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

Percentage Accurate: 95.7% → 97.4%

Time: 10.5s

Alternatives: 14

Speedup: 0.7×

• 28.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.7% 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: 97.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{y} - y\\ \mathbf{if}\;y \leq -4.5 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{t\_1 \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t\_1}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ t y) y)))
   (if (<= y -4.5e-16)
     (+ x (/ (* t_1 0.3333333333333333) z))
     (if (<= y 1.85e-72)
       (+ x (/ (/ (* t 0.3333333333333333) z) y))
       (+ x (/ t_1 (* z 3.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t / y) - y;
	double tmp;
	if (y <= -4.5e-16) {
		tmp = x + ((t_1 * 0.3333333333333333) / z);
	} else if (y <= 1.85e-72) {
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	} else {
		tmp = x + (t_1 / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t / y) - y
    if (y <= (-4.5d-16)) then
        tmp = x + ((t_1 * 0.3333333333333333d0) / z)
    else if (y <= 1.85d-72) then
        tmp = x + (((t * 0.3333333333333333d0) / z) / y)
    else
        tmp = x + (t_1 / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t / y) - y;
	double tmp;
	if (y <= -4.5e-16) {
		tmp = x + ((t_1 * 0.3333333333333333) / z);
	} else if (y <= 1.85e-72) {
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	} else {
		tmp = x + (t_1 / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t / y) - y
	tmp = 0
	if y <= -4.5e-16:
		tmp = x + ((t_1 * 0.3333333333333333) / z)
	elif y <= 1.85e-72:
		tmp = x + (((t * 0.3333333333333333) / z) / y)
	else:
		tmp = x + (t_1 / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t / y) - y)
	tmp = 0.0
	if (y <= -4.5e-16)
		tmp = Float64(x + Float64(Float64(t_1 * 0.3333333333333333) / z));
	elseif (y <= 1.85e-72)
		tmp = Float64(x + Float64(Float64(Float64(t * 0.3333333333333333) / z) / y));
	else
		tmp = Float64(x + Float64(t_1 / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t / y) - y;
	tmp = 0.0;
	if (y <= -4.5e-16)
		tmp = x + ((t_1 * 0.3333333333333333) / z);
	elseif (y <= 1.85e-72)
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	else
		tmp = x + (t_1 / (z * 3.0));
	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, -4.5e-16], N[(x + N[(N[(t$95$1 * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.85e-72], N[(x + N[(N[(N[(t * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.5000000000000002e-16

   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. +-commutative 99.7%

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

      4. associate--l+ 99.7%

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

      5. sub-neg 99.7%

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

      6. remove-double-neg 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. neg-mul-1 99.7%

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

      12. times-frac 99.7%

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

      13. distribute-frac-neg 99.7%

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

      14. neg-mul-1 99.7%

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

      15. *-commutative 99.7%

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

      16. associate-/l* 99.6%

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

      17. *-commutative 99.6%

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

   3. Simplified 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 99.7%

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

      1. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   if -4.5000000000000002e-16 < y < 1.8499999999999999e-72

   1. Initial program 88.7%

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

      1. +-commutative 88.7%

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

      2. associate-+r- 88.7%

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

      3. +-commutative 88.7%

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

      4. associate--l+ 88.7%

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

      5. sub-neg 88.7%

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

      6. remove-double-neg 88.7%

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

      7. distribute-frac-neg 88.7%

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

      8. distribute-neg-in 88.7%

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

      9. remove-double-neg 88.7%

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

      10. sub-neg 88.7%

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

      11. neg-mul-1 88.7%

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

      12. times-frac 89.7%

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

      13. distribute-frac-neg 89.7%

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

      14. neg-mul-1 89.7%

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

      15. *-commutative 89.7%

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

      16. associate-/l* 89.7%

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

      17. *-commutative 89.7%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in t around inf 88.5%

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

      1. associate-/r* 89.7%

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

      2. associate-*r/ 89.7%

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

      3. *-commutative 89.7%

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

      4. associate-*r/ 89.7%

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

   7. Simplified 89.7%

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

      1. associate-*l/ 99.8%

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

      2. associate-*r/ 99.8%

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

   9. Applied egg-rr 99.8%

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

   if 1.8499999999999999e-72 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+r- 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. remove-double-neg 99.9%

