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

Percentage Accurate: 95.9% → 95.6%

Time: 12.6s

Alternatives: 17

Speedup: N/A×

• 28.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 95.6% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 95.6%

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

3. Simplified 97.9%

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

   1. +-commutative 97.9%

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

   2. fma-def 97.9%

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

6. Applied egg-rr 97.9%

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

7. Final simplification 97.9%

   \[\leadsto \mathsf{fma}\left(\frac{0.3333333333333333}{z}, \frac{t}{y} - y, x\right) \]
8. Add Preprocessing

Alternative 2: 61.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -5.8 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -16500:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-33}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* z -3.0))))
   (if (<= y -5.8e+85)
     t_1
     (if (<= y -5.6e+32)
       x
       (if (<= y -16500.0)
         (/ -0.3333333333333333 (/ z y))
         (if (<= y 3.6e-33) (* 0.3333333333333333 (/ t (* z y))) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (y <= -5.8e+85) {
		tmp = t_1;
	} else if (y <= -5.6e+32) {
		tmp = x;
	} else if (y <= -16500.0) {
		tmp = -0.3333333333333333 / (z / y);
	} else if (y <= 3.6e-33) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (z * (-3.0d0))
    if (y <= (-5.8d+85)) then
        tmp = t_1
    else if (y <= (-5.6d+32)) then
        tmp = x
    else if (y <= (-16500.0d0)) then
        tmp = (-0.3333333333333333d0) / (z / y)
    else if (y <= 3.6d-33) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (y <= -5.8e+85) {
		tmp = t_1;
	} else if (y <= -5.6e+32) {
		tmp = x;
	} else if (y <= -16500.0) {
		tmp = -0.3333333333333333 / (z / y);
	} else if (y <= 3.6e-33) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (z * -3.0)
	tmp = 0
	if y <= -5.8e+85:
		tmp = t_1
	elif y <= -5.6e+32:
		tmp = x
	elif y <= -16500.0:
		tmp = -0.3333333333333333 / (z / y)
	elif y <= 3.6e-33:
		tmp = 0.3333333333333333 * (t / (z * y))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(z * -3.0))
	tmp = 0.0
	if (y <= -5.8e+85)
		tmp = t_1;
	elseif (y <= -5.6e+32)
		tmp = x;
	elseif (y <= -16500.0)
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	elseif (y <= 3.6e-33)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (z * -3.0);
	tmp = 0.0;
	if (y <= -5.8e+85)
		tmp = t_1;
	elseif (y <= -5.6e+32)
		tmp = x;
	elseif (y <= -16500.0)
		tmp = -0.3333333333333333 / (z / y);
	elseif (y <= 3.6e-33)
		tmp = 0.3333333333333333 * (t / (z * y));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.8e+85], t$95$1, If[LessEqual[y, -5.6e+32], x, If[LessEqual[y, -16500.0], N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-33], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.79999999999999995e85 or 3.60000000000000034e-33 < y

   1. Initial program 99.8%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-def 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 71.8%

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

      1. associate-*r/ 71.8%

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

      2. *-commutative 71.8%

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

      3. associate-/l* 71.9%

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

      4. div-inv 71.9%

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

      5. metadata-eval 71.9%

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

   9. Applied egg-rr 71.9%

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

   if -5.79999999999999995e85 < y < -5.6e32

   1. Initial program 99.9%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 58.4%

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

   if -5.6e32 < y < -16500

   1. Initial program 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-def 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around inf 58.3%

