z}{y}\right)}^{-1}} \]
   7. Step-by-step derivation

      1. unpow-1 99.8%

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

   8. Simplified 99.8%

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

   if -1.99999999999999988e-11 < (*.f64 z 3)

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. associate-+l+ 90.1%

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

      3. +-commutative 90.1%

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

      4. remove-double-neg 90.1%

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

      5. distribute-frac-neg 90.1%

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

      6. distribute-neg-in 90.1%

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

      7. remove-double-neg 90.1%

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

      8. sub-neg 90.1%

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

      9. neg-mul-1 90.1%

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

      10. times-frac 95.1%

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

      11. distribute-frac-neg 95.1%

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

      12. neg-mul-1 95.1%

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

      13. *-commutative 95.1%

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

      14. associate-/l* 95.1%

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

      15. *-commutative 95.1%

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

   3. Simplified 97.7%

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

      1. div-inv 97.7%

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

   6. Applied egg-rr 97.7%

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

      1. *-commutative 97.7%

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

      2. inv-pow 97.7%

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

      3. metadata-eval 97.7%

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

      4. unpow-prod-down 97.8%

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

      5. inv-pow 97.8%

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

   8. Applied egg-rr 97.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\left(\frac{t}{z \cdot \left(3 \cdot y\right)} + x\right) + \frac{1}{-3 \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{z \cdot 3} \cdot \left(\frac{t}{y} - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{y} - y\\ \mathbf{if}\;y \leq -5 \cdot 10^{-81}:\\ \;\;\;\;x + t\_1 \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1 \cdot \left(0.3333333333333333 \cdot \frac{1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ t y) y)))
   (if (<= y -5e-81)
     (+ x (* t_1 (/ 0.3333333333333333 z)))
     (if (<= y 9.8e-110)
       (+ x (/ (* t (/ 0.3333333333333333 z)) y))
       (+ x (* t_1 (* 0.3333333333333333 (/ 1.0 z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t / y) - y;
	double tmp;
	if (y <= -5e-81) {
		tmp = x + (t_1 * (0.3333333333333333 / z));
	} else if (y <= 9.8e-110) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x + (t_1 * (0.3333333333333333 * (1.0 / 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) :: t_1
    real(8) :: tmp
    t_1 = (t / y) - y
    if (y <= (-5d-81)) then
        tmp = x + (t_1 * (0.3333333333333333d0 / z))
    else if (y <= 9.8d-110) then
        tmp = x + ((t * (0.3333333333333333d0 / z)) / y)
    else
        tmp = x + (t_1 * (0.3333333333333333d0 * (1.0d0 / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t / y) - y;
	double tmp;
	if (y <= -5e-81) {
		tmp = x + (t_1 * (0.3333333333333333 / z));
	} else if (y <= 9.8e-110) {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	} else {
		tmp = x + (t_1 * (0.3333333333333333 * (1.0 / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t / y) - y
	tmp = 0
	if y <= -5e-81:
		tmp = x + (t_1 * (0.3333333333333333 / z))
	elif y <= 9.8e-110:
		tmp = x + ((t * (0.3333333333333333 / z)) / y)
	else:
		tmp = x + (t_1 * (0.3333333333333333 * (1.0 / z)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t / y) - y)
	tmp = 0.0
	if (y <= -5e-81)
		tmp = Float64(x + Float64(t_1 * Float64(0.3333333333333333 / z)));
	elseif (y <= 9.8e-110)
		tmp = Float64(x + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	else
		tmp = Float64(x + Float64(t_1 * Float64(0.3333333333333333 * Float64(1.0 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t / y) - y;
	tmp = 0.0;
	if (y <= -5e-81)
		tmp = x + (t_1 * (0.3333333333333333 / z));
	elseif (y <= 9.8e-110)
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	else
		tmp = x + (t_1 * (0.3333333333333333 * (1.0 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[y, -5e-81], N[(x + N[(t$95$1 * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e-110], N[(x + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 * N[(0.3333333333333333 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.99999999999999981e-81

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. associate-+l+ 96.1%

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

      3. +-commutative 96.1%

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

      4. remove-double-neg 96.1%

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

      5. distribute-frac-neg 96.1%

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

      6. distribute-neg-in 96.1%

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

      7. remove-double-neg 96.1%

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

      8. sub-neg 96.1%

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

      9. neg-mul-1 96.1%

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

      10. times-frac 96.1%

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

      11. distribute-frac-neg 96.1%

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

      12. neg-mul-1 96.1%

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

      13. *-commutative 96.1%

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

      14. associate-/l* 96.1%

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

      15. *-commutative 96.1%

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

   3. Simplified 99.7%

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

   if -4.99999999999999981e-81 < y < 9.7999999999999995e-110

   1. Initial program 86.0%

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

      1. sub-neg 86.0%

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

      2. associate-+l+ 86.0%

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

      3. +-commutative 86.0%

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

      4. remove-double-neg 86.0%

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

      5. distribute-frac-neg 86.0%

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

      6. distribute-neg-in 86.0%

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

      7. remove-double-neg 86.0%

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

      8. sub-neg 86.0%

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

      9. neg-mul-1 86.0%

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

      10. times-frac 86.1%

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

      11. distribute-frac-neg 86.1%

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

      12. neg-mul-1 86.1%

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

      13. *-commutative 86.1%

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

      14. associate-/l* 86.1%

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

      15. *-commutative 86.1%

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

   3. Simplified 86.1%

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

   5. Taylor expanded in y around 0 85.9%

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

      1. +-commutative 85.9%

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

   7. Simplified 85.9%

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

      1. metadata-eval 85.9%

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

      2. associate-/r* 86.2%

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

      3. times-frac 86.2%

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

      4. *-commutative 86.2%

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

      5. associate-*l/ 86.1%

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

      6. associate-*r/ 99.8%

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

      7. inv-pow 99.8%

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

      8. unpow-prod-down 99.7%

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

      9. inv-pow 99.7%

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

      10. metadata-eval 99.7%

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

      11. *-commutative 99.7%

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

      12. un-div-inv 99.7%

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

   9. Applied egg-rr 99.7%

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

   if 9.7999999999999995e-110 < 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. sub-neg 97.2%