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

      7. distribute-frac-neg 99.9%

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

      8. distribute-neg-in 99.9%

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

      9. remove-double-neg 99.9%

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

      10. sub-neg 99.9%

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

      11. neg-mul-1 99.9%

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

      12. times-frac 99.9%

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

      13. distribute-frac-neg 99.9%

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

      14. neg-mul-1 99.9%

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

      15. *-commutative 99.9%

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

      16. associate-/l* 99.8%

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

      17. *-commutative 99.8%

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

   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. metadata-eval 99.8%

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

      2. associate-/r* 99.8%

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

      3. *-commutative 99.8%

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

      4. associate-*l/ 99.9%

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

      5. *-un-lft-identity 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-16}:\\ \;\;\;\;x + \frac{\left(\frac{t}{y} - y\right) \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 1.85 \cdot 10^{-72}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-16} \lor \neg \left(y \leq 4.1 \cdot 10^{-90}\right):\\ \;\;\;\;x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.5e-16) (not (<= y 4.1e-90)))
   (+ 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 <= -4.5e-16) || !(y <= 4.1e-90)) {
		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 <= (-4.5d-16)) .or. (.not. (y <= 4.1d-90))) 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 <= -4.5e-16) || !(y <= 4.1e-90)) {
		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 <= -4.5e-16) or not (y <= 4.1e-90):
		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 <= -4.5e-16) || !(y <= 4.1e-90))
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(x + Float64(Float64(Float64(t * 0.3333333333333333) / z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.5e-16) || ~((y <= 4.1e-90)))
		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, -4.5e-16], N[Not[LessEqual[y, 4.1e-90]], $MachinePrecision]], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5000000000000002e-16 or 4.10000000000000035e-90 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. remove-double-neg 99.8%

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

      7. distribute-frac-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. sub-neg 99.8%

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

      11. neg-mul-1 99.8%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.8%

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

      17. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   if -4.5000000000000002e-16 < y < 4.10000000000000035e-90

   1. Initial program 88.2%

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

      1. +-commutative 88.2%

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

      2. associate-+r- 88.2%

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

      3. +-commutative 88.2%

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

      4. associate--l+ 88.2%

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

      5. sub-neg 88.2%

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

      6. remove-double-neg 88.2%

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

      7. distribute-frac-neg 88.2%

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

      8. distribute-neg-in 88.2%

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

      9. remove-double-neg 88.2%

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

      10. sub-neg 88.2%

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

      11. neg-mul-1 88.2%

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

      12. times-frac 89.3%

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

      13. distribute-frac-neg 89.3%

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

      14. neg-mul-1 89.3%

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

      15. *-commutative 89.3%

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

      16. associate-/l* 89.3%

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

      17. *-commutative 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in t around inf 88.1%

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

      1. associate-/r* 89.3%

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

      2. associate-*r/ 89.3%

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

      3. *-commutative 89.3%

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

      4. associate-*r/ 89.3%

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

   7. Simplified 89.3%

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

      1. associate-*l/ 99.8%

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

      2. associate-*r/ 99.8%

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

   9. Applied egg-rr 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-16} \lor \neg \left(y \leq 4.1 \cdot 10^{-90}\right):\\ \;\;\;\;x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{y} - y\\ \mathbf{if}\;y \leq -2.3 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{t\_1 \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1 \cdot \frac{0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ t y) y)))
   (if (<= y -2.3e-14)
     (+ x (/ (* t_1 0.3333333333333333) z))
     (if (<= y 3.4e-90)
       (+ x (/ (/ (* t 0.3333333333333333) z) y))
       (+ x (* t_1 (/ 0.3333333333333333 z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (t / y) - y;
	double tmp;
	if (y <= -2.3e-14) {
		tmp = x + ((t_1 * 0.3333333333333333) / z);
	} else if (y <= 3.4e-90) {
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	} else {
		tmp = x + (t_1 * (0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (t / y) - y
    if (y <= (-2.3d-14)) then
        tmp = x + ((t_1 * 0.3333333333333333d0) / z)
    else if (y <= 3.4d-90) then
        tmp = x + (((t * 0.3333333333333333d0) / z) / y)
    else
        tmp = x + (t_1 * (0.3333333333333333d0 / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (t / y) - y;
	double tmp;
	if (y <= -2.3e-14) {
		tmp = x + ((t_1 * 0.3333333333333333) / z);
	} else if (y <= 3.4e-90) {
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	} else {
		tmp = x + (t_1 * (0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (t / y) - y
	tmp = 0
	if y <= -2.3e-14:
		tmp = x + ((t_1 * 0.3333333333333333) / z)
	elif y <= 3.4e-90:
		tmp = x + (((t * 0.3333333333333333) / z) / y)
	else:
		tmp = x + (t_1 * (0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(t / y) - y)
	tmp = 0.0
	if (y <= -2.3e-14)
		tmp = Float64(x + Float64(Float64(t_1 * 0.3333333333333333) / z));
	elseif (y <= 3.4e-90)
		tmp = Float64(x + Float64(Float64(Float64(t * 0.3333333333333333) / z) / y));
	else
		tmp = Float64(x + Float64(t_1 * Float64(0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (t / y) - y;
	tmp = 0.0;
	if (y <= -2.3e-14)
		tmp = x + ((t_1 * 0.3333333333333333) / z);
	elseif (y <= 3.4e-90)
		tmp = x + (((t * 0.3333333333333333) / z) / y);
	else
		tmp = x + (t_1 * (0.3333333333333333 / 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, -2.3e-14], N[(x + N[(N[(t$95$1 * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e-90], N[(x + N[(N[(N[(t * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.29999999999999998e-14

