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

Percentage Accurate: 95.2% → 98.5%

Time: 11.8s

Alternatives: 15

Speedup: 0.7×

• 28.2% 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: 95.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -1.38 \cdot 10^{-105}:\\ \;\;\;\;x + \frac{t_1}{z \cdot -3}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{t_1}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- y (/ t y))))
   (if (<= y -1.38e-105)
     (+ x (/ t_1 (* z -3.0)))
     (if (<= y 9.2e-129)
       (+ x (/ (/ t z) (* y 3.0)))
       (+ x (/ -0.3333333333333333 (/ z t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -1.38e-105) {
		tmp = x + (t_1 / (z * -3.0));
	} else if (y <= 9.2e-129) {
		tmp = x + ((t / z) / (y * 3.0));
	} else {
		tmp = x + (-0.3333333333333333 / (z / t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (t / y)
    if (y <= (-1.38d-105)) then
        tmp = x + (t_1 / (z * (-3.0d0)))
    else if (y <= 9.2d-129) then
        tmp = x + ((t / z) / (y * 3.0d0))
    else
        tmp = x + ((-0.3333333333333333d0) / (z / t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -1.38e-105) {
		tmp = x + (t_1 / (z * -3.0));
	} else if (y <= 9.2e-129) {
		tmp = x + ((t / z) / (y * 3.0));
	} else {
		tmp = x + (-0.3333333333333333 / (z / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y - (t / y)
	tmp = 0
	if y <= -1.38e-105:
		tmp = x + (t_1 / (z * -3.0))
	elif y <= 9.2e-129:
		tmp = x + ((t / z) / (y * 3.0))
	else:
		tmp = x + (-0.3333333333333333 / (z / t_1))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y - Float64(t / y))
	tmp = 0.0
	if (y <= -1.38e-105)
		tmp = Float64(x + Float64(t_1 / Float64(z * -3.0)));
	elseif (y <= 9.2e-129)
		tmp = Float64(x + Float64(Float64(t / z) / Float64(y * 3.0)));
	else
		tmp = Float64(x + Float64(-0.3333333333333333 / Float64(z / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y - (t / y);
	tmp = 0.0;
	if (y <= -1.38e-105)
		tmp = x + (t_1 / (z * -3.0));
	elseif (y <= 9.2e-129)
		tmp = x + ((t / z) / (y * 3.0));
	else
		tmp = x + (-0.3333333333333333 / (z / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.38e-105], N[(x + N[(t$95$1 / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.2e-129], N[(x + N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-0.3333333333333333 / N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3800000000000001e-105

   1. Initial program 98.6%

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

   3. Simplified 99.7%

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

      1. clear-num 99.7%

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

      2. associate-*l/ 99.6%

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

      3. *-un-lft-identity 99.6%

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

      4. div-inv 99.8%

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

      5. metadata-eval 99.8%

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

   5. Applied egg-rr 99.8%

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

   if -1.3800000000000001e-105 < y < 9.1999999999999998e-129

   1. Initial program 91.9%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in y around 0 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-/r* 88.2%

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

      3. associate-*l/ 88.1%

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

      4. associate-*r/ 88.2%

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

   6. Simplified 88.2%

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

      1. associate-*r/ 88.1%

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

      2. associate-/l* 88.2%

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

      3. div-inv 88.2%

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

      4. metadata-eval 88.2%

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

      5. associate-/r* 91.9%

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

      6. *-commutative 91.9%

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

      7. associate-*l* 91.9%

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

      8. associate-/r* 99.3%

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

   8. Applied egg-rr 99.3%

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

   if 9.1999999999999998e-129 < y

   1. Initial program 97.7%

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

   3. Simplified 97.6%

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

      1. associate-*l/ 97.7%

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

      2. associate-/l* 97.7%

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

   5. Applied egg-rr 97.7%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.38 \cdot 10^{-105}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y - \frac{t}{y}}}\\ \end{array} \]

Alternative 2: 60.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-11}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* z -3.0))))
   (if (<= y -3.2e+36)
     t_1
     (if (<= y -4.1e-122)
       x
       (if (<= y 2.2e-11) (* 0.3333333333333333 (/ t (* y z))) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (y <= -3.2e+36) {
		tmp = t_1;
	} else if (y <= -4.1e-122) {
		tmp = x;
	} else if (y <= 2.2e-11) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (z * (-3.0d0))
    if (y <= (-3.2d+36)) then
        tmp = t_1
    else if (y <= (-4.1d-122)) then
        tmp = x
    else if (y <= 2.2d-11) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (y <= -3.2e+36) {
		tmp = t_1;
	} else if (y <= -4.1e-122) {
		tmp = x;
	} else if (y <= 2.2e-11) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (z * -3.0)
	tmp = 0
	if y <= -3.2e+36:
		tmp = t_1
	elif y <= -4.1e-122:
		tmp = x
	elif y <= 2.2e-11:
		tmp = 0.3333333333333333 * (t / (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(z * -3.0))
	tmp = 0.0
	if (y <= -3.2e+36)
		tmp = t_1;
	elseif (y <= -4.1e-122)
		tmp = x;
	elseif (y <= 2.2e-11)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (z * -3.0);
	tmp = 0.0;
	if (y <= -3.2e+36)
		tmp = t_1;
	elseif (y <= -4.1e-122)
		tmp = x;
	elseif (y <= 2.2e-11)
		tmp = 0.3333333333333333 * (t / (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.2e+36], t$95$1, If[LessEqual[y, -4.1e-122], x, If[LessEqual[y, 2.2e-11], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.1999999999999999e36 or 2.2000000000000002e-11 < 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. *-un-lft-identity 97.3%

