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

Percentage Accurate: 95.3% → 95.5%

Time: 9.0s

Alternatives: 13

Speedup: 1.4×

• 28.1% 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: 95.3% 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: 95.5% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

   1. associate-+l- 95.5%

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

   2. sub-neg 95.5%

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

   3. sub-neg 95.5%

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

   4. distribute-neg-in 95.5%

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

   5. unsub-neg 95.5%

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

   6. neg-mul-1 95.5%

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

   7. associate-*r/ 95.5%

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

   8. associate-*l/ 95.4%

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

   9. distribute-neg-frac 95.4%

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

   10. neg-mul-1 95.4%

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

   11. times-frac 97.5%

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

   12. distribute-lft-out-- 97.9%

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

   13. *-commutative 97.9%

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

   14. associate-/r* 97.9%

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

   15. metadata-eval 97.9%

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

3. Simplified 97.9%

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

   1. *-commutative 97.9%

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

   2. clear-num 97.9%

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

   3. un-div-inv 98.0%

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

   4. div-inv 98.0%

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

   5. metadata-eval 98.0%

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

5. Applied egg-rr 98.0%

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

6. Final simplification 98.0%

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

Alternative 2: 61.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ t_2 := x + 0.3333333333333333 \cdot \frac{y}{z}\\ t_3 := \frac{0.3333333333333333}{\frac{-z}{y}}\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{-27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+66}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.3333333333333333 (/ t (* y z))))
        (t_2 (+ x (* 0.3333333333333333 (/ y z))))
        (t_3 (/ 0.3333333333333333 (/ (- z) y))))
   (if (<= y -1.06e-27)
     t_3
     (if (<= y 1.95e-26)
       t_1
       (if (<= y 2.1e+19)
         t_2
         (if (<= y 7e+29)
           t_1
           (if (<= y 4.1e+66)
             (/ (* y -0.3333333333333333) z)
             (if (<= y 7.4e+99) t_2 t_3))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (y * z));
	double t_2 = x + (0.3333333333333333 * (y / z));
	double t_3 = 0.3333333333333333 / (-z / y);
	double tmp;
	if (y <= -1.06e-27) {
		tmp = t_3;
	} else if (y <= 1.95e-26) {
		tmp = t_1;
	} else if (y <= 2.1e+19) {
		tmp = t_2;
	} else if (y <= 7e+29) {
		tmp = t_1;
	} else if (y <= 4.1e+66) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 7.4e+99) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = 0.3333333333333333d0 * (t / (y * z))
    t_2 = x + (0.3333333333333333d0 * (y / z))
    t_3 = 0.3333333333333333d0 / (-z / y)
    if (y <= (-1.06d-27)) then
        tmp = t_3
    else if (y <= 1.95d-26) then
        tmp = t_1
    else if (y <= 2.1d+19) then
        tmp = t_2
    else if (y <= 7d+29) then
        tmp = t_1
    else if (y <= 4.1d+66) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= 7.4d+99) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (y * z));
	double t_2 = x + (0.3333333333333333 * (y / z));
	double t_3 = 0.3333333333333333 / (-z / y);
	double tmp;
	if (y <= -1.06e-27) {
		tmp = t_3;
	} else if (y <= 1.95e-26) {
		tmp = t_1;
	} else if (y <= 2.1e+19) {
		tmp = t_2;
	} else if (y <= 7e+29) {
		tmp = t_1;
	} else if (y <= 4.1e+66) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 7.4e+99) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 * (t / (y * z))
	t_2 = x + (0.3333333333333333 * (y / z))
	t_3 = 0.3333333333333333 / (-z / y)
	tmp = 0
	if y <= -1.06e-27:
		tmp = t_3
	elif y <= 1.95e-26:
		tmp = t_1
	elif y <= 2.1e+19:
		tmp = t_2
	elif y <= 7e+29:
		tmp = t_1
	elif y <= 4.1e+66:
		tmp = (y * -0.3333333333333333) / z
	elif y <= 7.4e+99:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 * Float64(t / Float64(y * z)))
	t_2 = Float64(x + Float64(0.3333333333333333 * Float64(y / z)))
	t_3 = Float64(0.3333333333333333 / Float64(Float64(-z) / y))
	tmp = 0.0
	if (y <= -1.06e-27)
		tmp = t_3;
	elseif (y <= 1.95e-26)
		tmp = t_1;
	elseif (y <= 2.1e+19)
		tmp = t_2;
	elseif (y <= 7e+29)
		tmp = t_1;
	elseif (y <= 4.1e+66)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= 7.4e+99)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 * (t / (y * z));
	t_2 = x + (0.3333333333333333 * (y / z));
	t_3 = 0.3333333333333333 / (-z / y);
	tmp = 0.0;
	if (y <= -1.06e-27)
		tmp = t_3;
	elseif (y <= 1.95e-26)
		tmp = t_1;
	elseif (y <= 2.1e+19)
		tmp = t_2;
	elseif (y <= 7e+29)
		tmp = t_1;
	elseif (y <= 4.1e+66)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= 7.4e+99)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(0.3333333333333333 / N[((-z) / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e-27], t$95$3, If[LessEqual[y, 1.95e-26], t$95$1, If[LessEqual[y, 2.1e+19], t$95$2, If[LessEqual[y, 7e+29], t$95$1, If[LessEqual[y, 4.1e+66], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 7.4e+99], t$95$2, t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.05999999999999998e-27 or 7.4000000000000002e99 < y

   1. Initial program 99.8%

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

      1. associate-/r* 96.3%

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

   3. Simplified 96.3%

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

      1. clear-num 96.3%

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

      2. inv-pow 96.3%

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

      3. *-commutative 96.3%

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

      4. *-un-lft-identity 96.3%

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

      5. times-frac 96.3%

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

      6. metadata-eval 96.3%

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

   5. Applied egg-rr 96.3%

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

      1. unpow-1 96.3%

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

   7. Simplified 96.3%

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

      1. associate-+l- 96.3%

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

      2. associate-/r* 96.3%

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

      3. metadata-eval 96.3%

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

   9. Applied egg-rr 96.3%

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

       1. associate--r- 96.3%

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

       2. +-commutative 96.3%

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

       3. associate-+r- 96.3%

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

       4. associate-/r/ 96.3%

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

       5. associate-/r* 95.5%

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

   11. Simplified 95.5%

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

   12. Taylor expanded in z around 0 77.0%

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

       1. distribute-lft-out-- 77.0%

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

       2. associate-/l* 77.0%

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

   14. Simplified 77.0%

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

   15. Taylor expanded in t around 0 73.4%

       \[\leadsto \frac{0.3333333333333333}{\color{blue}{-1 \cdot \frac{z}{y}}} \]
   16. Step-by-step derivation

