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

Percentage Accurate: 95.5% → 97.7%

Time: 13.7s

Alternatives: 18

Speedup: 0.7×

• 27.4% 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: 95.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.7% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 2e-5)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ (+ x (/ t (* z (* 3.0 y)))) (/ (/ y -3.0) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 2e-5) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x + (t / (z * (3.0 * y)))) + ((y / -3.0) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= 2d-5) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = (x + (t / (z * (3.0d0 * y)))) + ((y / (-3.0d0)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 2e-5) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x + (t / (z * (3.0 * y)))) + ((y / -3.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 2e-5:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = (x + (t / (z * (3.0 * y)))) + ((y / -3.0) / z)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-5], 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[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < 2.00000000000000016e-5

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-+r- 93.0%

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

      3. +-commutative 93.0%

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

      4. associate--l+ 93.0%

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

      5. sub-neg 93.0%

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

      6. remove-double-neg 93.0%

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

      7. distribute-frac-neg 93.0%

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

      8. distribute-neg-in 93.0%

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

      9. remove-double-neg 93.0%

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

      10. sub-neg 93.0%

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

      11. neg-mul-1 93.0%

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

      12. times-frac 98.3%

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

      13. distribute-frac-neg 98.3%

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

      14. neg-mul-1 98.3%

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

      15. *-commutative 98.3%

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

      16. associate-/l* 98.2%

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

      17. *-commutative 98.2%

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

   3. Simplified 99.2%

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

      1. *-commutative 99.2%

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

      2. clear-num 99.2%

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

      3. div-inv 99.2%

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

      4. metadata-eval 99.2%

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

      5. un-div-inv 99.3%

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

   6. Applied egg-rr 99.3%

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

   if 2.00000000000000016e-5 < (*.f64 z 3)

   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. Step-by-step derivation

      1. *-un-lft-identity 99.9%

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

      2. times-frac 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. associate-*l/ 100.0%

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

      2. *-lft-identity 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 99.5%

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

Alternative 2: 81.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{-40}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{elif}\;z \cdot 3 \leq 10^{+172}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= (* z 3.0) -4e-40)
     t_1
     (if (<= (* z 3.0) 2e-5)
       (* 0.3333333333333333 (/ (- (/ t y) y) z))
       (if (<= (* z 3.0) 1e+172)
         t_1
         (+ x (* 0.3333333333333333 (/ t (* z y)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((z * 3.0) <= -4e-40) {
		tmp = t_1;
	} else if ((z * 3.0) <= 2e-5) {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	} else if ((z * 3.0) <= 1e+172) {
		tmp = t_1;
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (z * 3.0d0))
    if ((z * 3.0d0) <= (-4d-40)) then
        tmp = t_1
    else if ((z * 3.0d0) <= 2d-5) then
        tmp = 0.3333333333333333d0 * (((t / y) - y) / z)
    else if ((z * 3.0d0) <= 1d+172) then
        tmp = t_1
    else
        tmp = x + (0.3333333333333333d0 * (t / (z * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if ((z * 3.0) <= -4e-40) {
		tmp = t_1;
	} else if ((z * 3.0) <= 2e-5) {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	} else if ((z * 3.0) <= 1e+172) {
		tmp = t_1;
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if (z * 3.0) <= -4e-40:
		tmp = t_1
	elif (z * 3.0) <= 2e-5:
		tmp = 0.3333333333333333 * (((t / y) - y) / z)
	elif (z * 3.0) <= 1e+172:
		tmp = t_1
	else:
		tmp = x + (0.3333333333333333 * (t / (z * y)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (Float64(z * 3.0) <= -4e-40)
		tmp = t_1;
	elseif (Float64(z * 3.0) <= 2e-5)
		tmp = Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z));
	elseif (Float64(z * 3.0) <= 1e+172)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if ((z * 3.0) <= -4e-40)
		tmp = t_1;
	elseif ((z * 3.0) <= 2e-5)
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	elseif ((z * 3.0) <= 1e+172)
		tmp = t_1;
	else
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * 3.0), $MachinePrecision], -4e-40], t$95$1, If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-5], N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 1e+172], t$95$1, N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -3.9999999999999997e-40 or 2.00000000000000016e-5 < (*.f64 z 3) < 1.0000000000000001e172

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 84.8%

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

      1. associate-*r/ 84.8%

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

      2. *-commutative 84.8%

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

   5. Applied egg-rr 84.8%

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

      1. associate-/l* 84.8%

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

      2. metadata-eval 84.8%

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

      3. associate-/r* 84.9%

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

      4. *-commutative 84.9%

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

      5. div-inv 84.9%

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

      6. add-cube-cbrt 84.3%

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

      7. associate-/l* 84.3%

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

      8. pow2 84.3%

         \[\leadsto x - \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{z \cdot 3} \]

   7. Applied egg-rr 84.3%

      \[\leadsto x - \color{blue}{{\left(\sqrt[3]{y}\right)}^{2} \cdot \frac{\sqrt[3]{y}}{z \cdot 3}} \]
   8. Step-by-step derivation

      1. associate-*r/ 84.3%

         \[\leadsto x - \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{z \cdot 3}} \]

      2. unpow2 84.3%

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

      3. rem-3cbrt-lft 84.9%

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

   9. Simplified 84.9%

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

   if -3.9999999999999997e-40 < (*.f64 z 3) < 2.00000000000000016e-5

   1. Initial program 89.9%

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

      1. +-commutative 89.9%

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

      2. associate-+r- 89.9%

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

      3. sub-neg 89.9%

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

      4. associate-*l* 89.9%

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

      5. *-commutative 89.9%

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

      6. distribute-frac-neg2 89.9%

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

      7. distribute-rgt-neg-in 89.9%

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

      8. metadata-eval 89.9%

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

   3. Simplified 89.9%

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

      1. clear-num 89.9%

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

      2. inv-pow 89.9%

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

   6. Applied egg-rr 89.9%

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

      1. unpow-1 89.9%

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

      2. associate-/l* 98.3%

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

   8. Simplified 98.3%

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

   9. Taylor expanded in z around 0 88.9%

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

       1. associate-*r/ 88.9%

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

       2. +-commutative 88.9%

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

       3. metadata-eval 88.9%

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

       4. cancel-sign-sub-inv 88.9%

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

       5. *-commutative 88.9%

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

       6. div-sub 87.3%

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

       7. *-commutative 87.3%

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

       8. associate-*r/ 87.4%

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

       9. associate-/l/ 80.4%

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

       10. *-commutative 80.4%

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

       11. associate-*r/ 80.4%

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

       12. distribute-lft-out-- 80.4%

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

       13. associate-/r* 87.4%

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

       14. div-sub 88.9%

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

   11. Simplified 88.9%

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

   if 1.0000000000000001e172 < (*.f64 z 3)

