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

Percentage Accurate: 95.9% → 98.1%

Time: 13.7s

Alternatives: 21

Speedup: 0.9×

• 29.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.6 \cdot 10^{-66}:\\ \;\;\;\;\left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{-1}{3 \cdot \frac{z}{y}}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.6e-66)
   (- (+ (/ (/ t z) (* y 3.0)) x) (* y (/ 0.3333333333333333 z)))
   (+ (+ x (/ -1.0 (* 3.0 (/ z y)))) (/ t (* y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.6e-66) {
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z));
	} else {
		tmp = (x + (-1.0 / (3.0 * (z / y)))) + (t / (y * (z * 3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.6d-66) then
        tmp = (((t / z) / (y * 3.0d0)) + x) - (y * (0.3333333333333333d0 / z))
    else
        tmp = (x + ((-1.0d0) / (3.0d0 * (z / y)))) + (t / (y * (z * 3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.6e-66) {
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z));
	} else {
		tmp = (x + (-1.0 / (3.0 * (z / y)))) + (t / (y * (z * 3.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.6e-66:
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z))
	else:
		tmp = (x + (-1.0 / (3.0 * (z / y)))) + (t / (y * (z * 3.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.6e-66)
		tmp = Float64(Float64(Float64(Float64(t / z) / Float64(y * 3.0)) + x) - Float64(y * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(Float64(x + Float64(-1.0 / Float64(3.0 * Float64(z / y)))) + Float64(t / Float64(y * Float64(z * 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.6e-66)
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z));
	else
		tmp = (x + (-1.0 / (3.0 * (z / y)))) + (t / (y * (z * 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.6e-66], N[(N[(N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x + N[(-1.0 / N[(3.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.59999999999999991e-66

   1. Initial program 94.1%

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

      1. associate-*l* 94.1%

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

      2. *-commutative 94.1%

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

   3. Simplified 94.1%

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

      1. +-commutative 94.1%

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

      2. *-commutative 94.1%

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

      3. associate-*l* 94.1%

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

      4. associate-+r- 94.1%

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

      5. associate-*l* 94.1%

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

      6. *-commutative 94.1%

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

      7. associate-/r* 98.2%

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

      8. div-inv 98.2%

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

      9. metadata-eval 98.2%

         \[\leadsto \left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{0.3333333333333333}}} \]

      10. div-inv 98.2%

          \[\leadsto \left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{1}{\color{blue}{\frac{z}{0.3333333333333333}}} \]

      11. clear-num 98.2%

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

   5. Applied egg-rr 98.2%

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

   if 1.59999999999999991e-66 < t

   1. Initial program 98.5%

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

      1. clear-num 98.6%

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

      2. inv-pow 98.6%

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

      3. *-commutative 98.6%

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

      4. *-un-lft-identity 98.6%

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

      5. times-frac 98.5%

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

      6. metadata-eval 98.5%

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

   3. Applied egg-rr 98.5%

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

      1. unpow-1 98.5%

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

   5. Simplified 98.5%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.6 \cdot 10^{-66}:\\ \;\;\;\;\left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\left(x + \frac{-1}{3 \cdot \frac{z}{y}}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]

Alternative 2: 88.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ t_2 := x + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+42}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-12}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* 0.3333333333333333 (/ t (* z y)))))
        (t_2 (+ x (* (/ 0.3333333333333333 z) (/ t y)))))
   (if (<= y -3.4e+74)
     (+ x (* y (/ -0.3333333333333333 z)))
     (if (<= y -9.5e+42)
       t_2
       (if (<= y -3.2e-12)
         (- x (* 0.3333333333333333 (/ y z)))
         (if (<= y 4.6e-204)
           t_1
           (if (<= y 8.5e-66)
             t_2
             (if (<= y 1.3e-41) t_1 (- x (/ y (* z 3.0)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (0.3333333333333333 * (t / (z * y)));
	double t_2 = x + ((0.3333333333333333 / z) * (t / y));
	double tmp;
	if (y <= -3.4e+74) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= -9.5e+42) {
		tmp = t_2;
	} else if (y <= -3.2e-12) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 4.6e-204) {
		tmp = t_1;
	} else if (y <= 8.5e-66) {
		tmp = t_2;
	} else if (y <= 1.3e-41) {
		tmp = t_1;
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (0.3333333333333333d0 * (t / (z * y)))
    t_2 = x + ((0.3333333333333333d0 / z) * (t / y))
    if (y <= (-3.4d+74)) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else if (y <= (-9.5d+42)) then
        tmp = t_2
    else if (y <= (-3.2d-12)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 4.6d-204) then
        tmp = t_1
    else if (y <= 8.5d-66) then
        tmp = t_2
    else if (y <= 1.3d-41) then
        tmp = t_1
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (0.3333333333333333 * (t / (z * y)));
	double t_2 = x + ((0.3333333333333333 / z) * (t / y));
	double tmp;
	if (y <= -3.4e+74) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (y <= -9.5e+42) {
		tmp = t_2;
	} else if (y <= -3.2e-12) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 4.6e-204) {
		tmp = t_1;
	} else if (y <= 8.5e-66) {
		tmp = t_2;
	} else if (y <= 1.3e-41) {
		tmp = t_1;
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (0.3333333333333333 * (t / (z * y)))
	t_2 = x + ((0.3333333333333333 / z) * (t / y))
	tmp = 0
	if y <= -3.4e+74:
		tmp = x + (y * (-0.3333333333333333 / z))
	elif y <= -9.5e+42:
		tmp = t_2
	elif y <= -3.2e-12:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 4.6e-204:
		tmp = t_1
	elif y <= 8.5e-66:
		tmp = t_2
	elif y <= 1.3e-41:
		tmp = t_1
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))))
	t_2 = Float64(x + Float64(Float64(0.3333333333333333 / z) * Float64(t / y)))
	tmp = 0.0
	if (y <= -3.4e+74)
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	elseif (y <= -9.5e+42)
		tmp = t_2;
	elseif (y <= -3.2e-12)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 4.6e-204)
		tmp = t_1;
	elseif (y <= 8.5e-66)
		tmp = t_2;
	elseif (y <= 1.3e-41)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (0.3333333333333333 * (t / (z * y)));
	t_2 = x + ((0.3333333333333333 / z) * (t / y));
	tmp = 0.0;
	if (y <= -3.4e+74)
		tmp = x + (y * (-0.3333333333333333 / z));
	elseif (y <= -9.5e+42)
		tmp = t_2;
	elseif (y <= -3.2e-12)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 4.6e-204)
		tmp = t_1;
	elseif (y <= 8.5e-66)
		tmp = t_2;
	elseif (y <= 1.3e-41)
		tmp = t_1;
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+74], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e+42], t$95$2, If[LessEqual[y, -3.2e-12], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.6e-204], t$95$1, If[LessEqual[y, 8.5e-66], t$95$2, If[LessEqual[y, 1.3e-41], t$95$1, N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.3999999999999999e74