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

      2. associate-+l+ 97.2%

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

      3. +-commutative 97.2%

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

      4. remove-double-neg 97.2%

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

      5. distribute-frac-neg 97.2%

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

      6. distribute-neg-in 97.2%

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

      7. remove-double-neg 97.2%

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

      8. sub-neg 97.2%

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

      9. neg-mul-1 97.2%

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

      10. times-frac 97.2%

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

      11. distribute-frac-neg 97.2%

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

      12. neg-mul-1 97.2%

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

      13. *-commutative 97.2%

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

      14. associate-/l* 97.2%

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

      15. *-commutative 97.2%

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

   3. Simplified 99.8%

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

      1. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-81}:\\ \;\;\;\;x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-110}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{t}{y} - y\right) \cdot \left(0.3333333333333333 \cdot \frac{1}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\left(x + \frac{t}{3 \cdot \left(z \cdot y\right)}\right) + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{z \cdot 3} \cdot \left(\frac{t}{y} - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -2e-11)
   (+ (+ x (/ t (* 3.0 (* z y)))) (/ y (* z -3.0)))
   (+ x (* (/ 1.0 (* z 3.0)) (- (/ t y) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -2e-11) {
		tmp = (x + (t / (3.0 * (z * y)))) + (y / (z * -3.0));
	} else {
		tmp = x + ((1.0 / (z * 3.0)) * ((t / y) - 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) <= (-2d-11)) then
        tmp = (x + (t / (3.0d0 * (z * y)))) + (y / (z * (-3.0d0)))
    else
        tmp = x + ((1.0d0 / (z * 3.0d0)) * ((t / y) - 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) <= -2e-11) {
		tmp = (x + (t / (3.0 * (z * y)))) + (y / (z * -3.0));
	} else {
		tmp = x + ((1.0 / (z * 3.0)) * ((t / y) - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -2e-11:
		tmp = (x + (t / (3.0 * (z * y)))) + (y / (z * -3.0))
	else:
		tmp = x + ((1.0 / (z * 3.0)) * ((t / y) - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -2e-11)
		tmp = Float64(Float64(x + Float64(t / Float64(3.0 * Float64(z * y)))) + Float64(y / Float64(z * -3.0)));
	else
		tmp = Float64(x + Float64(Float64(1.0 / Float64(z * 3.0)) * Float64(Float64(t / y) - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -2e-11)
		tmp = (x + (t / (3.0 * (z * y)))) + (y / (z * -3.0));
	else
		tmp = x + ((1.0 / (z * 3.0)) * ((t / y) - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -2e-11], N[(N[(x + N[(t / N[(3.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -1.99999999999999988e-11

   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. +-commutative 99.7%

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

      2. associate-+r- 99.7%

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

      3. sub-neg 99.7%

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

      4. associate-*l* 99.7%

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

      5. *-commutative 99.7%

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

      6. distribute-frac-neg2 99.7%

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

      7. distribute-rgt-neg-in 99.7%

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

      8. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   if -1.99999999999999988e-11 < (*.f64 z 3)

   1. Initial program 90.1%

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

      1. sub-neg 90.1%

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

      2. associate-+l+ 90.1%

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

      3. +-commutative 90.1%

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

      4. remove-double-neg 90.1%

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

      5. distribute-frac-neg 90.1%

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

      6. distribute-neg-in 90.1%

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

      7. remove-double-neg 90.1%

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

      8. sub-neg 90.1%

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

      9. neg-mul-1 90.1%

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

      10. times-frac 95.1%

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

      11. distribute-frac-neg 95.1%

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

      12. neg-mul-1 95.1%

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

      13. *-commutative 95.1%

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

      14. associate-/l* 95.1%

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

      15. *-commutative 95.1%

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

   3. Simplified 97.7%

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

      1. div-inv 97.7%

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

   6. Applied egg-rr 97.7%

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

      1. *-commutative 97.7%

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

      2. inv-pow 97.7%

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

      3. metadata-eval 97.7%

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

      4. unpow-prod-down 97.8%

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

      5. inv-pow 97.8%

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

   8. Applied egg-rr 97.8%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{-11}:\\ \;\;\;\;\left(x + \frac{t}{3 \cdot \left(z \cdot y\right)}\right) + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{z \cdot 3} \cdot \left(\frac{t}{y} - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{-75} \lor \neg \left(y \leq 6.4 \cdot 10^{-130}\right):\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.56e-75) (not (<= y 6.4e-130)))
   (+ x (* 0.3333333333333333 (/ (- (/ t y) y) z)))
   (+ x (/ (* t (/ 0.3333333333333333 z)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.56e-75) || !(y <= 6.4e-130)) {
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z));
	} else {
		tmp = x + ((t * (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 <= (-1.56d-75)) .or. (.not. (y <= 6.4d-130))) then
        tmp = x + (0.3333333333333333d0 * (((t / y) - y) / z))
    else
        tmp = x + ((t * (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 <= -1.56e-75) || !(y <= 6.4e-130)) {
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z));
	} else {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.56e-75) or not (y <= 6.4e-130):
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z))
	else:
		tmp = x + ((t * (0.3333333333333333 / z)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.56e-75) || !(y <= 6.4e-130))
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z)));
	else
		tmp = Float64(x + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.56e-75) || ~((y <= 6.4e-130)))
		tmp = x + (0.3333333333333333 * (((t / y) - y) / z));
	else
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.56e-75], N[Not[LessEqual[y, 6.4e-130]], $MachinePrecision]], N[(x + N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5600000000000001e-75 or 6.3999999999999999e-130 < y