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

      1. clear-num 58.3%

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

      2. div-inv 58.7%

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

   9. Applied egg-rr 58.7%

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

   if -16500 < y < 3.60000000000000034e-33

   1. Initial program 90.7%

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

   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%

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

      2. fma-def 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in t around inf 58.2%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+85}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -5.6 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -16500:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-33}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+83}:\\ \;\;\;\;\left(0.3333333333333333 \cdot y\right) \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -170000000:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-33}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -5.5e+83)
   (* (* 0.3333333333333333 y) (/ -1.0 z))
   (if (<= y -1.75e+34)
     x
     (if (<= y -170000000.0)
       (/ -0.3333333333333333 (/ z y))
       (if (<= y 3.6e-33)
         (* 0.3333333333333333 (/ t (* z y)))
         (/ y (* z -3.0)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e+83) {
		tmp = (0.3333333333333333 * y) * (-1.0 / z);
	} else if (y <= -1.75e+34) {
		tmp = x;
	} else if (y <= -170000000.0) {
		tmp = -0.3333333333333333 / (z / y);
	} else if (y <= 3.6e-33) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-5.5d+83)) then
        tmp = (0.3333333333333333d0 * y) * ((-1.0d0) / z)
    else if (y <= (-1.75d+34)) then
        tmp = x
    else if (y <= (-170000000.0d0)) then
        tmp = (-0.3333333333333333d0) / (z / y)
    else if (y <= 3.6d-33) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else
        tmp = y / (z * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -5.5e+83) {
		tmp = (0.3333333333333333 * y) * (-1.0 / z);
	} else if (y <= -1.75e+34) {
		tmp = x;
	} else if (y <= -170000000.0) {
		tmp = -0.3333333333333333 / (z / y);
	} else if (y <= 3.6e-33) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -5.5e+83:
		tmp = (0.3333333333333333 * y) * (-1.0 / z)
	elif y <= -1.75e+34:
		tmp = x
	elif y <= -170000000.0:
		tmp = -0.3333333333333333 / (z / y)
	elif y <= 3.6e-33:
		tmp = 0.3333333333333333 * (t / (z * y))
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -5.5e+83)
		tmp = Float64(Float64(0.3333333333333333 * y) * Float64(-1.0 / z));
	elseif (y <= -1.75e+34)
		tmp = x;
	elseif (y <= -170000000.0)
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	elseif (y <= 3.6e-33)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	else
		tmp = Float64(y / Float64(z * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -5.5e+83)
		tmp = (0.3333333333333333 * y) * (-1.0 / z);
	elseif (y <= -1.75e+34)
		tmp = x;
	elseif (y <= -170000000.0)
		tmp = -0.3333333333333333 / (z / y);
	elseif (y <= 3.6e-33)
		tmp = 0.3333333333333333 * (t / (z * y));
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -5.5e+83], N[(N[(0.3333333333333333 * y), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.75e+34], x, If[LessEqual[y, -170000000.0], N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e-33], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.4999999999999996e83

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 75.5%

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

      1. associate-*r/ 75.4%

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

      2. *-commutative 75.4%

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

   9. Applied egg-rr 75.4%

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

       1. frac-2neg 75.4%

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

       2. div-inv 75.6%

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

       3. distribute-rgt-neg-in 75.6%

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

       4. metadata-eval 75.6%

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

       5. metadata-eval 75.6%

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

       6. distribute-neg-frac 75.6%

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

       7. metadata-eval 75.6%

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

       8. frac-2neg 75.6%

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

       9. distribute-neg-frac 75.6%

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

       10. metadata-eval 75.6%

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

   11. Applied egg-rr 75.6%

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

   if -5.4999999999999996e83 < y < -1.74999999999999999e34

   1. Initial program 99.9%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 58.4%

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

   if -1.74999999999999999e34 < y < -1.7e8

   1. Initial program 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-def 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around inf 58.3%

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

      1. clear-num 58.3%

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

      2. div-inv 58.7%

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

   9. Applied egg-rr 58.7%

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

   if -1.7e8 < y < 3.60000000000000034e-33

   1. Initial program 90.7%

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

   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%

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

      2. fma-def 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in t around inf 58.2%

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

   if 3.60000000000000034e-33 < y

   1. Initial program 99.8%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-def 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around inf 69.6%

