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

Percentage Accurate: 95.6% → 99.5%

Time: 11.2s

Alternatives: 16

Speedup: 0.7×

• 28.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{-29} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{y}{z \cdot -3} + \left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -2e-29) (not (<= (* z 3.0) 2e+50)))
   (+ (/ y (* z -3.0)) (+ x (/ t (* z (* y 3.0)))))
   (+ x (* (/ -0.3333333333333333 z) (- y (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -2e-29) || !((z * 3.0) <= 2e+50)) {
		tmp = (y / (z * -3.0)) + (x + (t / (z * (y * 3.0))));
	} else {
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / 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-29)) .or. (.not. ((z * 3.0d0) <= 2d+50))) then
        tmp = (y / (z * (-3.0d0))) + (x + (t / (z * (y * 3.0d0))))
    else
        tmp = x + (((-0.3333333333333333d0) / z) * (y - (t / 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-29) || !((z * 3.0) <= 2e+50)) {
		tmp = (y / (z * -3.0)) + (x + (t / (z * (y * 3.0))));
	} else {
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -2e-29) or not ((z * 3.0) <= 2e+50):
		tmp = (y / (z * -3.0)) + (x + (t / (z * (y * 3.0))))
	else:
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -2e-29) || !(Float64(z * 3.0) <= 2e+50))
		tmp = Float64(Float64(y / Float64(z * -3.0)) + Float64(x + Float64(t / Float64(z * Float64(y * 3.0)))));
	else
		tmp = Float64(x + Float64(Float64(-0.3333333333333333 / z) * Float64(y - Float64(t / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -2e-29) || ~(((z * 3.0) <= 2e+50)))
		tmp = (y / (z * -3.0)) + (x + (t / (z * (y * 3.0))));
	else
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -2e-29], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 2e+50]], $MachinePrecision]], N[(N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(-0.3333333333333333 / z), $MachinePrecision] * N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z #s(literal 3 binary64)) < -1.99999999999999989e-29 or 2.0000000000000002e50 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. sub-neg 99.8%

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

      4. associate-*l* 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-frac-neg2 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   if -1.99999999999999989e-29 < (*.f64 z #s(literal 3 binary64)) < 2.0000000000000002e50

   1. Initial program 88.0%

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

      1. sub-neg 88.0%

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

      2. associate-+l+ 88.0%

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

      3. remove-double-neg 88.0%

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

      4. distribute-frac-neg 88.0%

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

      5. sub-neg 88.0%

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

      6. distribute-frac-neg 88.0%

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

      7. neg-mul-1 88.0%

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

      8. *-commutative 88.0%

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

      9. associate-/l* 88.0%

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

      10. *-commutative 88.0%

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

      11. neg-mul-1 88.0%

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

      12. times-frac 96.6%

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

      13. distribute-lft-out-- 99.8%

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

      14. *-commutative 99.8%

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

      15. associate-/r* 99.8%

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

      16. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{-29} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{y}{z \cdot -3} + \left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 61.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{if}\;y \leq -8 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.3333333333333333 (/ t (* y z)))))
   (if (<= y -8e+71)
     (/ y (* z -3.0))
     (if (<= y 9.5e-91)
       t_1
       (if (<= y 9.2e+46)
         x
         (if (<= y 3.1e+50) t_1 (* y (/ -0.3333333333333333 z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (y * z));
	double tmp;
	if (y <= -8e+71) {
		tmp = y / (z * -3.0);
	} else if (y <= 9.5e-91) {
		tmp = t_1;
	} else if (y <= 9.2e+46) {
		tmp = x;
	} else if (y <= 3.1e+50) {
		tmp = t_1;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.3333333333333333d0 * (t / (y * z))
    if (y <= (-8d+71)) then
        tmp = y / (z * (-3.0d0))
    else if (y <= 9.5d-91) then
        tmp = t_1
    else if (y <= 9.2d+46) then
        tmp = x
    else if (y <= 3.1d+50) then
        tmp = t_1
    else
        tmp = y * ((-0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (y * z));
	double tmp;
	if (y <= -8e+71) {
		tmp = y / (z * -3.0);
	} else if (y <= 9.5e-91) {
		tmp = t_1;
	} else if (y <= 9.2e+46) {
		tmp = x;
	} else if (y <= 3.1e+50) {
		tmp = t_1;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 * (t / (y * z))
	tmp = 0
	if y <= -8e+71:
		tmp = y / (z * -3.0)
	elif y <= 9.5e-91:
		tmp = t_1
	elif y <= 9.2e+46:
		tmp = x
	elif y <= 3.1e+50:
		tmp = t_1
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 * Float64(t / Float64(y * z)))
	tmp = 0.0
	if (y <= -8e+71)
		tmp = Float64(y / Float64(z * -3.0));
	elseif (y <= 9.5e-91)
		tmp = t_1;
	elseif (y <= 9.2e+46)
		tmp = x;
	elseif (y <= 3.1e+50)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 * (t / (y * z));
	tmp = 0.0;
	if (y <= -8e+71)
		tmp = y / (z * -3.0);
	elseif (y <= 9.5e-91)
		tmp = t_1;
	elseif (y <= 9.2e+46)
		tmp = x;
	elseif (y <= 3.1e+50)
		tmp = t_1;
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8e+71], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-91], t$95$1, If[LessEqual[y, 9.2e+46], x, If[LessEqual[y, 3.1e+50], t$95$1, N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.0000000000000003e71