   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 75.4%

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

      13. distribute-frac-neg 75.4%

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

      14. neg-mul-1 75.4%

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

      15. *-commutative 75.4%

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

      16. associate-/l* 75.4%

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

      17. *-commutative 75.4%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in t around inf 95.5%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{-40}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{-5}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{elif}\;z \cdot 3 \leq 10^{+172}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -2.8 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.44 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-130}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* z -3.0))))
   (if (<= y -2.8e-6)
     t_1
     (if (<= y -1.44e-142)
       x
       (if (<= y 3.8e-130)
         (* 0.3333333333333333 (/ t (* z y)))
         (if (<= y 1.65e+127) x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (y <= -2.8e-6) {
		tmp = t_1;
	} else if (y <= -1.44e-142) {
		tmp = x;
	} else if (y <= 3.8e-130) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 1.65e+127) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (z * (-3.0d0))
    if (y <= (-2.8d-6)) then
        tmp = t_1
    else if (y <= (-1.44d-142)) then
        tmp = x
    else if (y <= 3.8d-130) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else if (y <= 1.65d+127) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (y <= -2.8e-6) {
		tmp = t_1;
	} else if (y <= -1.44e-142) {
		tmp = x;
	} else if (y <= 3.8e-130) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 1.65e+127) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (z * -3.0)
	tmp = 0
	if y <= -2.8e-6:
		tmp = t_1
	elif y <= -1.44e-142:
		tmp = x
	elif y <= 3.8e-130:
		tmp = 0.3333333333333333 * (t / (z * y))
	elif y <= 1.65e+127:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(z * -3.0))
	tmp = 0.0
	if (y <= -2.8e-6)
		tmp = t_1;
	elseif (y <= -1.44e-142)
		tmp = x;
	elseif (y <= 3.8e-130)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	elseif (y <= 1.65e+127)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (z * -3.0);
	tmp = 0.0;
	if (y <= -2.8e-6)
		tmp = t_1;
	elseif (y <= -1.44e-142)
		tmp = x;
	elseif (y <= 3.8e-130)
		tmp = 0.3333333333333333 * (t / (z * y));
	elseif (y <= 1.65e+127)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.8e-6], t$95$1, If[LessEqual[y, -1.44e-142], x, If[LessEqual[y, 3.8e-130], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+127], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.79999999999999987e-6 or 1.64999999999999988e127 < y

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-+r- 99.0%

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

      3. +-commutative 99.0%

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

      4. associate--l+ 99.0%

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

      5. sub-neg 99.0%

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

      6. remove-double-neg 99.0%

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

      7. distribute-frac-neg 99.0%

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

      8. distribute-neg-in 99.0%

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

      9. remove-double-neg 99.0%

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

      10. sub-neg 99.0%

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

      11. neg-mul-1 99.0%

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

      12. times-frac 99.0%

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

      13. distribute-frac-neg 99.0%

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

      14. neg-mul-1 99.0%

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

      15. *-commutative 99.0%

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

      16. associate-/l* 98.8%

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

      17. *-commutative 98.8%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 90.1%

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

   6. Taylor expanded in x around 0 70.7%

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

      1. associate-*r/ 70.7%

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

      2. metadata-eval 70.7%

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

      3. div-inv 70.9%

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

      4. associate-/l/ 70.9%

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

   8. Applied egg-rr 70.9%

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

   if -2.79999999999999987e-6 < y < -1.4399999999999999e-142 or 3.7999999999999998e-130 < y < 1.64999999999999988e127

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. associate-+r- 97.8%

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

      3. +-commutative 97.8%

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

      4. associate--l+ 97.8%

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

      5. sub-neg 97.8%

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

      6. remove-double-neg 97.8%

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

      7. distribute-frac-neg 97.8%

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

      8. distribute-neg-in 97.8%

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

      9. remove-double-neg 97.8%

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

      10. sub-neg 97.8%

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

      11. neg-mul-1 97.8%

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

      12. times-frac 94.7%

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

      13. distribute-frac-neg 94.7%

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

      14. neg-mul-1 94.7%

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

      15. *-commutative 94.7%

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

      16. associate-/l* 94.6%

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

      17. *-commutative 94.6%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf 54.5%

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

   if -1.4399999999999999e-142 < y < 3.7999999999999998e-130

   1. Initial program 81.1%

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

      1. +-commutative 81.1%

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

      2. associate-+r- 81.1%

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

      3. sub-neg 81.1%

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

      4. associate-*l* 81.2%

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

      5. *-commutative 81.2%

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

      6. distribute-frac-neg2 81.2%

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

      7. distribute-rgt-neg-in 81.2%

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

      8. metadata-eval 81.2%

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

   3. Simplified 81.2%

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

      1. clear-num 81.2%

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

      2. inv-pow 81.2%

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

   6. Applied egg-rr 81.2%

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

      1. unpow-1 81.2%

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

      2. associate-/l* 92.7%

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

   8. Simplified 92.7%

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

   9. Taylor expanded in z around 0 74.6%

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

       1. associate-*r/ 74.6%

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

       2. +-commutative 74.6%

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

       3. metadata-eval 74.6%

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

       4. cancel-sign-sub-inv 74.6%

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

       5. *-commutative 74.6%

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

       6. div-sub 74.6%

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

       7. *-commutative 74.6%

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

       8. associate-*r/ 74.6%

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

       9. associate-/l/ 64.6%

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

       10. *-commutative 64.6%

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

       11. associate-*r/ 64.6%

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

       12. distribute-lft-out-- 64.6%

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

       13. associate-/r* 74.6%

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

       14. div-sub 74.6%

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

   11. Simplified 74.6%

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

   12. Taylor expanded in t around inf 64.6%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.8 \cdot 10^{-6}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -1.44 \cdot 10^{-142}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-130}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -1.2 \cdot 10^{-5}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-131}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* z -3.0))))
   (if (<= y -1.2e-5)
     t_1
     (if (<= y -1.6e-147)
       x
       (if (<= y 1.02e-131)
         (* 0.3333333333333333 (/ (/ t z) y))
         (if (<= y 7.5e+127) x t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (y <= -1.2e-5) {
		tmp = t_1;
	} else if (y <= -1.6e-147) {
		tmp = x;
	} else if (y <= 1.02e-131) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else if (y <= 7.5e+127) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (z * (-3.0d0))
    if (y <= (-1.2d-5)) then
        tmp = t_1
    else if (y <= (-1.6d-147)) then
        tmp = x
    else if (y <= 1.02d-131) then
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    else if (y <= 7.5d+127) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (y <= -1.2e-5) {
		tmp = t_1;
	} else if (y <= -1.6e-147) {
		tmp = x;
	} else if (y <= 1.02e-131) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else if (y <= 7.5e+127) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (z * -3.0)
	tmp = 0
	if y <= -1.2e-5:
		tmp = t_1
	elif y <= -1.6e-147:
		tmp = x
	elif y <= 1.02e-131:
		tmp = 0.3333333333333333 * ((t / z) / y)
	elif y <= 7.5e+127:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(z * -3.0))
	tmp = 0.0
	if (y <= -1.2e-5)
		tmp = t_1;
	elseif (y <= -1.6e-147)
		tmp = x;
	elseif (y <= 1.02e-131)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	elseif (y <= 7.5e+127)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (z * -3.0);
	tmp = 0.0;
	if (y <= -1.2e-5)
		tmp = t_1;
	elseif (y <= -1.6e-147)
		tmp = x;
	elseif (y <= 1.02e-131)
		tmp = 0.3333333333333333 * ((t / z) / y);
	elseif (y <= 7.5e+127)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.2e-5], t$95$1, If[LessEqual[y, -1.6e-147], x, If[LessEqual[y, 1.02e-131], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+127], x, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e-5 or 7.4999999999999996e127 < y