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

      1. associate-*r/ 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-/l* 69.7%

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

      4. div-inv 69.7%

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

      5. metadata-eval 69.7%

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

   9. Applied egg-rr 69.7%

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

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+83}:\\ \;\;\;\;\left(0.3333333333333333 \cdot y\right) \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -170000000:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-33}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{+22}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -4e+38)
   (- x (/ y (* z 3.0)))
   (if (<= (* z 3.0) 2e+22)
     (* 0.3333333333333333 (/ (- (/ t y) y) z))
     (+ x (/ (* y -0.3333333333333333) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -4e+38) {
		tmp = x - (y / (z * 3.0));
	} else if ((z * 3.0) <= 2e+22) {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	} else {
		tmp = x + ((y * -0.3333333333333333) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-4d+38)) then
        tmp = x - (y / (z * 3.0d0))
    else if ((z * 3.0d0) <= 2d+22) then
        tmp = 0.3333333333333333d0 * (((t / y) - y) / z)
    else
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -4e+38) {
		tmp = x - (y / (z * 3.0));
	} else if ((z * 3.0) <= 2e+22) {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	} else {
		tmp = x + ((y * -0.3333333333333333) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -4e+38:
		tmp = x - (y / (z * 3.0))
	elif (z * 3.0) <= 2e+22:
		tmp = 0.3333333333333333 * (((t / y) - y) / z)
	else:
		tmp = x + ((y * -0.3333333333333333) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -4e+38)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (Float64(z * 3.0) <= 2e+22)
		tmp = Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z));
	else
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -4e+38)
		tmp = x - (y / (z * 3.0));
	elseif ((z * 3.0) <= 2e+22)
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	else
		tmp = x + ((y * -0.3333333333333333) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -4e+38], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e+22], N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z 3) < -3.99999999999999991e38

   1. Initial program 97.9%

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

      1. associate-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 97.9%

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

      3. associate-+l- 97.9%

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

      4. *-commutative 97.9%

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

      5. associate-/r* 93.9%

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

      6. sub-div 93.9%

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

   6. Applied egg-rr 93.9%

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

      1. *-un-lft-identity 93.9%

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

      2. times-frac 95.7%

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

   8. Applied egg-rr 95.7%

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

   9. Taylor expanded in y around inf 85.9%

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

       1. *-commutative 85.9%

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

       2. associate-/r/ 85.9%

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

       3. metadata-eval 85.9%

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

       4. associate-/l* 86.0%

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

       5. /-rgt-identity 86.0%

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

   11. Simplified 86.0%

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

   if -3.99999999999999991e38 < (*.f64 z 3) < 2e22

   1. Initial program 93.5%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-def 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around 0 86.2%

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

   if 2e22 < (*.f64 z 3)

   1. Initial program 99.7%

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

   3. Simplified 94.7%

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

   5. Taylor expanded in t around 0 77.1%

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

      1. *-commutative 77.1%

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

      2. associate-*l/ 77.2%

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

      3. associate-*r/ 77.1%

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

   7. Simplified 77.1%

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

      1. associate-*r/ 77.2%

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

   9. Applied egg-rr 77.2%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+38}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{+22}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+83}:\\ \;\;\;\;\left(0.3333333333333333 \cdot y\right) \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-33}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.15e+83)
   (* (* 0.3333333333333333 y) (/ -1.0 z))
   (if (<= y -8e+14)
     x
     (if (<= y 3.6e-33)
       (* (/ t z) (/ 0.3333333333333333 y))
       (/ y (* z -3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e+83) {
		tmp = (0.3333333333333333 * y) * (-1.0 / z);
	} else if (y <= -8e+14) {
		tmp = x;
	} else if (y <= 3.6e-33) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.15d+83)) then
        tmp = (0.3333333333333333d0 * y) * ((-1.0d0) / z)
    else if (y <= (-8d+14)) then
        tmp = x
    else if (y <= 3.6d-33) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = y / (z * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.15e+83) {
		tmp = (0.3333333333333333 * y) * (-1.0 / z);
	} else if (y <= -8e+14) {
		tmp = x;
	} else if (y <= 3.6e-33) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.15e+83:
		tmp = (0.3333333333333333 * y) * (-1.0 / z)
	elif y <= -8e+14:
		tmp = x
	elif y <= 3.6e-33:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.15e+83)
		tmp = Float64(Float64(0.3333333333333333 * y) * Float64(-1.0 / z));
	elseif (y <= -8e+14)
		tmp = x;
	elseif (y <= 3.6e-33)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = Float64(y / Float64(z * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.15e+83)
		tmp = (0.3333333333333333 * y) * (-1.0 / z);
	elseif (y <= -8e+14)
		tmp = x;
	elseif (y <= 3.6e-33)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.15e+83], N[(N[(0.3333333333333333 * y), $MachinePrecision] * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -8e+14], x, If[LessEqual[y, 3.6e-33], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.14999999999999997e83