   1. Initial program 93.8%

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

      1. +-commutative 93.8%

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

      2. associate-+r- 93.8%

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

      3. sub-neg 93.8%

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

      4. associate-*l* 93.8%

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

      5. *-commutative 93.8%

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

      6. distribute-frac-neg2 93.8%

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

      7. distribute-rgt-neg-in 93.8%

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

      8. metadata-eval 93.8%

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

   3. Simplified 93.8%

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

      1. associate-/r* 90.0%

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

      2. div-inv 90.0%

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

   6. Applied egg-rr 90.0%

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

   7. Taylor expanded in y around inf 69.4%

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

      1. associate-*r/ 69.3%

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

      2. *-commutative 69.3%

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

      3. metadata-eval 69.3%

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

      4. div-inv 69.3%

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

      5. associate-/l/ 69.4%

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

   9. Applied egg-rr 69.4%

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

   if -8.0000000000000003e71 < y < 9.5e-91 or 9.2000000000000002e46 < y < 3.10000000000000003e50

   1. Initial program 92.7%

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

      1. +-commutative 92.7%

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

      2. associate-+r- 92.7%

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

      3. sub-neg 92.7%

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

      4. associate-*l* 92.7%

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

      5. *-commutative 92.7%

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

      6. distribute-frac-neg2 92.7%

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

      7. distribute-rgt-neg-in 92.7%

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

      8. metadata-eval 92.7%

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

   3. Simplified 92.7%

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

      1. *-un-lft-identity 92.7%

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

      2. times-frac 92.7%

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

   6. Applied egg-rr 92.7%

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

      1. associate-*l/ 92.7%

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

      2. *-lft-identity 92.7%

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

   8. Simplified 92.7%

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

   9. Taylor expanded in t around inf 64.9%

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

   if 9.5e-91 < y < 9.2000000000000002e46

   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. sub-neg 91.7%

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

      2. associate-+l+ 91.7%

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

      3. remove-double-neg 91.7%

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

      4. distribute-frac-neg 91.7%

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

      5. sub-neg 91.7%

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

      6. distribute-frac-neg 91.7%

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

      7. neg-mul-1 91.7%

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

      8. *-commutative 91.7%

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

      9. associate-/l* 91.6%

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

      10. *-commutative 91.6%

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

      11. neg-mul-1 91.6%

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

      12. times-frac 95.6%

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

      13. distribute-lft-out-- 95.7%

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

      14. *-commutative 95.7%

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

      15. associate-/r* 95.8%

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

      16. metadata-eval 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in x around inf 54.5%

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

   if 3.10000000000000003e50 < 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. associate-/r* 97.8%

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

      2. div-inv 97.8%

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

   6. Applied egg-rr 97.8%

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

   7. Taylor expanded in y around inf 64.4%

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

      1. *-commutative 64.4%

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

      2. associate-*l/ 64.5%

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

      3. associate-*r/ 64.6%

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

   9. Simplified 64.6%

      \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+71}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-91}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{+46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+50}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{t}{z} \cdot \frac{1}{y \cdot 3}\right) + \frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2e-116)
   (+ x (* (/ -0.3333333333333333 z) (- y (/ t y))))
   (+ (+ x (* (/ t z) (/ 1.0 (* y 3.0)))) (/ y (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e-116) {
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	} else {
		tmp = (x + ((t / z) * (1.0 / (y * 3.0)))) + (y / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2d-116)) then
        tmp = x + (((-0.3333333333333333d0) / z) * (y - (t / y)))
    else
        tmp = (x + ((t / z) * (1.0d0 / (y * 3.0d0)))) + (y / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2e-116) {
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	} else {
		tmp = (x + ((t / z) * (1.0 / (y * 3.0)))) + (y / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2e-116:
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)))
	else:
		tmp = (x + ((t / z) * (1.0 / (y * 3.0)))) + (y / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2e-116)
		tmp = Float64(x + Float64(Float64(-0.3333333333333333 / z) * Float64(y - Float64(t / y))));
	else
		tmp = Float64(Float64(x + Float64(Float64(t / z) * Float64(1.0 / Float64(y * 3.0)))) + Float64(y / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2e-116)
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	else
		tmp = (x + ((t / z) * (1.0 / (y * 3.0)))) + (y / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2e-116], N[(x + N[(N[(-0.3333333333333333 / z), $MachinePrecision] * N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(N[(t / z), $MachinePrecision] * N[(1.0 / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2e-116