       1. associate-*r/ 73.4%

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

       2. neg-mul-1 73.4%

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

   17. Simplified 73.4%

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

   if -1.05999999999999998e-27 < y < 1.94999999999999993e-26 or 2.1e19 < y < 6.99999999999999958e29

   1. Initial program 91.5%

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

      1. associate-/r* 99.1%

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

   3. Simplified 99.1%

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

      1. clear-num 99.0%

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

      2. inv-pow 99.0%

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

      3. *-commutative 99.0%

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

      4. *-un-lft-identity 99.0%

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

      5. times-frac 99.0%

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

      6. metadata-eval 99.0%

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

   5. Applied egg-rr 99.0%

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

      1. unpow-1 99.0%

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

   7. Simplified 99.0%

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

      1. associate-+l- 99.0%

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

      2. associate-/r* 99.0%

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

      3. metadata-eval 99.0%

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

   9. Applied egg-rr 99.0%

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

       1. associate--r- 99.0%

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

       2. +-commutative 99.0%

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

       3. associate-+r- 99.0%

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

       4. associate-/r/ 99.0%

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

       5. associate-/r* 99.0%

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

   11. Simplified 99.0%

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

   12. Taylor expanded in z around 0 62.6%

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

       1. distribute-lft-out-- 62.6%

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

       2. associate-/l* 62.6%

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

   14. Simplified 62.6%

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

   15. Taylor expanded in t around inf 57.2%

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

   if 1.94999999999999993e-26 < y < 2.1e19 or 4.09999999999999994e66 < y < 7.4000000000000002e99

   1. Initial program 93.5%

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

      1. associate-+l- 93.5%

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

      2. sub-neg 93.5%

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

      3. sub-neg 93.5%

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

      4. distribute-neg-in 93.5%

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

      5. unsub-neg 93.5%

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

      6. neg-mul-1 93.5%

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

      7. associate-*r/ 93.5%

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

      8. associate-*l/ 93.5%

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

      9. distribute-neg-frac 93.5%

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

      10. neg-mul-1 93.5%

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

      11. times-frac 93.6%

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

      12. distribute-lft-out-- 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-/r* 99.8%

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

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. un-div-inv 99.8%

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

      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%

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

   6. Taylor expanded in y around inf 87.4%

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

      1. associate-*r/ 87.5%

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

      2. associate-/l* 87.3%

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

   8. Simplified 87.3%

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

      1. add-sqr-sqrt 50.0%

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

      2. sqrt-unprod 81.2%

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

      3. frac-times 81.3%

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

      4. metadata-eval 81.3%

         \[\leadsto x + \sqrt{\frac{\color{blue}{0.1111111111111111}}{\frac{z}{y} \cdot \frac{z}{y}}} \]

      5. metadata-eval 81.3%

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

      6. frac-times 81.2%

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

      7. associate-/l* 81.3%

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

      8. associate-/l* 81.3%

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

      9. sqrt-unprod 31.3%

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

      10. add-sqr-sqrt 75.6%

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

      11. *-un-lft-identity 75.6%

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

      12. times-frac 75.6%

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

      13. metadata-eval 75.6%

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

      14. metadata-eval 75.6%

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

      15. times-frac 75.6%

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

      16. *-un-lft-identity 75.6%

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

      17. associate-/l/ 75.6%

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

      18. div-inv 75.6%

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

      19. metadata-eval 75.6%

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

   10. Applied egg-rr 75.6%

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

   if 6.99999999999999958e29 < y < 4.09999999999999994e66

   1. Initial program 100.0%

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

      1. associate-/r* 86.9%

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

   3. Simplified 86.9%

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

      1. clear-num 86.9%

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

      2. inv-pow 86.9%

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

      3. *-commutative 86.9%

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

      4. *-un-lft-identity 86.9%

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

      5. times-frac 86.9%

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

      6. metadata-eval 86.9%

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

   5. Applied egg-rr 86.9%

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

      1. unpow-1 86.9%

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

   7. Simplified 86.9%

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

      1. associate-+l- 86.9%

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

      2. associate-/r* 86.9%

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

      3. metadata-eval 86.9%

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

   9. Applied egg-rr 86.9%

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

       1. associate--r- 86.9%

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

       2. +-commutative 86.9%

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

       3. associate-+r- 86.9%

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

       4. associate-/r/ 86.9%

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

       5. associate-/r* 86.5%

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

   11. Simplified 86.5%

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

   12. Taylor expanded in z around 0 71.6%

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

       1. distribute-lft-out-- 71.6%

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

       2. associate-/l* 71.2%

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

   14. Simplified 71.2%

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

   15. Taylor expanded in t around 0 56.9%

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

       1. *-commutative 56.9%

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

       2. associate-*l/ 57.4%

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

   17. Simplified 57.4%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-27}:\\ \;\;\;\;\frac{0.3333333333333333}{\frac{-z}{y}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-26}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+19}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+29}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+66}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+99}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{\frac{-z}{y}}\\ \end{array} \]

