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

Percentage Accurate: 95.7% → 95.8%

Time: 14.3s

Alternatives: 18

Speedup: 1.4×

• 27.8% 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: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.8% 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 94.4%

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

   1. sub-neg 94.4%

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

   2. associate-+l+ 94.4%

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

   3. +-commutative 94.4%

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

   4. remove-double-neg 94.4%

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

   5. distribute-frac-neg 94.4%

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

   6. distribute-neg-in 94.4%

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

   7. remove-double-neg 94.4%

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

   8. sub-neg 94.4%

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

   9. neg-mul-1 94.4%

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

   10. times-frac 96.7%

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

   11. distribute-frac-neg 96.7%

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

   12. neg-mul-1 96.7%

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

   13. *-commutative 96.7%

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

   14. associate-/l* 96.7%

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

   15. *-commutative 96.7%

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

3. Simplified 97.5%

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

   1. *-commutative 97.5%

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

   2. clear-num 97.5%

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

   3. div-inv 97.5%

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

   4. metadata-eval 97.5%

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

   5. un-div-inv 97.6%

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

6. Applied egg-rr 97.6%

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

7. Final simplification 97.6%

   \[\leadsto x + \frac{\frac{t}{y} - y}{z \cdot 3} \]
8. Add Preprocessing

Alternative 2: 61.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot -0.3333333333333333\\ t_2 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{if}\;y \leq -6 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+27}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y z) -0.3333333333333333))
        (t_2 (* 0.3333333333333333 (/ t (* y z)))))
   (if (<= y -6e-14)
     t_1
     (if (<= y 7.2e-49)
       t_2
       (if (<= y 1.02e-16) x (if (<= y 7.8e+27) t_2 t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) * -0.3333333333333333;
	double t_2 = 0.3333333333333333 * (t / (y * z));
	double tmp;
	if (y <= -6e-14) {
		tmp = t_1;
	} else if (y <= 7.2e-49) {
		tmp = t_2;
	} else if (y <= 1.02e-16) {
		tmp = x;
	} else if (y <= 7.8e+27) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y / z) * (-0.3333333333333333d0)
    t_2 = 0.3333333333333333d0 * (t / (y * z))
    if (y <= (-6d-14)) then
        tmp = t_1
    else if (y <= 7.2d-49) then
        tmp = t_2
    else if (y <= 1.02d-16) then
        tmp = x
    else if (y <= 7.8d+27) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) * -0.3333333333333333;
	double t_2 = 0.3333333333333333 * (t / (y * z));
	double tmp;
	if (y <= -6e-14) {
		tmp = t_1;
	} else if (y <= 7.2e-49) {
		tmp = t_2;
	} else if (y <= 1.02e-16) {
		tmp = x;
	} else if (y <= 7.8e+27) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) * -0.3333333333333333
	t_2 = 0.3333333333333333 * (t / (y * z))
	tmp = 0
	if y <= -6e-14:
		tmp = t_1
	elif y <= 7.2e-49:
		tmp = t_2
	elif y <= 1.02e-16:
		tmp = x
	elif y <= 7.8e+27:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) * -0.3333333333333333)
	t_2 = Float64(0.3333333333333333 * Float64(t / Float64(y * z)))
	tmp = 0.0
	if (y <= -6e-14)
		tmp = t_1;
	elseif (y <= 7.2e-49)
		tmp = t_2;
	elseif (y <= 1.02e-16)
		tmp = x;
	elseif (y <= 7.8e+27)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) * -0.3333333333333333;
	t_2 = 0.3333333333333333 * (t / (y * z));
	tmp = 0.0;
	if (y <= -6e-14)
		tmp = t_1;
	elseif (y <= 7.2e-49)
		tmp = t_2;
	elseif (y <= 1.02e-16)
		tmp = x;
	elseif (y <= 7.8e+27)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]}, Block[{t$95$2 = N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -6e-14], t$95$1, If[LessEqual[y, 7.2e-49], t$95$2, If[LessEqual[y, 1.02e-16], x, If[LessEqual[y, 7.8e+27], t$95$2, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.9999999999999997e-14 or 7.7999999999999997e27 < y

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 72.7%

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

   4. Taylor expanded in t around 0 63.1%

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

      1. associate-/l* 63.1%

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

      2. *-commutative 63.1%

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

   6. Applied egg-rr 63.1%

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

   if -5.9999999999999997e-14 < y < 7.19999999999999939e-49 or 1.0200000000000001e-16 < y < 7.7999999999999997e27

   1. Initial program 91.9%

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

   3. Taylor expanded in z around 0 69.1%

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

      1. *-commutative 69.1%

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

      2. metadata-eval 69.1%

         \[\leadsto \frac{\frac{t}{y} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot y}{z} \]

      3. div-inv 69.2%

         \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   5. Applied egg-rr 69.2%

      \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   6. Taylor expanded in t around inf 61.9%