   1. Initial program 95.3%

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

      1. sub-neg 95.3%

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

      2. associate-+l+ 95.3%

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

      3. remove-double-neg 95.3%

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

      4. distribute-frac-neg 95.3%

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

      5. sub-neg 95.3%

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

      6. distribute-frac-neg 95.3%

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

      7. neg-mul-1 95.3%

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

      8. *-commutative 95.3%

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

      9. associate-/l* 95.3%

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

      10. *-commutative 95.3%

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

      11. neg-mul-1 95.3%

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

      12. times-frac 95.3%

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

      13. distribute-lft-out-- 99.7%

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

      14. *-commutative 99.7%

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

      15. associate-/r* 99.8%

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

      16. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   if -2e-116 < y

   1. Initial program 93.4%

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

      1. +-commutative 93.4%

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

      2. associate-+r- 93.4%

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

      3. sub-neg 93.4%

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

      4. associate-*l* 93.4%

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

      5. *-commutative 93.4%

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

      6. distribute-frac-neg2 93.4%

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

      7. distribute-rgt-neg-in 93.4%

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

      8. metadata-eval 93.4%

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

   3. Simplified 93.4%

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

      1. associate-/r* 99.2%

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

      2. div-inv 99.2%

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

   6. Applied egg-rr 99.2%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-116}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{t}{z} \cdot \frac{1}{y \cdot 3}\right) + \frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-134} \lor \neg \left(y \leq 1.48 \cdot 10^{-61}\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.2e-134) (not (<= y 1.48e-61)))
   (+ x (* (/ -0.3333333333333333 z) (- y (/ t y))))
   (+ x (/ 0.3333333333333333 (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.2e-134) || !(y <= 1.48e-61)) {
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	} else {
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	}
	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 <= (-8.2d-134)) .or. (.not. (y <= 1.48d-61))) then
        tmp = x + (((-0.3333333333333333d0) / z) * (y - (t / y)))
    else
        tmp = x + (0.3333333333333333d0 / (y * (z / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.2e-134) || !(y <= 1.48e-61)) {
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	} else {
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8.2e-134) or not (y <= 1.48e-61):
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)))
	else:
		tmp = x + (0.3333333333333333 / (y * (z / t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.2e-134) || !(y <= 1.48e-61))
		tmp = Float64(x + Float64(Float64(-0.3333333333333333 / z) * Float64(y - Float64(t / y))));
	else
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(y * Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8.2e-134) || ~((y <= 1.48e-61)))
		tmp = x + ((-0.3333333333333333 / z) * (y - (t / y)));
	else
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.2e-134], N[Not[LessEqual[y, 1.48e-61]], $MachinePrecision]], N[(x + N[(N[(-0.3333333333333333 / z), $MachinePrecision] * N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 / N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.2000000000000004e-134 or 1.4799999999999999e-61 < y

   1. Initial program 97.3%

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

      1. sub-neg 97.3%

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

      2. associate-+l+ 97.3%

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

      3. remove-double-neg 97.3%

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

      4. distribute-frac-neg 97.3%

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

      5. sub-neg 97.3%

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

      6. distribute-frac-neg 97.3%

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

      7. neg-mul-1 97.3%

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

      8. *-commutative 97.3%

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

      9. associate-/l* 97.2%

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

      10. *-commutative 97.2%

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

      11. neg-mul-1 97.2%

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

      12. times-frac 97.2%

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

      13. distribute-lft-out-- 99.7%

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

      14. *-commutative 99.7%

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

      15. associate-/r* 99.8%

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

      16. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   if -8.2000000000000004e-134 < y < 1.4799999999999999e-61

   1. Initial program 89.0%

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

      1. sub-neg 89.0%

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

      2. associate-+l+ 89.0%

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

      3. remove-double-neg 89.0%

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

      4. distribute-frac-neg 89.0%

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

      5. sub-neg 89.0%

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

      6. distribute-frac-neg 89.0%

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

      7. neg-mul-1 89.0%

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

      8. *-commutative 89.0%

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

      9. associate-/l* 89.0%

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

      10. *-commutative 89.0%

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

      11. neg-mul-1 89.0%

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

      12. times-frac 85.7%

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

      13. distribute-lft-out-- 85.7%

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

      14. *-commutative 85.7%

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

      15. associate-/r* 85.7%

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

      16. metadata-eval 85.7%

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

   3. Simplified 85.7%

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

   5. Taylor expanded in y around 0 87.7%

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

      1. metadata-eval 87.7%

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

      2. times-frac 87.7%

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

      3. *-commutative 87.7%

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

      4. *-lft-identity 87.7%

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

      5. associate-*r* 87.7%

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

   7. Simplified 87.7%

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

      1. associate-/r* 84.4%

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

      2. div-inv 84.4%

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

      3. frac-times 98.5%

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

      4. associate-/r* 98.4%

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

      5. associate-*r/ 98.5%

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

      6. times-frac 98.5%

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

      7. metadata-eval 98.5%

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

   9. Applied egg-rr 98.5%

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

       1. *-commutative 98.5%

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

       2. clear-num 98.5%

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

       3. un-div-inv 98.5%

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

       4. div-inv 98.5%

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

       5. clear-num 98.5%

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

   11. Applied egg-rr 98.5%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-134} \lor \neg \left(y \leq 1.48 \cdot 10^{-61}\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{z} \cdot \left(y - \frac{t}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+72}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+49}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.6e+72)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 2.35e+49)
     (+ x (* 0.3333333333333333 (/ t (* y z))))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+72) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 2.35e+49) {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.6d+72)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 2.35d+49) then
        tmp = x + (0.3333333333333333d0 * (t / (y * z)))
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.6e+72) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 2.35e+49) {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.6e+72:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 2.35e+49:
		tmp = x + (0.3333333333333333 * (t / (y * z)))
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.6e+72)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 2.35e+49)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(y * z))));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.6e+72)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 2.35e+49)
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.6e+72], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.35e+49], N[(x + N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.59999999999999981e72

   1. Initial program 93.7%

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

   3. Taylor expanded in t around 0 94.3%

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

   if -2.59999999999999981e72 < y < 2.3499999999999999e49

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. associate-+l+ 92.6%

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

      3. remove-double-neg 92.6%

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

      4. distribute-frac-neg 92.6%

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

      5. sub-neg 92.6%

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

      6. distribute-frac-neg 92.6%

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

      7. neg-mul-1 92.6%

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

      8. *-commutative 92.6%

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

      9. associate-/l* 92.6%

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

      10. *-commutative 92.6%

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

      11. neg-mul-1 92.6%

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

      12. times-frac 90.6%

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

      13. distribute-lft-out-- 91.2%

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

      14. *-commutative 91.2%

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

      15. associate-/r* 91.2%

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

      16. metadata-eval 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around 0 86.7%

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

   if 2.3499999999999999e49 < 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. sub-neg 99.9%

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

      2. associate-+l+ 99.9%

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

      3. remove-double-neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. neg-mul-1 99.9%

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

      8. *-commutative 99.9%

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

      9. associate-/l* 99.8%

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

      10. *-commutative 99.8%

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

      11. neg-mul-1 99.8%

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

      12. times-frac 99.7%

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

      13. distribute-lft-out-- 99.7%

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

      14. *-commutative 99.7%

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

      15. associate-/r* 99.9%

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

      16. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 97.6%

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

      1. +-commutative 97.6%

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

      2. associate-*r/ 97.8%

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

      3. associate-*l/ 97.8%

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

      4. *-commutative 97.8%

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

   7. Simplified 97.8%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+72}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+49}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+72}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+49}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e+72)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 1.6e+49)
     (+ x (* 0.3333333333333333 (/ (/ t z) y)))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e+72) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 1.6e+49) {
		tmp = x + (0.3333333333333333 * ((t / z) / y));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.5d+72)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 1.6d+49) then
        tmp = x + (0.3333333333333333d0 * ((t / z) / y))
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e+72) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 1.6e+49) {
		tmp = x + (0.3333333333333333 * ((t / z) / y));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e+72:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 1.6e+49:
		tmp = x + (0.3333333333333333 * ((t / z) / y))
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e+72)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 1.6e+49)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(Float64(t / z) / y)));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e+72)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 1.6e+49)
		tmp = x + (0.3333333333333333 * ((t / z) / y));
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e+72], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e+49], N[(x + N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999996e72