   1. Initial program 97.7%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-*l/ 97.6%

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

      3. associate-*r/ 97.7%

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

   6. Simplified 97.7%

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

   if -3.3999999999999999e74 < y < -9.50000000000000019e42 or 4.5999999999999998e-204 < y < 8.49999999999999966e-66

   1. Initial program 84.5%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in t around inf 92.8%

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

   if -9.50000000000000019e42 < y < -3.2000000000000001e-12

   1. Initial program 99.9%

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

      1. associate-*l* 99.9%

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

      2. *-commutative 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in t around 0 79.8%

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

   if -3.2000000000000001e-12 < y < 4.5999999999999998e-204 or 8.49999999999999966e-66 < y < 1.3e-41

   1. Initial program 94.9%

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

   3. Simplified 87.6%

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

   4. Taylor expanded in t around inf 93.6%

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

   if 1.3e-41 < 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-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. associate-+l- 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

      6. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 91.7%

      \[\leadsto x - \frac{\color{blue}{y}}{z \cdot 3} \]
3. Recombined 5 regimes into one program.

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq -3.2 \cdot 10^{-12}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-204}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-66}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-41}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 3: 90.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-37}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ -0.3333333333333333 z)))))
   (if (<= y -3.4e+74)
     t_1
     (if (<= y -4.1e+43)
       (+ x (* (/ 0.3333333333333333 z) (/ t y)))
       (if (<= y -3.15e+32)
         t_1
         (if (<= y -5.5e-37)
           (* -0.3333333333333333 (/ (- y (/ t y)) z))
           (if (<= y 1.3e-41)
             (+ x (/ 0.3333333333333333 (* y (/ z t))))
             (- x (/ y (* z 3.0))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -3.4e+74) {
		tmp = t_1;
	} else if (y <= -4.1e+43) {
		tmp = x + ((0.3333333333333333 / z) * (t / y));
	} else if (y <= -3.15e+32) {
		tmp = t_1;
	} else if (y <= -5.5e-37) {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	} else if (y <= 1.3e-41) {
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((-0.3333333333333333d0) / z))
    if (y <= (-3.4d+74)) then
        tmp = t_1
    else if (y <= (-4.1d+43)) then
        tmp = x + ((0.3333333333333333d0 / z) * (t / y))
    else if (y <= (-3.15d+32)) then
        tmp = t_1
    else if (y <= (-5.5d-37)) then
        tmp = (-0.3333333333333333d0) * ((y - (t / y)) / z)
    else if (y <= 1.3d-41) then
        tmp = x + (0.3333333333333333d0 / (y * (z / t)))
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -3.4e+74) {
		tmp = t_1;
	} else if (y <= -4.1e+43) {
		tmp = x + ((0.3333333333333333 / z) * (t / y));
	} else if (y <= -3.15e+32) {
		tmp = t_1;
	} else if (y <= -5.5e-37) {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	} else if (y <= 1.3e-41) {
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (-0.3333333333333333 / z))
	tmp = 0
	if y <= -3.4e+74:
		tmp = t_1
	elif y <= -4.1e+43:
		tmp = x + ((0.3333333333333333 / z) * (t / y))
	elif y <= -3.15e+32:
		tmp = t_1
	elif y <= -5.5e-37:
		tmp = -0.3333333333333333 * ((y - (t / y)) / z)
	elif y <= 1.3e-41:
		tmp = x + (0.3333333333333333 / (y * (z / t)))
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -3.4e+74)
		tmp = t_1;
	elseif (y <= -4.1e+43)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / z) * Float64(t / y)));
	elseif (y <= -3.15e+32)
		tmp = t_1;
	elseif (y <= -5.5e-37)
		tmp = Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z));
	elseif (y <= 1.3e-41)
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(y * Float64(z / t))));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (-0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -3.4e+74)
		tmp = t_1;
	elseif (y <= -4.1e+43)
		tmp = x + ((0.3333333333333333 / z) * (t / y));
	elseif (y <= -3.15e+32)
		tmp = t_1;
	elseif (y <= -5.5e-37)
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	elseif (y <= 1.3e-41)
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+74], t$95$1, If[LessEqual[y, -4.1e+43], N[(x + N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.15e+32], t$95$1, If[LessEqual[y, -5.5e-37], N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-41], N[(x + N[(0.3333333333333333 / N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.3999999999999999e74 or -4.1e43 < y < -3.1500000000000001e32

   1. Initial program 97.9%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 97.9%

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

      1. *-commutative 97.9%

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

      2. associate-*l/ 97.9%

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

      3. associate-*r/ 98.0%

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

   6. Simplified 98.0%

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

   if -3.3999999999999999e74 < y < -4.1e43

   1. Initial program 90.4%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around inf 85.1%

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

   if -3.1500000000000001e32 < y < -5.4999999999999998e-37

   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-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. associate-+l- 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.4%

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

      6. sub-div 99.4%

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

   5. Applied egg-rr 99.4%

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

   6. Taylor expanded in x around 0 99.4%

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

   if -5.4999999999999998e-37 < y < 1.3e-41

   1. Initial program 91.3%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 89.4%

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

      1. associate-*r/ 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-/r* 95.0%

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

      4. associate-*r/ 95.1%

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

   6. Simplified 95.1%

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

      1. associate-/l* 95.1%

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

      2. div-inv 95.0%

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

      3. div-inv 95.0%

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

      4. clear-num 95.0%

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

   8. Applied egg-rr 95.0%

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

      1. associate-*r/ 95.1%

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

      2. metadata-eval 95.1%

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

   10. Simplified 95.1%

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

   if 1.3e-41 < 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-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. associate-+l- 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