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-+r- 99.0%

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

      3. +-commutative 99.0%

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

      4. associate--l+ 99.0%

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

      5. sub-neg 99.0%

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

      6. remove-double-neg 99.0%

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

      7. distribute-frac-neg 99.0%

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

      8. distribute-neg-in 99.0%

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

      9. remove-double-neg 99.0%

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

      10. sub-neg 99.0%

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

      11. neg-mul-1 99.0%

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

      12. times-frac 99.0%

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

      13. distribute-frac-neg 99.0%

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

      14. neg-mul-1 99.0%

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

      15. *-commutative 99.0%

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

      16. associate-/l* 98.8%

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

      17. *-commutative 98.8%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 90.1%

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

   6. Taylor expanded in x around 0 70.7%

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

      1. associate-*r/ 70.7%

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

      2. metadata-eval 70.7%

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

      3. div-inv 70.9%

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

      4. associate-/l/ 70.9%

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

   8. Applied egg-rr 70.9%

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

   if -1.2e-5 < y < -1.5999999999999999e-147 or 1.02000000000000001e-131 < y < 7.4999999999999996e127

   1. Initial program 97.8%

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

      1. +-commutative 97.8%

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

      2. associate-+r- 97.8%

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

      3. +-commutative 97.8%

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

      4. associate--l+ 97.8%

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

      5. sub-neg 97.8%

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

      6. remove-double-neg 97.8%

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

      7. distribute-frac-neg 97.8%

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

      8. distribute-neg-in 97.8%

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

      9. remove-double-neg 97.8%

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

      10. sub-neg 97.8%

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

      11. neg-mul-1 97.8%

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

      12. times-frac 94.7%

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

      13. distribute-frac-neg 94.7%

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

      14. neg-mul-1 94.7%

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

      15. *-commutative 94.7%

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

      16. associate-/l* 94.6%

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

      17. *-commutative 94.6%

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

   3. Simplified 95.7%

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

   5. Taylor expanded in x around inf 54.5%

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

   if -1.5999999999999999e-147 < y < 1.02000000000000001e-131

   1. Initial program 81.1%

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

      1. +-commutative 81.1%

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

      2. associate-+r- 81.1%

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

      3. sub-neg 81.1%

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

      4. associate-*l* 81.2%

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

      5. *-commutative 81.2%

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

      6. distribute-frac-neg2 81.2%

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

      7. distribute-rgt-neg-in 81.2%

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

      8. metadata-eval 81.2%

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

   3. Simplified 81.2%

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

      1. clear-num 81.2%

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

      2. inv-pow 81.2%

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

   6. Applied egg-rr 81.2%

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

      1. unpow-1 81.2%

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

      2. associate-/l* 92.7%

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

   8. Simplified 92.7%

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

   9. Taylor expanded in z around 0 74.6%

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

       1. associate-*r/ 74.6%

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

       2. +-commutative 74.6%

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

       3. metadata-eval 74.6%

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

       4. cancel-sign-sub-inv 74.6%

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

       5. *-commutative 74.6%

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

       6. div-sub 74.6%

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

       7. *-commutative 74.6%

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

       8. associate-*r/ 74.6%

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

       9. associate-/l/ 64.6%

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

       10. *-commutative 64.6%

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

       11. associate-*r/ 64.6%

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

       12. distribute-lft-out-- 64.6%

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

       13. associate-/r* 74.6%

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

       14. div-sub 74.6%

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

   11. Simplified 74.6%

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

   12. Taylor expanded in t around inf 64.6%

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

       1. associate-/l/ 76.2%

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

   14. Simplified 76.2%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-147}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-131}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{-40} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -4e-40) (not (<= (* z 3.0) 2e-5)))
   (- x (/ y (* z 3.0)))
   (* 0.3333333333333333 (/ (- (/ t y) y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -4e-40) || !((z * 3.0) <= 2e-5)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * 3.0d0) <= (-4d-40)) .or. (.not. ((z * 3.0d0) <= 2d-5))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = 0.3333333333333333d0 * (((t / y) - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -4e-40) || !((z * 3.0) <= 2e-5)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -4e-40) or not ((z * 3.0) <= 2e-5):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = 0.3333333333333333 * (((t / y) - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -4e-40) || !(Float64(z * 3.0) <= 2e-5))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -4e-40) || ~(((z * 3.0) <= 2e-5)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -4e-40], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-5]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -3.9999999999999997e-40 or 2.00000000000000016e-5 < (*.f64 z 3)

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 82.1%

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

      1. associate-*r/ 82.2%

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

      2. *-commutative 82.2%

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

   5. Applied egg-rr 82.2%

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

      1. associate-/l* 82.1%

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

      2. metadata-eval 82.1%

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

      3. associate-/r* 82.2%

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

      4. *-commutative 82.2%

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

      5. div-inv 82.2%

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

      6. add-cube-cbrt 81.7%

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

      7. associate-/l* 81.7%

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

      8. pow2 81.7%

         \[\leadsto x - \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{z \cdot 3} \]

   7. Applied egg-rr 81.7%

      \[\leadsto x - \color{blue}{{\left(\sqrt[3]{y}\right)}^{2} \cdot \frac{\sqrt[3]{y}}{z \cdot 3}} \]
   8. Step-by-step derivation

      1. associate-*r/ 81.7%

         \[\leadsto x - \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{z \cdot 3}} \]