   1. Initial program 93.7%

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

   3. Taylor expanded in t around 0 94.3%

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

   if -2.49999999999999996e72 < y < 1.60000000000000007e49

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. associate-+l+ 92.6%

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

      3. remove-double-neg 92.6%

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

      4. distribute-frac-neg 92.6%

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

      5. sub-neg 92.6%

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

      6. distribute-frac-neg 92.6%

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

      7. neg-mul-1 92.6%

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

      8. *-commutative 92.6%

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

      9. associate-/l* 92.6%

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

      10. *-commutative 92.6%

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

      11. neg-mul-1 92.6%

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

      12. times-frac 90.6%

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

      13. distribute-lft-out-- 91.2%

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

      14. *-commutative 91.2%

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

      15. associate-/r* 91.2%

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

      16. metadata-eval 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around 0 86.7%

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

      1. metadata-eval 86.7%

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

      2. times-frac 86.7%

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

      3. *-commutative 86.7%

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

      4. *-lft-identity 86.7%

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

      5. associate-*r* 86.7%

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

   7. Simplified 86.7%

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

      1. associate-/r* 84.7%

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

      2. div-inv 84.6%

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

      3. frac-times 93.2%

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

      4. associate-/r* 93.2%

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

      5. associate-*r/ 93.2%

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

      6. times-frac 93.2%

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

      7. metadata-eval 93.2%

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

   9. Applied egg-rr 93.2%

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

   if 1.60000000000000007e49 < 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. sub-neg 99.9%

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

      2. associate-+l+ 99.9%

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

      3. remove-double-neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. neg-mul-1 99.9%

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

      8. *-commutative 99.9%

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

      9. associate-/l* 99.8%

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

      10. *-commutative 99.8%

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

      11. neg-mul-1 99.8%

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

      12. times-frac 99.7%

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

      13. distribute-lft-out-- 99.7%

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

      14. *-commutative 99.7%

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

      15. associate-/r* 99.9%

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

      16. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 97.6%

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

      1. +-commutative 97.6%

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

      2. associate-*r/ 97.8%

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

      3. associate-*l/ 97.8%

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

      4. *-commutative 97.8%

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

   7. Simplified 97.8%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+72}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+49}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+72}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.5e+72)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 2.8e+49)
     (+ x (/ 0.3333333333333333 (* y (/ z t))))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e+72) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 2.8e+49) {
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.5d+72)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 2.8d+49) then
        tmp = x + (0.3333333333333333d0 / (y * (z / t)))
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.5e+72) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 2.8e+49) {
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.5e+72:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 2.8e+49:
		tmp = x + (0.3333333333333333 / (y * (z / t)))
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.5e+72)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 2.8e+49)
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(y * Float64(z / t))));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.5e+72)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 2.8e+49)
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.5e+72], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+49], N[(x + N[(0.3333333333333333 / N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.49999999999999996e72

   1. Initial program 93.7%

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

   3. Taylor expanded in t around 0 94.3%

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

   if -2.49999999999999996e72 < y < 2.7999999999999998e49

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. associate-+l+ 92.6%

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

      3. remove-double-neg 92.6%

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

      4. distribute-frac-neg 92.6%

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

      5. sub-neg 92.6%

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

      6. distribute-frac-neg 92.6%

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

      7. neg-mul-1 92.6%

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

      8. *-commutative 92.6%

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

      9. associate-/l* 92.6%

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

      10. *-commutative 92.6%

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

      11. neg-mul-1 92.6%

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

      12. times-frac 90.6%

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

      13. distribute-lft-out-- 91.2%

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

      14. *-commutative 91.2%

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

      15. associate-/r* 91.2%

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

      16. metadata-eval 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around 0 86.7%

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

      1. metadata-eval 86.7%

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

      2. times-frac 86.7%

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

      3. *-commutative 86.7%

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

      4. *-lft-identity 86.7%

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

      5. associate-*r* 86.7%

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

   7. Simplified 86.7%

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

      1. associate-/r* 84.7%

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

      2. div-inv 84.6%

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

      3. frac-times 93.2%

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

      4. associate-/r* 93.2%

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

      5. associate-*r/ 93.2%

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

      6. times-frac 93.2%

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

      7. metadata-eval 93.2%

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

   9. Applied egg-rr 93.2%

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

       1. *-commutative 93.2%

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

       2. clear-num 93.2%

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

       3. un-div-inv 93.2%

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

       4. div-inv 93.2%

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

       5. clear-num 93.2%

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

   11. Applied egg-rr 93.2%

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

   if 2.7999999999999998e49 < 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. sub-neg 99.9%