      6. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 91.7%

      \[\leadsto x - \frac{\color{blue}{y}}{z \cdot 3} \]
3. Recombined 5 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq -3.15 \cdot 10^{+32}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-37}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 4: 90.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq -7.9 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-37}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ -0.3333333333333333 z)))))
   (if (<= y -3.4e+74)
     t_1
     (if (<= y -4.5e+42)
       (+ x (* (/ 0.3333333333333333 z) (/ t y)))
       (if (<= y -7.9e+27)
         t_1
         (if (<= y -7.5e-37)
           (* -0.3333333333333333 (/ (- y (/ t y)) z))
           (if (<= y 1.3e-41)
             (+ x (/ (* (/ t z) 0.3333333333333333) y))
             (- x (/ y (* z 3.0))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -3.4e+74) {
		tmp = t_1;
	} else if (y <= -4.5e+42) {
		tmp = x + ((0.3333333333333333 / z) * (t / y));
	} else if (y <= -7.9e+27) {
		tmp = t_1;
	} else if (y <= -7.5e-37) {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	} else if (y <= 1.3e-41) {
		tmp = x + (((t / z) * 0.3333333333333333) / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((-0.3333333333333333d0) / z))
    if (y <= (-3.4d+74)) then
        tmp = t_1
    else if (y <= (-4.5d+42)) then
        tmp = x + ((0.3333333333333333d0 / z) * (t / y))
    else if (y <= (-7.9d+27)) then
        tmp = t_1
    else if (y <= (-7.5d-37)) then
        tmp = (-0.3333333333333333d0) * ((y - (t / y)) / z)
    else if (y <= 1.3d-41) then
        tmp = x + (((t / z) * 0.3333333333333333d0) / y)
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -3.4e+74) {
		tmp = t_1;
	} else if (y <= -4.5e+42) {
		tmp = x + ((0.3333333333333333 / z) * (t / y));
	} else if (y <= -7.9e+27) {
		tmp = t_1;
	} else if (y <= -7.5e-37) {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	} else if (y <= 1.3e-41) {
		tmp = x + (((t / z) * 0.3333333333333333) / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (-0.3333333333333333 / z))
	tmp = 0
	if y <= -3.4e+74:
		tmp = t_1
	elif y <= -4.5e+42:
		tmp = x + ((0.3333333333333333 / z) * (t / y))
	elif y <= -7.9e+27:
		tmp = t_1
	elif y <= -7.5e-37:
		tmp = -0.3333333333333333 * ((y - (t / y)) / z)
	elif y <= 1.3e-41:
		tmp = x + (((t / z) * 0.3333333333333333) / y)
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -3.4e+74)
		tmp = t_1;
	elseif (y <= -4.5e+42)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / z) * Float64(t / y)));
	elseif (y <= -7.9e+27)
		tmp = t_1;
	elseif (y <= -7.5e-37)
		tmp = Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z));
	elseif (y <= 1.3e-41)
		tmp = Float64(x + Float64(Float64(Float64(t / z) * 0.3333333333333333) / y));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (-0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -3.4e+74)
		tmp = t_1;
	elseif (y <= -4.5e+42)
		tmp = x + ((0.3333333333333333 / z) * (t / y));
	elseif (y <= -7.9e+27)
		tmp = t_1;
	elseif (y <= -7.5e-37)
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	elseif (y <= 1.3e-41)
		tmp = x + (((t / z) * 0.3333333333333333) / y);
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+74], t$95$1, If[LessEqual[y, -4.5e+42], N[(x + N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -7.9e+27], t$95$1, If[LessEqual[y, -7.5e-37], N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.3e-41], N[(x + N[(N[(N[(t / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.3999999999999999e74 or -4.50000000000000012e42 < y < -7.89999999999999991e27

   1. Initial program 97.9%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 97.9%

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

      1. *-commutative 97.9%

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

      2. associate-*l/ 97.9%

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

      3. associate-*r/ 98.0%

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

   6. Simplified 98.0%

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

   if -3.3999999999999999e74 < y < -4.50000000000000012e42

   1. Initial program 90.4%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around inf 85.1%

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

   if -7.89999999999999991e27 < y < -7.5000000000000004e-37

   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-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. associate-+l- 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.4%

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

      6. sub-div 99.4%

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

   5. Applied egg-rr 99.4%

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

   6. Taylor expanded in x around 0 99.4%

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

   if -7.5000000000000004e-37 < y < 1.3e-41

   1. Initial program 91.3%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 89.4%

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

      1. associate-*r/ 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-/r* 95.0%

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

      4. associate-*r/ 95.1%

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

   6. Simplified 95.1%

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

   if 1.3e-41 < 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-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. associate-+l- 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

      6. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 91.7%

      \[\leadsto x - \frac{\color{blue}{y}}{z \cdot 3} \]
3. Recombined 5 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \mathbf{elif}\;y \leq -7.9 \cdot 10^{+27}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-37}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 5: 90.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{y}}{z}\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-36}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ -0.3333333333333333 z)))))
   (if (<= y -3.4e+74)
     t_1
     (if (<= y -1.16e+44)
       (+ x (/ (/ (* t 0.3333333333333333) y) z))
       (if (<= y -3.35e+31)
         t_1
         (if (<= y -1.15e-36)
           (* -0.3333333333333333 (/ (- y (/ t y)) z))
           (if (<= y 1.2e-41)
             (+ x (/ (* (/ t z) 0.3333333333333333) y))
             (- x (/ y (* z 3.0))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -3.4e+74) {
		tmp = t_1;
	} else if (y <= -1.16e+44) {
		tmp = x + (((t * 0.3333333333333333) / y) / z);
	} else if (y <= -3.35e+31) {
		tmp = t_1;
	} else if (y <= -1.15e-36) {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	} else if (y <= 1.2e-41) {
		tmp = x + (((t / z) * 0.3333333333333333) / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y * ((-0.3333333333333333d0) / z))
    if (y <= (-3.4d+74)) then
        tmp = t_1
    else if (y <= (-1.16d+44)) then
        tmp = x + (((t * 0.3333333333333333d0) / y) / z)
    else if (y <= (-3.35d+31)) then
        tmp = t_1
    else if (y <= (-1.15d-36)) then
        tmp = (-0.3333333333333333d0) * ((y - (t / y)) / z)
    else if (y <= 1.2d-41) then
        tmp = x + (((t / z) * 0.3333333333333333d0) / y)
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -3.4e+74) {
		tmp = t_1;
	} else if (y <= -1.16e+44) {
		tmp = x + (((t * 0.3333333333333333) / y) / z);
	} else if (y <= -3.35e+31) {
		tmp = t_1;
	} else if (y <= -1.15e-36) {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	} else if (y <= 1.2e-41) {
		tmp = x + (((t / z) * 0.3333333333333333) / y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (-0.3333333333333333 / z))
	tmp = 0
	if y <= -3.4e+74:
		tmp = t_1
	elif y <= -1.16e+44:
		tmp = x + (((t * 0.3333333333333333) / y) / z)
	elif y <= -3.35e+31:
		tmp = t_1
	elif y <= -1.15e-36:
		tmp = -0.3333333333333333 * ((y - (t / y)) / z)
	elif y <= 1.2e-41:
		tmp = x + (((t / z) * 0.3333333333333333) / y)
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -3.4e+74)
		tmp = t_1;
	elseif (y <= -1.16e+44)
		tmp = Float64(x + Float64(Float64(Float64(t * 0.3333333333333333) / y) / z));
	elseif (y <= -3.35e+31)
		tmp = t_1;
	elseif (y <= -1.15e-36)
		tmp = Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z));
	elseif (y <= 1.2e-41)
		tmp = Float64(x + Float64(Float64(Float64(t / z) * 0.3333333333333333) / y));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (-0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -3.4e+74)
		tmp = t_1;
	elseif (y <= -1.16e+44)
		tmp = x + (((t * 0.3333333333333333) / y) / z);
	elseif (y <= -3.35e+31)
		tmp = t_1;
	elseif (y <= -1.15e-36)
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	elseif (y <= 1.2e-41)
		tmp = x + (((t / z) * 0.3333333333333333) / y);
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+74], t$95$1, If[LessEqual[y, -1.16e+44], N[(x + N[(N[(N[(t * 0.3333333333333333), $MachinePrecision] / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.35e+31], t$95$1, If[LessEqual[y, -1.15e-36], N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-41], N[(x + N[(N[(N[(t / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -3.3999999999999999e74 or -1.1600000000000001e44 < y < -3.35000000000000008e31