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

      2. times-frac 97.2%

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

   3. Applied egg-rr 97.2%

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

   4. Taylor expanded in x around 0 70.5%

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

      1. cancel-sign-sub-inv 70.5%

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

      2. metadata-eval 70.5%

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

      3. +-commutative 70.5%

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

      4. associate-*r/ 70.5%

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

      5. associate-*l/ 70.5%

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

      6. *-commutative 70.5%

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

      7. associate-*r/ 70.5%

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

      8. associate-/l* 70.5%

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

      9. associate-*r/ 71.3%

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

      10. metadata-eval 71.3%

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

      11. associate-/r* 71.3%

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

      12. mul-1-neg 71.3%

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

      13. distribute-lft-neg-out 71.3%

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

      14. associate-*r/ 70.5%

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

      15. *-commutative 70.5%

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

      16. associate-/l* 70.5%

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

      17. *-commutative 70.5%

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

      18. metadata-eval 70.5%

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

      19. distribute-rgt-neg-in 70.5%

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

      20. distribute-lft-neg-in 70.5%

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

      21. associate-/l* 70.5%

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

      22. associate-/l* 70.5%

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

      23. neg-mul-1 70.5%

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

      24. associate-/r* 70.5%

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

   6. Simplified 73.0%

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

   7. Taylor expanded in y around inf 64.9%

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

      1. associate-*r/ 64.9%

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

      2. *-commutative 64.9%

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

      3. /-rgt-identity 64.9%

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

      4. associate-/l* 65.0%

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

      5. metadata-eval 65.0%

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

      6. associate-/l/ 65.0%

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

   9. Simplified 65.0%

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

   if -3.1999999999999999e36 < y < -4.1e-122

   1. Initial program 99.8%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 53.0%

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

   if -4.1e-122 < y < 2.2000000000000002e-11

   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. *-un-lft-identity 93.8%

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

      2. times-frac 93.8%

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

   3. Applied egg-rr 93.8%

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

   4. Taylor expanded in x around 0 68.7%

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

      1. cancel-sign-sub-inv 68.7%

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

      2. metadata-eval 68.7%

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

      3. +-commutative 68.7%

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

      4. associate-*r/ 68.7%

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

      5. associate-*l/ 68.7%

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

      6. *-commutative 68.7%

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

      7. associate-*r/ 68.7%

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

      8. associate-/l* 68.6%

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

      9. associate-*r/ 64.9%

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

      10. metadata-eval 64.9%

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

      11. associate-/r* 64.9%

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

      12. mul-1-neg 64.9%

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

      13. distribute-lft-neg-out 64.9%

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

      14. associate-*r/ 68.6%

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

      15. *-commutative 68.6%

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

      16. associate-/l* 68.7%

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

      17. *-commutative 68.7%

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

      18. metadata-eval 68.7%

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

      19. distribute-rgt-neg-in 68.7%

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

      20. distribute-lft-neg-in 68.7%

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

      21. associate-/l* 68.6%

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

      22. associate-/l* 68.6%

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

      23. neg-mul-1 68.6%

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

      24. associate-/r* 68.6%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in y around 0 66.2%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{+36}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-122}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.2 \cdot 10^{-11}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]

Alternative 3: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-105} \lor \neg \left(y \leq 2.25 \cdot 10^{-128}\right):\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.9e-105) (not (<= y 2.25e-128)))
   (+ x (* (- y (/ t y)) (/ -0.3333333333333333 z)))
   (+ x (/ (/ t z) (* y 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.9e-105) || !(y <= 2.25e-128)) {
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	} else {
		tmp = x + ((t / z) / (y * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.9d-105)) .or. (.not. (y <= 2.25d-128))) then
        tmp = x + ((y - (t / y)) * ((-0.3333333333333333d0) / z))
    else
        tmp = x + ((t / z) / (y * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.9e-105) || !(y <= 2.25e-128)) {
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	} else {
		tmp = x + ((t / z) / (y * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.9e-105) or not (y <= 2.25e-128):
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z))
	else:
		tmp = x + ((t / z) / (y * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.9e-105) || !(y <= 2.25e-128))
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(x + Float64(Float64(t / z) / Float64(y * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.9e-105) || ~((y <= 2.25e-128)))
		tmp = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	else
		tmp = x + ((t / z) / (y * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.9e-105], N[Not[LessEqual[y, 2.25e-128]], $MachinePrecision]], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9e-105 or 2.25e-128 < y

   1. Initial program 98.1%

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

   3. Simplified 98.5%

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

   if -3.9e-105 < y < 2.25e-128

   1. Initial program 91.9%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in y around 0 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-/r* 88.2%