      2. unpow2 81.7%

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

      3. rem-3cbrt-lft 82.2%

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

   9. Simplified 82.2%

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

   if -3.9999999999999997e-40 < (*.f64 z 3) < 2.00000000000000016e-5

   1. Initial program 89.9%

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

      1. +-commutative 89.9%

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

      2. associate-+r- 89.9%

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

      3. sub-neg 89.9%

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

      4. associate-*l* 89.9%

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

      5. *-commutative 89.9%

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

      6. distribute-frac-neg2 89.9%

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

      7. distribute-rgt-neg-in 89.9%

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

      8. metadata-eval 89.9%

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

   3. Simplified 89.9%

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

      1. clear-num 89.9%

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

      2. inv-pow 89.9%

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

   6. Applied egg-rr 89.9%

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

      1. unpow-1 89.9%

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

      2. associate-/l* 98.3%

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

   8. Simplified 98.3%

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

   9. Taylor expanded in z around 0 88.9%

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

       1. associate-*r/ 88.9%

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

       2. +-commutative 88.9%

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

       3. metadata-eval 88.9%

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

       4. cancel-sign-sub-inv 88.9%

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

       5. *-commutative 88.9%

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

       6. div-sub 87.3%

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

       7. *-commutative 87.3%

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

       8. associate-*r/ 87.4%

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

       9. associate-/l/ 80.4%

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

       10. *-commutative 80.4%

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

       11. associate-*r/ 80.4%

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

       12. distribute-lft-out-- 80.4%

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

       13. associate-/r* 87.4%

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

       14. div-sub 88.9%

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

   11. Simplified 88.9%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{-40} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{-5}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.7% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 2e-5)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ (/ y (* z -3.0)) (+ x (/ t (* 3.0 (* z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 2e-5) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (y / (z * -3.0)) + (x + (t / (3.0 * (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 ((z * 3.0d0) <= 2d-5) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = (y / (z * (-3.0d0))) + (x + (t / (3.0d0 * (z * y))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 2e-5) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (y / (z * -3.0)) + (x + (t / (3.0 * (z * y))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 2e-5:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = (y / (z * -3.0)) + (x + (t / (3.0 * (z * y))))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= 2e-5)
		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(3.0 * Float64(z * y)))));
	end
	return tmp
end

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-5], 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[(3.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < 2.00000000000000016e-5

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-+r- 93.0%

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

      3. +-commutative 93.0%

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

      4. associate--l+ 93.0%

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

      5. sub-neg 93.0%

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

      6. remove-double-neg 93.0%

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

      7. distribute-frac-neg 93.0%

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

      8. distribute-neg-in 93.0%

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

      9. remove-double-neg 93.0%

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

      10. sub-neg 93.0%

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

      11. neg-mul-1 93.0%

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

      12. times-frac 98.3%

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

      13. distribute-frac-neg 98.3%

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

      14. neg-mul-1 98.3%

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

      15. *-commutative 98.3%

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

      16. associate-/l* 98.2%

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

      17. *-commutative 98.2%

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

   3. Simplified 99.2%

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

      1. *-commutative 99.2%

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

      2. clear-num 99.2%

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

      3. div-inv 99.2%

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

      4. metadata-eval 99.2%

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

      5. un-div-inv 99.3%

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

   6. Applied egg-rr 99.3%

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

   if 2.00000000000000016e-5 < (*.f64 z 3)

   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 z around 0 99.9%

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

4. Final simplification 99.5%

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

Alternative 7: 97.7% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 2e-5)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ (+ x (/ t (* z (* 3.0 y)))) (/ y (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 2e-5) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x + (t / (z * (3.0 * y)))) + (y / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= 2d-5) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = (x + (t / (z * (3.0d0 * y)))) + (y / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 2e-5) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x + (t / (z * (3.0 * y)))) + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 2e-5:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = (x + (t / (z * (3.0 * y)))) + (y / (z * -3.0))
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-5], 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[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < 2.00000000000000016e-5

   1. Initial program 93.0%

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

      1. +-commutative 93.0%

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

      2. associate-+r- 93.0%

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

      3. +-commutative 93.0%

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

      4. associate--l+ 93.0%

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

      5. sub-neg 93.0%

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

      6. remove-double-neg 93.0%

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

      7. distribute-frac-neg 93.0%

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

      8. distribute-neg-in 93.0%

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

      9. remove-double-neg 93.0%

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

      10. sub-neg 93.0%

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

      11. neg-mul-1 93.0%

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

      12. times-frac 98.3%

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

      13. distribute-frac-neg 98.3%

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

      14. neg-mul-1 98.3%

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

      15. *-commutative 98.3%

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

      16. associate-/l* 98.2%

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

      17. *-commutative 98.2%

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

   3. Simplified 99.2%

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

      1. *-commutative 99.2%

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

      2. clear-num 99.2%

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

      3. div-inv 99.2%

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

      4. metadata-eval 99.2%

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

      5. un-div-inv 99.3%

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

   6. Applied egg-rr 99.3%

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

   if 2.00000000000000016e-5 < (*.f64 z 3)

   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
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

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

Alternative 8: 90.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.102 \lor \neg \left(y \leq 1.22 \cdot 10^{+98}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.102) (not (<= y 1.22e+98)))
   (- x (/ y (* z 3.0)))
   (+ x (/ (* t (/ 0.3333333333333333 z)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.102) || !(y <= 1.22e+98)) {
		tmp = x - (y / (z * 3.0));
	} 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 <= (-0.102d0)) .or. (.not. (y <= 1.22d+98))) then
        tmp = x - (y / (z * 3.0d0))
    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 <= -0.102) || !(y <= 1.22e+98)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.102) or not (y <= 1.22e+98):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + ((t * (0.3333333333333333 / z)) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.102) || !(y <= 1.22e+98))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.102) || ~((y <= 1.22e+98)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + ((t * (0.3333333333333333 / z)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.102], N[Not[LessEqual[y, 1.22e+98]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.101999999999999993 or 1.22e98 < y

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 90.9%

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

      1. associate-*r/ 90.9%

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

      2. *-commutative 90.9%

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

   5. Applied egg-rr 90.9%

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

      1. associate-/l* 90.9%

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

      2. metadata-eval 90.9%

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

      3. associate-/r* 90.9%

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

      4. *-commutative 90.9%

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

      5. div-inv 91.1%

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

      6. add-cube-cbrt 90.2%

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

      7. associate-/l* 90.2%

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

      8. pow2 90.2%

         \[\leadsto x - \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{z \cdot 3} \]

   7. Applied egg-rr 90.2%

      \[\leadsto x - \color{blue}{{\left(\sqrt[3]{y}\right)}^{2} \cdot \frac{\sqrt[3]{y}}{z \cdot 3}} \]
   8. Step-by-step derivation

      1. associate-*r/ 90.2%

         \[\leadsto x - \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{z \cdot 3}} \]