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

   if 7.19999999999999939e-49 < y < 1.0200000000000001e-16

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-+r- 100.0%

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

      3. sub-neg 100.0%

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

      4. associate-*l* 100.0%

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

      5. *-commutative 100.0%

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

      6. distribute-frac-neg2 100.0%

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

      7. distribute-rgt-neg-in 100.0%

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

      8. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 78.6%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-14}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-49}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 1.02 \cdot 10^{-16}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+27}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{if}\;y \leq -2.4 \cdot 10^{-12}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+30}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* (/ y z) -0.3333333333333333)))
   (if (<= y -2.4e-12)
     t_1
     (if (<= y 4.5e-53)
       (* 0.3333333333333333 (/ (/ t y) z))
       (if (<= y 1.65e-12)
         x
         (if (<= y 1.5e+30) (* 0.3333333333333333 (/ t (* y z))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (y / z) * -0.3333333333333333;
	double tmp;
	if (y <= -2.4e-12) {
		tmp = t_1;
	} else if (y <= 4.5e-53) {
		tmp = 0.3333333333333333 * ((t / y) / z);
	} else if (y <= 1.65e-12) {
		tmp = x;
	} else if (y <= 1.5e+30) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (y / z) * (-0.3333333333333333d0)
    if (y <= (-2.4d-12)) then
        tmp = t_1
    else if (y <= 4.5d-53) then
        tmp = 0.3333333333333333d0 * ((t / y) / z)
    else if (y <= 1.65d-12) then
        tmp = x
    else if (y <= 1.5d+30) then
        tmp = 0.3333333333333333d0 * (t / (y * z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (y / z) * -0.3333333333333333;
	double tmp;
	if (y <= -2.4e-12) {
		tmp = t_1;
	} else if (y <= 4.5e-53) {
		tmp = 0.3333333333333333 * ((t / y) / z);
	} else if (y <= 1.65e-12) {
		tmp = x;
	} else if (y <= 1.5e+30) {
		tmp = 0.3333333333333333 * (t / (y * z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (y / z) * -0.3333333333333333
	tmp = 0
	if y <= -2.4e-12:
		tmp = t_1
	elif y <= 4.5e-53:
		tmp = 0.3333333333333333 * ((t / y) / z)
	elif y <= 1.65e-12:
		tmp = x
	elif y <= 1.5e+30:
		tmp = 0.3333333333333333 * (t / (y * z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(y / z) * -0.3333333333333333)
	tmp = 0.0
	if (y <= -2.4e-12)
		tmp = t_1;
	elseif (y <= 4.5e-53)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / y) / z));
	elseif (y <= 1.65e-12)
		tmp = x;
	elseif (y <= 1.5e+30)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (y / z) * -0.3333333333333333;
	tmp = 0.0;
	if (y <= -2.4e-12)
		tmp = t_1;
	elseif (y <= 4.5e-53)
		tmp = 0.3333333333333333 * ((t / y) / z);
	elseif (y <= 1.65e-12)
		tmp = x;
	elseif (y <= 1.5e+30)
		tmp = 0.3333333333333333 * (t / (y * z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]}, If[LessEqual[y, -2.4e-12], t$95$1, If[LessEqual[y, 4.5e-53], N[(0.3333333333333333 * N[(N[(t / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e-12], x, If[LessEqual[y, 1.5e+30], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.39999999999999987e-12 or 1.49999999999999989e30 < y

   1. Initial program 97.1%

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

   3. Taylor expanded in z around 0 72.7%

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

   4. Taylor expanded in t around 0 63.1%

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

      1. associate-/l* 63.1%

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

      2. *-commutative 63.1%

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

   6. Applied egg-rr 63.1%

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

   if -2.39999999999999987e-12 < y < 4.49999999999999985e-53

   1. Initial program 91.2%

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

   3. Taylor expanded in z around 0 68.3%

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

      1. *-commutative 68.3%

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

      2. metadata-eval 68.3%

         \[\leadsto \frac{\frac{t}{y} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot y}{z} \]

      3. div-inv 68.3%

         \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   5. Applied egg-rr 68.3%

      \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   6. Taylor expanded in t around inf 61.9%

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

      1. associate-/r* 66.0%

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

   8. Simplified 66.0%

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

   if 4.49999999999999985e-53 < y < 1.65e-12

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-+r- 100.0%

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

      3. sub-neg 100.0%

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

      4. associate-*l* 100.0%

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

      5. *-commutative 100.0%

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

      6. distribute-frac-neg2 100.0%

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

      7. distribute-rgt-neg-in 100.0%

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

      8. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 78.6%

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

   if 1.65e-12 < y < 1.49999999999999989e30

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 79.9%

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

      1. *-commutative 79.9%

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

      2. metadata-eval 79.9%

         \[\leadsto \frac{\frac{t}{y} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot y}{z} \]

      3. div-inv 80.1%

         \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   5. Applied egg-rr 80.1%

      \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   6. Taylor expanded in t around inf 60.9%

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

4. Final simplification 65.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-12}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-53}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{-12}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+30}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+85}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{+91}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -2e+85)
   (- x (/ (/ y z) 3.0))
   (if (<= (* z 3.0) 2e+91)
     (* 0.3333333333333333 (/ (- (/ t y) y) z))
     (- x (/ 0.3333333333333333 (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -2e+85) {
		tmp = x - ((y / z) / 3.0);
	} else if ((z * 3.0) <= 2e+91) {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	} else {
		tmp = x - (0.3333333333333333 / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-2d+85)) then
        tmp = x - ((y / z) / 3.0d0)
    else if ((z * 3.0d0) <= 2d+91) then
        tmp = 0.3333333333333333d0 * (((t / y) - y) / z)
    else
        tmp = x - (0.3333333333333333d0 / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -2e+85) {
		tmp = x - ((y / z) / 3.0);
	} else if ((z * 3.0) <= 2e+91) {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	} else {
		tmp = x - (0.3333333333333333 / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -2e+85:
		tmp = x - ((y / z) / 3.0)
	elif (z * 3.0) <= 2e+91:
		tmp = 0.3333333333333333 * (((t / y) - y) / z)
	else:
		tmp = x - (0.3333333333333333 / (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -2e+85)
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	elseif (Float64(z * 3.0) <= 2e+91)
		tmp = Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z));
	else
		tmp = Float64(x - Float64(0.3333333333333333 / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -2e+85)
		tmp = x - ((y / z) / 3.0);
	elseif ((z * 3.0) <= 2e+91)
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	else
		tmp = x - (0.3333333333333333 / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+85], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e+91], N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -2e85