   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. +-commutative 99.7%

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

      4. associate--l+ 99.7%

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

      5. sub-neg 99.7%

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

      6. remove-double-neg 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. neg-mul-1 99.7%

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

      12. times-frac 99.7%

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

      13. distribute-frac-neg 99.7%

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

      14. neg-mul-1 99.7%

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

      15. *-commutative 99.7%

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

      16. associate-/l* 99.6%

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

      17. *-commutative 99.6%

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

   3. Simplified 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 99.7%

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

      1. associate-*r/ 99.8%

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

   7. Simplified 99.8%

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

   if -2.29999999999999998e-14 < y < 3.39999999999999994e-90

   1. Initial program 88.2%

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

      1. +-commutative 88.2%

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

      2. associate-+r- 88.2%

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

      3. +-commutative 88.2%

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

      4. associate--l+ 88.2%

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

      5. sub-neg 88.2%

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

      6. remove-double-neg 88.2%

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

      7. distribute-frac-neg 88.2%

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

      8. distribute-neg-in 88.2%

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

      9. remove-double-neg 88.2%

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

      10. sub-neg 88.2%

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

      11. neg-mul-1 88.2%

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

      12. times-frac 89.3%

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

      13. distribute-frac-neg 89.3%

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

      14. neg-mul-1 89.3%

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

      15. *-commutative 89.3%

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

      16. associate-/l* 89.3%

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

      17. *-commutative 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in t around inf 88.1%

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

      1. associate-/r* 89.3%

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

      2. associate-*r/ 89.3%

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

      3. *-commutative 89.3%

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

      4. associate-*r/ 89.3%

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

   7. Simplified 89.3%

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

      1. associate-*l/ 99.8%

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

      2. associate-*r/ 99.8%

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

   9. Applied egg-rr 99.8%

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

   if 3.39999999999999994e-90 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+r- 99.9%

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

      3. +-commutative 99.9%

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

      4. associate--l+ 99.9%

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

      5. sub-neg 99.9%

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

      6. remove-double-neg 99.9%

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

      7. distribute-frac-neg 99.9%

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

      8. distribute-neg-in 99.9%

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

      9. remove-double-neg 99.9%

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

      10. sub-neg 99.9%

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

      11. neg-mul-1 99.9%

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

      12. times-frac 99.9%

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

      13. distribute-frac-neg 99.9%

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

      14. neg-mul-1 99.9%

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

      15. *-commutative 99.9%

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

      16. associate-/l* 99.8%

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

      17. *-commutative 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3 \cdot 10^{-14}:\\ \;\;\;\;x + \frac{\left(\frac{t}{y} - y\right) \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-90}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 7.7 \cdot 10^{+121}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right) + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 7.7e+121)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ (+ x (/ t (* z (* y 3.0)))) (/ y (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 7.7e+121) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x + (t / (z * (y * 3.0)))) + (y / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 7.7d+121) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = (x + (t / (z * (y * 3.0d0)))) + (y / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 7.7e+121) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x + (t / (z * (y * 3.0)))) + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 7.7e+121:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = (x + (t / (z * (y * 3.0)))) + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 7.7e+121)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(x + Float64(t / Float64(z * Float64(y * 3.0)))) + Float64(y / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 7.7e+121)
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = (x + (t / (z * (y * 3.0)))) + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 7.7e+121], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 7.70000000000000028e121