      2. unpow2 90.2%

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

      3. rem-3cbrt-lft 91.1%

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

   9. Simplified 91.1%

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

   if -0.101999999999999993 < y < 1.22e98

   1. Initial program 91.1%

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

      1. +-commutative 91.1%

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

      2. associate-+r- 91.1%

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

      3. +-commutative 91.1%

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

      4. associate--l+ 91.1%

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

      5. sub-neg 91.1%

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

      6. remove-double-neg 91.1%

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

      7. distribute-frac-neg 91.1%

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

      8. distribute-neg-in 91.1%

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

      9. remove-double-neg 91.1%

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

      10. sub-neg 91.1%

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

      11. neg-mul-1 91.1%

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

      12. times-frac 93.6%

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

      13. distribute-frac-neg 93.6%

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

      14. neg-mul-1 93.6%

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

      15. *-commutative 93.6%

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

      16. associate-/l* 93.5%

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

      17. *-commutative 93.5%

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

   3. Simplified 94.3%

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

      1. *-commutative 94.3%

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

      2. clear-num 94.3%

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

      3. div-inv 94.3%

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

      4. metadata-eval 94.3%

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

      5. un-div-inv 94.4%

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

   6. Applied egg-rr 94.4%

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

   7. Taylor expanded in t around inf 84.0%

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

      1. associate-*r/ 84.1%

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

      2. *-commutative 84.1%

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

      3. times-frac 85.9%

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

      4. *-commutative 85.9%

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

      5. associate-*l/ 90.0%

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

   9. Simplified 90.0%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.102 \lor \neg \left(y \leq 1.22 \cdot 10^{+98}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 95.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 10^{+172}:\\ \;\;\;\;x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 1e+172)
   (+ x (* (- (/ t y) y) (/ 0.3333333333333333 z)))
   (+ x (* 0.3333333333333333 (/ t (* z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 1e+172) {
		tmp = x + (((t / y) - y) * (0.3333333333333333 / z));
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= 1d+172) then
        tmp = x + (((t / y) - y) * (0.3333333333333333d0 / z))
    else
        tmp = x + (0.3333333333333333d0 * (t / (z * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 1e+172) {
		tmp = x + (((t / y) - y) * (0.3333333333333333 / z));
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 1e+172:
		tmp = x + (((t / y) - y) * (0.3333333333333333 / z))
	else:
		tmp = x + (0.3333333333333333 * (t / (z * y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= 1e+172)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= 1e+172)
		tmp = x + (((t / y) - y) * (0.3333333333333333 / z));
	else
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 1e+172], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < 1.0000000000000001e172

   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 98.1%

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

      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* 98.0%

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

      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 98.9%

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

   if 1.0000000000000001e172 < (*.f64 z 3)

   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 75.4%

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

      13. distribute-frac-neg 75.4%

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

      14. neg-mul-1 75.4%

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

      15. *-commutative 75.4%

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

      16. associate-/l* 75.4%

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

      17. *-commutative 75.4%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in t around inf 95.5%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 10^{+172}:\\ \;\;\;\;x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 95.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 10^{+172}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 1e+172)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ x (* 0.3333333333333333 (/ t (* z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 1e+172) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= 1d+172) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = x + (0.3333333333333333d0 * (t / (z * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 1e+172) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 1e+172:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = x + (0.3333333333333333 * (t / (z * y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= 1e+172)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= 1e+172)
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 1e+172], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < 1.0000000000000001e172

   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 98.1%

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

      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* 98.0%

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

      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 98.9%

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

      1. *-commutative 98.9%

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

      2. clear-num 98.9%

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

      3. div-inv 98.9%

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

      4. metadata-eval 98.9%

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

      5. un-div-inv 99.0%

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

   6. Applied egg-rr 99.0%

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

   if 1.0000000000000001e172 < (*.f64 z 3)

   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 75.4%

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

      13. distribute-frac-neg 75.4%

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

      14. neg-mul-1 75.4%

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

      15. *-commutative 75.4%

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

      16. associate-/l* 75.4%

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

      17. *-commutative 75.4%

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

   3. Simplified 75.3%

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

   5. Taylor expanded in t around inf 95.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 10^{+172}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.44 \cdot 10^{-142} \lor \neg \left(y \leq 6.5 \cdot 10^{-132}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.44e-142) (not (<= y 6.5e-132)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* 0.3333333333333333 (/ (/ t z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.44e-142) || !(y <= 6.5e-132)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * ((t / z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.44d-142)) .or. (.not. (y <= 6.5d-132))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.44e-142) || !(y <= 6.5e-132)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * ((t / z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.44e-142) or not (y <= 6.5e-132):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * ((t / z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.44e-142) || !(y <= 6.5e-132))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.44e-142) || ~((y <= 6.5e-132)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * ((t / z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.44e-142], N[Not[LessEqual[y, 6.5e-132]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4399999999999999e-142 or 6.49999999999999991e-132 < y

   1. Initial program 98.4%

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

      1. +-commutative 98.4%

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

      2. associate-+r- 98.4%

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

      3. +-commutative 98.4%

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

      4. associate--l+ 98.4%

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

      5. sub-neg 98.4%

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

      6. remove-double-neg 98.4%

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

      7. distribute-frac-neg 98.4%

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

      8. distribute-neg-in 98.4%

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

      9. remove-double-neg 98.4%

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

      10. sub-neg 98.4%

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

      11. neg-mul-1 98.4%

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

      12. times-frac 97.0%

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

      13. distribute-frac-neg 97.0%

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

      14. neg-mul-1 97.0%

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

      15. *-commutative 97.0%

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

      16. associate-/l* 96.9%

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

      17. *-commutative 96.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around 0 80.9%