   1. Initial program 97.9%

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

   3. Taylor expanded in t around 0 78.1%

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

      1. metadata-eval 78.1%

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

      2. times-frac 78.1%

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

      3. *-un-lft-identity 78.1%

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

      4. *-commutative 78.1%

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

      5. associate-/r* 78.2%

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

   5. Applied egg-rr 78.2%

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

   if -2e85 < (*.f64 z 3) < 2.00000000000000016e91

   1. Initial program 92.2%

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

   3. Taylor expanded in z around 0 86.1%

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

      1. distribute-lft-out-- 86.1%

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

      2. *-commutative 86.1%

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

   5. Applied egg-rr 86.1%

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

   6. Taylor expanded in z around 0 86.1%

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

   if 2.00000000000000016e91 < (*.f64 z 3)

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 86.9%

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

      1. clear-num 87.0%

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

      2. un-div-inv 87.0%

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

   5. Applied egg-rr 87.0%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+85}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{+91}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 81.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+86}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{+91}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -1e+86)
   (- x (/ (/ y z) 3.0))
   (if (<= (* z 3.0) 2e+91)
     (* (- (/ t y) y) (/ 0.3333333333333333 z))
     (- x (/ 0.3333333333333333 (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -1e+86) {
		tmp = x - ((y / z) / 3.0);
	} else if ((z * 3.0) <= 2e+91) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} else {
		tmp = x - (0.3333333333333333 / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-1d+86)) then
        tmp = x - ((y / z) / 3.0d0)
    else if ((z * 3.0d0) <= 2d+91) then
        tmp = ((t / y) - y) * (0.3333333333333333d0 / z)
    else
        tmp = x - (0.3333333333333333d0 / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -1e+86) {
		tmp = x - ((y / z) / 3.0);
	} else if ((z * 3.0) <= 2e+91) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} else {
		tmp = x - (0.3333333333333333 / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -1e+86:
		tmp = x - ((y / z) / 3.0)
	elif (z * 3.0) <= 2e+91:
		tmp = ((t / y) - y) * (0.3333333333333333 / z)
	else:
		tmp = x - (0.3333333333333333 / (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -1e+86)
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	elseif (Float64(z * 3.0) <= 2e+91)
		tmp = Float64(Float64(Float64(t / y) - y) * Float64(0.3333333333333333 / z));
	else
		tmp = Float64(x - Float64(0.3333333333333333 / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -1e+86)
		tmp = x - ((y / z) / 3.0);
	elseif ((z * 3.0) <= 2e+91)
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	else
		tmp = x - (0.3333333333333333 / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -1e+86], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e+91], N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -1e86

   1. Initial program 97.9%

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

   3. Taylor expanded in t around 0 77.7%

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

      1. metadata-eval 77.7%

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

      2. times-frac 77.7%

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

      3. *-un-lft-identity 77.7%

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

      4. *-commutative 77.7%

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

      5. associate-/r* 77.7%

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

   5. Applied egg-rr 77.7%

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

   if -1e86 < (*.f64 z 3) < 2.00000000000000016e91

   1. Initial program 92.3%

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

   3. Taylor expanded in z around 0 86.2%

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

      1. distribute-lft-out-- 86.2%

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

      2. *-commutative 86.2%

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

   5. Applied egg-rr 86.2%

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

      1. associate-/l* 86.2%

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

      2. metadata-eval 86.2%

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

      3. associate-/r* 86.2%

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

      4. *-commutative 86.2%

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

      5. *-commutative 86.2%

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

      6. *-commutative 86.2%

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

      7. associate-/r* 86.2%

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

      8. metadata-eval 86.2%

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

   7. Applied egg-rr 86.2%

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

   if 2.00000000000000016e91 < (*.f64 z 3)

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 86.9%

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

      1. clear-num 87.0%

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

      2. un-div-inv 87.0%

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

   5. Applied egg-rr 87.0%

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

4. Final simplification 84.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+86}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{+91}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-12}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.2e-12)
   (- x (/ (/ y z) 3.0))
   (if (<= y 2.5e+30)
     (+ x (* (/ t y) (/ 0.3333333333333333 z)))
     (- x (/ (/ y 3.0) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.2e-12) {
		tmp = x - ((y / z) / 3.0);
	} else if (y <= 2.5e+30) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} else {
		tmp = x - ((y / 3.0) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.2d-12)) then
        tmp = x - ((y / z) / 3.0d0)
    else if (y <= 2.5d+30) then
        tmp = x + ((t / y) * (0.3333333333333333d0 / z))
    else
        tmp = x - ((y / 3.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.2e-12) {
		tmp = x - ((y / z) / 3.0);
	} else if (y <= 2.5e+30) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} else {
		tmp = x - ((y / 3.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.2e-12:
		tmp = x - ((y / z) / 3.0)
	elif y <= 2.5e+30:
		tmp = x + ((t / y) * (0.3333333333333333 / z))
	else:
		tmp = x - ((y / 3.0) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.2e-12)
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	elseif (y <= 2.5e+30)
		tmp = Float64(x + Float64(Float64(t / y) * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.2e-12)
		tmp = x - ((y / z) / 3.0);
	elseif (y <= 2.5e+30)
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	else
		tmp = x - ((y / 3.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.2e-12], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+30], N[(x + N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.19999999999999992e-12