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

      2. associate-+l+ 99.9%

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

      3. remove-double-neg 99.9%

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

      4. distribute-frac-neg 99.9%

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

      5. sub-neg 99.9%

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

      6. distribute-frac-neg 99.9%

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

      7. neg-mul-1 99.9%

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

      8. *-commutative 99.9%

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

      9. associate-/l* 99.8%

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

      10. *-commutative 99.8%

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

      11. neg-mul-1 99.8%

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

      12. times-frac 99.7%

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

      13. distribute-lft-out-- 99.7%

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

      14. *-commutative 99.7%

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

      15. associate-/r* 99.9%

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

      16. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 97.6%

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

      1. +-commutative 97.6%

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

      2. associate-*r/ 97.8%

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

      3. associate-*l/ 97.8%

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

      4. *-commutative 97.8%

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

   7. Simplified 97.8%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+72}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+49}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-74} \lor \neg \left(y \leq 1.4 \cdot 10^{-90}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.2e-74) (not (<= y 1.4e-90)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* 0.3333333333333333 (/ t (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2e-74) || !(y <= 1.4e-90)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (t / (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 <= (-4.2d-74)) .or. (.not. (y <= 1.4d-90))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = 0.3333333333333333d0 * (t / (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 <= -4.2e-74) || !(y <= 1.4e-90)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (t / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.2e-74) or not (y <= 1.4e-90):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * (t / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.2e-74) || !(y <= 1.4e-90))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.2e-74) || ~((y <= 1.4e-90)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * (t / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.2e-74], N[Not[LessEqual[y, 1.4e-90]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e-74 or 1.3999999999999999e-90 < y

   1. Initial program 96.0%

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

      1. sub-neg 96.0%

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

      2. associate-+l+ 96.0%

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

      3. remove-double-neg 96.0%

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

      4. distribute-frac-neg 96.0%

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

      5. sub-neg 96.0%

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

      6. distribute-frac-neg 96.0%

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

      7. neg-mul-1 96.0%

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

      8. *-commutative 96.0%

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

      9. associate-/l* 95.9%

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

      10. *-commutative 95.9%

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

      11. neg-mul-1 95.9%

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

      12. times-frac 96.5%

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

      13. distribute-lft-out-- 99.1%

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

      14. *-commutative 99.1%

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

      15. associate-/r* 99.2%

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

      16. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in t around 0 82.4%

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

      1. +-commutative 82.4%

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

      2. associate-*r/ 82.4%

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

      3. associate-*l/ 82.4%

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

      4. *-commutative 82.4%

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

   7. Simplified 82.4%

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

   if -4.2e-74 < y < 1.3999999999999999e-90

   1. Initial program 91.2%

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

      1. +-commutative 91.2%

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

      2. associate-+r- 91.2%

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

      3. sub-neg 91.2%

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

      4. associate-*l* 91.2%

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

      5. *-commutative 91.2%

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

      6. distribute-frac-neg2 91.2%

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

      7. distribute-rgt-neg-in 91.2%

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

      8. metadata-eval 91.2%

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

   3. Simplified 91.2%

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

      1. *-un-lft-identity 91.2%

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

      2. times-frac 91.2%

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

   6. Applied egg-rr 91.2%

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

      1. associate-*l/ 91.2%

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

      2. *-lft-identity 91.2%

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

   8. Simplified 91.2%

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

   9. Taylor expanded in t around inf 72.9%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-74} \lor \neg \left(y \leq 1.4 \cdot 10^{-90}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-79}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-90}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.35e-79)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 1.4e-90)
     (* 0.3333333333333333 (/ t (* y z)))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.35e-79) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 1.4e-90) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.35d-79)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 1.4d-90) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.35e-79) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 1.4e-90) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.35e-79:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 1.4e-90:
		tmp = 0.3333333333333333 * (t / (y * z))
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.35e-79)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 1.4e-90)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.35e-79)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 1.4e-90)
		tmp = 0.3333333333333333 * (t / (y * z));
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.35e-79], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-90], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.3500000000000001e-79

   1. Initial program 95.0%

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

   3. Taylor expanded in t around 0 81.5%

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

   if -2.3500000000000001e-79 < y < 1.3999999999999999e-90

   1. Initial program 91.2%

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

      1. +-commutative 91.2%

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

      2. associate-+r- 91.2%

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

      3. sub-neg 91.2%

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

      4. associate-*l* 91.2%

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

      5. *-commutative 91.2%

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

      6. distribute-frac-neg2 91.2%

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

      7. distribute-rgt-neg-in 91.2%

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

      8. metadata-eval 91.2%

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

   3. Simplified 91.2%

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

      1. *-un-lft-identity 91.2%

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

      2. times-frac 91.2%

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

   6. Applied egg-rr 91.2%

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

      1. associate-*l/ 91.2%

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

      2. *-lft-identity 91.2%

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

   8. Simplified 91.2%

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

   9. Taylor expanded in t around inf 72.9%

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

   if 1.3999999999999999e-90 < y

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. associate-+l+ 97.1%

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

      3. remove-double-neg 97.1%

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

      4. distribute-frac-neg 97.1%

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

      5. sub-neg 97.1%

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

      6. distribute-frac-neg 97.1%

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

      7. neg-mul-1 97.1%

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

      8. *-commutative 97.1%

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

      9. associate-/l* 96.9%

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

      10. *-commutative 96.9%

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

      11. neg-mul-1 96.9%

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

      12. times-frac 98.3%

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

      13. distribute-lft-out-- 98.3%

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

      14. *-commutative 98.3%

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

      15. associate-/r* 98.5%

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

      16. metadata-eval 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. associate-*r/ 83.5%

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

      3. associate-*l/ 83.5%

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

      4. *-commutative 83.5%

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

   7. Simplified 83.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{-79}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-90}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-76}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-90}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.2e-76)
   (- x (/ (* y 0.3333333333333333) z))
   (if (<= y 3.7e-90)
     (* 0.3333333333333333 (/ t (* y z)))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e-76) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 3.7e-90) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.2d-76)) then
        tmp = x - ((y * 0.3333333333333333d0) / z)
    else if (y <= 3.7d-90) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.2e-76) {
		tmp = x - ((y * 0.3333333333333333) / z);
	} else if (y <= 3.7e-90) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.2e-76:
		tmp = x - ((y * 0.3333333333333333) / z)
	elif y <= 3.7e-90:
		tmp = 0.3333333333333333 * (t / (y * z))
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.2e-76)
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	elseif (y <= 3.7e-90)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.2e-76)
		tmp = x - ((y * 0.3333333333333333) / z);
	elseif (y <= 3.7e-90)
		tmp = 0.3333333333333333 * (t / (y * z));
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.2e-76], N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.7e-90], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.20000000000000007e-76