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

      3. associate-*l/ 88.1%

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

      4. associate-*r/ 88.2%

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

   6. Simplified 88.2%

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

      1. associate-*r/ 88.1%

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

      2. associate-/l* 88.2%

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

      3. div-inv 88.2%

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

      4. metadata-eval 88.2%

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

      5. associate-/r* 91.9%

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

      6. *-commutative 91.9%

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

      7. associate-*l* 91.9%

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

      8. associate-/r* 99.3%

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

   8. Applied egg-rr 99.3%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-105} \lor \neg \left(y \leq 2.25 \cdot 10^{-128}\right):\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \]

Alternative 4: 98.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -1.7 \cdot 10^{-103}:\\ \;\;\;\;x + t_1 \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{t_1}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- y (/ t y))))
   (if (<= y -1.7e-103)
     (+ x (* t_1 (/ -0.3333333333333333 z)))
     (if (<= y 2.75e-129)
       (+ x (/ (/ t z) (* y 3.0)))
       (+ x (/ -0.3333333333333333 (/ z t_1)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -1.7e-103) {
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	} else if (y <= 2.75e-129) {
		tmp = x + ((t / z) / (y * 3.0));
	} else {
		tmp = x + (-0.3333333333333333 / (z / t_1));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (t / y)
    if (y <= (-1.7d-103)) then
        tmp = x + (t_1 * ((-0.3333333333333333d0) / z))
    else if (y <= 2.75d-129) then
        tmp = x + ((t / z) / (y * 3.0d0))
    else
        tmp = x + ((-0.3333333333333333d0) / (z / t_1))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -1.7e-103) {
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	} else if (y <= 2.75e-129) {
		tmp = x + ((t / z) / (y * 3.0));
	} else {
		tmp = x + (-0.3333333333333333 / (z / t_1));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y - (t / y)
	tmp = 0
	if y <= -1.7e-103:
		tmp = x + (t_1 * (-0.3333333333333333 / z))
	elif y <= 2.75e-129:
		tmp = x + ((t / z) / (y * 3.0))
	else:
		tmp = x + (-0.3333333333333333 / (z / t_1))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y - Float64(t / y))
	tmp = 0.0
	if (y <= -1.7e-103)
		tmp = Float64(x + Float64(t_1 * Float64(-0.3333333333333333 / z)));
	elseif (y <= 2.75e-129)
		tmp = Float64(x + Float64(Float64(t / z) / Float64(y * 3.0)));
	else
		tmp = Float64(x + Float64(-0.3333333333333333 / Float64(z / t_1)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y - (t / y);
	tmp = 0.0;
	if (y <= -1.7e-103)
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	elseif (y <= 2.75e-129)
		tmp = x + ((t / z) / (y * 3.0));
	else
		tmp = x + (-0.3333333333333333 / (z / t_1));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.7e-103], N[(x + N[(t$95$1 * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.75e-129], N[(x + N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-0.3333333333333333 / N[(z / t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.70000000000000001e-103

   1. Initial program 98.6%

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

   3. Simplified 99.7%

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

   if -1.70000000000000001e-103 < y < 2.75000000000000012e-129

   1. Initial program 91.9%

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

   3. Simplified 88.7%

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

   4. Taylor expanded in y around 0 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-/r* 88.2%

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

      3. associate-*l/ 88.1%

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

      4. associate-*r/ 88.2%

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

   6. Simplified 88.2%

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

      1. associate-*r/ 88.1%

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

      2. associate-/l* 88.2%

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

      3. div-inv 88.2%

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

      4. metadata-eval 88.2%

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

      5. associate-/r* 91.9%

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

      6. *-commutative 91.9%

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

      7. associate-*l* 91.9%

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

      8. associate-/r* 99.3%

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

   8. Applied egg-rr 99.3%

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

   if 2.75000000000000012e-129 < y

   1. Initial program 97.7%

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

   3. Simplified 97.6%

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

      1. associate-*l/ 97.7%

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

      2. associate-/l* 97.7%

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

   5. Applied egg-rr 97.7%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{-103}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-129}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y - \frac{t}{y}}}\\ \end{array} \]

Alternative 5: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+98}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.3e+98)
   (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))
   (+ x (/ (- y (/ t y)) (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.3e+98) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} else {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4.3d+98)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    else
        tmp = x + ((y - (t / y)) / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.3e+98) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} else {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.3e+98:
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))
	else:
		tmp = x + ((y - (t / y)) / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.3e+98)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))));
	else
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.3e+98)
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	else
		tmp = x + ((y - (t / y)) / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.3e+98], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.3000000000000001e98

   1. Initial program 99.8%

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

   if -4.3000000000000001e98 < t

   1. Initial program 95.1%

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

   3. Simplified 97.5%

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

      1. clear-num 97.5%

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

      2. associate-*l/ 97.5%

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

      3. *-un-lft-identity 97.5%

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

      4. div-inv 97.6%

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

      5. metadata-eval 97.6%

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

   5. Applied egg-rr 97.6%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{+98}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \]