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 87.0%

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

      1. metadata-eval 87.0%

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

      2. times-frac 86.9%

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

      3. *-un-lft-identity 86.9%

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

      4. *-commutative 86.9%

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

      5. associate-/r* 87.1%

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

   5. Applied egg-rr 87.1%

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

   if -2.19999999999999992e-12 < y < 2.4999999999999999e30

   1. Initial program 92.4%

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

      1. sub-neg 92.4%

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

      2. associate-+l+ 92.4%

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

      3. +-commutative 92.4%

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

      4. remove-double-neg 92.4%

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

      5. distribute-frac-neg 92.4%

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

      6. distribute-neg-in 92.4%

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

      7. remove-double-neg 92.4%

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

      8. sub-neg 92.4%

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

      9. neg-mul-1 92.4%

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

      10. times-frac 95.8%

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

      11. distribute-frac-neg 95.8%

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

      12. neg-mul-1 95.8%

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

      13. *-commutative 95.8%

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

      14. associate-/l* 95.8%

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

      15. *-commutative 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around inf 92.5%

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

   if 2.4999999999999999e30 < y

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0 93.2%

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

      1. metadata-eval 93.2%

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

      2. times-frac 93.2%

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

      3. *-un-lft-identity 93.2%

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

      4. associate-/r* 93.3%

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

   5. Applied egg-rr 93.3%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.2 \cdot 10^{-12}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+30}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-13}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.5e-13)
   (- x (/ (/ y z) 3.0))
   (if (<= y 2.8e+29) (+ x (/ (/ t y) (* z 3.0))) (- x (/ (/ y 3.0) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e-13) {
		tmp = x - ((y / z) / 3.0);
	} else if (y <= 2.8e+29) {
		tmp = x + ((t / y) / (z * 3.0));
	} else {
		tmp = x - ((y / 3.0) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9.5d-13)) then
        tmp = x - ((y / z) / 3.0d0)
    else if (y <= 2.8d+29) then
        tmp = x + ((t / y) / (z * 3.0d0))
    else
        tmp = x - ((y / 3.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e-13) {
		tmp = x - ((y / z) / 3.0);
	} else if (y <= 2.8e+29) {
		tmp = x + ((t / y) / (z * 3.0));
	} else {
		tmp = x - ((y / 3.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.5e-13:
		tmp = x - ((y / z) / 3.0)
	elif y <= 2.8e+29:
		tmp = x + ((t / y) / (z * 3.0))
	else:
		tmp = x - ((y / 3.0) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.5e-13)
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	elseif (y <= 2.8e+29)
		tmp = Float64(x + Float64(Float64(t / y) / Float64(z * 3.0)));
	else
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9.5e-13)
		tmp = x - ((y / z) / 3.0);
	elseif (y <= 2.8e+29)
		tmp = x + ((t / y) / (z * 3.0));
	else
		tmp = x - ((y / 3.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.5e-13], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+29], N[(x + N[(N[(t / y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.49999999999999991e-13

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 87.0%

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

      1. metadata-eval 87.0%

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

      2. times-frac 86.9%

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

      3. *-un-lft-identity 86.9%

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

      4. *-commutative 86.9%

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

      5. associate-/r* 87.1%

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

   5. Applied egg-rr 87.1%

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

   if -9.49999999999999991e-13 < y < 2.8e29

   1. Initial program 92.4%

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

      1. sub-neg 92.4%

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

      2. associate-+l+ 92.4%

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

      3. +-commutative 92.4%

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

      4. remove-double-neg 92.4%

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

      5. distribute-frac-neg 92.4%

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

      6. distribute-neg-in 92.4%

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

      7. remove-double-neg 92.4%

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

      8. sub-neg 92.4%

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

      9. neg-mul-1 92.4%

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

      10. times-frac 95.8%

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

      11. distribute-frac-neg 95.8%

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

      12. neg-mul-1 95.8%

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

      13. *-commutative 95.8%

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

      14. associate-/l* 95.8%

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

      15. *-commutative 95.8%

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

   3. Simplified 95.8%

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

      1. *-commutative 95.8%

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

      2. clear-num 95.8%

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

      3. div-inv 95.8%

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

      4. metadata-eval 95.8%

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

      5. un-div-inv 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in t around inf 92.6%