   1. Initial program 97.9%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in t around 0 97.9%

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

      1. *-commutative 97.9%

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

      2. associate-*l/ 97.9%

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

      3. associate-*r/ 98.0%

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

   6. Simplified 98.0%

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

   if -3.3999999999999999e74 < y < -1.1600000000000001e44

   1. Initial program 90.4%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 75.5%

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

      1. +-commutative 75.5%

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

      2. associate-*r/ 75.5%

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

      3. associate-/r* 85.1%

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

   6. Simplified 85.1%

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

   if -3.35000000000000008e31 < y < -1.14999999999999998e-36

   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-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. associate-+l- 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.4%

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

      6. sub-div 99.4%

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

   5. Applied egg-rr 99.4%

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

   6. Taylor expanded in x around 0 99.4%

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

   if -1.14999999999999998e-36 < y < 1.20000000000000011e-41

   1. Initial program 91.3%

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

   3. Simplified 90.8%

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

   4. Taylor expanded in t around inf 89.4%

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

      1. associate-*r/ 89.4%

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

      2. *-commutative 89.4%

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

      3. associate-/r* 95.0%

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

      4. associate-*r/ 95.1%

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

   6. Simplified 95.1%

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

   if 1.20000000000000011e-41 < 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-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. associate-+l- 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

      6. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 91.7%

      \[\leadsto x - \frac{\color{blue}{y}}{z \cdot 3} \]
3. Recombined 5 regimes into one program.

4. Final simplification 94.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+74}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{+44}:\\ \;\;\;\;x + \frac{\frac{t \cdot 0.3333333333333333}{y}}{z}\\ \mathbf{elif}\;y \leq -3.35 \cdot 10^{+31}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-36}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-41}:\\ \;\;\;\;x + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]

Alternative 6: 81.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+45} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{-45}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -1e+45) (not (<= (* z 3.0) 2e-45)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* -0.3333333333333333 (/ (- y (/ t y)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -1e+45) || !((z * 3.0) <= 2e-45)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = -0.3333333333333333 * ((y - (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 (((z * 3.0d0) <= (-1d+45)) .or. (.not. ((z * 3.0d0) <= 2d-45))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = (-0.3333333333333333d0) * ((y - (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 (((z * 3.0) <= -1e+45) || !((z * 3.0) <= 2e-45)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -1e+45) or not ((z * 3.0) <= 2e-45):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = -0.3333333333333333 * ((y - (t / y)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -1e+45) || !(Float64(z * 3.0) <= 2e-45))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -1e+45) || ~(((z * 3.0) <= 2e-45)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -1e+45], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-45]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -9.9999999999999993e44 or 1.99999999999999997e-45 < (*.f64 z 3)

   1. Initial program 99.0%

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

   3. Simplified 91.9%

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

   4. Taylor expanded in t around 0 77.4%

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

      1. *-commutative 77.4%

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

      2. associate-*l/ 77.5%

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

      3. associate-*r/ 77.5%

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

   6. Simplified 77.5%

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

   if -9.9999999999999993e44 < (*.f64 z 3) < 1.99999999999999997e-45

   1. Initial program 92.5%

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

      1. associate-*l* 92.5%

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

      2. *-commutative 92.5%

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

   3. Simplified 92.5%

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

      1. *-commutative 92.5%

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

      2. associate-*l* 92.5%

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

      3. associate-+l- 92.5%

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

      4. *-commutative 92.5%

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

      5. associate-/r* 99.1%

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

      6. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 93.0%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+45} \lor \neg \left(z \cdot 3 \leq 2 \cdot 10^{-45}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \]

Alternative 7: 97.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 10^{-71}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1e-71)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ (- x (/ y (* z 3.0))) (/ t (* z (* y 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1e-71) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x - (y / (z * 3.0))) + (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 (t <= 1d-71) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = (x - (y / (z * 3.0d0))) + (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 (t <= 1e-71) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1e-71:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1e-71)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(z * Float64(y * 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1e-71)
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1e-71], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 9.9999999999999992e-72

   1. Initial program 94.1%

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

      1. associate-*l* 94.1%

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

      2. *-commutative 94.1%

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

   3. Simplified 94.1%

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

      1. *-commutative 94.1%

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

      2. associate-*l* 94.1%

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

      3. associate-+l- 94.1%

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

      4. *-commutative 94.1%

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

      5. associate-/r* 98.1%

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

      6. sub-div 98.1%

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

   5. Applied egg-rr 98.1%

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

   if 9.9999999999999992e-72 < t

   1. Initial program 98.5%

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

      1. associate-*l* 98.5%

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

      2. *-commutative 98.5%

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

   3. Simplified 98.5%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 10^{-71}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \end{array} \]