Alternative 3: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ t_2 := x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-131}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-82}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 0.3333333333333333 (* z (/ y t))))
        (t_2 (+ x (/ -0.3333333333333333 (/ z y)))))
   (if (<= y -6.8e-42)
     t_2
     (if (<= y -4.8e-159)
       t_1
       (if (<= y -3.7e-191)
         t_2
         (if (<= y 4.2e-131)
           t_1
           (if (<= y 1.15e-82)
             t_2
             (if (<= y 2e-26) t_1 (- x (/ (* y 0.3333333333333333) z))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 / (z * (y / t));
	double t_2 = x + (-0.3333333333333333 / (z / y));
	double tmp;
	if (y <= -6.8e-42) {
		tmp = t_2;
	} else if (y <= -4.8e-159) {
		tmp = t_1;
	} else if (y <= -3.7e-191) {
		tmp = t_2;
	} else if (y <= 4.2e-131) {
		tmp = t_1;
	} else if (y <= 1.15e-82) {
		tmp = t_2;
	} else if (y <= 2e-26) {
		tmp = t_1;
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.3333333333333333d0 / (z * (y / t))
    t_2 = x + ((-0.3333333333333333d0) / (z / y))
    if (y <= (-6.8d-42)) then
        tmp = t_2
    else if (y <= (-4.8d-159)) then
        tmp = t_1
    else if (y <= (-3.7d-191)) then
        tmp = t_2
    else if (y <= 4.2d-131) then
        tmp = t_1
    else if (y <= 1.15d-82) then
        tmp = t_2
    else if (y <= 2d-26) then
        tmp = t_1
    else
        tmp = x - ((y * 0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 / (z * (y / t));
	double t_2 = x + (-0.3333333333333333 / (z / y));
	double tmp;
	if (y <= -6.8e-42) {
		tmp = t_2;
	} else if (y <= -4.8e-159) {
		tmp = t_1;
	} else if (y <= -3.7e-191) {
		tmp = t_2;
	} else if (y <= 4.2e-131) {
		tmp = t_1;
	} else if (y <= 1.15e-82) {
		tmp = t_2;
	} else if (y <= 2e-26) {
		tmp = t_1;
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 / (z * (y / t))
	t_2 = x + (-0.3333333333333333 / (z / y))
	tmp = 0
	if y <= -6.8e-42:
		tmp = t_2
	elif y <= -4.8e-159:
		tmp = t_1
	elif y <= -3.7e-191:
		tmp = t_2
	elif y <= 4.2e-131:
		tmp = t_1
	elif y <= 1.15e-82:
		tmp = t_2
	elif y <= 2e-26:
		tmp = t_1
	else:
		tmp = x - ((y * 0.3333333333333333) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 / Float64(z * Float64(y / t)))
	t_2 = Float64(x + Float64(-0.3333333333333333 / Float64(z / y)))
	tmp = 0.0
	if (y <= -6.8e-42)
		tmp = t_2;
	elseif (y <= -4.8e-159)
		tmp = t_1;
	elseif (y <= -3.7e-191)
		tmp = t_2;
	elseif (y <= 4.2e-131)
		tmp = t_1;
	elseif (y <= 1.15e-82)
		tmp = t_2;
	elseif (y <= 2e-26)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 / (z * (y / t));
	t_2 = x + (-0.3333333333333333 / (z / y));
	tmp = 0.0;
	if (y <= -6.8e-42)
		tmp = t_2;
	elseif (y <= -4.8e-159)
		tmp = t_1;
	elseif (y <= -3.7e-191)
		tmp = t_2;
	elseif (y <= 4.2e-131)
		tmp = t_1;
	elseif (y <= 1.15e-82)
		tmp = t_2;
	elseif (y <= 2e-26)
		tmp = t_1;
	else
		tmp = x - ((y * 0.3333333333333333) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 / N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6.8e-42], t$95$2, If[LessEqual[y, -4.8e-159], t$95$1, If[LessEqual[y, -3.7e-191], t$95$2, If[LessEqual[y, 4.2e-131], t$95$1, If[LessEqual[y, 1.15e-82], t$95$2, If[LessEqual[y, 2e-26], t$95$1, N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.80000000000000045e-42 or -4.79999999999999995e-159 < y < -3.6999999999999997e-191 or 4.19999999999999994e-131 < y < 1.14999999999999998e-82

   1. Initial program 98.1%

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

      1. associate-+l- 98.1%

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

      2. sub-neg 98.1%

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

      3. sub-neg 98.1%

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

      4. distribute-neg-in 98.1%

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

      5. unsub-neg 98.1%

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

      6. neg-mul-1 98.1%

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

      7. associate-*r/ 98.1%

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

      8. associate-*l/ 98.0%

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

      9. distribute-neg-frac 98.0%

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

      10. neg-mul-1 98.0%

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

      11. times-frac 97.8%

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

      12. distribute-lft-out-- 97.8%

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

      13. *-commutative 97.8%

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

      14. associate-/r* 97.8%

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

      15. metadata-eval 97.8%

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

   3. Simplified 97.8%

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

      1. *-commutative 97.8%

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

      2. clear-num 97.8%

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

      3. un-div-inv 97.9%

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

      4. div-inv 97.9%

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

      5. metadata-eval 97.9%

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

   5. Applied egg-rr 97.9%

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

   6. Taylor expanded in y around inf 87.6%

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

      1. associate-*r/ 88.4%

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

      2. associate-/l* 88.5%

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

   8. Simplified 88.5%

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

   if -6.80000000000000045e-42 < y < -4.79999999999999995e-159 or -3.6999999999999997e-191 < y < 4.19999999999999994e-131 or 1.14999999999999998e-82 < y < 2.0000000000000001e-26

   1. Initial program 90.9%

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

      1. associate-/r* 98.8%

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

   3. Simplified 98.8%

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

      1. clear-num 98.8%

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

      2. inv-pow 98.8%

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

      3. *-commutative 98.8%

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

      4. *-un-lft-identity 98.8%

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

      5. times-frac 98.8%

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

      6. metadata-eval 98.8%

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

   5. Applied egg-rr 98.8%

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

      1. unpow-1 98.8%

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

   7. Simplified 98.8%

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

      1. associate-+l- 98.8%

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

      2. associate-/r* 98.8%

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

      3. metadata-eval 98.8%

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

   9. Applied egg-rr 98.8%

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

       1. associate--r- 98.8%

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

       2. +-commutative 98.8%

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

       3. associate-+r- 98.8%

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

       4. associate-/r/ 98.8%

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

       5. associate-/r* 98.8%

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

   11. Simplified 98.8%

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

   12. Taylor expanded in z around 0 70.0%

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

       1. distribute-lft-out-- 70.0%

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

       2. associate-/l* 69.9%

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

   14. Simplified 69.9%

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

   15. Taylor expanded in t around inf 63.7%

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

       1. *-commutative 63.7%

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

       2. associate-*r/ 68.7%

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

   17. Simplified 68.7%

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

   if 2.0000000000000001e-26 < y

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 98.2%

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

      1. cancel-sign-sub-inv 98.2%

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

      2. metadata-eval 98.2%

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

      3. +-commutative 98.2%

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

      4. associate-+r+ 98.2%

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

      5. +-commutative 98.2%

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

      6. associate-/r* 98.2%

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

      7. associate-*r/ 98.2%

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

      8. metadata-eval 98.2%

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

      9. cancel-sign-sub-inv 98.2%

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

      10. associate-*r/ 98.2%

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

      11. div-sub 99.8%

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

      12. distribute-lft-out-- 99.8%

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

      13. metadata-eval 99.8%

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

      14. associate-*r* 99.8%

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

      15. distribute-lft-out-- 99.8%

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

      16. associate-*r/ 99.8%

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

      17. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in t around 0 91.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-42}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-159}:\\ \;\;\;\;\frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ \mathbf{elif}\;y \leq -3.7 \cdot 10^{-191}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{-131}:\\ \;\;\;\;\frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-82}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-26}:\\ \;\;\;\;\frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \]