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

   if 2.8e29 < y

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0 93.2%

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

      1. metadata-eval 93.2%

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

      2. times-frac 93.2%

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

      3. *-un-lft-identity 93.2%

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

      4. associate-/r* 93.3%

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

   5. Applied egg-rr 93.3%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-13}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;x + \frac{\frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{\frac{t}{y \cdot 3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.5e-13)
   (- x (/ (/ y z) 3.0))
   (if (<= y 3.3e+27) (+ x (/ (/ t (* y 3.0)) z)) (- x (/ (/ y 3.0) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.5e-13) {
		tmp = x - ((y / z) / 3.0);
	} else if (y <= 3.3e+27) {
		tmp = x + ((t / (y * 3.0)) / z);
	} else {
		tmp = x - ((y / 3.0) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-8.5d-13)) then
        tmp = x - ((y / z) / 3.0d0)
    else if (y <= 3.3d+27) then
        tmp = x + ((t / (y * 3.0d0)) / z)
    else
        tmp = x - ((y / 3.0d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.5e-13) {
		tmp = x - ((y / z) / 3.0);
	} else if (y <= 3.3e+27) {
		tmp = x + ((t / (y * 3.0)) / z);
	} else {
		tmp = x - ((y / 3.0) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.5e-13:
		tmp = x - ((y / z) / 3.0)
	elif y <= 3.3e+27:
		tmp = x + ((t / (y * 3.0)) / z)
	else:
		tmp = x - ((y / 3.0) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.5e-13)
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	elseif (y <= 3.3e+27)
		tmp = Float64(x + Float64(Float64(t / Float64(y * 3.0)) / z));
	else
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -8.5e-13)
		tmp = x - ((y / z) / 3.0);
	elseif (y <= 3.3e+27)
		tmp = x + ((t / (y * 3.0)) / z);
	else
		tmp = x - ((y / 3.0) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.5e-13], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.3e+27], N[(x + N[(N[(t / N[(y * 3.0), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.5000000000000001e-13

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 87.0%

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

      1. metadata-eval 87.0%

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

      2. times-frac 86.9%

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

      3. *-un-lft-identity 86.9%

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

      4. *-commutative 86.9%

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

      5. associate-/r* 87.1%

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

   5. Applied egg-rr 87.1%

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

   if -8.5000000000000001e-13 < y < 3.2999999999999998e27

   1. Initial program 92.4%

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

      1. sub-neg 92.4%

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

      2. associate-+l+ 92.4%

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

      3. +-commutative 92.4%

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

      4. remove-double-neg 92.4%

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

      5. distribute-frac-neg 92.4%

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

      6. distribute-neg-in 92.4%

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

      7. remove-double-neg 92.4%

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

      8. sub-neg 92.4%

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

      9. neg-mul-1 92.4%

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

      10. times-frac 95.8%

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

      11. distribute-frac-neg 95.8%

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

      12. neg-mul-1 95.8%

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

      13. *-commutative 95.8%

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

      14. associate-/l* 95.8%

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

      15. *-commutative 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in t around inf 89.6%

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

      1. metadata-eval 89.6%

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

      2. associate-/r* 92.4%

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

      3. times-frac 92.6%

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

      4. *-commutative 92.6%

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

      5. times-frac 92.5%

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

      6. associate-/r* 92.5%

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

      7. associate-*l/ 92.6%

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

      8. *-lft-identity 92.6%

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

   7. Simplified 92.6%

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

   if 3.2999999999999998e27 < y

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0 93.2%

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

      1. metadata-eval 93.2%

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

      2. times-frac 93.2%

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

      3. *-un-lft-identity 93.2%

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

      4. associate-/r* 93.3%

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

   5. Applied egg-rr 93.3%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-13}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+27}:\\ \;\;\;\;x + \frac{\frac{t}{y \cdot 3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-15} \lor \neg \left(y \leq 2.15 \cdot 10^{-69}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.5e-15) (not (<= y 2.15e-69)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* 0.3333333333333333 (/ (/ t y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e-15) || !(y <= 2.15e-69)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * ((t / y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-9.5d-15)) .or. (.not. (y <= 2.15d-69))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = 0.3333333333333333d0 * ((t / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e-15) || !(y <= 2.15e-69)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * ((t / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.5e-15) or not (y <= 2.15e-69):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * ((t / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.5e-15) || !(y <= 2.15e-69))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -9.5e-15) || ~((y <= 2.15e-69)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * ((t / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.5e-15], N[Not[LessEqual[y, 2.15e-69]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(t / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5000000000000005e-15 or 2.15e-69 < y

   1. Initial program 96.9%

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

      1. sub-neg 96.9%

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

      2. associate-+l+ 96.9%

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

      3. +-commutative 96.9%

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

      4. remove-double-neg 96.9%

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

      5. distribute-frac-neg 96.9%

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

      6. distribute-neg-in 96.9%

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

      7. remove-double-neg 96.9%

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

      8. sub-neg 96.9%

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

      9. neg-mul-1 96.9%

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

      10. times-frac 98.3%

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

      11. distribute-frac-neg 98.3%

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

      12. neg-mul-1 98.3%

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

      13. *-commutative 98.3%

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

      14. associate-/l* 98.2%

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

      15. *-commutative 98.2%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 83.8%

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

      1. metadata-eval 83.8%

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

      2. distribute-lft-neg-in 83.8%

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

      3. *-commutative 83.8%

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

      4. associate-*l/ 83.8%

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

      5. associate-*r/ 83.8%

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

      6. distribute-rgt-neg-out 83.8%

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

      7. distribute-neg-frac 83.8%

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

      8. metadata-eval 83.8%

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

   7. Simplified 83.8%

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

   if -9.5000000000000005e-15 < y < 2.15e-69

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. metadata-eval 68.1%

         \[\leadsto \frac{\frac{t}{y} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot y}{z} \]

      3. div-inv 68.2%

         \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   5. Applied egg-rr 68.2%

      \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   6. Taylor expanded in t around inf 63.0%