   1. Initial program 94.3%

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

      1. +-commutative 94.3%

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

      2. associate-+r- 94.3%

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

      3. +-commutative 94.3%

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

      4. associate--l+ 94.3%

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

      5. sub-neg 94.3%

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

      6. remove-double-neg 94.3%

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

      7. distribute-frac-neg 94.3%

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

      8. distribute-neg-in 94.3%

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

      9. remove-double-neg 94.3%

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

      10. sub-neg 94.3%

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

      11. neg-mul-1 94.3%

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

      12. times-frac 98.0%

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

      13. distribute-frac-neg 98.0%

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

      14. neg-mul-1 98.0%

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

      15. *-commutative 98.0%

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

      16. associate-/l* 98.0%

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

      17. *-commutative 98.0%

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

   3. Simplified 98.0%

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

      1. metadata-eval 98.0%

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

      2. associate-/r* 98.0%

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

      3. *-commutative 98.0%

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

      4. associate-*l/ 98.1%

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

      5. *-un-lft-identity 98.1%

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

   6. Applied egg-rr 98.1%

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

   if 7.70000000000000028e121 < t

   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. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. sub-neg 99.8%

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

      4. associate-*l* 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 7.7 \cdot 10^{+121}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right) + \frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{+138}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3} + \left(x + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 6.5e+138)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ (/ y (* z -3.0)) (+ x (* t (/ (/ 0.3333333333333333 z) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 6.5e+138) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (y / (z * -3.0)) + (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 (t <= 6.5d+138) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = (y / (z * (-3.0d0))) + (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 (t <= 6.5e+138) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (y / (z * -3.0)) + (x + (t * ((0.3333333333333333 / z) / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 6.5e+138:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = (y / (z * -3.0)) + (x + (t * ((0.3333333333333333 / z) / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 6.5e+138)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(y / Float64(z * -3.0)) + Float64(x + Float64(t * Float64(Float64(0.3333333333333333 / z) / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 6.5e+138)
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = (y / (z * -3.0)) + (x + (t * ((0.3333333333333333 / z) / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 6.5e+138], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 6.50000000000000054e138

   1. Initial program 94.4%

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

      1. +-commutative 94.4%

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

      2. associate-+r- 94.4%

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

      3. +-commutative 94.4%

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

      4. associate--l+ 94.4%

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

      5. sub-neg 94.4%

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

      6. remove-double-neg 94.4%

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

      7. distribute-frac-neg 94.4%

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

      8. distribute-neg-in 94.4%

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

      9. remove-double-neg 94.4%

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

      10. sub-neg 94.4%

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

      11. neg-mul-1 94.4%

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

      12. times-frac 98.1%

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

      13. distribute-frac-neg 98.1%

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

      14. neg-mul-1 98.1%

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

      15. *-commutative 98.1%

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

      16. associate-/l* 98.1%

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

      17. *-commutative 98.1%

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

   3. Simplified 98.1%

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

      1. metadata-eval 98.1%

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

      2. associate-/r* 98.1%

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

      3. *-commutative 98.1%

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

      4. associate-*l/ 98.1%

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

      5. *-un-lft-identity 98.1%

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

   6. Applied egg-rr 98.1%

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

   if 6.50000000000000054e138 < t

   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. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. sub-neg 99.8%

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

      4. associate-*l* 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-*l* 99.7%

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

      5. associate-/r* 99.7%

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

      6. *-commutative 99.7%

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

      7. associate-/r* 99.8%

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

      8. metadata-eval 99.8%

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

   6. Applied egg-rr 99.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 6.5 \cdot 10^{+138}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3} + \left(x + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-5}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.02e+29)
   (+ x (/ (/ y -3.0) z))
   (if (<= y 1.25e-5)
     (+ x (* 0.3333333333333333 (/ t (* y z))))
     (+ x (/ y (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e+29) {
		tmp = x + ((y / -3.0) / z);
	} else if (y <= 1.25e-5) {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.02d+29)) then
        tmp = x + ((y / (-3.0d0)) / z)
    else if (y <= 1.25d-5) then
        tmp = x + (0.3333333333333333d0 * (t / (y * z)))
    else
        tmp = x + (y / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.02e+29) {
		tmp = x + ((y / -3.0) / z);
	} else if (y <= 1.25e-5) {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.02e+29:
		tmp = x + ((y / -3.0) / z)
	elif y <= 1.25e-5:
		tmp = x + (0.3333333333333333 * (t / (y * z)))
	else:
		tmp = x + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.02e+29)
		tmp = Float64(x + Float64(Float64(y / -3.0) / z));
	elseif (y <= 1.25e-5)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(y * z))));
	else
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.02e+29)
		tmp = x + ((y / -3.0) / z);
	elseif (y <= 1.25e-5)
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	else
		tmp = x + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.02e+29], N[(x + N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.25e-5], N[(x + N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0200000000000001e29