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. associate-+l+ 96.1%

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

      3. +-commutative 96.1%

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

      4. remove-double-neg 96.1%

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

      5. distribute-frac-neg 96.1%

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

      6. distribute-neg-in 96.1%

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

      7. remove-double-neg 96.1%

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

      8. sub-neg 96.1%

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

      9. neg-mul-1 96.1%

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

      10. times-frac 96.7%

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

      11. distribute-frac-neg 96.7%

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

      12. neg-mul-1 96.7%

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

      13. *-commutative 96.7%

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

      14. associate-/l* 96.7%

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

      15. *-commutative 96.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.6%

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

   if -1.5600000000000001e-75 < y < 6.3999999999999999e-130

   1. Initial program 86.5%

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

      1. sub-neg 86.5%

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

      2. associate-+l+ 86.5%

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

      3. +-commutative 86.5%

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

      4. remove-double-neg 86.5%

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

      5. distribute-frac-neg 86.5%

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

      6. distribute-neg-in 86.5%

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

      7. remove-double-neg 86.5%

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

      8. sub-neg 86.5%

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

      9. neg-mul-1 86.5%

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

      10. times-frac 85.5%

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

      11. distribute-frac-neg 85.5%

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

      12. neg-mul-1 85.5%

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

      13. *-commutative 85.5%

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

      14. associate-/l* 85.5%

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

      15. *-commutative 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in y around 0 86.3%

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

      1. +-commutative 86.3%

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

   7. Simplified 86.3%

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

      1. metadata-eval 86.3%

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

      2. associate-/r* 85.6%

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

      3. times-frac 85.6%

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

      4. *-commutative 85.6%

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

      5. associate-*l/ 85.5%

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

      6. associate-*r/ 99.8%

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

      7. inv-pow 99.8%

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

      8. unpow-prod-down 99.7%

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

      9. inv-pow 99.7%

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

      10. metadata-eval 99.7%

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

      11. *-commutative 99.7%

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

      12. un-div-inv 99.7%

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

   9. Applied egg-rr 99.7%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{-75} \lor \neg \left(y \leq 6.4 \cdot 10^{-130}\right):\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-76} \lor \neg \left(y \leq 6.8 \cdot 10^{-130}\right):\\ \;\;\;\;x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.2e-76) (not (<= y 6.8e-130)))
   (+ x (* (- (/ t y) y) (/ 0.3333333333333333 z)))
   (+ x (/ (* t (/ 0.3333333333333333 z)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.2e-76) || !(y <= 6.8e-130)) {
		tmp = x + (((t / y) - y) * (0.3333333333333333 / z));
	} else {
		tmp = x + ((t * (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 <= (-1.2d-76)) .or. (.not. (y <= 6.8d-130))) then
        tmp = x + (((t / y) - y) * (0.3333333333333333d0 / z))
    else
        tmp = x + ((t * (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 <= -1.2e-76) || !(y <= 6.8e-130)) {
		tmp = x + (((t / y) - y) * (0.3333333333333333 / z));
	} else {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.2e-76) or not (y <= 6.8e-130):
		tmp = x + (((t / y) - y) * (0.3333333333333333 / z))
	else:
		tmp = x + ((t * (0.3333333333333333 / z)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.2e-76) || !(y <= 6.8e-130))
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(x + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.2e-76) || ~((y <= 6.8e-130)))
		tmp = x + (((t / y) - y) * (0.3333333333333333 / z));
	else
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.2e-76], N[Not[LessEqual[y, 6.8e-130]], $MachinePrecision]], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.20000000000000007e-76 or 6.8000000000000001e-130 < y