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

      1. metadata-eval 80.9%

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

      2. distribute-lft-neg-in 80.9%

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

      3. *-commutative 80.9%

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

      4. associate-*l/ 80.9%

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

      5. associate-*r/ 80.9%

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

      6. distribute-rgt-neg-out 80.9%

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

      7. distribute-neg-frac 80.9%

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

      8. metadata-eval 80.9%

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

   7. Simplified 80.9%

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

   if -1.4399999999999999e-142 < y < 6.49999999999999991e-132

   1. Initial program 81.1%

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

      1. +-commutative 81.1%

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

      2. associate-+r- 81.1%

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

      3. sub-neg 81.1%

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

      4. associate-*l* 81.2%

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

      5. *-commutative 81.2%

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

      6. distribute-frac-neg2 81.2%

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

      7. distribute-rgt-neg-in 81.2%

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

      8. metadata-eval 81.2%

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

   3. Simplified 81.2%

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

      1. clear-num 81.2%

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

      2. inv-pow 81.2%

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

   6. Applied egg-rr 81.2%

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

      1. unpow-1 81.2%

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

      2. associate-/l* 92.7%

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

   8. Simplified 92.7%

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

   9. Taylor expanded in z around 0 74.6%

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

       1. associate-*r/ 74.6%

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

       2. +-commutative 74.6%

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

       3. metadata-eval 74.6%

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

       4. cancel-sign-sub-inv 74.6%

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

       5. *-commutative 74.6%

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

       6. div-sub 74.6%

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

       7. *-commutative 74.6%

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

       8. associate-*r/ 74.6%

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

       9. associate-/l/ 64.6%

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

       10. *-commutative 64.6%

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

       11. associate-*r/ 64.6%

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

       12. distribute-lft-out-- 64.6%

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

       13. associate-/r* 74.6%

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

       14. div-sub 74.6%

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

   11. Simplified 74.6%

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

   12. Taylor expanded in t around inf 64.6%

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

       1. associate-/l/ 76.2%

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

   14. Simplified 76.2%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.44 \cdot 10^{-142} \lor \neg \left(y \leq 6.5 \cdot 10^{-132}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 77.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-151} \lor \neg \left(y \leq 6 \cdot 10^{-133}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.75e-151) (not (<= y 6e-133)))
   (- x (/ y (* z 3.0)))
   (* 0.3333333333333333 (/ (/ t z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.75e-151) || !(y <= 6e-133)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 * ((t / z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.75d-151)) .or. (.not. (y <= 6d-133))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.75e-151) || !(y <= 6e-133)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 * ((t / z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.75e-151) or not (y <= 6e-133):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = 0.3333333333333333 * ((t / z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.75e-151) || !(y <= 6e-133))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.75e-151) || ~((y <= 6e-133)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = 0.3333333333333333 * ((t / z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.75e-151], N[Not[LessEqual[y, 6e-133]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.7499999999999999e-151 or 6.00000000000000038e-133 < y

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0 80.9%

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

      1. associate-*r/ 80.9%

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

      2. *-commutative 80.9%

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

   5. Applied egg-rr 80.9%

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

      1. associate-/l* 80.9%

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

      2. metadata-eval 80.9%

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

      3. associate-/r* 80.9%

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

      4. *-commutative 80.9%

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

      5. div-inv 81.0%

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

      6. add-cube-cbrt 80.4%

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

      7. associate-/l* 80.4%

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

      8. pow2 80.4%

         \[\leadsto x - \color{blue}{{\left(\sqrt[3]{y}\right)}^{2}} \cdot \frac{\sqrt[3]{y}}{z \cdot 3} \]

   7. Applied egg-rr 80.4%

      \[\leadsto x - \color{blue}{{\left(\sqrt[3]{y}\right)}^{2} \cdot \frac{\sqrt[3]{y}}{z \cdot 3}} \]
   8. Step-by-step derivation

      1. associate-*r/ 80.4%

         \[\leadsto x - \color{blue}{\frac{{\left(\sqrt[3]{y}\right)}^{2} \cdot \sqrt[3]{y}}{z \cdot 3}} \]

      2. unpow2 80.4%

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

      3. rem-3cbrt-lft 81.0%

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

   9. Simplified 81.0%

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

   if -2.7499999999999999e-151 < y < 6.00000000000000038e-133

   1. Initial program 81.1%

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

      1. +-commutative 81.1%

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

      2. associate-+r- 81.1%

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

      3. sub-neg 81.1%

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

      4. associate-*l* 81.2%

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

      5. *-commutative 81.2%

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

      6. distribute-frac-neg2 81.2%

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

      7. distribute-rgt-neg-in 81.2%

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

      8. metadata-eval 81.2%

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

   3. Simplified 81.2%

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

      1. clear-num 81.2%

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

      2. inv-pow 81.2%

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

   6. Applied egg-rr 81.2%

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

      1. unpow-1 81.2%

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

      2. associate-/l* 92.7%

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

   8. Simplified 92.7%

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

   9. Taylor expanded in z around 0 74.6%

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

       1. associate-*r/ 74.6%

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

       2. +-commutative 74.6%

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

       3. metadata-eval 74.6%

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

       4. cancel-sign-sub-inv 74.6%

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

       5. *-commutative 74.6%

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

       6. div-sub 74.6%

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

       7. *-commutative 74.6%

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

       8. associate-*r/ 74.6%

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

       9. associate-/l/ 64.6%

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

       10. *-commutative 64.6%

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

       11. associate-*r/ 64.6%

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

       12. distribute-lft-out-- 64.6%

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

       13. associate-/r* 74.6%

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

       14. div-sub 74.6%

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

   11. Simplified 74.6%

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

   12. Taylor expanded in t around inf 64.6%

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

       1. associate-/l/ 76.2%

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

   14. Simplified 76.2%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-151} \lor \neg \left(y \leq 6 \cdot 10^{-133}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.44 \cdot 10^{-142}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-130}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.44e-142)
   (+ x (* y (/ -0.3333333333333333 z)))
   (if (<= y 3.8e-130)
     (* 0.3333333333333333 (/ (/ t z) y))
     (- x (* 0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.44e-142) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= 3.8e-130) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.44d-142)) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else if (y <= 3.8d-130) then
        tmp = 0.3333333333333333d0 * ((t / z) / y)
    else
        tmp = x - (0.3333333333333333d0 * (y / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.44e-142) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= 3.8e-130) {
		tmp = 0.3333333333333333 * ((t / z) / y);
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.44e-142:
		tmp = x + (y * (-0.3333333333333333 / z))
	elif y <= 3.8e-130:
		tmp = 0.3333333333333333 * ((t / z) / y)
	else:
		tmp = x - (0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.44e-142)
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	elseif (y <= 3.8e-130)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / z) / y));
	else
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.44e-142)
		tmp = x + (y * (-0.3333333333333333 / z));
	elseif (y <= 3.8e-130)
		tmp = 0.3333333333333333 * ((t / z) / y);
	else
		tmp = x - (0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.44e-142], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.8e-130], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4399999999999999e-142

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. associate-+r- 98.0%

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

      3. +-commutative 98.0%

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

      4. associate--l+ 98.0%

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

      5. sub-neg 98.0%

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

      6. remove-double-neg 98.0%

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

      7. distribute-frac-neg 98.0%

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

      8. distribute-neg-in 98.0%

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

      9. remove-double-neg 98.0%

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

      10. sub-neg 98.0%

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

      11. neg-mul-1 98.0%

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

      12. times-frac 97.0%

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

      13. distribute-frac-neg 97.0%

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

      14. neg-mul-1 97.0%

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

      15. *-commutative 97.0%

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

      16. associate-/l* 96.9%

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

      17. *-commutative 96.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in t around 0 81.7%