Alternative 6: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+98}:\\ \;\;\;\;x + \left(-0.3333333333333333 \cdot \frac{y}{z} + \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.5e+98)
   (+ x (+ (* -0.3333333333333333 (/ y z)) (/ t (* z (* y 3.0)))))
   (+ x (/ (- y (/ t y)) (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.5e+98) {
		tmp = x + ((-0.3333333333333333 * (y / z)) + (t / (z * (y * 3.0))));
	} else {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-4.5d+98)) then
        tmp = x + (((-0.3333333333333333d0) * (y / z)) + (t / (z * (y * 3.0d0))))
    else
        tmp = x + ((y - (t / y)) / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.5e+98) {
		tmp = x + ((-0.3333333333333333 * (y / z)) + (t / (z * (y * 3.0))));
	} else {
		tmp = x + ((y - (t / y)) / (z * -3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.5e+98:
		tmp = x + ((-0.3333333333333333 * (y / z)) + (t / (z * (y * 3.0))))
	else:
		tmp = x + ((y - (t / y)) / (z * -3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.5e+98)
		tmp = Float64(x + Float64(Float64(-0.3333333333333333 * Float64(y / z)) + Float64(t / Float64(z * Float64(y * 3.0)))));
	else
		tmp = Float64(x + Float64(Float64(y - Float64(t / y)) / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.5e+98)
		tmp = x + ((-0.3333333333333333 * (y / z)) + (t / (z * (y * 3.0))));
	else
		tmp = x + ((y - (t / y)) / (z * -3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.5e+98], N[(x + N[(N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.5000000000000002e98

   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. sub-neg 99.8%

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

      3. distribute-frac-neg 99.8%

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

      4. associate-+r+ 99.8%

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

      5. --rgt-identity 99.8%

         \[\leadsto \color{blue}{\left(\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - 0\right)} + \frac{-y}{z \cdot 3} \]

      6. +-commutative 99.8%

         \[\leadsto \left(\color{blue}{\left(x + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} - 0\right) + \frac{-y}{z \cdot 3} \]

      7. associate--l+ 99.8%

         \[\leadsto \color{blue}{\left(x + \left(\frac{t}{\left(z \cdot 3\right) \cdot y} - 0\right)\right)} + \frac{-y}{z \cdot 3} \]

      8. associate-+l+ 99.8%

         \[\leadsto \color{blue}{x + \left(\left(\frac{t}{\left(z \cdot 3\right) \cdot y} - 0\right) + \frac{-y}{z \cdot 3}\right)} \]

      9. associate--r- 99.8%

         \[\leadsto x + \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} - \left(0 - \frac{-y}{z \cdot 3}\right)\right)} \]

      10. neg-sub0 99.8%

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

      11. distribute-frac-neg 99.8%

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

      12. remove-double-neg 99.8%

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

      13. sub-neg 99.8%

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

      14. distribute-frac-neg 99.8%

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

      15. +-commutative 99.8%

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

   3. Simplified 99.6%

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

   if -4.5000000000000002e98 < t

   1. Initial program 95.1%

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

   3. Simplified 97.5%

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

      1. clear-num 97.5%

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

      2. associate-*l/ 97.5%

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

      3. *-un-lft-identity 97.5%

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

      4. div-inv 97.6%

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

      5. metadata-eval 97.6%

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

   5. Applied egg-rr 97.6%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.5 \cdot 10^{+98}:\\ \;\;\;\;x + \left(-0.3333333333333333 \cdot \frac{y}{z} + \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z \cdot -3}\\ \end{array} \]

Alternative 7: 82.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+69} \lor \neg \left(z \leq 1.4 \cdot 10^{+39}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -6.5e+69) (not (<= z 1.4e+39)))
   (+ x (/ y (* z -3.0)))
   (* (- y (/ t y)) (/ -0.3333333333333333 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.5e+69) || !(z <= 1.4e+39)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = (y - (t / y)) * (-0.3333333333333333 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-6.5d+69)) .or. (.not. (z <= 1.4d+39))) then
        tmp = x + (y / (z * (-3.0d0)))
    else
        tmp = (y - (t / y)) * ((-0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -6.5e+69) || !(z <= 1.4e+39)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = (y - (t / y)) * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -6.5e+69) or not (z <= 1.4e+39):
		tmp = x + (y / (z * -3.0))
	else:
		tmp = (y - (t / y)) * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -6.5e+69) || !(z <= 1.4e+39))
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	else
		tmp = Float64(Float64(y - Float64(t / y)) * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -6.5e+69) || ~((z <= 1.4e+39)))
		tmp = x + (y / (z * -3.0));
	else
		tmp = (y - (t / y)) * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -6.5e+69], N[Not[LessEqual[z, 1.4e+39]], $MachinePrecision]], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -6.5000000000000001e69 or 1.40000000000000001e39 < z

   1. Initial program 99.0%

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

   3. Simplified 91.2%

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

      1. associate-*l/ 91.2%

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

      2. associate-/l* 91.2%

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

   5. Applied egg-rr 91.2%

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

   6. Taylor expanded in y around inf 78.8%

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

      1. div-inv 78.8%

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

      2. metadata-eval 78.8%

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

      3. clear-num 78.8%

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

      4. times-frac 78.9%

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

      5. *-commutative 78.9%

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

      6. times-frac 78.9%

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

   8. Applied egg-rr 78.9%

      \[\leadsto x + \color{blue}{\frac{1}{z} \cdot \frac{y}{-3}} \]
   9. Step-by-step derivation