   1. Initial program 96.1%

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

      1. sub-neg 96.1%

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

      2. associate-+l+ 96.1%

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

      3. +-commutative 96.1%

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

      4. remove-double-neg 96.1%

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

      5. distribute-frac-neg 96.1%

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

      6. distribute-neg-in 96.1%

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

      7. remove-double-neg 96.1%

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

      8. sub-neg 96.1%

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

      9. neg-mul-1 96.1%

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

      10. times-frac 96.7%

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

      11. distribute-frac-neg 96.7%

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

      12. neg-mul-1 96.7%

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

      13. *-commutative 96.7%

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

      14. associate-/l* 96.7%

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

      15. *-commutative 96.7%

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

   3. Simplified 99.7%

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

   if -1.20000000000000007e-76 < y < 6.8000000000000001e-130

   1. Initial program 86.5%

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

      1. sub-neg 86.5%

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

      2. associate-+l+ 86.5%

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

      3. +-commutative 86.5%

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

      4. remove-double-neg 86.5%

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

      5. distribute-frac-neg 86.5%

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

      6. distribute-neg-in 86.5%

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

      7. remove-double-neg 86.5%

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

      8. sub-neg 86.5%

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

      9. neg-mul-1 86.5%

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

      10. times-frac 85.5%

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

      11. distribute-frac-neg 85.5%

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

      12. neg-mul-1 85.5%

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

      13. *-commutative 85.5%

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

      14. associate-/l* 85.5%

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

      15. *-commutative 85.5%

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

   3. Simplified 85.5%

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

   5. Taylor expanded in y around 0 86.3%

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

      1. +-commutative 86.3%

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

   7. Simplified 86.3%

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

      1. metadata-eval 86.3%

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

      2. associate-/r* 85.6%

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

      3. times-frac 85.6%

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

      4. *-commutative 85.6%

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

      5. associate-*l/ 85.5%

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

      6. associate-*r/ 99.8%

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

      7. inv-pow 99.8%

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

      8. unpow-prod-down 99.7%

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

      9. inv-pow 99.7%

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

      10. metadata-eval 99.7%

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

      11. *-commutative 99.7%

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

      12. un-div-inv 99.7%

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

   9. Applied egg-rr 99.7%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-76} \lor \neg \left(y \leq 6.8 \cdot 10^{-130}\right):\\ \;\;\;\;x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+62} \lor \neg \left(y \leq 2.7 \cdot 10^{+76}\right):\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2e+62) (not (<= y 2.7e+76)))
   (- x (/ 0.3333333333333333 (/ z y)))
   (+ x (* 0.3333333333333333 (/ (/ t z) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e+62) || !(y <= 2.7e+76)) {
		tmp = x - (0.3333333333333333 / (z / y));
	} else {
		tmp = x + (0.3333333333333333 * ((t / z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2d+62)) .or. (.not. (y <= 2.7d+76))) then
        tmp = x - (0.3333333333333333d0 / (z / y))
    else
        tmp = x + (0.3333333333333333d0 * ((t / z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2e+62) || !(y <= 2.7e+76)) {
		tmp = x - (0.3333333333333333 / (z / y));
	} else {
		tmp = x + (0.3333333333333333 * ((t / z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2e+62) or not (y <= 2.7e+76):
		tmp = x - (0.3333333333333333 / (z / y))
	else:
		tmp = x + (0.3333333333333333 * ((t / z) / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2e+62) || !(y <= 2.7e+76))
		tmp = Float64(x - Float64(0.3333333333333333 / Float64(z / y)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(Float64(t / z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2e+62) || ~((y <= 2.7e+76)))
		tmp = x - (0.3333333333333333 / (z / y));
	else
		tmp = x + (0.3333333333333333 * ((t / z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2e+62], N[Not[LessEqual[y, 2.7e+76]], $MachinePrecision]], N[(x - N[(0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.00000000000000007e62 or 2.6999999999999999e76 < y

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0 96.8%

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

      1. clear-num 96.9%

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

      2. un-div-inv 97.0%

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

   5. Applied egg-rr 97.0%

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

   if -2.00000000000000007e62 < y < 2.6999999999999999e76

   1. Initial program 89.9%

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

      1. sub-neg 89.9%

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

      2. associate-+l+ 89.9%

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

      3. +-commutative 89.9%

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

      4. remove-double-neg 89.9%

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

      5. distribute-frac-neg 89.9%

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

      6. distribute-neg-in 89.9%

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

      7. remove-double-neg 89.9%

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

      8. sub-neg 89.9%

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

      9. neg-mul-1 89.9%

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

      10. times-frac 89.9%

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

      11. distribute-frac-neg 89.9%

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

      12. neg-mul-1 89.9%

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

      13. *-commutative 89.9%

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

      14. associate-/l* 89.9%

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

      15. *-commutative 89.9%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in t around inf 86.7%

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

      1. *-commutative 86.7%

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

      2. *-commutative 86.7%

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

      3. metadata-eval 86.7%

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

      4. times-frac 86.8%

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

      5. *-rgt-identity 86.8%

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

      6. associate-*r* 86.8%

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

      7. associate-/r* 95.4%

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

      8. *-lft-identity 95.4%

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

      9. *-commutative 95.4%

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

      10. times-frac 95.3%

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

      11. metadata-eval 95.3%

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

   7. Simplified 95.3%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+62} \lor \neg \left(y \leq 2.7 \cdot 10^{+76}\right):\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+60} \lor \neg \left(y \leq 2.9 \cdot 10^{+76}\right):\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9e+60) (not (<= y 2.9e+76)))
   (- x (/ 0.3333333333333333 (/ z y)))
   (+ x (/ (* t (/ 0.3333333333333333 z)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e+60) || !(y <= 2.9e+76)) {
		tmp = x - (0.3333333333333333 / (z / y));
	} else {
		tmp = x + ((t * (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 <= (-9d+60)) .or. (.not. (y <= 2.9d+76))) then
        tmp = x - (0.3333333333333333d0 / (z / y))
    else
        tmp = x + ((t * (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 <= -9e+60) || !(y <= 2.9e+76)) {
		tmp = x - (0.3333333333333333 / (z / y));
	} else {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9e+60) or not (y <= 2.9e+76):
		tmp = x - (0.3333333333333333 / (z / y))
	else:
		tmp = x + ((t * (0.3333333333333333 / z)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9e+60) || !(y <= 2.9e+76))
		tmp = Float64(x - Float64(0.3333333333333333 / Float64(z / y)));
	else
		tmp = Float64(x + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9e+60) || ~((y <= 2.9e+76)))
		tmp = x - (0.3333333333333333 / (z / y));
	else
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9e+60], N[Not[LessEqual[y, 2.9e+76]], $MachinePrecision]], N[(x - N[(0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.00000000000000026e60 or 2.9000000000000002e76 < y

   1. Initial program 96.8%

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

   3. Taylor expanded in t around 0 96.8%

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

      1. clear-num 96.9%

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

      2. un-div-inv 97.0%

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

   5. Applied egg-rr 97.0%

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

   if -9.00000000000000026e60 < y < 2.9000000000000002e76

   1. Initial program 89.9%

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

      1. sub-neg 89.9%

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

      2. associate-+l+ 89.9%

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

      3. +-commutative 89.9%

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

      4. remove-double-neg 89.9%

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

      5. distribute-frac-neg 89.9%

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

      6. distribute-neg-in 89.9%

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

      7. remove-double-neg 89.9%

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

      8. sub-neg 89.9%

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

      9. neg-mul-1 89.9%

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

      10. times-frac 89.9%

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

      11. distribute-frac-neg 89.9%

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

      12. neg-mul-1 89.9%

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

      13. *-commutative 89.9%

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

      14. associate-/l* 89.9%

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

      15. *-commutative 89.9%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around 0 86.7%