Alternative 4: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-40} \lor \neg \left(y \leq 5.3 \cdot 10^{-133}\right) \land \left(y \leq 1.3 \cdot 10^{-83} \lor \neg \left(y \leq 1.35 \cdot 10^{-26}\right)\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.3e-40)
         (and (not (<= y 5.3e-133)) (or (<= y 1.3e-83) (not (<= y 1.35e-26)))))
   (+ 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 <= -4.3e-40) || (!(y <= 5.3e-133) && ((y <= 1.3e-83) || !(y <= 1.35e-26)))) {
		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 <= (-4.3d-40)) .or. (.not. (y <= 5.3d-133)) .and. (y <= 1.3d-83) .or. (.not. (y <= 1.35d-26))) 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 <= -4.3e-40) || (!(y <= 5.3e-133) && ((y <= 1.3e-83) || !(y <= 1.35e-26)))) {
		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 <= -4.3e-40) or (not (y <= 5.3e-133) and ((y <= 1.3e-83) or not (y <= 1.35e-26))):
		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 <= -4.3e-40) || (!(y <= 5.3e-133) && ((y <= 1.3e-83) || !(y <= 1.35e-26))))
		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 <= -4.3e-40) || (~((y <= 5.3e-133)) && ((y <= 1.3e-83) || ~((y <= 1.35e-26)))))
		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, -4.3e-40], And[N[Not[LessEqual[y, 5.3e-133]], $MachinePrecision], Or[LessEqual[y, 1.3e-83], N[Not[LessEqual[y, 1.35e-26]], $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 < -4.3000000000000003e-40 or 5.29999999999999983e-133 < y < 1.30000000000000004e-83 or 1.34999999999999991e-26 < y

   1. Initial program 98.0%

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

      1. associate-+l- 98.0%

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

      2. sub-neg 98.0%

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

      3. sub-neg 98.0%

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

      4. distribute-neg-in 98.0%

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

      5. unsub-neg 98.0%

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

      6. neg-mul-1 98.0%

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

      7. associate-*r/ 98.0%

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

      8. associate-*l/ 97.9%

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

      9. distribute-neg-frac 97.9%

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

      10. neg-mul-1 97.9%

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

      11. times-frac 98.4%

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

      12. distribute-lft-out-- 99.1%

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

      13. *-commutative 99.1%

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

      14. associate-/r* 99.1%

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

      15. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

      1. *-commutative 99.1%

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

      2. clear-num 99.1%

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

      3. un-div-inv 99.2%

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

      4. div-inv 99.2%

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

      5. metadata-eval 99.2%

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

   5. Applied egg-rr 99.2%

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

   6. Taylor expanded in y around inf 90.7%

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

      1. associate-*r/ 91.3%

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

      2. associate-/l* 91.3%

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

   8. Simplified 91.3%

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

   if -4.3000000000000003e-40 < y < 5.29999999999999983e-133 or 1.30000000000000004e-83 < y < 1.34999999999999991e-26