      1. associate-*r/ 78.8%

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

      2. associate-*l/ 78.8%

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

      3. *-lft-identity 78.8%

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

      4. rem-square-sqrt 39.6%

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

      5. associate-/r* 39.6%

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

      6. rem-square-sqrt 78.9%

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

   10. Simplified 78.9%

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

   if -6.5000000000000001e69 < z < 1.40000000000000001e39

   1. Initial program 93.9%

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

      1. *-un-lft-identity 93.9%

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

      2. times-frac 93.9%

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

   3. Applied egg-rr 93.9%

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

   4. Taylor expanded in x around 0 85.3%

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

      1. cancel-sign-sub-inv 85.3%

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

      2. metadata-eval 85.3%

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

      3. +-commutative 85.3%

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

      4. associate-*r/ 85.3%

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

      5. associate-*l/ 85.2%

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

      6. *-commutative 85.2%

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

      7. associate-*r/ 85.3%

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

      8. associate-/l* 85.3%

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

      9. associate-*r/ 87.9%

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

      10. metadata-eval 87.9%

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

      11. associate-/r* 87.9%

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

      12. mul-1-neg 87.9%

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

      13. distribute-lft-neg-out 87.9%

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

      14. associate-*r/ 85.3%

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

      15. *-commutative 85.3%

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

      16. associate-/l* 85.3%

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

      17. *-commutative 85.3%

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

      18. metadata-eval 85.3%

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

      19. distribute-rgt-neg-in 85.3%

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

      20. distribute-lft-neg-in 85.3%

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

      21. associate-/l* 85.2%

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

      22. associate-/l* 85.3%

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

      23. neg-mul-1 85.3%

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

      24. associate-/r* 85.3%

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

   6. Simplified 89.3%

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

4. Final simplification 84.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+69} \lor \neg \left(z \leq 1.4 \cdot 10^{+39}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 8: 88.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-55} \lor \neg \left(y \leq 2.7 \cdot 10^{-13}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.6e-55) (not (<= y 2.7e-13)))
   (+ x (/ y (* z -3.0)))
   (+ x (* (/ t y) (/ 0.3333333333333333 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.6e-55) || !(y <= 2.7e-13)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.6d-55)) .or. (.not. (y <= 2.7d-13))) then
        tmp = x + (y / (z * (-3.0d0)))
    else
        tmp = x + ((t / y) * (0.3333333333333333d0 / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.6e-55) || !(y <= 2.7e-13)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.6e-55) or not (y <= 2.7e-13):
		tmp = x + (y / (z * -3.0))
	else:
		tmp = x + ((t / y) * (0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.6e-55) || !(y <= 2.7e-13))
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	else
		tmp = Float64(x + Float64(Float64(t / y) * Float64(0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.6e-55) || ~((y <= 2.7e-13)))
		tmp = x + (y / (z * -3.0));
	else
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.6e-55], N[Not[LessEqual[y, 2.7e-13]], $MachinePrecision]], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.6000000000000001e-55 or 2.70000000000000011e-13 < y

   1. Initial program 97.6%

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

   3. Simplified 99.6%

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

      1. associate-*l/ 99.6%

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

      2. associate-/l* 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 89.8%

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

      1. div-inv 89.7%

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

      2. metadata-eval 89.7%

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

      3. clear-num 89.8%

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

      4. times-frac 90.0%

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

      5. *-commutative 90.0%

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

      6. times-frac 89.9%

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

   8. Applied egg-rr 89.9%

      \[\leadsto x + \color{blue}{\frac{1}{z} \cdot \frac{y}{-3}} \]
   9. Step-by-step derivation

      1. associate-*r/ 89.8%

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

      2. associate-*l/ 89.8%

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

      3. *-lft-identity 89.8%

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

      4. rem-square-sqrt 43.7%

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

      5. associate-/r* 43.7%

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

      6. rem-square-sqrt 90.0%

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

   10. Simplified 90.0%

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

   if -3.6000000000000001e-55 < y < 2.70000000000000011e-13

   1. Initial program 94.3%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in y around 0 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-/r* 87.7%

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

      3. associate-*l/ 87.7%

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

      4. associate-*r/ 87.7%

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

   6. Simplified 87.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-55} \lor \neg \left(y \leq 2.7 \cdot 10^{-13}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \end{array} \]

Alternative 9: 88.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-55} \lor \neg \left(y \leq 5.8 \cdot 10^{-8}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.7e-55) (not (<= y 5.8e-8)))
   (+ x (/ y (* z -3.0)))
   (+ x (/ t (* y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.7e-55) || !(y <= 5.8e-8)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = x + (t / (y * (z * 3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-4.7d-55)) .or. (.not. (y <= 5.8d-8))) then
        tmp = x + (y / (z * (-3.0d0)))
    else
        tmp = x + (t / (y * (z * 3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.7e-55) || !(y <= 5.8e-8)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = x + (t / (y * (z * 3.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.7e-55) or not (y <= 5.8e-8):
		tmp = x + (y / (z * -3.0))
	else:
		tmp = x + (t / (y * (z * 3.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.7e-55) || !(y <= 5.8e-8))
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	else
		tmp = Float64(x + Float64(t / Float64(y * Float64(z * 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.7e-55) || ~((y <= 5.8e-8)))
		tmp = x + (y / (z * -3.0));
	else
		tmp = x + (t / (y * (z * 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.7e-55], N[Not[LessEqual[y, 5.8e-8]], $MachinePrecision]], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7e-55 or 5.8000000000000003e-8 < y