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

      1. associate-/r* 67.2%

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

   8. Simplified 67.2%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-15} \lor \neg \left(y \leq 2.15 \cdot 10^{-69}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-14} \lor \neg \left(y \leq 6.5 \cdot 10^{-69}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.5e-14) (not (<= y 6.5e-69)))
   (- x (* 0.3333333333333333 (/ y z)))
   (* 0.3333333333333333 (/ (/ t y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.5e-14) || !(y <= 6.5e-69)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = 0.3333333333333333 * ((t / y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.5d-14)) .or. (.not. (y <= 6.5d-69))) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else
        tmp = 0.3333333333333333d0 * ((t / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.5e-14) || !(y <= 6.5e-69)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = 0.3333333333333333 * ((t / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.5e-14) or not (y <= 6.5e-69):
		tmp = x - (0.3333333333333333 * (y / z))
	else:
		tmp = 0.3333333333333333 * ((t / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.5e-14) || !(y <= 6.5e-69))
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.5e-14) || ~((y <= 6.5e-69)))
		tmp = x - (0.3333333333333333 * (y / z));
	else
		tmp = 0.3333333333333333 * ((t / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.5e-14], N[Not[LessEqual[y, 6.5e-69]], $MachinePrecision]], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(t / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4999999999999999e-14 or 6.49999999999999951e-69 < y

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0 83.8%

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

   if -1.4999999999999999e-14 < y < 6.49999999999999951e-69

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. metadata-eval 68.1%

         \[\leadsto \frac{\frac{t}{y} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot y}{z} \]

      3. div-inv 68.2%

         \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   5. Applied egg-rr 68.2%

      \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   6. Taylor expanded in t around inf 63.0%

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

      1. associate-/r* 67.2%

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

   8. Simplified 67.2%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.5 \cdot 10^{-14} \lor \neg \left(y \leq 6.5 \cdot 10^{-69}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-14} \lor \neg \left(y \leq 5.2 \cdot 10^{-69}\right):\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.06e-14) (not (<= y 5.2e-69)))
   (- x (/ 0.3333333333333333 (/ z y)))
   (* 0.3333333333333333 (/ (/ t y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.06e-14) || !(y <= 5.2e-69)) {
		tmp = x - (0.3333333333333333 / (z / y));
	} else {
		tmp = 0.3333333333333333 * ((t / y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.06d-14)) .or. (.not. (y <= 5.2d-69))) then
        tmp = x - (0.3333333333333333d0 / (z / y))
    else
        tmp = 0.3333333333333333d0 * ((t / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.06e-14) || !(y <= 5.2e-69)) {
		tmp = x - (0.3333333333333333 / (z / y));
	} else {
		tmp = 0.3333333333333333 * ((t / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.06e-14) or not (y <= 5.2e-69):
		tmp = x - (0.3333333333333333 / (z / y))
	else:
		tmp = 0.3333333333333333 * ((t / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.06e-14) || !(y <= 5.2e-69))
		tmp = Float64(x - Float64(0.3333333333333333 / Float64(z / y)));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.06e-14) || ~((y <= 5.2e-69)))
		tmp = x - (0.3333333333333333 / (z / y));
	else
		tmp = 0.3333333333333333 * ((t / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.06e-14], N[Not[LessEqual[y, 5.2e-69]], $MachinePrecision]], N[(x - N[(0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(t / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.06e-14 or 5.2000000000000004e-69 < y

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0 83.8%

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

      1. clear-num 83.8%

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

      2. un-div-inv 83.8%

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

   5. Applied egg-rr 83.8%

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

   if -1.06e-14 < y < 5.2000000000000004e-69

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. metadata-eval 68.1%

         \[\leadsto \frac{\frac{t}{y} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot y}{z} \]

      3. div-inv 68.2%

         \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   5. Applied egg-rr 68.2%

      \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   6. Taylor expanded in t around inf 63.0%

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

      1. associate-/r* 67.2%

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

   8. Simplified 67.2%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-14} \lor \neg \left(y \leq 5.2 \cdot 10^{-69}\right):\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-69}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.7e-15)
   (- x (/ (/ y 3.0) z))
   (if (<= y 4.8e-69)
     (* 0.3333333333333333 (/ (/ t y) z))
     (- x (/ 0.3333333333333333 (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.7e-15) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 4.8e-69) {
		tmp = 0.3333333333333333 * ((t / y) / z);
	} else {
		tmp = x - (0.3333333333333333 / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.7d-15)) then
        tmp = x - ((y / 3.0d0) / z)
    else if (y <= 4.8d-69) then
        tmp = 0.3333333333333333d0 * ((t / y) / z)
    else
        tmp = x - (0.3333333333333333d0 / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.7e-15) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 4.8e-69) {
		tmp = 0.3333333333333333 * ((t / y) / z);
	} else {
		tmp = x - (0.3333333333333333 / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.7e-15:
		tmp = x - ((y / 3.0) / z)
	elif y <= 4.8e-69:
		tmp = 0.3333333333333333 * ((t / y) / z)
	else:
		tmp = x - (0.3333333333333333 / (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.7e-15)
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	elseif (y <= 4.8e-69)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / y) / z));
	else
		tmp = Float64(x - Float64(0.3333333333333333 / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.7e-15)
		tmp = x - ((y / 3.0) / z);
	elseif (y <= 4.8e-69)
		tmp = 0.3333333333333333 * ((t / y) / z);
	else
		tmp = x - (0.3333333333333333 / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.7e-15], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.8e-69], N[(0.3333333333333333 * N[(N[(t / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.6999999999999999e-15

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 87.0%

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

      1. metadata-eval 87.0%

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

      2. times-frac 86.9%

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

      3. *-un-lft-identity 86.9%

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

      4. associate-/r* 87.1%

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

   5. Applied egg-rr 87.1%

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

   if -4.6999999999999999e-15 < y < 4.8000000000000002e-69

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. metadata-eval 68.1%

         \[\leadsto \frac{\frac{t}{y} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot y}{z} \]