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

      1. +-commutative 86.7%

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

   7. Simplified 86.7%

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

      1. metadata-eval 86.7%

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

      2. associate-/r* 86.9%

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

      3. times-frac 86.9%

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

      4. *-commutative 86.9%

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

      5. associate-*l/ 86.9%

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

      6. associate-*r/ 95.4%

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

      7. inv-pow 95.4%

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

      8. unpow-prod-down 95.3%

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

      9. inv-pow 95.3%

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

      10. metadata-eval 95.3%

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

      11. *-commutative 95.3%

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

      12. un-div-inv 95.4%

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

   9. Applied egg-rr 95.4%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+60} \lor \neg \left(y \leq 2.9 \cdot 10^{+76}\right):\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+60} \lor \neg \left(y \leq 2.7 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9e+60) (not (<= y 2.7e+76)))
   (/ -0.3333333333333333 (/ z y))
   (* 0.3333333333333333 (/ t (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e+60) || !(y <= 2.7e+76)) {
		tmp = -0.3333333333333333 / (z / y);
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9d+60)) .or. (.not. (y <= 2.7d+76))) then
        tmp = (-0.3333333333333333d0) / (z / y)
    else
        tmp = 0.3333333333333333d0 * (t / (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9e+60) || !(y <= 2.7e+76)) {
		tmp = -0.3333333333333333 / (z / y);
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9e+60) or not (y <= 2.7e+76):
		tmp = -0.3333333333333333 / (z / y)
	else:
		tmp = 0.3333333333333333 * (t / (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9e+60) || !(y <= 2.7e+76))
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	else
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9e+60) || ~((y <= 2.7e+76)))
		tmp = -0.3333333333333333 / (z / y);
	else
		tmp = 0.3333333333333333 * (t / (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9e+60], N[Not[LessEqual[y, 2.7e+76]], $MachinePrecision]], N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.00000000000000026e60 or 2.6999999999999999e76 < y

   1. Initial program 96.8%

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

      1. +-commutative 96.8%

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

      2. associate-+r- 96.8%

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

      3. sub-neg 96.8%

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

      4. associate-*l* 96.8%

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

      5. *-commutative 96.8%

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

      6. distribute-frac-neg2 96.8%

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

      7. distribute-rgt-neg-in 96.8%

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

      8. metadata-eval 96.8%

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

   3. Simplified 96.8%

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

      1. *-un-lft-identity 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*l* 96.8%

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

      4. *-commutative 96.8%

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

      5. times-frac 90.0%

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

      6. *-un-lft-identity 90.0%

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

      7. *-commutative 90.0%

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

      8. times-frac 90.0%

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

      9. metadata-eval 90.0%

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

   6. Applied egg-rr 90.0%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 90.0%

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

      2. *-lft-identity 90.0%

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

   8. Simplified 90.0%

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

   9. Taylor expanded in y around inf 70.7%

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

       1. clear-num 70.7%

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

       2. div-inv 70.8%

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

   11. Applied egg-rr 70.8%

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

   if -9.00000000000000026e60 < y < 2.6999999999999999e76

   1. Initial program 89.9%

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

      1. +-commutative 89.9%

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

      2. associate-+r- 89.9%

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

      3. sub-neg 89.9%

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

      4. associate-*l* 89.9%

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

      5. *-commutative 89.9%

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

      6. distribute-frac-neg2 89.9%

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

      7. distribute-rgt-neg-in 89.9%

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

      8. metadata-eval 89.9%

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

   3. Simplified 89.9%

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

      1. *-un-lft-identity 89.9%

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

      2. *-commutative 89.9%

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

      3. associate-*l* 89.9%

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

      4. *-commutative 89.9%

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

      5. times-frac 98.4%

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

      6. *-un-lft-identity 98.4%

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

      7. *-commutative 98.4%

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

      8. times-frac 98.3%

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

      9. metadata-eval 98.3%

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

   6. Applied egg-rr 98.3%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 98.4%

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

      2. *-lft-identity 98.4%

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

   8. Simplified 98.4%

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

      1. clear-num 98.4%

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

      2. inv-pow 98.4%

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

      3. *-commutative 98.4%

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

      4. *-un-lft-identity 98.4%

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

      5. times-frac 98.4%

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

      6. metadata-eval 98.4%

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

   10. Applied egg-rr 98.4%

       \[\leadsto \left(\frac{0.3333333333333333 \cdot \frac{t}{z}}{y} + x\right) + \color{blue}{{\left(-3 \cdot \frac{z}{y}\right)}^{-1}} \]
   11. Step-by-step derivation

       1. unpow-1 98.4%

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

   12. Simplified 98.4%

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

   13. Taylor expanded in t around inf 60.6%

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

4. Final simplification 64.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+60} \lor \neg \left(y \leq 2.7 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+62} \lor \neg \left(y \leq 2.7 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.8e+62) (not (<= y 2.7e+76)))
   (/ -0.3333333333333333 (/ z y))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+62) || !(y <= 2.7e+76)) {
		tmp = -0.3333333333333333 / (z / y);
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.8d+62)) .or. (.not. (y <= 2.7d+76))) then
        tmp = (-0.3333333333333333d0) / (z / y)
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.8e+62) || !(y <= 2.7e+76)) {
		tmp = -0.3333333333333333 / (z / y);
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.8e+62) or not (y <= 2.7e+76):
		tmp = -0.3333333333333333 / (z / y)
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.8e+62) || !(y <= 2.7e+76))
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.8e+62) || ~((y <= 2.7e+76)))
		tmp = -0.3333333333333333 / (z / y);
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.8e+62], N[Not[LessEqual[y, 2.7e+76]], $MachinePrecision]], N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.79999999999999984e62 or 2.6999999999999999e76 < y

   1. Initial program 96.8%

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

      1. +-commutative 96.8%

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

      2. associate-+r- 96.8%

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

      3. sub-neg 96.8%

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

      4. associate-*l* 96.8%

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

      5. *-commutative 96.8%

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

      6. distribute-frac-neg2 96.8%

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

      7. distribute-rgt-neg-in 96.8%

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

      8. metadata-eval 96.8%

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

   3. Simplified 96.8%

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

      1. *-un-lft-identity 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*l* 96.8%