   1. Initial program 97.6%

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

   3. Simplified 99.6%

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

      1. associate-*l/ 99.6%

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

      2. associate-/l* 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 89.8%

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

      1. div-inv 89.7%

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

      2. metadata-eval 89.7%

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

      3. clear-num 89.8%

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

      4. times-frac 90.0%

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

      5. *-commutative 90.0%

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

      6. times-frac 89.9%

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

   8. Applied egg-rr 89.9%

      \[\leadsto x + \color{blue}{\frac{1}{z} \cdot \frac{y}{-3}} \]
   9. Step-by-step derivation

      1. associate-*r/ 89.8%

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

      2. associate-*l/ 89.8%

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

      3. *-lft-identity 89.8%

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

      4. rem-square-sqrt 43.7%

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

      5. associate-/r* 43.7%

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

      6. rem-square-sqrt 90.0%

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

   10. Simplified 90.0%

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

   if -4.7e-55 < y < 5.8000000000000003e-8

   1. Initial program 94.3%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in y around 0 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-/r* 87.7%

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

      3. associate-*l/ 87.7%

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

      4. associate-*r/ 87.7%

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

   6. Simplified 87.7%

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

      1. associate-*r/ 87.7%

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

      2. associate-/l* 87.7%

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

      3. div-inv 87.7%

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

      4. metadata-eval 87.7%

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

      5. associate-/r* 92.0%

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

      6. *-commutative 92.0%

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

      7. associate-*l* 91.9%

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

   8. Applied egg-rr 91.9%

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

   9. Taylor expanded in z around 0 92.0%

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

       1. *-commutative 92.0%

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

       2. associate-*l* 92.0%

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

   11. Simplified 92.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-55} \lor \neg \left(y \leq 5.8 \cdot 10^{-8}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]

Alternative 10: 91.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-55} \lor \neg \left(y \leq 7.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.7e-55) (not (<= y 7.5e-8)))
   (+ x (/ y (* z -3.0)))
   (+ x (/ (/ t z) (* y 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.7e-55) || !(y <= 7.5e-8)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = x + ((t / z) / (y * 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 <= (-4.7d-55)) .or. (.not. (y <= 7.5d-8))) then
        tmp = x + (y / (z * (-3.0d0)))
    else
        tmp = x + ((t / z) / (y * 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 <= -4.7e-55) || !(y <= 7.5e-8)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = x + ((t / z) / (y * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.7e-55) or not (y <= 7.5e-8):
		tmp = x + (y / (z * -3.0))
	else:
		tmp = x + ((t / z) / (y * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.7e-55) || !(y <= 7.5e-8))
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	else
		tmp = Float64(x + Float64(Float64(t / z) / Float64(y * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.7e-55) || ~((y <= 7.5e-8)))
		tmp = x + (y / (z * -3.0));
	else
		tmp = x + ((t / z) / (y * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.7e-55], N[Not[LessEqual[y, 7.5e-8]], $MachinePrecision]], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.7e-55 or 7.4999999999999997e-8 < y

   1. Initial program 97.6%

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

   3. Simplified 99.6%

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

      1. associate-*l/ 99.6%

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

      2. associate-/l* 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 89.8%

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

      1. div-inv 89.7%

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

      2. metadata-eval 89.7%

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

      3. clear-num 89.8%

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

      4. times-frac 90.0%

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

      5. *-commutative 90.0%

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

      6. times-frac 89.9%

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

   8. Applied egg-rr 89.9%

      \[\leadsto x + \color{blue}{\frac{1}{z} \cdot \frac{y}{-3}} \]
   9. Step-by-step derivation

      1. associate-*r/ 89.8%

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

      2. associate-*l/ 89.8%

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

      3. *-lft-identity 89.8%

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

      4. rem-square-sqrt 43.7%

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

      5. associate-/r* 43.7%

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

      6. rem-square-sqrt 90.0%

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

   10. Simplified 90.0%

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

   if -4.7e-55 < y < 7.4999999999999997e-8

   1. Initial program 94.3%

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

   3. Simplified 90.4%

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

   4. Taylor expanded in y around 0 91.9%

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

      1. *-commutative 91.9%

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

      2. associate-/r* 87.7%

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

      3. associate-*l/ 87.7%

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

      4. associate-*r/ 87.7%

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

   6. Simplified 87.7%

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

      1. associate-*r/ 87.7%

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

      2. associate-/l* 87.7%

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

      3. div-inv 87.7%

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

      4. metadata-eval 87.7%

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

      5. associate-/r* 92.0%

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

      6. *-commutative 92.0%

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

      7. associate-*l* 91.9%

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

      8. associate-/r* 97.0%

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

   8. Applied egg-rr 97.0%

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

4. Final simplification 93.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-55} \lor \neg \left(y \leq 7.5 \cdot 10^{-8}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \]