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

      1. metadata-eval 81.7%

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

      2. distribute-lft-neg-in 81.7%

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

      3. *-commutative 81.7%

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

      4. associate-*l/ 81.8%

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

      5. associate-*r/ 81.8%

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

      6. distribute-rgt-neg-out 81.8%

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

      7. distribute-neg-frac 81.8%

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

      8. metadata-eval 81.8%

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

   7. Simplified 81.8%

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

   if -1.4399999999999999e-142 < y < 3.7999999999999998e-130

   1. Initial program 81.1%

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

      1. +-commutative 81.1%

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

      2. associate-+r- 81.1%

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

      3. sub-neg 81.1%

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

      4. associate-*l* 81.2%

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

      5. *-commutative 81.2%

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

      6. distribute-frac-neg2 81.2%

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

      7. distribute-rgt-neg-in 81.2%

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

      8. metadata-eval 81.2%

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

   3. Simplified 81.2%

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

      1. clear-num 81.2%

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

      2. inv-pow 81.2%

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

   6. Applied egg-rr 81.2%

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

      1. unpow-1 81.2%

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

      2. associate-/l* 92.7%

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

   8. Simplified 92.7%

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

   9. Taylor expanded in z around 0 74.6%

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

       1. associate-*r/ 74.6%

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

       2. +-commutative 74.6%

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

       3. metadata-eval 74.6%

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

       4. cancel-sign-sub-inv 74.6%

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

       5. *-commutative 74.6%

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

       6. div-sub 74.6%

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

       7. *-commutative 74.6%

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

       8. associate-*r/ 74.6%

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

       9. associate-/l/ 64.6%

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

       10. *-commutative 64.6%

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

       11. associate-*r/ 64.6%

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

       12. distribute-lft-out-- 64.6%

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

       13. associate-/r* 74.6%

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

       14. div-sub 74.6%

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

   11. Simplified 74.6%

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

   12. Taylor expanded in t around inf 64.6%

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

       1. associate-/l/ 76.2%

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

   14. Simplified 76.2%

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

   if 3.7999999999999998e-130 < y

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 80.0%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.44 \cdot 10^{-142}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-130}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 46.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.000155 \lor \neg \left(y \leq 9.8 \cdot 10^{+126}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -0.000155) (not (<= y 9.8e+126)))
   (* -0.3333333333333333 (/ y z))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.000155) || !(y <= 9.8e+126)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-0.000155d0)) .or. (.not. (y <= 9.8d+126))) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -0.000155) || !(y <= 9.8e+126)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -0.000155) or not (y <= 9.8e+126):
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -0.000155) || !(y <= 9.8e+126))
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -0.000155) || ~((y <= 9.8e+126)))
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -0.000155], N[Not[LessEqual[y, 9.8e+126]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e-4 or 9.80000000000000002e126 < y

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-+r- 99.0%

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

      3. sub-neg 99.0%

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

      4. associate-*l* 99.0%

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

      5. *-commutative 99.0%

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

      6. distribute-frac-neg2 99.0%

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

      7. distribute-rgt-neg-in 99.0%

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

      8. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

      1. clear-num 98.9%

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

      2. inv-pow 98.9%

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

   6. Applied egg-rr 98.9%

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

      1. unpow-1 98.9%

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

      2. associate-/l* 99.0%

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

   8. Simplified 99.0%

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

   9. Taylor expanded in y around inf 70.7%

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

   if -1.55e-4 < y < 9.80000000000000002e126

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-+r- 91.7%

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

      3. +-commutative 91.7%

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

      4. associate--l+ 91.7%

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

      5. sub-neg 91.7%

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

      6. remove-double-neg 91.7%

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

      7. distribute-frac-neg 91.7%

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

      8. distribute-neg-in 91.7%

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

      9. remove-double-neg 91.7%

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

      10. sub-neg 91.7%

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

      11. neg-mul-1 91.7%

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

      12. times-frac 94.0%

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

      13. distribute-frac-neg 94.0%

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

      14. neg-mul-1 94.0%

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

      15. *-commutative 94.0%

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

      16. associate-/l* 93.9%

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

      17. *-commutative 93.9%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around inf 42.5%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.000155 \lor \neg \left(y \leq 9.8 \cdot 10^{+126}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \lor \neg \left(y \leq 10^{+127}\right):\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.1) (not (<= y 1e+127))) (/ y (* z -3.0)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1) || !(y <= 1e+127)) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.1d0)) .or. (.not. (y <= 1d+127))) then
        tmp = y / (z * (-3.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1) || !(y <= 1e+127)) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.1) or not (y <= 1e+127):
		tmp = y / (z * -3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.1) || !(y <= 1e+127))
		tmp = Float64(y / Float64(z * -3.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.1) || ~((y <= 1e+127)))
		tmp = y / (z * -3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.1], N[Not[LessEqual[y, 1e+127]], $MachinePrecision]], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.10000000000000009 or 9.99999999999999955e126 < y

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-+r- 99.0%

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

      3. +-commutative 99.0%

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

      4. associate--l+ 99.0%

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

      5. sub-neg 99.0%

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

      6. remove-double-neg 99.0%

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

      7. distribute-frac-neg 99.0%

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

      8. distribute-neg-in 99.0%

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

      9. remove-double-neg 99.0%

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

      10. sub-neg 99.0%

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

      11. neg-mul-1 99.0%

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

      12. times-frac 99.0%

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

      13. distribute-frac-neg 99.0%

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

      14. neg-mul-1 99.0%

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

      15. *-commutative 99.0%

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

      16. associate-/l* 98.8%

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

      17. *-commutative 98.8%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 90.1%

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

   6. Taylor expanded in x around 0 70.7%

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

      1. associate-*r/ 70.7%

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

      2. metadata-eval 70.7%

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

      3. div-inv 70.9%

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

      4. associate-/l/ 70.9%

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

   8. Applied egg-rr 70.9%

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

   if -3.10000000000000009 < y < 9.99999999999999955e126

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-+r- 91.7%

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

      3. +-commutative 91.7%

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

      4. associate--l+ 91.7%

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

      5. sub-neg 91.7%

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

      6. remove-double-neg 91.7%

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

      7. distribute-frac-neg 91.7%

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

      8. distribute-neg-in 91.7%

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

      9. remove-double-neg 91.7%

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

      10. sub-neg 91.7%

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

      11. neg-mul-1 91.7%

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

      12. times-frac 94.0%

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

      13. distribute-frac-neg 94.0%

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

      14. neg-mul-1 94.0%

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

      15. *-commutative 94.0%

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

      16. associate-/l* 93.9%

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

      17. *-commutative 93.9%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around inf 42.5%

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

4. Final simplification 54.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \lor \neg \left(y \leq 10^{+127}\right):\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.122:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.122)
   (* y (/ -0.3333333333333333 z))
   (if (<= y 9.8e+126) x (* -0.3333333333333333 (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.122) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 9.8e+126) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-0.122d0)) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else if (y <= 9.8d+126) then
        tmp = x
    else
        tmp = (-0.3333333333333333d0) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.122) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 9.8e+126) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.122:
		tmp = y * (-0.3333333333333333 / z)
	elif y <= 9.8e+126:
		tmp = x
	else:
		tmp = -0.3333333333333333 * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.122)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	elseif (y <= 9.8e+126)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.122)
		tmp = y * (-0.3333333333333333 / z);
	elseif (y <= 9.8e+126)
		tmp = x;
	else
		tmp = -0.3333333333333333 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.122], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e+126], x, N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.122