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

      4. *-commutative 96.8%

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

      5. times-frac 90.0%

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

      6. *-un-lft-identity 90.0%

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

      7. *-commutative 90.0%

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

      8. times-frac 90.0%

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

      9. metadata-eval 90.0%

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

   6. Applied egg-rr 90.0%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 90.0%

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

      2. *-lft-identity 90.0%

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

   8. Simplified 90.0%

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

   9. Taylor expanded in y around inf 70.7%

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

       1. clear-num 70.7%

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

       2. div-inv 70.8%

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

   11. Applied egg-rr 70.8%

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

   if -3.79999999999999984e62 < y < 2.6999999999999999e76

   1. Initial program 89.9%

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

      1. +-commutative 89.9%

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

      2. associate-+r- 89.9%

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

      3. sub-neg 89.9%

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

      4. associate-*l* 89.9%

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

      5. *-commutative 89.9%

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

      6. distribute-frac-neg2 89.9%

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

      7. distribute-rgt-neg-in 89.9%

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

      8. metadata-eval 89.9%

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

   3. Simplified 89.9%

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

      1. *-un-lft-identity 89.9%

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

      2. *-commutative 89.9%

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

      3. associate-*l* 89.9%

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

      4. *-commutative 89.9%

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

      5. times-frac 98.4%

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

      6. *-un-lft-identity 98.4%

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

      7. *-commutative 98.4%

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

      8. times-frac 98.3%

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

      9. metadata-eval 98.3%

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

   6. Applied egg-rr 98.3%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 98.4%

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

      2. *-lft-identity 98.4%

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

   8. Simplified 98.4%

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

      1. clear-num 98.4%

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

      2. inv-pow 98.4%

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

      3. *-commutative 98.4%

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

      4. *-un-lft-identity 98.4%

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

      5. times-frac 98.4%

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

      6. metadata-eval 98.4%

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

   10. Applied egg-rr 98.4%

       \[\leadsto \left(\frac{0.3333333333333333 \cdot \frac{t}{z}}{y} + x\right) + \color{blue}{{\left(-3 \cdot \frac{z}{y}\right)}^{-1}} \]
   11. Step-by-step derivation

       1. unpow-1 98.4%

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

   12. Simplified 98.4%

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

   13. Taylor expanded in t around inf 60.6%

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

       1. associate-*r/ 60.6%

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

       2. times-frac 66.5%

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

       3. *-commutative 66.5%

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

   15. Simplified 66.5%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+62} \lor \neg \left(y \leq 2.7 \cdot 10^{+76}\right):\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-111} \lor \neg \left(y \leq 6.4 \cdot 10^{+69}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e-111) (not (<= y 6.4e+69)))
   (- x (* 0.3333333333333333 (/ y z)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e-111) || !(y <= 6.4e+69)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.15d-111)) .or. (.not. (y <= 6.4d+69))) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e-111) || !(y <= 6.4e+69)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.15e-111) or not (y <= 6.4e+69):
		tmp = x - (0.3333333333333333 * (y / z))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.15e-111) || !(y <= 6.4e+69))
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.15e-111) || ~((y <= 6.4e+69)))
		tmp = x - (0.3333333333333333 * (y / z));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.15e-111], N[Not[LessEqual[y, 6.4e+69]], $MachinePrecision]], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e-111 or 6.3999999999999997e69 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in t around 0 87.1%

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

   if -1.15e-111 < y < 6.3999999999999997e69

   1. Initial program 89.5%

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

      1. +-commutative 89.5%

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

      2. associate-+r- 89.5%

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

      3. sub-neg 89.5%

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

      4. associate-*l* 89.5%

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

      5. *-commutative 89.5%

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

      6. distribute-frac-neg2 89.5%

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

      7. distribute-rgt-neg-in 89.5%

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

      8. metadata-eval 89.5%

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

   3. Simplified 89.5%

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

      1. *-un-lft-identity 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*l* 89.5%

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

      4. *-commutative 89.5%

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

      5. times-frac 98.9%

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

      6. *-un-lft-identity 98.9%

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

      7. *-commutative 98.9%

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

      8. times-frac 98.8%

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

      9. metadata-eval 98.8%

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

   6. Applied egg-rr 98.8%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 98.8%

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

      2. *-lft-identity 98.8%

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

   8. Simplified 98.8%

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

      1. clear-num 98.8%

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

      2. inv-pow 98.8%

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

      3. *-commutative 98.8%

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

      4. *-un-lft-identity 98.8%

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

      5. times-frac 98.8%

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

      6. metadata-eval 98.8%

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

   10. Applied egg-rr 98.8%

       \[\leadsto \left(\frac{0.3333333333333333 \cdot \frac{t}{z}}{y} + x\right) + \color{blue}{{\left(-3 \cdot \frac{z}{y}\right)}^{-1}} \]
   11. Step-by-step derivation

       1. unpow-1 98.8%

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

   12. Simplified 98.8%

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

   13. Taylor expanded in t around inf 66.4%

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

       1. associate-*r/ 66.4%

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

       2. times-frac 73.2%

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

       3. *-commutative 73.2%

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

   15. Simplified 73.2%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-111} \lor \neg \left(y \leq 6.4 \cdot 10^{+69}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-111} \lor \neg \left(y \leq 6.4 \cdot 10^{+69}\right):\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.05e-111) (not (<= y 6.4e+69)))
   (- x (/ 0.3333333333333333 (/ z y)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-111) || !(y <= 6.4e+69)) {
		tmp = x - (0.3333333333333333 / (z / y));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.05d-111)) .or. (.not. (y <= 6.4d+69))) then
        tmp = x - (0.3333333333333333d0 / (z / y))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-111) || !(y <= 6.4e+69)) {
		tmp = x - (0.3333333333333333 / (z / y));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.05e-111) or not (y <= 6.4e+69):
		tmp = x - (0.3333333333333333 / (z / y))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.05e-111) || !(y <= 6.4e+69))
		tmp = Float64(x - Float64(0.3333333333333333 / Float64(z / y)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.05e-111) || ~((y <= 6.4e+69)))
		tmp = x - (0.3333333333333333 / (z / y));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.05e-111], N[Not[LessEqual[y, 6.4e+69]], $MachinePrecision]], N[(x - N[(0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.0499999999999999e-111 or 6.3999999999999997e69 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in t around 0 87.1%

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

      1. clear-num 87.2%

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

      2. un-div-inv 87.3%

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

   5. Applied egg-rr 87.3%

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

   if -1.0499999999999999e-111 < y < 6.3999999999999997e69

   1. Initial program 89.5%

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

      1. +-commutative 89.5%

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

      2. associate-+r- 89.5%

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

      3. sub-neg 89.5%

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

      4. associate-*l* 89.5%

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

      5. *-commutative 89.5%

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

      6. distribute-frac-neg2 89.5%

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

      7. distribute-rgt-neg-in 89.5%

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

      8. metadata-eval 89.5%

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

   3. Simplified 89.5%

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

      1. *-un-lft-identity 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*l* 89.5%