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 75.5%

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

      1. associate-*r/ 75.4%

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

      2. *-commutative 75.4%

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

   9. Applied egg-rr 75.4%

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

       1. frac-2neg 75.4%

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

       2. div-inv 75.6%

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

       3. distribute-rgt-neg-in 75.6%

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

       4. metadata-eval 75.6%

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

       5. metadata-eval 75.6%

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

       6. distribute-neg-frac 75.6%

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

       7. metadata-eval 75.6%

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

       8. frac-2neg 75.6%

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

       9. distribute-neg-frac 75.6%

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

       10. metadata-eval 75.6%

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

   11. Applied egg-rr 75.6%

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

   if -1.14999999999999997e83 < y < -8e14

   1. Initial program 99.8%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 54.1%

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

   if -8e14 < y < 3.60000000000000034e-33

   1. Initial program 90.9%

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

   3. Simplified 95.9%

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

      1. +-commutative 95.9%

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

      2. fma-def 95.9%

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

   6. Applied egg-rr 95.9%

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

   7. Taylor expanded in t around inf 58.0%

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

      1. associate-*r/ 58.1%

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

      2. *-commutative 58.1%

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

      3. *-commutative 58.1%

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

      4. times-frac 62.3%

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

   9. Simplified 62.3%

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

   if 3.60000000000000034e-33 < y

   1. Initial program 99.8%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-def 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around inf 69.6%

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

      1. associate-*r/ 69.6%

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

      2. *-commutative 69.6%

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

      3. associate-/l* 69.7%

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

      4. div-inv 69.7%

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

      5. metadata-eval 69.7%

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

   9. Applied egg-rr 69.7%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{+83}:\\ \;\;\;\;\left(0.3333333333333333 \cdot y\right) \cdot \frac{-1}{z}\\ \mathbf{elif}\;y \leq -8 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-33}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 88.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+63} \lor \neg \left(y \leq 2.8 \cdot 10^{-33}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.6e+63) (not (<= y 2.8e-33)))
   (- x (/ y (* z 3.0)))
   (+ x (* (/ 0.3333333333333333 z) (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e+63) || !(y <= 2.8e-33)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((0.3333333333333333 / z) * (t / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.6d+63)) .or. (.not. (y <= 2.8d-33))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + ((0.3333333333333333d0 / z) * (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e+63) || !(y <= 2.8e-33)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((0.3333333333333333 / z) * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.6e+63) or not (y <= 2.8e-33):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + ((0.3333333333333333 / z) * (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.6e+63) || !(y <= 2.8e-33))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / z) * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.6e+63) || ~((y <= 2.8e-33)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + ((0.3333333333333333 / z) * (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.6e+63], N[Not[LessEqual[y, 2.8e-33]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.60000000000000006e63 or 2.8e-33 < y

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. associate-+l- 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