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      2. associate-+r- 98.6%

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

      3. +-commutative 98.6%

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

      4. associate--l+ 98.6%

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

      5. sub-neg 98.6%

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

      6. remove-double-neg 98.6%

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

      7. distribute-frac-neg 98.6%

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

      8. distribute-neg-in 98.6%

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

      9. remove-double-neg 98.6%

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

      10. sub-neg 98.6%

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

      11. neg-mul-1 98.6%

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

      12. times-frac 98.5%

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

      13. distribute-frac-neg 98.5%

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

      14. neg-mul-1 98.5%

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

      15. *-commutative 98.5%

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

      16. associate-/l* 98.4%

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

      17. *-commutative 98.4%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 85.9%

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

   6. Taylor expanded in x around 0 65.4%

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

   if -0.122 < y < 9.80000000000000002e126

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-+r- 91.7%

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

      3. +-commutative 91.7%

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

      4. associate--l+ 91.7%

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

      5. sub-neg 91.7%

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

      6. remove-double-neg 91.7%

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

      7. distribute-frac-neg 91.7%

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

      8. distribute-neg-in 91.7%

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

      9. remove-double-neg 91.7%

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

      10. sub-neg 91.7%

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

      11. neg-mul-1 91.7%

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

      12. times-frac 94.0%

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

      13. distribute-frac-neg 94.0%

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

      14. neg-mul-1 94.0%

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

      15. *-commutative 94.0%

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

      16. associate-/l* 93.9%

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

      17. *-commutative 93.9%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around inf 42.5%

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

   if 9.80000000000000002e126 < 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. 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. inv-pow 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. unpow-1 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-/l* 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around inf 82.6%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.122:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{+126}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 47.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.2)
   (/ -0.3333333333333333 (/ z y))
   (if (<= y 1e+127) x (* -0.3333333333333333 (/ y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2) {
		tmp = -0.3333333333333333 / (z / y);
	} else if (y <= 1e+127) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 * (y / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.2d0)) then
        tmp = (-0.3333333333333333d0) / (z / y)
    else if (y <= 1d+127) then
        tmp = x
    else
        tmp = (-0.3333333333333333d0) * (y / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.2) {
		tmp = -0.3333333333333333 / (z / y);
	} else if (y <= 1e+127) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 * (y / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.2:
		tmp = -0.3333333333333333 / (z / y)
	elif y <= 1e+127:
		tmp = x
	else:
		tmp = -0.3333333333333333 * (y / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.2)
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	elseif (y <= 1e+127)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.2)
		tmp = -0.3333333333333333 / (z / y);
	elseif (y <= 1e+127)
		tmp = x;
	else
		tmp = -0.3333333333333333 * (y / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.2], N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1e+127], x, N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.2000000000000002

   1. Initial program 98.6%

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

      1. +-commutative 98.6%

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

      2. associate-+r- 98.6%

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

      3. sub-neg 98.6%

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

      4. associate-*l* 98.6%

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

      5. *-commutative 98.6%

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

      6. distribute-frac-neg2 98.6%

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

      7. distribute-rgt-neg-in 98.6%

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

      8. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

      1. clear-num 98.5%

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

      2. inv-pow 98.5%

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

   6. Applied egg-rr 98.5%

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

      1. unpow-1 98.5%

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

      2. associate-/l* 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in y around inf 65.3%

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

       1. clear-num 65.3%

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

       2. un-div-inv 65.4%

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

   11. Applied egg-rr 65.4%

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

   if -3.2000000000000002 < y < 9.99999999999999955e126

   1. Initial program 91.7%

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

      1. +-commutative 91.7%

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

      2. associate-+r- 91.7%

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

      3. +-commutative 91.7%

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

      4. associate--l+ 91.7%

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

      5. sub-neg 91.7%

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

      6. remove-double-neg 91.7%

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

      7. distribute-frac-neg 91.7%

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

      8. distribute-neg-in 91.7%

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

      9. remove-double-neg 91.7%

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

      10. sub-neg 91.7%

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

      11. neg-mul-1 91.7%

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

      12. times-frac 94.0%

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

      13. distribute-frac-neg 94.0%

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

      14. neg-mul-1 94.0%

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

      15. *-commutative 94.0%

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

      16. associate-/l* 93.9%

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

      17. *-commutative 93.9%

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

   3. Simplified 94.6%

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

   5. Taylor expanded in x around inf 42.5%

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

   if 9.99999999999999955e126 < 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. 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. inv-pow 99.9%

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

   6. Applied egg-rr 99.9%

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

      1. unpow-1 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-/l* 99.9%

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

   8. Simplified 99.9%

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

   9. Taylor expanded in y around inf 82.6%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 10^{+127}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 30.1% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 94.8%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Step-by-step derivation

   1. +-commutative 94.8%

      \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

   2. associate-+r- 94.8%

      \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

   3. +-commutative 94.8%

      \[\leadsto \color{blue}{\left(x + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} - \frac{y}{z \cdot 3} \]

   4. associate--l+ 94.8%

      \[\leadsto \color{blue}{x + \left(\frac{t}{\left(z \cdot 3\right) \cdot y} - \frac{y}{z \cdot 3}\right)} \]

   5. sub-neg 94.8%

      \[\leadsto x + \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(-\frac{y}{z \cdot 3}\right)\right)} \]

   6. remove-double-neg 94.8%

      \[\leadsto x + \left(\color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   7. distribute-frac-neg 94.8%

      \[\leadsto x + \left(\left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   8. distribute-neg-in 94.8%

      \[\leadsto x + \color{blue}{\left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \frac{y}{z \cdot 3}\right)\right)} \]

   9. remove-double-neg 94.8%

      \[\leadsto x + \left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(-\left(-\frac{y}{z \cdot 3}\right)\right)}\right)\right) \]

   10. sub-neg 94.8%

       \[\leadsto x + \left(-\color{blue}{\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)}\right) \]

   11. neg-mul-1 94.8%

       \[\leadsto x + \left(-\left(\frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   12. times-frac 96.1%

       \[\leadsto x + \left(-\left(\color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   13. distribute-frac-neg 96.1%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-y}{z \cdot 3}}\right)\right) \]

   14. neg-mul-1 96.1%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{-1 \cdot y}}{z \cdot 3}\right)\right) \]

   15. *-commutative 96.1%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{y \cdot -1}}{z \cdot 3}\right)\right) \]

   16. associate-/l* 96.0%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{y \cdot \frac{-1}{z \cdot 3}}\right)\right) \]

   17. *-commutative 96.0%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-1}{z \cdot 3} \cdot y}\right)\right) \]

3. Simplified 96.8%

   \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 33.3%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 33.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y)))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x - (y / (z * 3.0d0))) + ((t / (z * 3.0d0)) / y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y)

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(t / Float64(z * 3.0)) / y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024055 
(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))))