   1. Initial program 95.0%

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

   3. Taylor expanded in t around 0 81.5%

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

      1. associate-*r/ 81.5%

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

   5. Applied egg-rr 81.5%

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

   if -1.20000000000000007e-76 < y < 3.70000000000000018e-90

   1. Initial program 91.2%

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

      1. +-commutative 91.2%

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

      2. associate-+r- 91.2%

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

      3. sub-neg 91.2%

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

      4. associate-*l* 91.2%

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

      5. *-commutative 91.2%

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

      6. distribute-frac-neg2 91.2%

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

      7. distribute-rgt-neg-in 91.2%

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

      8. metadata-eval 91.2%

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

   3. Simplified 91.2%

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

      1. *-un-lft-identity 91.2%

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

      2. times-frac 91.2%

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

   6. Applied egg-rr 91.2%

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

      1. associate-*l/ 91.2%

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

      2. *-lft-identity 91.2%

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

   8. Simplified 91.2%

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

   9. Taylor expanded in t around inf 72.9%

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

   if 3.70000000000000018e-90 < y

   1. Initial program 97.1%

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

      1. sub-neg 97.1%

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

      2. associate-+l+ 97.1%

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

      3. remove-double-neg 97.1%

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

      4. distribute-frac-neg 97.1%

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

      5. sub-neg 97.1%

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

      6. distribute-frac-neg 97.1%

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

      7. neg-mul-1 97.1%

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

      8. *-commutative 97.1%

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

      9. associate-/l* 96.9%

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

      10. *-commutative 96.9%

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

      11. neg-mul-1 96.9%

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

      12. times-frac 98.3%

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

      13. distribute-lft-out-- 98.3%

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

      14. *-commutative 98.3%

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

      15. associate-/r* 98.5%

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

      16. metadata-eval 98.5%

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

   3. Simplified 98.5%

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

   5. Taylor expanded in t around 0 83.4%

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

      1. +-commutative 83.4%

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

      2. associate-*r/ 83.5%

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

      3. associate-*l/ 83.5%

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

      4. *-commutative 83.5%

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

   7. Simplified 83.5%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{-76}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.7 \cdot 10^{-90}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 46.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+85}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.2e-68) x (if (<= x 3.7e+85) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.2e-68) {
		tmp = x;
	} else if (x <= 3.7e+85) {
		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 (x <= (-6.2d-68)) then
        tmp = x
    else if (x <= 3.7d+85) 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 (x <= -6.2e-68) {
		tmp = x;
	} else if (x <= 3.7e+85) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.2e-68:
		tmp = x
	elif x <= 3.7e+85:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.2e-68)
		tmp = x;
	elseif (x <= 3.7e+85)
		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 (x <= -6.2e-68)
		tmp = x;
	elseif (x <= 3.7e+85)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.2e-68], x, If[LessEqual[x, 3.7e+85], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.1999999999999999e-68 or 3.7000000000000002e85 < x

   1. Initial program 89.8%

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

      1. sub-neg 89.8%

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

      2. associate-+l+ 89.8%

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

      3. remove-double-neg 89.8%

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

      4. distribute-frac-neg 89.8%

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

      5. sub-neg 89.8%

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

      6. distribute-frac-neg 89.8%

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

      7. neg-mul-1 89.8%

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

      8. *-commutative 89.8%

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

      9. associate-/l* 89.8%

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

      10. *-commutative 89.8%

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

      11. neg-mul-1 89.8%

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

      12. times-frac 93.0%

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

      13. distribute-lft-out-- 95.4%

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

      14. *-commutative 95.4%

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

      15. associate-/r* 95.4%

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

      16. metadata-eval 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in x around inf 49.1%

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

   if -6.1999999999999999e-68 < x < 3.7000000000000002e85

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-+r- 98.2%

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

      3. sub-neg 98.2%

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

      4. associate-*l* 98.2%

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

      5. *-commutative 98.2%

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

      6. distribute-frac-neg2 98.2%

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

      7. distribute-rgt-neg-in 98.2%

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

      8. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

      1. associate-/r* 97.4%

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

      2. div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in y around inf 43.6%

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

4. Final simplification 46.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.2 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{+85}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 46.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -8.5e-68) x (if (<= x 1.05e+84) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -8.5e-68) {
		tmp = x;
	} else if (x <= 1.05e+84) {
		tmp = y * (-0.3333333333333333 / 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 (x <= (-8.5d-68)) then
        tmp = x
    else if (x <= 1.05d+84) then
        tmp = y * ((-0.3333333333333333d0) / 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 (x <= -8.5e-68) {
		tmp = x;
	} else if (x <= 1.05e+84) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -8.5e-68:
		tmp = x
	elif x <= 1.05e+84:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -8.5e-68)
		tmp = x;
	elseif (x <= 1.05e+84)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -8.5e-68)
		tmp = x;
	elseif (x <= 1.05e+84)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -8.5e-68], x, If[LessEqual[x, 1.05e+84], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -8.50000000000000026e-68 or 1.05000000000000009e84 < x