Alternative 8: 97.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 4.6 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(z \cdot 3\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 4.6e-69)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ (/ t (* y (* z 3.0))) (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4.6e-69) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (t / (y * (z * 3.0))) + (x - (y / (z * 3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 4.6d-69) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = (t / (y * (z * 3.0d0))) + (x - (y / (z * 3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 4.6e-69) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (t / (y * (z * 3.0))) + (x - (y / (z * 3.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 4.6e-69:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = (t / (y * (z * 3.0))) + (x - (y / (z * 3.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 4.6e-69)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(t / Float64(y * Float64(z * 3.0))) + Float64(x - Float64(y / Float64(z * 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 4.6e-69)
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = (t / (y * (z * 3.0))) + (x - (y / (z * 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 4.6e-69], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 4.6000000000000001e-69

   1. Initial program 94.1%

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

      1. associate-*l* 94.1%

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

      2. *-commutative 94.1%

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

   3. Simplified 94.1%

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

      1. *-commutative 94.1%

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

      2. associate-*l* 94.1%

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

      3. associate-+l- 94.1%

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

      4. *-commutative 94.1%

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

      5. associate-/r* 98.1%

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

      6. sub-div 98.1%

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

   5. Applied egg-rr 98.1%

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

   if 4.6000000000000001e-69 < t

   1. Initial program 98.5%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 4.6 \cdot 10^{-69}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(z \cdot 3\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\ \end{array} \]

Alternative 9: 98.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.02 \cdot 10^{-66}:\\ \;\;\;\;\left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(z \cdot 3\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.02e-66)
   (- (+ (/ (/ t z) (* y 3.0)) x) (* y (/ 0.3333333333333333 z)))
   (+ (/ t (* y (* z 3.0))) (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.02e-66) {
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z));
	} else {
		tmp = (t / (y * (z * 3.0))) + (x - (y / (z * 3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.02d-66) then
        tmp = (((t / z) / (y * 3.0d0)) + x) - (y * (0.3333333333333333d0 / z))
    else
        tmp = (t / (y * (z * 3.0d0))) + (x - (y / (z * 3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.02e-66) {
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z));
	} else {
		tmp = (t / (y * (z * 3.0))) + (x - (y / (z * 3.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.02e-66:
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z))
	else:
		tmp = (t / (y * (z * 3.0))) + (x - (y / (z * 3.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.02e-66)
		tmp = Float64(Float64(Float64(Float64(t / z) / Float64(y * 3.0)) + x) - Float64(y * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(Float64(t / Float64(y * Float64(z * 3.0))) + Float64(x - Float64(y / Float64(z * 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.02e-66)
		tmp = (((t / z) / (y * 3.0)) + x) - (y * (0.3333333333333333 / z));
	else
		tmp = (t / (y * (z * 3.0))) + (x - (y / (z * 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.02e-66], N[(N[(N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.01999999999999996e-66

   1. Initial program 94.1%

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

      1. associate-*l* 94.1%

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

      2. *-commutative 94.1%

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

   3. Simplified 94.1%

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

      1. +-commutative 94.1%

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

      2. *-commutative 94.1%

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

      3. associate-*l* 94.1%

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

      4. associate-+r- 94.1%

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

      5. associate-*l* 94.1%

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

      6. *-commutative 94.1%

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

      7. associate-/r* 98.2%

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

      8. div-inv 98.2%

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

      9. metadata-eval 98.2%

         \[\leadsto \left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{0.3333333333333333}}} \]

      10. div-inv 98.2%

          \[\leadsto \left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{1}{\color{blue}{\frac{z}{0.3333333333333333}}} \]

      11. clear-num 98.2%

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

   5. Applied egg-rr 98.2%

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

   if 1.01999999999999996e-66 < t

   1. Initial program 98.5%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.02 \cdot 10^{-66}:\\ \;\;\;\;\left(\frac{\frac{t}{z}}{y \cdot 3} + x\right) - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{y \cdot \left(z \cdot 3\right)} + \left(x - \frac{y}{z \cdot 3}\right)\\ \end{array} \]

Alternative 10: 61.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -3.3 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-58}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* y (/ -0.3333333333333333 z))))
   (if (<= y -3.3e-12)
     t_1
     (if (<= y 8e-58)
       (* 0.3333333333333333 (/ t (* z y)))
       (if (<= y 1.7e-13)
         x
         (if (<= y 3.9e+43)
           t_1
           (if (<= y 4e+101) x (/ (* y -0.3333333333333333) z))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y * (-0.3333333333333333 / z);
	double tmp;
	if (y <= -3.3e-12) {
		tmp = t_1;
	} else if (y <= 8e-58) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 1.7e-13) {
		tmp = x;
	} else if (y <= 3.9e+43) {
		tmp = t_1;
	} else if (y <= 4e+101) {
		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) :: t_1
    real(8) :: tmp
    t_1 = y * ((-0.3333333333333333d0) / z)
    if (y <= (-3.3d-12)) then
        tmp = t_1
    else if (y <= 8d-58) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else if (y <= 1.7d-13) then
        tmp = x
    else if (y <= 3.9d+43) then
        tmp = t_1
    else if (y <= 4d+101) 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 t_1 = y * (-0.3333333333333333 / z);
	double tmp;
	if (y <= -3.3e-12) {
		tmp = t_1;
	} else if (y <= 8e-58) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else if (y <= 1.7e-13) {
		tmp = x;
	} else if (y <= 3.9e+43) {
		tmp = t_1;
	} else if (y <= 4e+101) {
		tmp = x;
	} else {
		tmp = (y * -0.3333333333333333) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y * (-0.3333333333333333 / z)
	tmp = 0
	if y <= -3.3e-12:
		tmp = t_1
	elif y <= 8e-58:
		tmp = 0.3333333333333333 * (t / (z * y))
	elif y <= 1.7e-13:
		tmp = x
	elif y <= 3.9e+43:
		tmp = t_1
	elif y <= 4e+101:
		tmp = x
	else:
		tmp = (y * -0.3333333333333333) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y * Float64(-0.3333333333333333 / z))
	tmp = 0.0
	if (y <= -3.3e-12)
		tmp = t_1;
	elseif (y <= 8e-58)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	elseif (y <= 1.7e-13)
		tmp = x;
	elseif (y <= 3.9e+43)
		tmp = t_1;
	elseif (y <= 4e+101)
		tmp = x;
	else
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y * (-0.3333333333333333 / z);
	tmp = 0.0;
	if (y <= -3.3e-12)
		tmp = t_1;
	elseif (y <= 8e-58)
		tmp = 0.3333333333333333 * (t / (z * y));
	elseif (y <= 1.7e-13)
		tmp = x;
	elseif (y <= 3.9e+43)
		tmp = t_1;
	elseif (y <= 4e+101)
		tmp = x;
	else
		tmp = (y * -0.3333333333333333) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.3e-12], t$95$1, If[LessEqual[y, 8e-58], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.7e-13], x, If[LessEqual[y, 3.9e+43], t$95$1, If[LessEqual[y, 4e+101], x, N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.3000000000000001e-12 or 1.70000000000000008e-13 < y < 3.9000000000000001e43