   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. +-commutative 99.7%

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

      4. associate--l+ 99.7%

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

      5. sub-neg 99.7%

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

      6. remove-double-neg 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. neg-mul-1 99.7%

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

      12. times-frac 99.7%

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

      13. distribute-frac-neg 99.7%

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

      14. neg-mul-1 99.7%

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

      15. *-commutative 99.7%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   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 t around 0 98.0%

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

      1. metadata-eval 98.0%

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

      2. times-frac 98.0%

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

      3. *-un-lft-identity 98.0%

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

      4. associate-/r* 98.1%

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

   7. Applied egg-rr 98.1%

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

   if -1.0200000000000001e29 < y < 1.25000000000000006e-5

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-+r- 90.9%

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

      3. +-commutative 90.9%

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

      4. associate--l+ 90.9%

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

      5. sub-neg 90.9%

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

      6. remove-double-neg 90.9%

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

      7. distribute-frac-neg 90.9%

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

      8. distribute-neg-in 90.9%

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

      9. remove-double-neg 90.9%

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

      10. sub-neg 90.9%

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

      11. neg-mul-1 90.9%

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

      12. times-frac 91.7%

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

      13. distribute-frac-neg 91.7%

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

      14. neg-mul-1 91.7%

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

      15. *-commutative 91.7%

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

      16. associate-/l* 91.7%

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

      17. *-commutative 91.7%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in t around inf 87.0%

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

   if 1.25000000000000006e-5 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+r- 99.9%

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

      3. sub-neg 99.9%

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

      4. associate-*l* 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 94.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.02 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-5}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 88.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;y \leq 0.00026:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -7e+29)
   (+ x (/ (/ y -3.0) z))
   (if (<= y 0.00026)
     (+ x (* (/ t y) (/ 0.3333333333333333 z)))
     (+ x (/ y (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e+29) {
		tmp = x + ((y / -3.0) / z);
	} else if (y <= 0.00026) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-7d+29)) then
        tmp = x + ((y / (-3.0d0)) / z)
    else if (y <= 0.00026d0) then
        tmp = x + ((t / y) * (0.3333333333333333d0 / z))
    else
        tmp = x + (y / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -7e+29) {
		tmp = x + ((y / -3.0) / z);
	} else if (y <= 0.00026) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -7e+29:
		tmp = x + ((y / -3.0) / z)
	elif y <= 0.00026:
		tmp = x + ((t / y) * (0.3333333333333333 / z))
	else:
		tmp = x + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -7e+29)
		tmp = Float64(x + Float64(Float64(y / -3.0) / z));
	elseif (y <= 0.00026)
		tmp = Float64(x + Float64(Float64(t / y) * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -7e+29)
		tmp = x + ((y / -3.0) / z);
	elseif (y <= 0.00026)
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	else
		tmp = x + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -7e+29], N[(x + N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.00026], N[(x + N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.99999999999999958e29

   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. +-commutative 99.7%

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

      4. associate--l+ 99.7%

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

      5. sub-neg 99.7%

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

      6. remove-double-neg 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. neg-mul-1 99.7%

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

      12. times-frac 99.7%

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

      13. distribute-frac-neg 99.7%

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

      14. neg-mul-1 99.7%

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

      15. *-commutative 99.7%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   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 t around 0 98.0%

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

      1. metadata-eval 98.0%

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

      2. times-frac 98.0%

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

      3. *-un-lft-identity 98.0%

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

      4. associate-/r* 98.1%

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

   7. Applied egg-rr 98.1%

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

   if -6.99999999999999958e29 < y < 2.59999999999999977e-4

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-+r- 90.9%

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

      3. +-commutative 90.9%

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

      4. associate--l+ 90.9%

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

      5. sub-neg 90.9%

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

      6. remove-double-neg 90.9%

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

      7. distribute-frac-neg 90.9%

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

      8. distribute-neg-in 90.9%

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

      9. remove-double-neg 90.9%

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

      10. sub-neg 90.9%

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

      11. neg-mul-1 90.9%

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

      12. times-frac 91.7%

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

      13. distribute-frac-neg 91.7%

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

      14. neg-mul-1 91.7%

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

      15. *-commutative 91.7%

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

      16. associate-/l* 91.7%

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

      17. *-commutative 91.7%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in t around inf 87.0%