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

      4. *-commutative 89.5%

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

      5. times-frac 98.9%

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

      6. *-un-lft-identity 98.9%

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

      7. *-commutative 98.9%

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

      8. times-frac 98.8%

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

      9. metadata-eval 98.8%

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

   6. Applied egg-rr 98.8%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 98.8%

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

      2. *-lft-identity 98.8%

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

   8. Simplified 98.8%

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

      1. clear-num 98.8%

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

      2. inv-pow 98.8%

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

      3. *-commutative 98.8%

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

      4. *-un-lft-identity 98.8%

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

      5. times-frac 98.8%

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

      6. metadata-eval 98.8%

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

   10. Applied egg-rr 98.8%

       \[\leadsto \left(\frac{0.3333333333333333 \cdot \frac{t}{z}}{y} + x\right) + \color{blue}{{\left(-3 \cdot \frac{z}{y}\right)}^{-1}} \]
   11. Step-by-step derivation

       1. unpow-1 98.8%

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

   12. Simplified 98.8%

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

   13. Taylor expanded in t around inf 66.4%

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

       1. associate-*r/ 66.4%

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

       2. times-frac 73.2%

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

       3. *-commutative 73.2%

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

   15. Simplified 73.2%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-111} \lor \neg \left(y \leq 6.4 \cdot 10^{+69}\right):\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 75.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-111} \lor \neg \left(y \leq 6.4 \cdot 10^{+69}\right):\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e-111) (not (<= y 6.4e+69)))
   (- x (/ 0.3333333333333333 (/ z y)))
   (/ (* t (/ 0.3333333333333333 z)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e-111) || !(y <= 6.4e+69)) {
		tmp = x - (0.3333333333333333 / (z / y));
	} else {
		tmp = (t * (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 <= (-1.15d-111)) .or. (.not. (y <= 6.4d+69))) then
        tmp = x - (0.3333333333333333d0 / (z / y))
    else
        tmp = (t * (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 <= -1.15e-111) || !(y <= 6.4e+69)) {
		tmp = x - (0.3333333333333333 / (z / y));
	} else {
		tmp = (t * (0.3333333333333333 / z)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.15e-111) or not (y <= 6.4e+69):
		tmp = x - (0.3333333333333333 / (z / y))
	else:
		tmp = (t * (0.3333333333333333 / z)) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.15e-111) || !(y <= 6.4e+69))
		tmp = Float64(x - Float64(0.3333333333333333 / Float64(z / y)));
	else
		tmp = Float64(Float64(t * Float64(0.3333333333333333 / z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.15e-111) || ~((y <= 6.4e+69)))
		tmp = x - (0.3333333333333333 / (z / y));
	else
		tmp = (t * (0.3333333333333333 / z)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.15e-111], N[Not[LessEqual[y, 6.4e+69]], $MachinePrecision]], N[(x - N[(0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.15e-111 or 6.3999999999999997e69 < y

   1. Initial program 95.4%

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

   3. Taylor expanded in t around 0 87.1%

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

      1. clear-num 87.2%

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

      2. un-div-inv 87.3%

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

   5. Applied egg-rr 87.3%

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

   if -1.15e-111 < y < 6.3999999999999997e69

   1. Initial program 89.5%

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

      1. +-commutative 89.5%

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

      2. associate-+r- 89.5%

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

      3. sub-neg 89.5%

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

      4. associate-*l* 89.5%

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

      5. *-commutative 89.5%

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

      6. distribute-frac-neg2 89.5%

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

      7. distribute-rgt-neg-in 89.5%

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

      8. metadata-eval 89.5%

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

   3. Simplified 89.5%

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

      1. *-un-lft-identity 89.5%

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

      2. *-commutative 89.5%

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

      3. associate-*l* 89.5%

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

      4. *-commutative 89.5%

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

      5. times-frac 98.9%

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

      6. *-un-lft-identity 98.9%

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

      7. *-commutative 98.9%

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

      8. times-frac 98.8%

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

      9. metadata-eval 98.8%

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

   6. Applied egg-rr 98.8%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 98.8%

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

      2. *-lft-identity 98.8%

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

   8. Simplified 98.8%

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

      1. clear-num 98.8%

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

      2. inv-pow 98.8%

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

      3. *-commutative 98.8%

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

      4. *-un-lft-identity 98.8%

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

      5. times-frac 98.8%

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

      6. metadata-eval 98.8%

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

   10. Applied egg-rr 98.8%

       \[\leadsto \left(\frac{0.3333333333333333 \cdot \frac{t}{z}}{y} + x\right) + \color{blue}{{\left(-3 \cdot \frac{z}{y}\right)}^{-1}} \]
   11. Step-by-step derivation

       1. unpow-1 98.8%

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

   12. Simplified 98.8%

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

   13. Taylor expanded in t around inf 66.4%

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

       1. metadata-eval 88.0%

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

       2. associate-/r* 87.4%

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

       3. times-frac 87.5%

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

       4. *-commutative 87.5%

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

       5. associate-*l/ 87.4%

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

       6. associate-*r/ 97.5%

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

       7. inv-pow 97.5%

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

       8. unpow-prod-down 97.4%

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

       9. inv-pow 97.4%

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

       10. metadata-eval 97.4%

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

       11. *-commutative 97.4%

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

       12. un-div-inv 97.4%

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

   15. Applied egg-rr 73.3%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-111} \lor \neg \left(y \leq 6.4 \cdot 10^{+69}\right):\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -4.3e+76) x (if (<= z 4.5e-26) (* (/ y z) -0.3333333333333333) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -4.3e+76) {
		tmp = x;
	} else if (z <= 4.5e-26) {
		tmp = (y / z) * -0.3333333333333333;
	} 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 (z <= (-4.3d+76)) then
        tmp = x
    else if (z <= 4.5d-26) then
        tmp = (y / z) * (-0.3333333333333333d0)
    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 (z <= -4.3e+76) {
		tmp = x;
	} else if (z <= 4.5e-26) {
		tmp = (y / z) * -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -4.3e+76:
		tmp = x
	elif z <= 4.5e-26:
		tmp = (y / z) * -0.3333333333333333
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -4.3e+76)
		tmp = x;
	elseif (z <= 4.5e-26)
		tmp = Float64(Float64(y / z) * -0.3333333333333333);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -4.3e+76)
		tmp = x;
	elseif (z <= 4.5e-26)
		tmp = (y / z) * -0.3333333333333333;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -4.3e+76], x, If[LessEqual[z, 4.5e-26], N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -4.29999999999999978e76 or 4.4999999999999999e-26 < z