Alternative 11: 75.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-122} \lor \neg \left(y \leq 3.1 \cdot 10^{-14}\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.1e-122) (not (<= y 3.1e-14)))
   (+ x (/ -0.3333333333333333 (/ z y)))
   (* 0.3333333333333333 (/ t (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.1e-122) || !(y <= 3.1e-14)) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} 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 <= (-4.1d-122)) .or. (.not. (y <= 3.1d-14))) then
        tmp = x + ((-0.3333333333333333d0) / (z / y))
    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 <= -4.1e-122) || !(y <= 3.1e-14)) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else {
		tmp = 0.3333333333333333 * (t / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.1e-122) or not (y <= 3.1e-14):
		tmp = x + (-0.3333333333333333 / (z / y))
	else:
		tmp = 0.3333333333333333 * (t / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.1e-122) || !(y <= 3.1e-14))
		tmp = Float64(x + Float64(-0.3333333333333333 / Float64(z / y)));
	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 <= -4.1e-122) || ~((y <= 3.1e-14)))
		tmp = x + (-0.3333333333333333 / (z / y));
	else
		tmp = 0.3333333333333333 * (t / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.1e-122], N[Not[LessEqual[y, 3.1e-14]], $MachinePrecision]], N[(x + N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1e-122 or 3.10000000000000004e-14 < y

   1. Initial program 97.8%

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

   3. Simplified 99.7%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 88.5%

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

   if -4.1e-122 < y < 3.10000000000000004e-14

   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. *-un-lft-identity 93.8%

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

      2. times-frac 93.8%

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

   3. Applied egg-rr 93.8%

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

   4. Taylor expanded in x around 0 68.7%

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

      1. cancel-sign-sub-inv 68.7%

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

      2. metadata-eval 68.7%

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

      3. +-commutative 68.7%

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

      4. associate-*r/ 68.7%

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

      5. associate-*l/ 68.7%

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

      6. *-commutative 68.7%

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

      7. associate-*r/ 68.7%

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

      8. associate-/l* 68.6%

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

      9. associate-*r/ 64.9%

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

      10. metadata-eval 64.9%

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

      11. associate-/r* 64.9%

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

      12. mul-1-neg 64.9%

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

      13. distribute-lft-neg-out 64.9%

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

      14. associate-*r/ 68.6%

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

      15. *-commutative 68.6%

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

      16. associate-/l* 68.7%

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

      17. *-commutative 68.7%

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

      18. metadata-eval 68.7%

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

      19. distribute-rgt-neg-in 68.7%

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

      20. distribute-lft-neg-in 68.7%

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

      21. associate-/l* 68.6%

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

      22. associate-/l* 68.6%

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

      23. neg-mul-1 68.6%

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

      24. associate-/r* 68.6%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in y around 0 66.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.1 \cdot 10^{-122} \lor \neg \left(y \leq 3.1 \cdot 10^{-14}\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 12: 75.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-123} \lor \neg \left(y \leq 5.4 \cdot 10^{-14}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.2e-123) (not (<= y 5.4e-14)))
   (+ x (/ y (* z -3.0)))
   (* 0.3333333333333333 (/ t (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.2e-123) || !(y <= 5.4e-14)) {
		tmp = x + (y / (z * -3.0));
	} 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 <= (-9.2d-123)) .or. (.not. (y <= 5.4d-14))) then
        tmp = x + (y / (z * (-3.0d0)))
    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 <= -9.2e-123) || !(y <= 5.4e-14)) {
		tmp = x + (y / (z * -3.0));
	} else {
		tmp = 0.3333333333333333 * (t / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.2e-123) or not (y <= 5.4e-14):
		tmp = x + (y / (z * -3.0))
	else:
		tmp = 0.3333333333333333 * (t / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.2e-123) || !(y <= 5.4e-14))
		tmp = Float64(x + Float64(y / Float64(z * -3.0)));
	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 <= -9.2e-123) || ~((y <= 5.4e-14)))
		tmp = x + (y / (z * -3.0));
	else
		tmp = 0.3333333333333333 * (t / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.2e-123], N[Not[LessEqual[y, 5.4e-14]], $MachinePrecision]], N[(x + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.19999999999999947e-123 or 5.3999999999999997e-14 < y

   1. Initial program 97.8%

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

   3. Simplified 99.7%

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

      1. associate-*l/ 99.7%

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

      2. associate-/l* 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 88.5%

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

      1. div-inv 88.4%

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

      2. metadata-eval 88.4%

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

      3. clear-num 88.5%

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

      4. times-frac 88.7%

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

      5. *-commutative 88.7%

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

      6. times-frac 88.6%

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

   8. Applied egg-rr 88.6%

      \[\leadsto x + \color{blue}{\frac{1}{z} \cdot \frac{y}{-3}} \]
   9. Step-by-step derivation