   1. Initial program 89.8%

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

      1. sub-neg 89.8%

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

      2. associate-+l+ 89.8%

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

      3. remove-double-neg 89.8%

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

      4. distribute-frac-neg 89.8%

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

      5. sub-neg 89.8%

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

      6. distribute-frac-neg 89.8%

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

      7. neg-mul-1 89.8%

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

      8. *-commutative 89.8%

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

      9. associate-/l* 89.8%

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

      10. *-commutative 89.8%

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

      11. neg-mul-1 89.8%

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

      12. times-frac 93.0%

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

      13. distribute-lft-out-- 95.4%

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

      14. *-commutative 95.4%

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

      15. associate-/r* 95.4%

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

      16. metadata-eval 95.4%

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

   3. Simplified 95.4%

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

   5. Taylor expanded in x around inf 49.1%

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

   if -8.50000000000000026e-68 < x < 1.05000000000000009e84

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-+r- 98.2%

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

      3. sub-neg 98.2%

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

      4. associate-*l* 98.2%

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

      5. *-commutative 98.2%

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

      6. distribute-frac-neg2 98.2%

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

      7. distribute-rgt-neg-in 98.2%

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

      8. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

      1. associate-/r* 97.4%

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

      2. div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in y around inf 43.6%

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

      1. *-commutative 43.6%

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

      2. associate-*l/ 43.6%

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

      3. associate-*r/ 43.6%

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

   9. Simplified 43.6%

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

4. Final simplification 46.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-68}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 44.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -2.5e-68)
   (* y (/ x y))
   (if (<= x 4e+85) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -2.5e-68) {
		tmp = y * (x / y);
	} else if (x <= 4e+85) {
		tmp = y * (-0.3333333333333333 / 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 (x <= (-2.5d-68)) then
        tmp = y * (x / y)
    else if (x <= 4d+85) then
        tmp = y * ((-0.3333333333333333d0) / 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 (x <= -2.5e-68) {
		tmp = y * (x / y);
	} else if (x <= 4e+85) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -2.5e-68:
		tmp = y * (x / y)
	elif x <= 4e+85:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -2.5e-68)
		tmp = Float64(y * Float64(x / y));
	elseif (x <= 4e+85)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -2.5e-68)
		tmp = y * (x / y);
	elseif (x <= 4e+85)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -2.5e-68], N[(y * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+85], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if x < -2.49999999999999986e-68

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. associate-+l+ 92.6%

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

      3. remove-double-neg 92.6%

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

      4. distribute-frac-neg 92.6%

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

      5. sub-neg 92.6%

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

      6. distribute-frac-neg 92.6%

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

      7. neg-mul-1 92.6%

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

      8. *-commutative 92.6%

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

      9. associate-/l* 92.6%

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

      10. *-commutative 92.6%

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

      11. neg-mul-1 92.6%

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

      12. times-frac 91.6%

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

      13. distribute-lft-out-- 94.1%

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

      14. *-commutative 94.1%

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

      15. associate-/r* 94.1%

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

      16. metadata-eval 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in y around inf 57.4%

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

   6. Taylor expanded in x around inf 46.9%

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

   if -2.49999999999999986e-68 < x < 4.0000000000000001e85

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-+r- 98.2%

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

      3. sub-neg 98.2%

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

      4. associate-*l* 98.2%

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

      5. *-commutative 98.2%

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

      6. distribute-frac-neg2 98.2%

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

      7. distribute-rgt-neg-in 98.2%

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

      8. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

      1. associate-/r* 97.4%

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

      2. div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in y around inf 43.6%

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

      1. *-commutative 43.6%

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

      2. associate-*l/ 43.6%

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

      3. associate-*r/ 43.6%

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

   9. Simplified 43.6%

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

   if 4.0000000000000001e85 < x

   1. Initial program 84.9%

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

      1. sub-neg 84.9%

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

      2. associate-+l+ 84.9%

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

      3. remove-double-neg 84.9%

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

      4. distribute-frac-neg 84.9%

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

      5. sub-neg 84.9%

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

      6. distribute-frac-neg 84.9%

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

      7. neg-mul-1 84.9%

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

      8. *-commutative 84.9%

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

      9. associate-/l* 84.9%

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

      10. *-commutative 84.9%

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

      11. neg-mul-1 84.9%

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

      12. times-frac 95.6%

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

      13. distribute-lft-out-- 97.8%

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

      14. *-commutative 97.8%

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

      15. associate-/r* 97.8%

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

      16. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf 56.7%

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

4. Final simplification 47.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.5 \cdot 10^{-68}:\\ \;\;\;\;y \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-68}:\\ \;\;\;\;z \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -9.5e-68)
   (* z (/ x z))
   (if (<= x 4e+85) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -9.5e-68) {
		tmp = z * (x / z);
	} else if (x <= 4e+85) {
		tmp = y * (-0.3333333333333333 / 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 (x <= (-9.5d-68)) then
        tmp = z * (x / z)
    else if (x <= 4d+85) then
        tmp = y * ((-0.3333333333333333d0) / 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 (x <= -9.5e-68) {
		tmp = z * (x / z);
	} else if (x <= 4e+85) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -9.5e-68:
		tmp = z * (x / z)
	elif x <= 4e+85:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -9.5e-68)
		tmp = Float64(z * Float64(x / z));
	elseif (x <= 4e+85)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -9.5e-68)
		tmp = z * (x / z);
	elseif (x <= 4e+85)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -9.5e-68], N[(z * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+85], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if x < -9.4999999999999997e-68

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. associate-+l+ 92.6%

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

      3. remove-double-neg 92.6%

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

      4. distribute-frac-neg 92.6%

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

      5. sub-neg 92.6%

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

      6. distribute-frac-neg 92.6%

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

      7. neg-mul-1 92.6%

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

      8. *-commutative 92.6%

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

      9. associate-/l* 92.6%

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

      10. *-commutative 92.6%

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

      11. neg-mul-1 92.6%

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

      12. times-frac 91.6%

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

      13. distribute-lft-out-- 94.1%

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

      14. *-commutative 94.1%

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

      15. associate-/r* 94.1%

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

      16. metadata-eval 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in y around inf 57.4%