   1. Initial program 97.5%

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

      1. associate-*l* 97.4%

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

      2. *-commutative 97.4%

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

   3. Simplified 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*l* 97.5%

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

      3. associate-+l- 97.5%

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

      4. *-commutative 97.5%

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

      5. associate-/r* 98.6%

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

      6. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 79.8%

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

      1. associate-*r/ 79.8%

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

   8. Applied egg-rr 79.8%

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

   9. Taylor expanded in y around inf 65.4%

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

       1. associate-*r/ 65.5%

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

       2. *-commutative 65.5%

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

       3. associate-*r/ 65.6%

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

   11. Simplified 65.6%

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

   if -3.3000000000000001e-12 < y < 8.0000000000000002e-58

   1. Initial program 91.0%

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

      1. associate-*l* 91.0%

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

      2. *-commutative 91.0%

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

   3. Simplified 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*l* 91.0%

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

      3. associate-+l- 91.0%

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

      4. *-commutative 91.0%

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

      5. associate-/r* 90.5%

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

      6. sub-div 90.5%

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

   5. Applied egg-rr 90.5%

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

   6. Taylor expanded in x around 0 69.2%

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

      1. associate-*r/ 69.2%

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

   8. Applied egg-rr 69.2%

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

   9. Taylor expanded in y around 0 70.7%

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

   if 8.0000000000000002e-58 < y < 1.70000000000000008e-13 or 3.9000000000000001e43 < y < 3.9999999999999999e101

   1. Initial program 99.9%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 62.8%

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

   if 3.9999999999999999e101 < 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-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. associate-+l- 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

      6. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in x around 0 74.0%

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

      1. associate-*r/ 74.0%

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

   8. Applied egg-rr 74.0%

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

   9. Taylor expanded in y around inf 74.1%

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

       1. *-commutative 74.1%

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

   11. Simplified 74.1%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{-12}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-58}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{+43}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+101}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]

Alternative 11: 89.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-12} \lor \neg \left(y \leq 3.7 \cdot 10^{-42}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.5e-12) (not (<= y 3.7e-42)))
   (- x (/ y (* z 3.0)))
   (+ x (* 0.3333333333333333 (/ t (* z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e-12) || !(y <= 3.7e-42)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.5d-12)) .or. (.not. (y <= 3.7d-42))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + (0.3333333333333333d0 * (t / (z * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e-12) || !(y <= 3.7e-42)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.5e-12) or not (y <= 3.7e-42):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + (0.3333333333333333 * (t / (z * y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.5e-12) || !(y <= 3.7e-42))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.5e-12) || ~((y <= 3.7e-42)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.5e-12], N[Not[LessEqual[y, 3.7e-42]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999985e-12 or 3.7000000000000002e-42 < y

   1. Initial program 98.5%

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

      1. associate-*l* 98.5%

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

      2. *-commutative 98.5%

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

   3. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. associate-*l* 98.5%

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

      3. associate-+l- 98.5%

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

      4. *-commutative 98.5%

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

      5. associate-/r* 99.1%

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

      6. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 89.3%

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

   if -2.49999999999999985e-12 < y < 3.7000000000000002e-42

   1. Initial program 91.4%

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

   3. Simplified 90.9%

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

   4. Taylor expanded in t around inf 89.6%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-12} \lor \neg \left(y \leq 3.7 \cdot 10^{-42}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]

Alternative 12: 78.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-15} \lor \neg \left(y \leq 1.06 \cdot 10^{-58}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{\frac{-t}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.35e-15) (not (<= y 1.06e-58)))
   (- x (/ y (* z 3.0)))
   (* -0.3333333333333333 (/ (/ (- t) z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.35e-15) || !(y <= 1.06e-58)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = -0.3333333333333333 * ((-t / z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.35d-15)) .or. (.not. (y <= 1.06d-58))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (-0.3333333333333333d0) * ((-t / z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.35e-15) || !(y <= 1.06e-58)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = -0.3333333333333333 * ((-t / z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.35e-15) or not (y <= 1.06e-58):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = -0.3333333333333333 * ((-t / z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.35e-15) || !(y <= 1.06e-58))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(-0.3333333333333333 * Float64(Float64(Float64(-t) / z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.35e-15) || ~((y <= 1.06e-58)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = -0.3333333333333333 * ((-t / z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.35e-15], N[Not[LessEqual[y, 1.06e-58]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(N[((-t) / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.35000000000000005e-15 or 1.0600000000000001e-58 < y

   1. Initial program 98.5%

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

      1. associate-*l* 98.5%

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

      2. *-commutative 98.5%

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

   3. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. associate-*l* 98.5%

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

      3. associate-+l- 98.5%

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

      4. *-commutative 98.5%

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

      5. associate-/r* 99.1%

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

      6. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 88.9%

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

   if -1.35000000000000005e-15 < y < 1.0600000000000001e-58

   1. Initial program 91.0%

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

      1. associate-*l* 91.0%

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

      2. *-commutative 91.0%

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

   3. Simplified 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*l* 91.0%

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

      3. associate-+l- 91.0%

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

      4. *-commutative 91.0%

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

      5. associate-/r* 90.5%

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

      6. sub-div 90.5%

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

   5. Applied egg-rr 90.5%

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

   6. Taylor expanded in x around 0 69.2%

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

   7. Taylor expanded in y around 0 70.7%

      \[\leadsto -0.3333333333333333 \cdot \color{blue}{\left(-1 \cdot \frac{t}{y \cdot z}\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 70.7%

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

      2. distribute-neg-frac 70.7%

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

   9. Simplified 70.7%

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

   10. Taylor expanded in t around 0 70.7%

       \[\leadsto -0.3333333333333333 \cdot \color{blue}{\left(-1 \cdot \frac{t}{y \cdot z}\right)} \]
   11. Step-by-step derivation

       1. associate-*r/ 70.7%

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

       2. *-commutative 70.7%

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

       3. associate-/r* 74.5%

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

       4. mul-1-neg 74.5%

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

   12. Simplified 74.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-15} \lor \neg \left(y \leq 1.06 \cdot 10^{-58}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{\frac{-t}{z}}{y}\\ \end{array} \]