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

      1. associate-/r* 88.0%

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

      2. associate-*r/ 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*r/ 88.0%

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

   7. Simplified 88.0%

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

   if 2.59999999999999977e-4 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+r- 99.9%

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

      3. sub-neg 99.9%

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

      4. associate-*l* 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 94.4%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;y \leq 0.00026:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.2e+21)
   (+ x (/ (/ y -3.0) z))
   (if (<= y 2.5e-5)
     (+ x (* (/ t z) (/ 0.3333333333333333 y)))
     (+ x (/ y (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e+21) {
		tmp = x + ((y / -3.0) / z);
	} else if (y <= 2.5e-5) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.2d+21)) then
        tmp = x + ((y / (-3.0d0)) / z)
    else if (y <= 2.5d-5) then
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    else
        tmp = x + (y / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2e+21) {
		tmp = x + ((y / -3.0) / z);
	} else if (y <= 2.5e-5) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.2e+21:
		tmp = x + ((y / -3.0) / z)
	elif y <= 2.5e-5:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	else:
		tmp = x + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.2e+21)
		tmp = Float64(x + Float64(Float64(y / -3.0) / z));
	elseif (y <= 2.5e-5)
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	else
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.2e+21)
		tmp = x + ((y / -3.0) / z);
	elseif (y <= 2.5e-5)
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	else
		tmp = x + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.2e+21], N[(x + N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-5], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2e21

   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. +-commutative 99.7%

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

      4. associate--l+ 99.7%

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

      5. sub-neg 99.7%

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

      6. remove-double-neg 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. neg-mul-1 99.7%

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

      12. times-frac 99.7%

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

      13. distribute-frac-neg 99.7%

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

      14. neg-mul-1 99.7%

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

      15. *-commutative 99.7%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   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 t around 0 98.0%

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

      1. metadata-eval 98.0%

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

      2. times-frac 98.0%

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

      3. *-un-lft-identity 98.0%

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

      4. associate-/r* 98.1%

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

   7. Applied egg-rr 98.1%

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

   if -3.2e21 < y < 2.50000000000000012e-5

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-+r- 90.9%

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

      3. +-commutative 90.9%

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

      4. associate--l+ 90.9%

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

      5. sub-neg 90.9%

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

      6. remove-double-neg 90.9%

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

      7. distribute-frac-neg 90.9%

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

      8. distribute-neg-in 90.9%

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

      9. remove-double-neg 90.9%

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

      10. sub-neg 90.9%

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

      11. neg-mul-1 90.9%

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

      12. times-frac 91.7%

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

      13. distribute-frac-neg 91.7%

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

      14. neg-mul-1 91.7%

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

      15. *-commutative 91.7%

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

      16. associate-/l* 91.7%

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

      17. *-commutative 91.7%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in t around inf 87.0%

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

      1. associate-/r* 88.0%

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

      2. associate-*r/ 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*r/ 88.0%

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

   7. Simplified 88.0%

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

      1. associate-*l/ 96.0%

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

      2. associate-*r/ 96.1%

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

   9. Applied egg-rr 96.1%

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

   10. Taylor expanded in t around 0 87.0%

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

       1. associate-*r/ 87.1%

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

       2. times-frac 96.0%

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

       3. *-commutative 96.0%

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

   12. Simplified 96.0%

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

   if 2.50000000000000012e-5 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+r- 99.9%

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

      3. sub-neg 99.9%

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

      4. associate-*l* 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 94.4%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+21}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-5}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;y \leq 0.0001:\\ \;\;\;\;x + \frac{\frac{0.3333333333333333}{\frac{z}{t}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.2e+23)
   (+ x (/ (/ y -3.0) z))
   (if (<= y 0.0001)
     (+ x (/ (/ 0.3333333333333333 (/ z t)) y))
     (+ x (/ y (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e+23) {
		tmp = x + ((y / -3.0) / z);
	} else if (y <= 0.0001) {
		tmp = x + ((0.3333333333333333 / (z / t)) / y);
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.2d+23)) then
        tmp = x + ((y / (-3.0d0)) / z)
    else if (y <= 0.0001d0) then
        tmp = x + ((0.3333333333333333d0 / (z / t)) / y)
    else
        tmp = x + (y / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.2e+23) {
		tmp = x + ((y / -3.0) / z);
	} else if (y <= 0.0001) {
		tmp = x + ((0.3333333333333333 / (z / t)) / y);
	} else {
		tmp = x + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.2e+23:
		tmp = x + ((y / -3.0) / z)
	elif y <= 0.0001:
		tmp = x + ((0.3333333333333333 / (z / t)) / y)
	else:
		tmp = x + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.2e+23)
		tmp = Float64(x + Float64(Float64(y / -3.0) / z));
	elseif (y <= 0.0001)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / Float64(z / t)) / y));
	else
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.2e+23)
		tmp = x + ((y / -3.0) / z);
	elseif (y <= 0.0001)
		tmp = x + ((0.3333333333333333 / (z / t)) / y);
	else
		tmp = x + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.2e+23], N[(x + N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.0001], N[(x + N[(N[(0.3333333333333333 / N[(z / t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.19999999999999983e23