   1. Initial program 91.9%

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

      1. associate-/r* 99.0%

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

   3. Simplified 99.0%

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

      1. clear-num 98.9%

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

      2. inv-pow 98.9%

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

      3. *-commutative 98.9%

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

      4. *-un-lft-identity 98.9%

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

      5. times-frac 98.9%

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

      6. metadata-eval 98.9%

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

   5. Applied egg-rr 98.9%

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

      1. unpow-1 98.9%

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

   7. Simplified 98.9%

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

      1. associate-+l- 98.9%

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

      2. associate-/r* 98.9%

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

      3. metadata-eval 98.9%

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

   9. Applied egg-rr 98.9%

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

       1. associate--r- 98.9%

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

       2. +-commutative 98.9%

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

       3. associate-+r- 98.9%

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

       4. associate-/r/ 98.9%

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

       5. associate-/r* 98.9%

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

   11. Simplified 98.9%

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

   12. Taylor expanded in z around 0 65.2%

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

       1. distribute-lft-out-- 65.2%

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

       2. associate-/l* 65.2%

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

   14. Simplified 65.2%

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

   15. Taylor expanded in t around inf 60.5%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.3 \cdot 10^{-40} \lor \neg \left(y \leq 5.3 \cdot 10^{-133}\right) \land \left(y \leq 1.3 \cdot 10^{-83} \lor \neg \left(y \leq 1.35 \cdot 10^{-26}\right)\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 5: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ t_2 := x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -1.75 \cdot 10^{-42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-83}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-26}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.3333333333333333 (/ t (* y z))))
        (t_2 (+ x (/ -0.3333333333333333 (/ z y)))))
   (if (<= y -1.75e-42)
     t_2
     (if (<= y 3.6e-130)
       t_1
       (if (<= y 1.9e-83)
         t_2
         (if (<= y 3.9e-26) t_1 (- x (/ (* y 0.3333333333333333) z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (y * z));
	double t_2 = x + (-0.3333333333333333 / (z / y));
	double tmp;
	if (y <= -1.75e-42) {
		tmp = t_2;
	} else if (y <= 3.6e-130) {
		tmp = t_1;
	} else if (y <= 1.9e-83) {
		tmp = t_2;
	} else if (y <= 3.9e-26) {
		tmp = t_1;
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = 0.3333333333333333d0 * (t / (y * z))
    t_2 = x + ((-0.3333333333333333d0) / (z / y))
    if (y <= (-1.75d-42)) then
        tmp = t_2
    else if (y <= 3.6d-130) then
        tmp = t_1
    else if (y <= 1.9d-83) then
        tmp = t_2
    else if (y <= 3.9d-26) then
        tmp = t_1
    else
        tmp = x - ((y * 0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (y * z));
	double t_2 = x + (-0.3333333333333333 / (z / y));
	double tmp;
	if (y <= -1.75e-42) {
		tmp = t_2;
	} else if (y <= 3.6e-130) {
		tmp = t_1;
	} else if (y <= 1.9e-83) {
		tmp = t_2;
	} else if (y <= 3.9e-26) {
		tmp = t_1;
	} else {
		tmp = x - ((y * 0.3333333333333333) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 * (t / (y * z))
	t_2 = x + (-0.3333333333333333 / (z / y))
	tmp = 0
	if y <= -1.75e-42:
		tmp = t_2
	elif y <= 3.6e-130:
		tmp = t_1
	elif y <= 1.9e-83:
		tmp = t_2
	elif y <= 3.9e-26:
		tmp = t_1
	else:
		tmp = x - ((y * 0.3333333333333333) / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 * Float64(t / Float64(y * z)))
	t_2 = Float64(x + Float64(-0.3333333333333333 / Float64(z / y)))
	tmp = 0.0
	if (y <= -1.75e-42)
		tmp = t_2;
	elseif (y <= 3.6e-130)
		tmp = t_1;
	elseif (y <= 1.9e-83)
		tmp = t_2;
	elseif (y <= 3.9e-26)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(y * 0.3333333333333333) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 * (t / (y * z));
	t_2 = x + (-0.3333333333333333 / (z / y));
	tmp = 0.0;
	if (y <= -1.75e-42)
		tmp = t_2;
	elseif (y <= 3.6e-130)
		tmp = t_1;
	elseif (y <= 1.9e-83)
		tmp = t_2;
	elseif (y <= 3.9e-26)
		tmp = t_1;
	else
		tmp = x - ((y * 0.3333333333333333) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.75e-42], t$95$2, If[LessEqual[y, 3.6e-130], t$95$1, If[LessEqual[y, 1.9e-83], t$95$2, If[LessEqual[y, 3.9e-26], t$95$1, N[(x - N[(N[(y * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7500000000000001e-42 or 3.6000000000000001e-130 < y < 1.89999999999999988e-83

   1. Initial program 97.8%

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

      1. associate-+l- 97.8%

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

      2. sub-neg 97.8%

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

      3. sub-neg 97.8%

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

      4. distribute-neg-in 97.8%

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

      5. unsub-neg 97.8%

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

      6. neg-mul-1 97.8%

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

      7. associate-*r/ 97.8%

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

      8. associate-*l/ 97.7%

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

      9. distribute-neg-frac 97.7%

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

      10. neg-mul-1 97.7%

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

      11. times-frac 98.6%

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

      12. distribute-lft-out-- 98.6%

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

      13. *-commutative 98.6%

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

      14. associate-/r* 98.6%

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

      15. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

      1. *-commutative 98.6%

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

      2. clear-num 98.6%

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

      3. un-div-inv 98.7%

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

      4. div-inv 98.7%

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

      5. metadata-eval 98.7%

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

   5. Applied egg-rr 98.7%

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

   6. Taylor expanded in y around inf 90.5%

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

      1. associate-*r/ 91.5%

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

      2. associate-/l* 91.5%

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

   8. Simplified 91.5%

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

   if -1.7500000000000001e-42 < y < 3.6000000000000001e-130 or 1.89999999999999988e-83 < y < 3.89999999999999986e-26

   1. Initial program 91.9%

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

      1. associate-/r* 99.0%

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

   3. Simplified 99.0%

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

      1. clear-num 98.9%

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

      2. inv-pow 98.9%

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

      3. *-commutative 98.9%

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

      4. *-un-lft-identity 98.9%

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

      5. times-frac 98.9%

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

      6. metadata-eval 98.9%

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

   5. Applied egg-rr 98.9%

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

      1. unpow-1 98.9%

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

   7. Simplified 98.9%

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

      1. associate-+l- 98.9%

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

      2. associate-/r* 98.9%

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

      3. metadata-eval 98.9%

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

   9. Applied egg-rr 98.9%

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

       1. associate--r- 98.9%

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

       2. +-commutative 98.9%

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

       3. associate-+r- 98.9%

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

       4. associate-/r/ 98.9%

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

       5. associate-/r* 98.9%

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

   11. Simplified 98.9%

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

   12. Taylor expanded in z around 0 65.2%

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

       1. distribute-lft-out-- 65.2%

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

       2. associate-/l* 65.2%

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

   14. Simplified 65.2%

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

   15. Taylor expanded in t around inf 60.5%

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

   if 3.89999999999999986e-26 < y

   1. Initial program 98.3%

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

   2. Taylor expanded in x around 0 98.2%

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

      1. cancel-sign-sub-inv 98.2%

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

      2. metadata-eval 98.2%

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

      3. +-commutative 98.2%

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

      4. associate-+r+ 98.2%

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

      5. +-commutative 98.2%

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

      6. associate-/r* 98.2%

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

      7. associate-*r/ 98.2%

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

      8. metadata-eval 98.2%

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

      9. cancel-sign-sub-inv 98.2%

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

      10. associate-*r/ 98.2%

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

      11. div-sub 99.8%

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

      12. distribute-lft-out-- 99.8%

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

      13. metadata-eval 99.8%

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

      14. associate-*r* 99.8%

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

      15. distribute-lft-out-- 99.8%

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

      16. associate-*r/ 99.8%

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

      17. +-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in t around 0 91.0%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-42}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-130}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-83}:\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-26}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot 0.3333333333333333}{z}\\ \end{array} \]

Alternative 6: 88.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-27} \lor \neg \left(y \leq 3.2 \cdot 10^{+36}\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.06e-27) (not (<= y 3.2e+36)))
   (+ x (/ -0.3333333333333333 (/ z y)))
   (+ x (* t (/ 0.3333333333333333 (* y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.06e-27) || !(y <= 3.2e+36)) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else {
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.06d-27)) .or. (.not. (y <= 3.2d+36))) then
        tmp = x + ((-0.3333333333333333d0) / (z / y))
    else
        tmp = x + (t * (0.3333333333333333d0 / (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.06e-27) || !(y <= 3.2e+36)) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else {
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.06e-27) or not (y <= 3.2e+36):
		tmp = x + (-0.3333333333333333 / (z / y))
	else:
		tmp = x + (t * (0.3333333333333333 / (y * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.06e-27) || !(y <= 3.2e+36))
		tmp = Float64(x + Float64(-0.3333333333333333 / Float64(z / y)));
	else
		tmp = Float64(x + Float64(t * Float64(0.3333333333333333 / Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.06e-27) || ~((y <= 3.2e+36)))
		tmp = x + (-0.3333333333333333 / (z / y));
	else
		tmp = x + (t * (0.3333333333333333 / (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.06e-27], N[Not[LessEqual[y, 3.2e+36]], $MachinePrecision]], N[(x + N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(0.3333333333333333 / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05999999999999998e-27 or 3.1999999999999999e36 < y