Alternative 13: 77.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-19} \lor \neg \left(y \leq 8.2 \cdot 10^{-58}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7e-19) (not (<= y 8.2e-58)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* 0.3333333333333333 (/ t (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e-19) || !(y <= 8.2e-58)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7d-19)) .or. (.not. (y <= 8.2d-58))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = 0.3333333333333333d0 * (t / (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e-19) || !(y <= 8.2e-58)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7e-19) or not (y <= 8.2e-58):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * (t / (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7e-19) || !(y <= 8.2e-58))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7e-19) || ~((y <= 8.2e-58)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * (t / (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7e-19], N[Not[LessEqual[y, 8.2e-58]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.00000000000000031e-19 or 8.20000000000000056e-58 < y

   1. Initial program 98.5%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in t around 0 88.8%

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

      1. *-commutative 88.8%

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

      2. associate-*l/ 88.9%

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

      3. associate-*r/ 88.9%

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

   6. Simplified 88.9%

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

   if -7.00000000000000031e-19 < y < 8.20000000000000056e-58

   1. Initial program 91.0%

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

      1. associate-*l* 91.0%

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

      2. *-commutative 91.0%

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

   3. Simplified 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*l* 91.0%

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

      3. associate-+l- 91.0%

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

      4. *-commutative 91.0%

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

      5. associate-/r* 90.5%

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

      6. sub-div 90.5%

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

   5. Applied egg-rr 90.5%

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

   6. Taylor expanded in x around 0 69.2%

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

      1. associate-*r/ 69.2%

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

   8. Applied egg-rr 69.2%

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

   9. Taylor expanded in y around 0 70.7%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-19} \lor \neg \left(y \leq 8.2 \cdot 10^{-58}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]

Alternative 14: 77.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-17} \lor \neg \left(y \leq 8.2 \cdot 10^{-58}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.2e-17) (not (<= y 8.2e-58)))
   (- x (/ y (* z 3.0)))
   (* 0.3333333333333333 (/ t (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.2e-17) || !(y <= 8.2e-58)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.2d-17)) .or. (.not. (y <= 8.2d-58))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = 0.3333333333333333d0 * (t / (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.2e-17) || !(y <= 8.2e-58)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.2e-17) or not (y <= 8.2e-58):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = 0.3333333333333333 * (t / (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.2e-17) || !(y <= 8.2e-58))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.2e-17) || ~((y <= 8.2e-58)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = 0.3333333333333333 * (t / (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.2e-17], N[Not[LessEqual[y, 8.2e-58]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.2e-17 or 8.20000000000000056e-58 < y

   1. Initial program 98.5%

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

      1. associate-*l* 98.5%

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

      2. *-commutative 98.5%

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

   3. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. associate-*l* 98.5%

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

      3. associate-+l- 98.5%

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

      4. *-commutative 98.5%

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

      5. associate-/r* 99.1%

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

      6. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 88.9%

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

   if -2.2e-17 < y < 8.20000000000000056e-58

   1. Initial program 91.0%

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

      1. associate-*l* 91.0%

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

      2. *-commutative 91.0%

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

   3. Simplified 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*l* 91.0%

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

      3. associate-+l- 91.0%

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

      4. *-commutative 91.0%

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

      5. associate-/r* 90.5%

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

      6. sub-div 90.5%

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

   5. Applied egg-rr 90.5%

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

   6. Taylor expanded in x around 0 69.2%

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

      1. associate-*r/ 69.2%

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

   8. Applied egg-rr 69.2%

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

   9. Taylor expanded in y around 0 70.7%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-17} \lor \neg \left(y \leq 8.2 \cdot 10^{-58}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]

Alternative 15: 78.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-17} \lor \neg \left(y \leq 7 \cdot 10^{-58}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.05e-17) (not (<= y 7e-58)))
   (- x (/ y (* z 3.0)))
   (/ (/ 0.3333333333333333 y) (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-17) || !(y <= 7e-58)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (0.3333333333333333 / y) / (z / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.05d-17)) .or. (.not. (y <= 7d-58))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (0.3333333333333333d0 / y) / (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.05e-17) || !(y <= 7e-58)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (0.3333333333333333 / y) / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.05e-17) or not (y <= 7e-58):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = (0.3333333333333333 / y) / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.05e-17) || !(y <= 7e-58))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(0.3333333333333333 / y) / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.05e-17) || ~((y <= 7e-58)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = (0.3333333333333333 / y) / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.05e-17], N[Not[LessEqual[y, 7e-58]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.3333333333333333 / y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.04999999999999996e-17 or 6.9999999999999998e-58 < y

   1. Initial program 98.5%

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

      1. associate-*l* 98.5%

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

      2. *-commutative 98.5%

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

   3. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. associate-*l* 98.5%

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

      3. associate-+l- 98.5%

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

      4. *-commutative 98.5%

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

      5. associate-/r* 99.1%

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

      6. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 88.9%

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

   if -1.04999999999999996e-17 < y < 6.9999999999999998e-58

   1. Initial program 91.0%

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

      1. associate-*l* 91.0%

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

      2. *-commutative 91.0%

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

   3. Simplified 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*l* 91.0%

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

      3. associate-+l- 91.0%

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

      4. *-commutative 91.0%

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

      5. associate-/r* 90.5%

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

      6. sub-div 90.5%

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

   5. Applied egg-rr 90.5%

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

   6. Taylor expanded in x around 0 69.2%

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

   7. Taylor expanded in y around 0 70.7%

      \[\leadsto -0.3333333333333333 \cdot \color{blue}{\left(-1 \cdot \frac{t}{y \cdot z}\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 70.7%

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

      2. distribute-neg-frac 70.7%

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

   9. Simplified 70.7%

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

       1. associate-*r/ 70.7%

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

       2. clear-num 70.7%

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

       3. neg-mul-1 70.7%

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

       4. associate-*r* 70.7%

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

       5. metadata-eval 70.7%

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

       6. associate-/l/ 70.7%

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

       7. associate-*r/ 74.4%

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

       8. clear-num 74.5%

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

       9. associate-/r* 74.5%

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

   11. Applied egg-rr 74.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-17} \lor \neg \left(y \leq 7 \cdot 10^{-58}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}\\ \end{array} \]