   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. sub-neg 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-frac-neg 99.8%

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

      6. distribute-neg-in 99.8%

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

      7. remove-double-neg 99.8%

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

      8. sub-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. times-frac 87.0%

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

      11. distribute-frac-neg 87.0%

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

      12. neg-mul-1 87.0%

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

      13. *-commutative 87.0%

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

      14. associate-/l* 87.0%

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

      15. *-commutative 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in x around inf 55.0%

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

   if -4.29999999999999978e76 < z < 4.4999999999999999e-26

   1. Initial program 87.7%

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

      1. +-commutative 87.7%

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

      2. associate-+r- 87.7%

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

      3. sub-neg 87.7%

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

      4. associate-*l* 87.7%

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

      5. *-commutative 87.7%

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

      6. distribute-frac-neg2 87.7%

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

      7. distribute-rgt-neg-in 87.7%

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

      8. metadata-eval 87.7%

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

   3. Simplified 87.7%

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

      1. *-un-lft-identity 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-*l* 87.7%

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

      4. *-commutative 87.7%

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

      5. times-frac 92.0%

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

      6. *-un-lft-identity 92.0%

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

      7. *-commutative 92.0%

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

      8. times-frac 91.9%

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

      9. metadata-eval 91.9%

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

   6. Applied egg-rr 91.9%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 91.9%

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

      2. *-lft-identity 91.9%

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

   8. Simplified 91.9%

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

   9. Taylor expanded in y around inf 39.8%

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

4. Final simplification 45.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+76}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-26}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.65e+72) x (if (<= z 2.1e-26) (/ -0.3333333333333333 (/ z y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.65e+72) {
		tmp = x;
	} else if (z <= 2.1e-26) {
		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 (z <= (-1.65d+72)) then
        tmp = x
    else if (z <= 2.1d-26) 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 (z <= -1.65e+72) {
		tmp = x;
	} else if (z <= 2.1e-26) {
		tmp = -0.3333333333333333 / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.65e+72:
		tmp = x
	elif z <= 2.1e-26:
		tmp = -0.3333333333333333 / (z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.65e+72)
		tmp = x;
	elseif (z <= 2.1e-26)
		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 (z <= -1.65e+72)
		tmp = x;
	elseif (z <= 2.1e-26)
		tmp = -0.3333333333333333 / (z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.65e+72], x, If[LessEqual[z, 2.1e-26], N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e72 or 2.10000000000000008e-26 < z

   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. sub-neg 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-frac-neg 99.8%

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

      6. distribute-neg-in 99.8%

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

      7. remove-double-neg 99.8%

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

      8. sub-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. times-frac 87.0%

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

      11. distribute-frac-neg 87.0%

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

      12. neg-mul-1 87.0%

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

      13. *-commutative 87.0%

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

      14. associate-/l* 87.0%

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

      15. *-commutative 87.0%

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

   3. Simplified 87.0%

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

   5. Taylor expanded in x around inf 55.0%

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

   if -1.65e72 < z < 2.10000000000000008e-26

   1. Initial program 87.7%

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

      1. +-commutative 87.7%

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

      2. associate-+r- 87.7%

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

      3. sub-neg 87.7%

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

      4. associate-*l* 87.7%

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

      5. *-commutative 87.7%

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

      6. distribute-frac-neg2 87.7%

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

      7. distribute-rgt-neg-in 87.7%

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

      8. metadata-eval 87.7%

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

   3. Simplified 87.7%

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

      1. *-un-lft-identity 87.7%

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

      2. *-commutative 87.7%

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

      3. associate-*l* 87.7%

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

      4. *-commutative 87.7%

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

      5. times-frac 92.0%

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

      6. *-un-lft-identity 92.0%

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

      7. *-commutative 92.0%

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

      8. times-frac 91.9%

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

      9. metadata-eval 91.9%

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

   6. Applied egg-rr 91.9%

      \[\leadsto \left(\color{blue}{\frac{1}{y} \cdot \left(0.3333333333333333 \cdot \frac{t}{z}\right)} + x\right) + \frac{y}{z \cdot -3} \]
   7. Step-by-step derivation

      1. associate-*l/ 91.9%

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

      2. *-lft-identity 91.9%

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

   8. Simplified 91.9%

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

   9. Taylor expanded in y around inf 39.8%

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

       1. clear-num 39.8%

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

       2. div-inv 39.9%

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

   11. Applied egg-rr 39.9%

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

4. Final simplification 46.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{+72}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-26}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.1% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 92.6%

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

   1. sub-neg 92.6%

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

   2. associate-+l+ 92.6%

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

   3. +-commutative 92.6%

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

   4. remove-double-neg 92.6%

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

   5. distribute-frac-neg 92.6%

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

   6. distribute-neg-in 92.6%

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

   7. remove-double-neg 92.6%

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

   8. sub-neg 92.6%

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

   9. neg-mul-1 92.6%

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

   10. times-frac 92.6%

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

   11. distribute-frac-neg 92.6%

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

   12. neg-mul-1 92.6%

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

   13. *-commutative 92.6%

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

   14. associate-/l* 92.6%

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

   15. *-commutative 92.6%

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

3. Simplified 94.6%

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

5. Taylor expanded in x around inf 28.4%

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

6. Final simplification 28.4%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024039 
(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))))