   1. Initial program 99.0%

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

      1. associate-+l- 99.0%

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

      2. sub-neg 99.0%

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

      3. sub-neg 99.0%

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

      4. distribute-neg-in 99.0%

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

      5. unsub-neg 99.0%

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

      6. neg-mul-1 99.0%

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

      7. associate-*r/ 99.0%

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

      8. associate-*l/ 98.9%

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

      9. distribute-neg-frac 98.9%

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

      10. neg-mul-1 98.9%

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

      11. times-frac 98.9%

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

      12. distribute-lft-out-- 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/r* 99.7%

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

      15. metadata-eval 99.7%

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

   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. *-commutative 99.7%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.8%

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

      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%

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

   6. Taylor expanded in y around inf 94.3%

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

      1. associate-*r/ 95.0%

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

      2. associate-/l* 95.0%

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

   8. Simplified 95.0%

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

   if -1.05999999999999998e-27 < y < 3.1999999999999999e36

   1. Initial program 92.1%

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

      1. associate-+l- 92.1%

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

      2. sub-neg 92.1%

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

      3. sub-neg 92.1%

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

      4. distribute-neg-in 92.1%

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

      5. unsub-neg 92.1%

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

      6. neg-mul-1 92.1%

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

      7. associate-*r/ 92.1%

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

      8. associate-*l/ 92.1%

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

      9. distribute-neg-frac 92.1%

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

      10. neg-mul-1 92.1%

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

      11. times-frac 96.2%

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

      12. distribute-lft-out-- 96.2%

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

      13. *-commutative 96.2%

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

      14. associate-/r* 96.2%

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

      15. metadata-eval 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in y around 0 88.9%

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

      1. metadata-eval 88.9%

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

      2. times-frac 89.0%

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

      3. associate-*r* 88.9%

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

      4. *-commutative 88.9%

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

      5. *-lft-identity 88.9%

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

      6. associate-/r* 95.9%

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

      7. *-commutative 95.9%

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

   6. Simplified 95.9%

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

   7. Taylor expanded in t around 0 88.9%

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

      1. associate-*r/ 89.0%

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

      2. *-commutative 89.0%

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

      3. associate-*r/ 87.9%

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

   9. Simplified 87.9%

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

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-27} \lor \neg \left(y \leq 3.2 \cdot 10^{+36}\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{0.3333333333333333}{y \cdot z}\\ \end{array} \]

Alternative 7: 91.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-30} \lor \neg \left(y \leq 3.9 \cdot 10^{+36}\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.6e-30) (not (<= y 3.9e+36)))
   (+ x (/ -0.3333333333333333 (/ z y)))
   (+ x (/ (/ t z) (* y 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.6e-30) || !(y <= 3.9e+36)) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} 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 <= (-3.6d-30)) .or. (.not. (y <= 3.9d+36))) then
        tmp = x + ((-0.3333333333333333d0) / (z / y))
    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 <= -3.6e-30) || !(y <= 3.9e+36)) {
		tmp = x + (-0.3333333333333333 / (z / y));
	} else {
		tmp = x + ((t / z) / (y * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.6e-30) or not (y <= 3.9e+36):
		tmp = x + (-0.3333333333333333 / (z / y))
	else:
		tmp = x + ((t / z) / (y * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.6e-30) || !(y <= 3.9e+36))
		tmp = Float64(x + Float64(-0.3333333333333333 / Float64(z / y)));
	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 <= -3.6e-30) || ~((y <= 3.9e+36)))
		tmp = x + (-0.3333333333333333 / (z / y));
	else
		tmp = x + ((t / z) / (y * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.6e-30], N[Not[LessEqual[y, 3.9e+36]], $MachinePrecision]], N[(x + N[(-0.3333333333333333 / N[(z / y), $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 < -3.6000000000000003e-30 or 3.90000000000000021e36 < y

   1. Initial program 99.0%

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

      1. associate-+l- 99.0%

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

      2. sub-neg 99.0%

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

      3. sub-neg 99.0%

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

      4. distribute-neg-in 99.0%

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

      5. unsub-neg 99.0%

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

      6. neg-mul-1 99.0%

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

      7. associate-*r/ 99.0%

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

      8. associate-*l/ 98.9%

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

      9. distribute-neg-frac 98.9%

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

      10. neg-mul-1 98.9%

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

      11. times-frac 98.9%

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

      12. distribute-lft-out-- 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/r* 99.7%

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

      15. metadata-eval 99.7%

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

   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. *-commutative 99.7%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.8%

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

      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%

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

   6. Taylor expanded in y around inf 94.3%

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

      1. associate-*r/ 95.0%

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

      2. associate-/l* 95.0%

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

   8. Simplified 95.0%

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

   if -3.6000000000000003e-30 < y < 3.90000000000000021e36

   1. Initial program 92.1%

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

      1. associate-+l- 92.1%

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

      2. sub-neg 92.1%

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

      3. sub-neg 92.1%

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

      4. distribute-neg-in 92.1%

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

      5. unsub-neg 92.1%

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

      6. neg-mul-1 92.1%

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

      7. associate-*r/ 92.1%

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

      8. associate-*l/ 92.1%

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

      9. distribute-neg-frac 92.1%

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

      10. neg-mul-1 92.1%

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

      11. times-frac 96.2%

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

      12. distribute-lft-out-- 96.2%

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

      13. *-commutative 96.2%

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

      14. associate-/r* 96.2%

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

      15. metadata-eval 96.2%

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

   3. Simplified 96.2%

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

   4. Taylor expanded in y around 0 88.9%

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

      1. metadata-eval 88.9%

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

      2. times-frac 89.0%

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

      3. associate-*r* 88.9%

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

      4. *-commutative 88.9%

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

      5. *-lft-identity 88.9%

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

      6. associate-/r* 95.9%

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

      7. *-commutative 95.9%

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

   6. Simplified 95.9%

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

4. Final simplification 95.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{-30} \lor \neg \left(y \leq 3.9 \cdot 10^{+36}\right):\\ \;\;\;\;x + \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \]