Alternative 16: 78.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-21} \lor \neg \left(y \leq 3.05 \cdot 10^{-58}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{0.3333333333333333}{\frac{z}{t}}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6e-21) (not (<= y 3.05e-58)))
   (- x (/ y (* z 3.0)))
   (/ (/ 0.3333333333333333 (/ z t)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6e-21) || !(y <= 3.05e-58)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (0.3333333333333333 / (z / t)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6d-21)) .or. (.not. (y <= 3.05d-58))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (0.3333333333333333d0 / (z / t)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6e-21) || !(y <= 3.05e-58)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (0.3333333333333333 / (z / t)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6e-21) or not (y <= 3.05e-58):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = (0.3333333333333333 / (z / t)) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6e-21) || !(y <= 3.05e-58))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(0.3333333333333333 / Float64(z / t)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6e-21) || ~((y <= 3.05e-58)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = (0.3333333333333333 / (z / t)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6e-21], N[Not[LessEqual[y, 3.05e-58]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.3333333333333333 / N[(z / t), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999982e-21 or 3.0500000000000002e-58 < y

   1. Initial program 98.5%

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

      1. associate-*l* 98.5%

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

      2. *-commutative 98.5%

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

   3. Simplified 98.5%

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

      1. *-commutative 98.5%

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

      2. associate-*l* 98.5%

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

      3. associate-+l- 98.5%

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

      4. *-commutative 98.5%

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

      5. associate-/r* 99.1%

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

      6. sub-div 99.8%

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

   5. Applied egg-rr 99.8%

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

   6. Taylor expanded in y around inf 88.9%

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

   if -5.99999999999999982e-21 < y < 3.0500000000000002e-58

   1. Initial program 91.0%

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

      1. associate-*l* 91.0%

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

      2. *-commutative 91.0%

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

   3. Simplified 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*l* 91.0%

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

      3. associate-+l- 91.0%

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

      4. *-commutative 91.0%

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

      5. associate-/r* 90.5%

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

      6. sub-div 90.5%

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

   5. Applied egg-rr 90.5%

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

   6. Taylor expanded in x around 0 69.2%

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

   7. Taylor expanded in y around 0 70.7%

      \[\leadsto -0.3333333333333333 \cdot \color{blue}{\left(-1 \cdot \frac{t}{y \cdot z}\right)} \]
   8. Step-by-step derivation

      1. mul-1-neg 70.7%

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

      2. distribute-neg-frac 70.7%

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

   9. Simplified 70.7%

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

       1. associate-*r/ 70.7%

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

       2. clear-num 70.7%

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

       3. neg-mul-1 70.7%

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

       4. associate-*r* 70.7%

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

       5. metadata-eval 70.7%

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

       6. associate-/l/ 70.7%

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

       7. associate-*r/ 74.4%

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

       8. clear-num 74.5%

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

       9. *-commutative 74.5%

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

       10. associate-/r* 74.5%

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

   11. Applied egg-rr 74.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-21} \lor \neg \left(y \leq 3.05 \cdot 10^{-58}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{0.3333333333333333}{\frac{z}{t}}}{y}\\ \end{array} \]

Alternative 17: 95.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + ((0.3333333333333333 / z) * ((t / y) - 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 + ((0.3333333333333333d0 / z) * ((t / y) - y))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.5%

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

3. Simplified 96.1%

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

4. Final simplification 96.1%

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

Alternative 18: 95.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x + (((t / y) - 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 + (((t / y) - y) / (z * 3.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

   2. *-commutative 95.5%

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

3. Simplified 95.5%

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

   1. *-commutative 95.5%

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

   2. associate-*l* 95.5%

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

   3. associate-+l- 95.5%

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

   4. *-commutative 95.5%

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

   5. associate-/r* 95.7%

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

   6. sub-div 96.1%

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

5. Applied egg-rr 96.1%

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

6. Final simplification 96.1%

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

Alternative 19: 47.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+55}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.6e+80) x (if (<= x 1.22e+55) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.6e+80) {
		tmp = x;
	} else if (x <= 1.22e+55) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.6d+80)) then
        tmp = x
    else if (x <= 1.22d+55) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.6e+80) {
		tmp = x;
	} else if (x <= 1.22e+55) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.6e+80:
		tmp = x
	elif x <= 1.22e+55:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.6e+80)
		tmp = x;
	elseif (x <= 1.22e+55)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.6e+80)
		tmp = x;
	elseif (x <= 1.22e+55)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.6e+80], x, If[LessEqual[x, 1.22e+55], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.59999999999999995e80 or 1.22e55 < x

   1. Initial program 94.5%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 54.2%

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

   if -1.59999999999999995e80 < x < 1.22e55

   1. Initial program 96.1%

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

      1. associate-*l* 96.1%

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

      2. *-commutative 96.1%

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

   3. Simplified 96.1%

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

      1. *-commutative 96.1%

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

      2. associate-*l* 96.1%

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

      3. associate-+l- 96.1%

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

      4. *-commutative 96.1%

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

      5. associate-/r* 95.7%

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

      6. sub-div 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in x around 0 84.6%

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

   7. Taylor expanded in y around inf 50.9%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{+55}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 20: 47.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.7e+80) x (if (<= x 1.25e+58) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.7e+80) {
		tmp = x;
	} else if (x <= 1.25e+58) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.7d+80)) then
        tmp = x
    else if (x <= 1.25d+58) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.7e+80) {
		tmp = x;
	} else if (x <= 1.25e+58) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.7e+80:
		tmp = x
	elif x <= 1.25e+58:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.7e+80)
		tmp = x;
	elseif (x <= 1.25e+58)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.7e+80)
		tmp = x;
	elseif (x <= 1.25e+58)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.7e+80], x, If[LessEqual[x, 1.25e+58], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.69999999999999996e80 or 1.24999999999999996e58 < x

   1. Initial program 94.5%

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

   3. Simplified 96.8%

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

   4. Taylor expanded in x around inf 54.2%

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

   if -1.69999999999999996e80 < x < 1.24999999999999996e58

   1. Initial program 96.1%

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

      1. associate-*l* 96.1%

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

      2. *-commutative 96.1%

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

   3. Simplified 96.1%

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

      1. *-commutative 96.1%

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

      2. associate-*l* 96.1%

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

      3. associate-+l- 96.1%

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

      4. *-commutative 96.1%

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

      5. associate-/r* 95.7%

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

      6. sub-div 95.7%

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

   5. Applied egg-rr 95.7%

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

   6. Taylor expanded in x around 0 84.6%

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

      1. associate-*r/ 84.7%

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

   8. Applied egg-rr 84.7%

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

   9. Taylor expanded in y around inf 50.9%

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

       1. associate-*r/ 51.0%

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

       2. *-commutative 51.0%

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

       3. associate-*r/ 51.0%

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

   11. Simplified 51.0%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+80}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+58}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21: 29.8% 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%

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

3. Simplified 96.1%

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

4. Taylor expanded in x around inf 27.4%

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

5. Final simplification 27.4%

   \[\leadsto x \]

Developer target: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023332 
(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))))