      1. associate-*r/ 88.5%

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

      2. associate-*l/ 88.6%

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

      3. *-lft-identity 88.6%

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

      4. rem-square-sqrt 40.8%

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

      5. associate-/r* 40.7%

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

      6. rem-square-sqrt 88.7%

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

   10. Simplified 88.7%

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

   if -9.19999999999999947e-123 < y < 5.3999999999999997e-14

   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. *-un-lft-identity 93.8%

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

      2. times-frac 93.8%

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

   3. Applied egg-rr 93.8%

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

   4. Taylor expanded in x around 0 68.7%

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

      1. cancel-sign-sub-inv 68.7%

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

      2. metadata-eval 68.7%

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

      3. +-commutative 68.7%

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

      4. associate-*r/ 68.7%

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

      5. associate-*l/ 68.7%

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

      6. *-commutative 68.7%

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

      7. associate-*r/ 68.7%

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

      8. associate-/l* 68.6%

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

      9. associate-*r/ 64.9%

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

      10. metadata-eval 64.9%

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

      11. associate-/r* 64.9%

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

      12. mul-1-neg 64.9%

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

      13. distribute-lft-neg-out 64.9%

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

      14. associate-*r/ 68.6%

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

      15. *-commutative 68.6%

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

      16. associate-/l* 68.7%

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

      17. *-commutative 68.7%

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

      18. metadata-eval 68.7%

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

      19. distribute-rgt-neg-in 68.7%

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

      20. distribute-lft-neg-in 68.7%

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

      21. associate-/l* 68.6%

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

      22. associate-/l* 68.6%

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

      23. neg-mul-1 68.6%

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

      24. associate-/r* 68.6%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in y around 0 66.2%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{-123} \lor \neg \left(y \leq 5.4 \cdot 10^{-14}\right):\\ \;\;\;\;x + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 13: 46.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 102000:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.4e+179)
   x
   (if (<= x 102000.0) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.4e+179) {
		tmp = x;
	} else if (x <= 102000.0) {
		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 <= (-1.4d+179)) then
        tmp = x
    else if (x <= 102000.0d0) 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 <= -1.4e+179) {
		tmp = x;
	} else if (x <= 102000.0) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.4e+179:
		tmp = x
	elif x <= 102000.0:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.4e+179)
		tmp = x;
	elseif (x <= 102000.0)
		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 <= -1.4e+179)
		tmp = x;
	elseif (x <= 102000.0)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.4e+179], x, If[LessEqual[x, 102000.0], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4e179 or 102000 < x

   1. Initial program 94.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 63.3%

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

   if -1.4e179 < x < 102000

   1. Initial program 96.8%

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

      1. *-un-lft-identity 96.8%

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

      2. times-frac 96.8%

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

   3. Applied egg-rr 96.8%

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

   4. Taylor expanded in y around inf 43.1%

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

4. Final simplification 50.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 102000:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14: 46.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 61000000:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.4e+179) x (if (<= x 61000000.0) (/ y (* z -3.0)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.4e+179) {
		tmp = x;
	} else if (x <= 61000000.0) {
		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 <= (-1.4d+179)) then
        tmp = x
    else if (x <= 61000000.0d0) 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 <= -1.4e+179) {
		tmp = x;
	} else if (x <= 61000000.0) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.4e+179:
		tmp = x
	elif x <= 61000000.0:
		tmp = y / (z * -3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.4e+179)
		tmp = x;
	elseif (x <= 61000000.0)
		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 <= -1.4e+179)
		tmp = x;
	elseif (x <= 61000000.0)
		tmp = y / (z * -3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.4e+179], x, If[LessEqual[x, 61000000.0], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4e179 or 6.1e7 < x

   1. Initial program 94.8%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 63.3%

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

   if -1.4e179 < x < 6.1e7

   1. Initial program 96.8%

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

      1. *-un-lft-identity 96.8%

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

      2. times-frac 96.8%

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

   3. Applied egg-rr 96.8%

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

   4. Taylor expanded in x around 0 85.5%

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

      1. cancel-sign-sub-inv 85.5%

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

      2. metadata-eval 85.5%

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

      3. +-commutative 85.5%

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

      4. associate-*r/ 85.5%

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

      5. associate-*l/ 85.5%

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

      6. *-commutative 85.5%

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

      7. associate-*r/ 85.4%

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

      8. associate-/l* 85.4%

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

      9. associate-*r/ 83.5%

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

      10. metadata-eval 83.5%

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

      11. associate-/r* 83.5%

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

      12. mul-1-neg 83.5%

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

      13. distribute-lft-neg-out 83.5%

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

      14. associate-*r/ 85.4%

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

      15. *-commutative 85.4%

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

      16. associate-/l* 85.4%

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

      17. *-commutative 85.4%

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

      18. metadata-eval 85.4%

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

      19. distribute-rgt-neg-in 85.4%

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

      20. distribute-lft-neg-in 85.4%

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

      21. associate-/l* 85.4%

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

      22. associate-/l* 85.4%

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

      23. neg-mul-1 85.4%

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

      24. associate-/r* 85.4%

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

   6. Simplified 83.3%

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

   7. Taylor expanded in y around inf 43.1%

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

      1. associate-*r/ 43.1%

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

      2. *-commutative 43.1%

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

      3. /-rgt-identity 43.1%

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

      4. associate-/l* 43.2%

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

      5. metadata-eval 43.2%

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

      6. associate-/l/ 43.2%

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

   9. Simplified 43.2%

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

4. Final simplification 50.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{+179}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 61000000:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 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 96.1%

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

3. Simplified 95.3%

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

4. Taylor expanded in x around inf 31.2%

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

5. Final simplification 31.2%

   \[\leadsto x \]

Developer target: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023336 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

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

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