   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. +-commutative 99.7%

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

      4. associate--l+ 99.7%

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

      5. sub-neg 99.7%

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

      6. remove-double-neg 99.7%

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

      7. distribute-frac-neg 99.7%

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

      8. distribute-neg-in 99.7%

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

      9. remove-double-neg 99.7%

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

      10. sub-neg 99.7%

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

      11. neg-mul-1 99.7%

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

      12. times-frac 99.7%

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

      13. distribute-frac-neg 99.7%

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

      14. neg-mul-1 99.7%

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

      15. *-commutative 99.7%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   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 t around 0 98.0%

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

      1. metadata-eval 98.0%

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

      2. times-frac 98.0%

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

      3. *-un-lft-identity 98.0%

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

      4. associate-/r* 98.1%

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

   7. Applied egg-rr 98.1%

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

   if -5.19999999999999983e23 < y < 1.00000000000000005e-4

   1. Initial program 90.9%

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

      1. +-commutative 90.9%

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

      2. associate-+r- 90.9%

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

      3. +-commutative 90.9%

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

      4. associate--l+ 90.9%

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

      5. sub-neg 90.9%

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

      6. remove-double-neg 90.9%

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

      7. distribute-frac-neg 90.9%

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

      8. distribute-neg-in 90.9%

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

      9. remove-double-neg 90.9%

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

      10. sub-neg 90.9%

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

      11. neg-mul-1 90.9%

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

      12. times-frac 91.7%

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

      13. distribute-frac-neg 91.7%

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

      14. neg-mul-1 91.7%

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

      15. *-commutative 91.7%

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

      16. associate-/l* 91.7%

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

      17. *-commutative 91.7%

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

   3. Simplified 91.8%

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

   5. Taylor expanded in t around inf 87.0%

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

      1. associate-/r* 88.0%

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

      2. associate-*r/ 88.0%

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

      3. *-commutative 88.0%

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

      4. associate-*r/ 88.0%

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

   7. Simplified 88.0%

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

      1. associate-*l/ 96.0%

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

      2. associate-*r/ 96.1%

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

   9. Applied egg-rr 96.1%

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

       1. clear-num 96.0%

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

       2. inv-pow 96.0%

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

       3. div-inv 95.9%

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

       4. clear-num 96.0%

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

       5. *-un-lft-identity 96.0%

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

       6. *-commutative 96.0%

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

       7. times-frac 96.0%

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

       8. metadata-eval 96.0%

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

   11. Applied egg-rr 96.0%

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

       1. unpow-1 96.0%

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

       2. *-commutative 96.0%

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

       3. associate-/r* 96.0%

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

       4. associate-/r* 96.1%

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

       5. metadata-eval 96.1%

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

   13. Simplified 96.1%

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

   if 1.00000000000000005e-4 < y

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-+r- 99.9%

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

      3. sub-neg 99.9%

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

      4. associate-*l* 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 94.4%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+23}:\\ \;\;\;\;x + \frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;y \leq 0.0001:\\ \;\;\;\;x + \frac{\frac{0.3333333333333333}{\frac{z}{t}}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.0% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