      3. div-inv 68.2%

         \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   5. Applied egg-rr 68.2%

      \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   6. Taylor expanded in t around inf 63.0%

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

      1. associate-/r* 67.2%

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

   8. Simplified 67.2%

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

   if 4.8000000000000002e-69 < y

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0 81.8%

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

      1. clear-num 81.8%

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

      2. un-div-inv 81.8%

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

   5. Applied egg-rr 81.8%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-69}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-69}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9.5e-15)
   (- x (/ (/ y z) 3.0))
   (if (<= y 6.5e-69)
     (* 0.3333333333333333 (/ (/ t y) z))
     (- x (/ 0.3333333333333333 (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e-15) {
		tmp = x - ((y / z) / 3.0);
	} else if (y <= 6.5e-69) {
		tmp = 0.3333333333333333 * ((t / y) / z);
	} else {
		tmp = x - (0.3333333333333333 / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9.5d-15)) then
        tmp = x - ((y / z) / 3.0d0)
    else if (y <= 6.5d-69) then
        tmp = 0.3333333333333333d0 * ((t / y) / z)
    else
        tmp = x - (0.3333333333333333d0 / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9.5e-15) {
		tmp = x - ((y / z) / 3.0);
	} else if (y <= 6.5e-69) {
		tmp = 0.3333333333333333 * ((t / y) / z);
	} else {
		tmp = x - (0.3333333333333333 / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9.5e-15:
		tmp = x - ((y / z) / 3.0)
	elif y <= 6.5e-69:
		tmp = 0.3333333333333333 * ((t / y) / z)
	else:
		tmp = x - (0.3333333333333333 / (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9.5e-15)
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	elseif (y <= 6.5e-69)
		tmp = Float64(0.3333333333333333 * Float64(Float64(t / y) / z));
	else
		tmp = Float64(x - Float64(0.3333333333333333 / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9.5e-15)
		tmp = x - ((y / z) / 3.0);
	elseif (y <= 6.5e-69)
		tmp = 0.3333333333333333 * ((t / y) / z);
	else
		tmp = x - (0.3333333333333333 / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9.5e-15], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.5e-69], N[(0.3333333333333333 * N[(N[(t / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.5000000000000005e-15

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 87.0%

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

      1. metadata-eval 87.0%

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

      2. times-frac 86.9%

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

      3. *-un-lft-identity 86.9%

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

      4. *-commutative 86.9%

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

      5. associate-/r* 87.1%

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

   5. Applied egg-rr 87.1%

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

   if -9.5000000000000005e-15 < y < 6.49999999999999951e-69

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 68.1%

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

      1. *-commutative 68.1%

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

      2. metadata-eval 68.1%

         \[\leadsto \frac{\frac{t}{y} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot y}{z} \]

      3. div-inv 68.2%

         \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   5. Applied egg-rr 68.2%

      \[\leadsto \frac{\color{blue}{\frac{\frac{t}{y}}{3}} - 0.3333333333333333 \cdot y}{z} \]

   6. Taylor expanded in t around inf 63.0%

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

      1. associate-/r* 67.2%

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

   8. Simplified 67.2%

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

   if 6.49999999999999951e-69 < y

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0 81.8%

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

      1. clear-num 81.8%

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

      2. un-div-inv 81.8%

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

   5. Applied egg-rr 81.8%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-69}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{t}{y} \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.45e-15)
   (- x (/ (/ y z) 3.0))
   (if (<= y 2.4e-69)
     (/ (* (/ t y) 0.3333333333333333) z)
     (- x (/ 0.3333333333333333 (/ z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-15) {
		tmp = x - ((y / z) / 3.0);
	} else if (y <= 2.4e-69) {
		tmp = ((t / y) * 0.3333333333333333) / z;
	} else {
		tmp = x - (0.3333333333333333 / (z / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.45d-15)) then
        tmp = x - ((y / z) / 3.0d0)
    else if (y <= 2.4d-69) then
        tmp = ((t / y) * 0.3333333333333333d0) / z
    else
        tmp = x - (0.3333333333333333d0 / (z / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.45e-15) {
		tmp = x - ((y / z) / 3.0);
	} else if (y <= 2.4e-69) {
		tmp = ((t / y) * 0.3333333333333333) / z;
	} else {
		tmp = x - (0.3333333333333333 / (z / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.45e-15:
		tmp = x - ((y / z) / 3.0)
	elif y <= 2.4e-69:
		tmp = ((t / y) * 0.3333333333333333) / z
	else:
		tmp = x - (0.3333333333333333 / (z / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.45e-15)
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	elseif (y <= 2.4e-69)
		tmp = Float64(Float64(Float64(t / y) * 0.3333333333333333) / z);
	else
		tmp = Float64(x - Float64(0.3333333333333333 / Float64(z / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.45e-15)
		tmp = x - ((y / z) / 3.0);
	elseif (y <= 2.4e-69)
		tmp = ((t / y) * 0.3333333333333333) / z;
	else
		tmp = x - (0.3333333333333333 / (z / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.45e-15], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e-69], N[(N[(N[(t / y), $MachinePrecision] * 0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], N[(x - N[(0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.45000000000000009e-15