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

   6. Taylor expanded in z around 0 35.7%

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

   7. Taylor expanded in y around 0 25.1%

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

      1. *-commutative 25.1%

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

      2. associate-/l* 51.9%

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

   9. Applied egg-rr 51.9%

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

   if -9.4999999999999997e-68 < x < 4.0000000000000001e85

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-+r- 98.2%

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

      3. sub-neg 98.2%

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

      4. associate-*l* 98.2%

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

      5. *-commutative 98.2%

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

      6. distribute-frac-neg2 98.2%

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

      7. distribute-rgt-neg-in 98.2%

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

      8. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

      1. associate-/r* 97.4%

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

      2. div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in y around inf 43.6%

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

      1. *-commutative 43.6%

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

      2. associate-*l/ 43.6%

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

      3. associate-*r/ 43.6%

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

   9. Simplified 43.6%

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

   if 4.0000000000000001e85 < x

   1. Initial program 84.9%

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

      1. sub-neg 84.9%

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

      2. associate-+l+ 84.9%

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

      3. remove-double-neg 84.9%

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

      4. distribute-frac-neg 84.9%

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

      5. sub-neg 84.9%

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

      6. distribute-frac-neg 84.9%

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

      7. neg-mul-1 84.9%

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

      8. *-commutative 84.9%

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

      9. associate-/l* 84.9%

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

      10. *-commutative 84.9%

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

      11. neg-mul-1 84.9%

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

      12. times-frac 95.6%

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

      13. distribute-lft-out-- 97.8%

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

      14. *-commutative 97.8%

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

      15. associate-/r* 97.8%

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

      16. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf 56.7%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-68}:\\ \;\;\;\;z \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.42e-67) (* z (/ x z)) (if (<= x 1.35e+84) (/ y (* z -3.0)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.42e-67) {
		tmp = z * (x / z);
	} else if (x <= 1.35e+84) {
		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 (x <= (-1.42d-67)) then
        tmp = z * (x / z)
    else if (x <= 1.35d+84) 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 (x <= -1.42e-67) {
		tmp = z * (x / z);
	} else if (x <= 1.35e+84) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.42e-67:
		tmp = z * (x / z)
	elif x <= 1.35e+84:
		tmp = y / (z * -3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.42e-67)
		tmp = Float64(z * Float64(x / z));
	elseif (x <= 1.35e+84)
		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 (x <= -1.42e-67)
		tmp = z * (x / z);
	elseif (x <= 1.35e+84)
		tmp = y / (z * -3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.42e-67], N[(z * N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e+84], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if x < -1.42000000000000004e-67

   1. Initial program 92.6%

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

      1. sub-neg 92.6%

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

      2. associate-+l+ 92.6%

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

      3. remove-double-neg 92.6%

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

      4. distribute-frac-neg 92.6%

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

      5. sub-neg 92.6%

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

      6. distribute-frac-neg 92.6%

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

      7. neg-mul-1 92.6%

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

      8. *-commutative 92.6%

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

      9. associate-/l* 92.6%

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

      10. *-commutative 92.6%

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

      11. neg-mul-1 92.6%

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

      12. times-frac 91.6%

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

      13. distribute-lft-out-- 94.1%

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

      14. *-commutative 94.1%

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

      15. associate-/r* 94.1%

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

      16. metadata-eval 94.1%

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

   3. Simplified 94.1%

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

   5. Taylor expanded in y around inf 57.4%

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

   6. Taylor expanded in z around 0 35.7%

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

   7. Taylor expanded in y around 0 25.1%

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

      1. *-commutative 25.1%

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

      2. associate-/l* 51.9%

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

   9. Applied egg-rr 51.9%

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

   if -1.42000000000000004e-67 < x < 1.35e84

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. associate-+r- 98.2%

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

      3. sub-neg 98.2%

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

      4. associate-*l* 98.2%

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

      5. *-commutative 98.2%

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

      6. distribute-frac-neg2 98.2%

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

      7. distribute-rgt-neg-in 98.2%

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

      8. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

      1. associate-/r* 97.4%

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

      2. div-inv 97.4%

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

   6. Applied egg-rr 97.4%

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

   7. Taylor expanded in y around inf 43.6%

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

      1. associate-*r/ 43.6%

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

      2. *-commutative 43.6%

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

      3. metadata-eval 43.6%

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

      4. div-inv 43.7%

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

      5. associate-/l/ 43.7%

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

   9. Applied egg-rr 43.7%

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

   if 1.35e84 < x

   1. Initial program 84.9%

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

      1. sub-neg 84.9%

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

      2. associate-+l+ 84.9%

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

      3. remove-double-neg 84.9%

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

      4. distribute-frac-neg 84.9%

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

      5. sub-neg 84.9%

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

      6. distribute-frac-neg 84.9%

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

      7. neg-mul-1 84.9%

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

      8. *-commutative 84.9%

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

      9. associate-/l* 84.9%

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

      10. *-commutative 84.9%

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

      11. neg-mul-1 84.9%

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

      12. times-frac 95.6%

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

      13. distribute-lft-out-- 97.8%

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

      14. *-commutative 97.8%

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

      15. associate-/r* 97.8%

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

      16. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in x around inf 56.7%

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

4. Final simplification 48.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.42 \cdot 10^{-67}:\\ \;\;\;\;z \cdot \frac{x}{z}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+84}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 30.5% 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 94.1%

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

   1. sub-neg 94.1%

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

   2. associate-+l+ 94.1%

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

   3. remove-double-neg 94.1%

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

   4. distribute-frac-neg 94.1%

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

   5. sub-neg 94.1%

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

   6. distribute-frac-neg 94.1%

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

   7. neg-mul-1 94.1%

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

   8. *-commutative 94.1%

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

   9. associate-/l* 94.0%

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

   10. *-commutative 94.0%

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

   11. neg-mul-1 94.0%

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

   12. times-frac 92.7%

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

   13. distribute-lft-out-- 94.3%

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

   14. *-commutative 94.3%

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

   15. associate-/r* 94.3%

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

   16. metadata-eval 94.3%

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

3. Simplified 94.3%

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

5. Taylor expanded in x around inf 31.3%

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

6. Final simplification 31.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024095 
(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))))