   1. +-commutative 95.3%

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

   2. associate-+r- 95.3%

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

   3. +-commutative 95.3%

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

   4. associate--l+ 95.3%

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

   5. sub-neg 95.3%

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

   6. remove-double-neg 95.3%

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

   7. distribute-frac-neg 95.3%

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

   8. distribute-neg-in 95.3%

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

   9. remove-double-neg 95.3%

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

   10. sub-neg 95.3%

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

   11. neg-mul-1 95.3%

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

   12. times-frac 95.7%

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

   13. distribute-frac-neg 95.7%

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

   14. neg-mul-1 95.7%

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

   15. *-commutative 95.7%

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

   16. associate-/l* 95.7%

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

   17. *-commutative 95.7%

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

3. Simplified 95.7%

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

5. Taylor expanded in t around 0 65.2%

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

6. Final simplification 65.2%

   \[\leadsto x + -0.3333333333333333 \cdot \frac{y}{z} \]
7. Add Preprocessing

Alternative 11: 64.0% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

   1. +-commutative 95.3%

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

   2. associate-+r- 95.3%

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

   3. +-commutative 95.3%

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

   4. associate--l+ 95.3%

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

   5. sub-neg 95.3%

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

   6. remove-double-neg 95.3%

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

   7. distribute-frac-neg 95.3%

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

   8. distribute-neg-in 95.3%

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

   9. remove-double-neg 95.3%

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

   10. sub-neg 95.3%

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

   11. neg-mul-1 95.3%

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

   12. times-frac 95.7%

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

   13. distribute-frac-neg 95.7%

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

   14. neg-mul-1 95.7%

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

   15. *-commutative 95.7%

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

   16. associate-/l* 95.7%

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

   17. *-commutative 95.7%

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

3. Simplified 95.7%

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

5. Taylor expanded in t around 0 65.2%

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

   1. *-commutative 65.2%

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

   2. associate-*l/ 65.2%

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

   3. associate-/l* 65.2%

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

7. Simplified 65.2%

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

8. Final simplification 65.2%

   \[\leadsto x + y \cdot \frac{-0.3333333333333333}{z} \]
9. Add Preprocessing

Alternative 12: 64.0% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

   1. +-commutative 95.3%

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

   2. associate-+r- 95.3%

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

   3. sub-neg 95.3%

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

   4. associate-*l* 95.3%

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

   5. *-commutative 95.3%

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

   6. distribute-frac-neg2 95.3%

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

   7. distribute-rgt-neg-in 95.3%

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

   8. metadata-eval 95.3%

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

3. Simplified 95.3%

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

5. Taylor expanded in t around 0 65.3%

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

6. Final simplification 65.3%

   \[\leadsto x + \frac{y}{z \cdot -3} \]
7. Add Preprocessing

Alternative 13: 64.1% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

   1. +-commutative 95.3%

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

   2. associate-+r- 95.3%

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

   3. +-commutative 95.3%

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

   4. associate--l+ 95.3%

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

   5. sub-neg 95.3%

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

   6. remove-double-neg 95.3%

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

   7. distribute-frac-neg 95.3%

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

   8. distribute-neg-in 95.3%

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

   9. remove-double-neg 95.3%

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

   10. sub-neg 95.3%

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

   11. neg-mul-1 95.3%

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

   12. times-frac 95.7%

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

   13. distribute-frac-neg 95.7%

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

   14. neg-mul-1 95.7%

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

   15. *-commutative 95.7%

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

   16. associate-/l* 95.7%

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

   17. *-commutative 95.7%

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

3. Simplified 95.7%

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

5. Taylor expanded in t around 0 65.2%

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

   1. metadata-eval 65.2%

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

   2. times-frac 65.3%

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

   3. *-un-lft-identity 65.3%

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

   4. associate-/r* 65.3%

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

7. Applied egg-rr 65.3%

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

8. Final simplification 65.3%

   \[\leadsto x + \frac{\frac{y}{-3}}{z} \]
9. Add Preprocessing

Alternative 14: 29.9% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 95.3%

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

   1. +-commutative 95.3%

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

   2. associate-+r- 95.3%

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

   3. +-commutative 95.3%

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

   4. associate--l+ 95.3%

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

   5. sub-neg 95.3%

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

   6. remove-double-neg 95.3%

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

   7. distribute-frac-neg 95.3%

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

   8. distribute-neg-in 95.3%

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

   9. remove-double-neg 95.3%

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

   10. sub-neg 95.3%

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

   11. neg-mul-1 95.3%

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

   12. times-frac 95.7%

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

   13. distribute-frac-neg 95.7%

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

   14. neg-mul-1 95.7%

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

   15. *-commutative 95.7%

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

   16. associate-/l* 95.7%

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

   17. *-commutative 95.7%

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

3. Simplified 95.7%

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

5. Taylor expanded in t around 0 65.2%

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

6. Taylor expanded in x around inf 30.0%

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

7. Final simplification 30.0%

   \[\leadsto x \]
8. Add Preprocessing

Developer target: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024067 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :alt
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))