Alternative 8: 60.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-33}:\\ \;\;\;\;\frac{0.3333333333333333}{\frac{-z}{y}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-27}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.7e-33)
   (/ 0.3333333333333333 (/ (- z) y))
   (if (<= y 8e-27)
     (* 0.3333333333333333 (/ t (* y z)))
     (if (<= y 4e+44) x (/ (* y -0.3333333333333333) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e-33) {
		tmp = 0.3333333333333333 / (-z / y);
	} else if (y <= 8e-27) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else if (y <= 4e+44) {
		tmp = x;
	} else {
		tmp = (y * -0.3333333333333333) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.7d-33)) then
        tmp = 0.3333333333333333d0 / (-z / y)
    else if (y <= 8d-27) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else if (y <= 4d+44) then
        tmp = x
    else
        tmp = (y * (-0.3333333333333333d0)) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.7e-33) {
		tmp = 0.3333333333333333 / (-z / y);
	} else if (y <= 8e-27) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else if (y <= 4e+44) {
		tmp = x;
	} else {
		tmp = (y * -0.3333333333333333) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.7e-33:
		tmp = 0.3333333333333333 / (-z / y)
	elif y <= 8e-27:
		tmp = 0.3333333333333333 * (t / (y * z))
	elif y <= 4e+44:
		tmp = x
	else:
		tmp = (y * -0.3333333333333333) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.7e-33)
		tmp = Float64(0.3333333333333333 / Float64(Float64(-z) / y));
	elseif (y <= 8e-27)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	elseif (y <= 4e+44)
		tmp = x;
	else
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.7e-33)
		tmp = 0.3333333333333333 / (-z / y);
	elseif (y <= 8e-27)
		tmp = 0.3333333333333333 * (t / (y * z));
	elseif (y <= 4e+44)
		tmp = x;
	else
		tmp = (y * -0.3333333333333333) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.7e-33], N[(0.3333333333333333 / N[((-z) / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-27], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+44], x, N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.7000000000000001e-33

   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. associate-/r* 98.4%

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

   3. Simplified 98.4%

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

      1. clear-num 98.4%

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

      2. inv-pow 98.4%

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

      3. *-commutative 98.4%

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

      4. *-un-lft-identity 98.4%

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

      5. times-frac 98.4%

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

      6. metadata-eval 98.4%

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

   5. Applied egg-rr 98.4%

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

      1. unpow-1 98.4%

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

   7. Simplified 98.4%

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

      1. associate-+l- 98.4%

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

      2. associate-/r* 98.4%

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

      3. metadata-eval 98.4%

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

   9. Applied egg-rr 98.4%

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

       1. associate--r- 98.4%

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

       2. +-commutative 98.4%

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

       3. associate-+r- 98.4%

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

       4. associate-/r/ 98.4%

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

       5. associate-/r* 97.2%

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

   11. Simplified 97.2%

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

   12. Taylor expanded in z around 0 77.5%

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

       1. distribute-lft-out-- 77.5%

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

       2. associate-/l* 77.5%

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

   14. Simplified 77.5%

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

   15. Taylor expanded in t around 0 71.9%

       \[\leadsto \frac{0.3333333333333333}{\color{blue}{-1 \cdot \frac{z}{y}}} \]
   16. Step-by-step derivation

       1. associate-*r/ 71.9%

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

       2. neg-mul-1 71.9%

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

   17. Simplified 71.9%

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

   if -2.7000000000000001e-33 < y < 8.0000000000000003e-27

   1. Initial program 91.3%

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

      1. associate-/r* 99.0%

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

   3. Simplified 99.0%

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

      1. clear-num 99.0%

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

      2. inv-pow 99.0%

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

      3. *-commutative 99.0%

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

      4. *-un-lft-identity 99.0%

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

      5. times-frac 99.0%

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

      6. metadata-eval 99.0%

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

   5. Applied egg-rr 99.0%

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

      1. unpow-1 99.0%

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

   7. Simplified 99.0%

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

      1. associate-+l- 99.0%

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

      2. associate-/r* 99.0%

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

      3. metadata-eval 99.0%

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

   9. Applied egg-rr 99.0%

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

       1. associate--r- 99.0%

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

       2. +-commutative 99.0%

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

       3. associate-+r- 99.0%

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

       4. associate-/r/ 99.0%

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

       5. associate-/r* 99.0%

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

   11. Simplified 99.0%

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

   12. Taylor expanded in z around 0 62.2%

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

       1. distribute-lft-out-- 62.2%

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

       2. associate-/l* 62.1%

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

   14. Simplified 62.1%

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

   15. Taylor expanded in t around inf 56.6%

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

   if 8.0000000000000003e-27 < y < 4.0000000000000004e44

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 63.1%

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

   if 4.0000000000000004e44 < y

   1. Initial program 97.9%

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

      1. associate-/r* 90.7%

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

   3. Simplified 90.7%

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

      1. clear-num 90.7%

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

      2. inv-pow 90.7%

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

      3. *-commutative 90.7%

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

      4. *-un-lft-identity 90.7%

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

      5. times-frac 90.7%

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

      6. metadata-eval 90.7%

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

   5. Applied egg-rr 90.7%

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

      1. unpow-1 90.7%

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

   7. Simplified 90.7%

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

      1. associate-+l- 90.7%

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

      2. associate-/r* 90.7%

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

      3. metadata-eval 90.7%

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

   9. Applied egg-rr 90.7%

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

       1. associate--r- 90.7%

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

       2. +-commutative 90.7%

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

       3. associate-+r- 90.7%

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

       4. associate-/r/ 90.7%

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

       5. associate-/r* 90.7%

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

   11. Simplified 90.7%

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

   12. Taylor expanded in z around 0 72.8%

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

       1. distribute-lft-out-- 72.8%

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

       2. associate-/l* 72.7%

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

   14. Simplified 72.7%

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

   15. Taylor expanded in t around 0 68.9%

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

       1. *-commutative 68.9%

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

       2. associate-*l/ 69.0%

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

   17. Simplified 69.0%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.7 \cdot 10^{-33}:\\ \;\;\;\;\frac{0.3333333333333333}{\frac{-z}{y}}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-27}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]