   1. Initial program 98.0%

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

   3. Taylor expanded in t around 0 87.0%

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

      1. metadata-eval 87.0%

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

      2. times-frac 86.9%

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

      3. *-un-lft-identity 86.9%

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

      4. *-commutative 86.9%

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

      5. associate-/r* 87.1%

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

   5. Applied egg-rr 87.1%

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

   if -1.45000000000000009e-15 < y < 2.4000000000000001e-69

   1. Initial program 91.5%

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

   3. Taylor expanded in z around 0 68.1%

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

      1. distribute-lft-out-- 68.1%

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

      2. *-commutative 68.1%

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

   5. Applied egg-rr 68.1%

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

   6. Taylor expanded in t around inf 67.2%

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

   if 2.4000000000000001e-69 < y

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0 81.8%

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

      1. clear-num 81.8%

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

      2. un-div-inv 81.8%

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

   5. Applied egg-rr 81.8%

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

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.45 \cdot 10^{-15}:\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{-69}:\\ \;\;\;\;\frac{\frac{t}{y} \cdot 0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.9e+58) x (if (<= x 3.2e-69) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.9e+58) {
		tmp = x;
	} else if (x <= 3.2e-69) {
		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 <= (-1.9d+58)) then
        tmp = x
    else if (x <= 3.2d-69) 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 <= -1.9e+58) {
		tmp = x;
	} else if (x <= 3.2e-69) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.9e+58:
		tmp = x
	elif x <= 3.2e-69:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.9e+58)
		tmp = x;
	elseif (x <= 3.2e-69)
		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 <= -1.9e+58)
		tmp = x;
	elseif (x <= 3.2e-69)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.9e+58], x, If[LessEqual[x, 3.2e-69], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8999999999999999e58 or 3.19999999999999999e-69 < x

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. associate-+r- 95.8%

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

      3. sub-neg 95.8%

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

      4. associate-*l* 95.8%

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

      5. *-commutative 95.8%

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

      6. distribute-frac-neg2 95.8%

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

      7. distribute-rgt-neg-in 95.8%

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

      8. metadata-eval 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in z around inf 52.2%

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

   if -1.8999999999999999e58 < x < 3.19999999999999999e-69

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 89.8%

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

   4. Taylor expanded in t around 0 44.0%

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

   5. Taylor expanded in y around 0 44.1%

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

      1. *-commutative 44.1%

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

      2. associate-*l/ 44.0%

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

      3. associate-*r/ 44.1%

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

   7. Simplified 44.1%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-69}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.8e+56) x (if (<= x 2.2e-69) (* (/ y z) -0.3333333333333333) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.8e+56) {
		tmp = x;
	} else if (x <= 2.2e-69) {
		tmp = (y / z) * -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-6.8d+56)) then
        tmp = x
    else if (x <= 2.2d-69) then
        tmp = (y / z) * (-0.3333333333333333d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.8e+56) {
		tmp = x;
	} else if (x <= 2.2e-69) {
		tmp = (y / z) * -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.8e+56:
		tmp = x
	elif x <= 2.2e-69:
		tmp = (y / z) * -0.3333333333333333
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.8e+56)
		tmp = x;
	elseif (x <= 2.2e-69)
		tmp = Float64(Float64(y / z) * -0.3333333333333333);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -6.8e+56)
		tmp = x;
	elseif (x <= 2.2e-69)
		tmp = (y / z) * -0.3333333333333333;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.8e+56], x, If[LessEqual[x, 2.2e-69], N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -6.80000000000000002e56 or 2.2e-69 < x

   1. Initial program 95.8%

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

      1. +-commutative 95.8%

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

      2. associate-+r- 95.8%

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

      3. sub-neg 95.8%

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

      4. associate-*l* 95.8%

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

      5. *-commutative 95.8%

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

      6. distribute-frac-neg2 95.8%

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

      7. distribute-rgt-neg-in 95.8%

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

      8. metadata-eval 95.8%

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

   3. Simplified 95.8%

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

   5. Taylor expanded in z around inf 52.2%

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

   if -6.80000000000000002e56 < x < 2.2e-69

   1. Initial program 93.0%

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

   3. Taylor expanded in z around 0 89.8%

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

   4. Taylor expanded in t around 0 44.0%

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

      1. associate-/l* 44.1%

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

      2. *-commutative 44.1%

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

   6. Applied egg-rr 44.1%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{+56}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.2 \cdot 10^{-69}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 95.7% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.4%

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

   1. sub-neg 94.4%

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

   2. associate-+l+ 94.4%

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

   3. +-commutative 94.4%

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

   4. remove-double-neg 94.4%

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

   5. distribute-frac-neg 94.4%

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

   6. distribute-neg-in 94.4%

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

   7. remove-double-neg 94.4%

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

   8. sub-neg 94.4%

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

   9. neg-mul-1 94.4%

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

   10. times-frac 96.7%

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

   11. distribute-frac-neg 96.7%

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

   12. neg-mul-1 96.7%

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

   13. *-commutative 96.7%

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

   14. associate-/l* 96.7%

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

   15. *-commutative 96.7%

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

3. Simplified 97.5%

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

5. Final simplification 97.5%

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

Alternative 18: 30.3% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 94.4%

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

   1. +-commutative 94.4%

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

   2. associate-+r- 94.4%

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

   3. sub-neg 94.4%

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

   4. associate-*l* 94.4%

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

   5. *-commutative 94.4%

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

   6. distribute-frac-neg2 94.4%

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

   7. distribute-rgt-neg-in 94.4%

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

   8. metadata-eval 94.4%

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

3. Simplified 94.4%

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

5. Taylor expanded in z around inf 31.9%

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

6. Final simplification 31.9%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024044 
(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))))