Alternative 9: 95.5% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

   1. associate-+l- 95.5%

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

   2. sub-neg 95.5%

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

   3. sub-neg 95.5%

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

   4. distribute-neg-in 95.5%

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

   5. unsub-neg 95.5%

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

   6. neg-mul-1 95.5%

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

   7. associate-*r/ 95.5%

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

   8. associate-*l/ 95.4%

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

   9. distribute-neg-frac 95.4%

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

   10. neg-mul-1 95.4%

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

   11. times-frac 97.5%

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

   12. distribute-lft-out-- 97.9%

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

   13. *-commutative 97.9%

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

   14. associate-/r* 97.9%

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

   15. metadata-eval 97.9%

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

3. Simplified 97.9%

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

4. Taylor expanded in z around 0 97.6%

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

5. Final simplification 97.6%

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

Alternative 10: 95.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

   1. associate-+l- 95.5%

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

   2. sub-neg 95.5%

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

   3. sub-neg 95.5%

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

   4. distribute-neg-in 95.5%

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

   5. unsub-neg 95.5%

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

   6. neg-mul-1 95.5%

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

   7. associate-*r/ 95.5%

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

   8. associate-*l/ 95.4%

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

   9. distribute-neg-frac 95.4%

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

   10. neg-mul-1 95.4%

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

   11. times-frac 97.5%

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

   12. distribute-lft-out-- 97.9%

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

   13. *-commutative 97.9%

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

   14. associate-/r* 97.9%

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

   15. metadata-eval 97.9%

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

3. Simplified 97.9%

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

4. Final simplification 97.9%

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

Alternative 11: 48.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+59} \lor \neg \left(y \leq 8.4 \cdot 10^{+44}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.55e+59) (not (<= y 8.4e+44)))
   (* -0.3333333333333333 (/ y z))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.55e+59) || !(y <= 8.4e+44)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.55d+59)) .or. (.not. (y <= 8.4d+44))) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.55e+59) || !(y <= 8.4e+44)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.55e+59) or not (y <= 8.4e+44):
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.55e+59) || !(y <= 8.4e+44))
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.55e+59) || ~((y <= 8.4e+44)))
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.55e+59], N[Not[LessEqual[y, 8.4e+44]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.55000000000000007e59 or 8.39999999999999947e44 < y

   1. Initial program 98.9%

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

      1. associate-/r* 94.5%

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

   3. Simplified 94.5%

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

      1. clear-num 94.5%

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

      2. inv-pow 94.5%

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

      3. *-commutative 94.5%

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

      4. *-un-lft-identity 94.5%

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

      5. times-frac 94.5%

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

      6. metadata-eval 94.5%

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

   5. Applied egg-rr 94.5%

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

      1. unpow-1 94.5%

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

   7. Simplified 94.5%

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

      1. associate-+l- 94.5%

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

      2. associate-/r* 94.5%

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

      3. metadata-eval 94.5%

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

   9. Applied egg-rr 94.5%

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

       1. associate--r- 94.5%

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

       2. +-commutative 94.5%

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

       3. associate-+r- 94.5%

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

       4. associate-/r/ 94.5%

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

       5. associate-/r* 93.8%

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

   11. Simplified 93.8%

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

   12. Taylor expanded in z around 0 77.0%

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

       1. distribute-lft-out-- 77.0%

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

       2. associate-/l* 77.0%

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

   14. Simplified 77.0%

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

   15. Taylor expanded in t around 0 73.6%

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

   if -1.55000000000000007e59 < y < 8.39999999999999947e44

   1. Initial program 92.9%

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

   2. Taylor expanded in x around inf 37.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+59} \lor \neg \left(y \leq 8.4 \cdot 10^{+44}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 48.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+57} \lor \neg \left(y \leq 7.1 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.22e+57) (not (<= y 7.1e+43)))
   (/ (* y -0.3333333333333333) z)
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.22e+57) || !(y <= 7.1e+43)) {
		tmp = (y * -0.3333333333333333) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.22d+57)) .or. (.not. (y <= 7.1d+43))) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.22e+57) || !(y <= 7.1e+43)) {
		tmp = (y * -0.3333333333333333) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.22e+57) or not (y <= 7.1e+43):
		tmp = (y * -0.3333333333333333) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.22e+57) || !(y <= 7.1e+43))
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.22e+57) || ~((y <= 7.1e+43)))
		tmp = (y * -0.3333333333333333) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.22e+57], N[Not[LessEqual[y, 7.1e+43]], $MachinePrecision]], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.22e57 or 7.09999999999999972e43 < y

   1. Initial program 98.9%

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

      1. associate-/r* 94.5%

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

   3. Simplified 94.5%

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

      1. clear-num 94.5%

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

      2. inv-pow 94.5%

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

      3. *-commutative 94.5%

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

      4. *-un-lft-identity 94.5%

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

      5. times-frac 94.5%

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

      6. metadata-eval 94.5%

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

   5. Applied egg-rr 94.5%

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

      1. unpow-1 94.5%

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

   7. Simplified 94.5%

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

      1. associate-+l- 94.5%

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

      2. associate-/r* 94.5%

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

      3. metadata-eval 94.5%

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

   9. Applied egg-rr 94.5%

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

       1. associate--r- 94.5%

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

       2. +-commutative 94.5%

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

       3. associate-+r- 94.5%

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

       4. associate-/r/ 94.5%

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

       5. associate-/r* 93.8%

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

   11. Simplified 93.8%

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

   12. Taylor expanded in z around 0 77.0%

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

       1. distribute-lft-out-- 77.0%

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

       2. associate-/l* 77.0%

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

   14. Simplified 77.0%

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

   15. Taylor expanded in t around 0 73.6%

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

       1. *-commutative 73.6%

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

       2. associate-*l/ 74.3%

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

   17. Simplified 74.3%

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

   if -1.22e57 < y < 7.09999999999999972e43

   1. Initial program 92.9%

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

   2. Taylor expanded in x around inf 37.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{+57} \lor \neg \left(y \leq 7.1 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 30.3% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

2. Taylor expanded in x around inf 31.8%

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

3. Final simplification 31.8%

   \[\leadsto x \]

Developer target: 95.8% 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 2023229 
(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))))