      6. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. *-un-lft-identity 99.8%

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

      2. times-frac 99.6%

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

   8. Applied egg-rr 99.6%

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

   9. Taylor expanded in y around inf 96.1%

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

       1. *-commutative 96.1%

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

       2. associate-/r/ 96.2%

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

       3. metadata-eval 96.2%

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

       4. associate-/l* 96.2%

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

       5. /-rgt-identity 96.2%

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

   11. Simplified 96.2%

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

   if -1.60000000000000006e63 < y < 2.8e-33

   1. Initial program 91.8%

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

   3. Simplified 96.2%

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

   5. Taylor expanded in t around inf 85.6%

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

      1. associate-/r* 89.6%

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

      2. associate-*r/ 89.6%

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

      3. associate-*l/ 89.5%

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

      4. *-commutative 89.5%

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

   7. Simplified 89.5%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+63} \lor \neg \left(y \leq 2.8 \cdot 10^{-33}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 92.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -106 \lor \neg \left(y \leq 3.6 \cdot 10^{-33}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{0.3333333333333333}{z} \cdot t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -106.0) (not (<= y 3.6e-33)))
   (- x (/ y (* z 3.0)))
   (+ x (/ (* (/ 0.3333333333333333 z) t) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -106.0) || !(y <= 3.6e-33)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (((0.3333333333333333 / z) * t) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-106.0d0)) .or. (.not. (y <= 3.6d-33))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + (((0.3333333333333333d0 / z) * t) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -106.0) || !(y <= 3.6e-33)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (((0.3333333333333333 / z) * t) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -106.0) or not (y <= 3.6e-33):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + (((0.3333333333333333 / z) * t) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -106.0) || !(y <= 3.6e-33))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(Float64(0.3333333333333333 / z) * t) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -106.0) || ~((y <= 3.6e-33)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + (((0.3333333333333333 / z) * t) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -106.0], N[Not[LessEqual[y, 3.6e-33]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(0.3333333333333333 / z), $MachinePrecision] * t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -106 or 3.60000000000000034e-33 < y

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. associate-+l- 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

      6. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. *-un-lft-identity 99.8%

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

      2. times-frac 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in y around inf 93.1%

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

       1. *-commutative 93.1%

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

       2. associate-/r/ 93.1%

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

       3. metadata-eval 93.1%

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

       4. associate-/l* 93.1%

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

       5. /-rgt-identity 93.1%

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

   11. Simplified 93.1%

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

   if -106 < y < 3.60000000000000034e-33

   1. Initial program 90.7%

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

   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 87.3%

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

      1. associate-/r* 91.8%

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

      2. associate-*r/ 91.8%

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

      3. associate-*l/ 91.8%

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

      4. *-commutative 91.8%

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

   7. Simplified 91.8%

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

      1. associate-*l/ 93.8%

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

   9. Applied egg-rr 93.8%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -106 \lor \neg \left(y \leq 3.6 \cdot 10^{-33}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{0.3333333333333333}{z} \cdot t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -28 \lor \neg \left(y \leq 1.4 \cdot 10^{-33}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -28.0) (not (<= y 1.4e-33)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -28.0) || !(y <= 1.4e-33)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / 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 <= (-28.0d0)) .or. (.not. (y <= 1.4d-33))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -28.0) || !(y <= 1.4e-33)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -28.0) or not (y <= 1.4e-33):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -28.0) || !(y <= 1.4e-33))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -28.0) || ~((y <= 1.4e-33)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -28.0], N[Not[LessEqual[y, 1.4e-33]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -28 or 1.4e-33 < y

   1. Initial program 99.8%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 93.1%

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

      1. *-commutative 93.1%

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

      2. associate-*l/ 93.0%

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

      3. associate-*r/ 93.0%

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

   7. Simplified 93.0%

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

   if -28 < y < 1.4e-33

   1. Initial program 90.7%

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

   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%

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

      2. fma-def 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in t around inf 58.6%

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

      1. associate-*r/ 58.7%

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

      2. *-commutative 58.7%

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

      3. *-commutative 58.7%

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

      4. times-frac 63.0%

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

   9. Simplified 63.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -28 \lor \neg \left(y \leq 1.4 \cdot 10^{-33}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \lor \neg \left(y \leq 6.2 \cdot 10^{-34}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.25) (not (<= y 6.2e-34)))
   (- x (* 0.3333333333333333 (/ y z)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.25) || !(y <= 6.2e-34)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / 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 <= (-1.25d0)) .or. (.not. (y <= 6.2d-34))) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.25) || !(y <= 6.2e-34)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.25) or not (y <= 6.2e-34):
		tmp = x - (0.3333333333333333 * (y / z))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.25) || !(y <= 6.2e-34))
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.25) || ~((y <= 6.2e-34)))
		tmp = x - (0.3333333333333333 * (y / z));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.25], N[Not[LessEqual[y, 6.2e-34]], $MachinePrecision]], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.25 or 6.1999999999999996e-34 < y

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 93.1%

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

   if -1.25 < y < 6.1999999999999996e-34

   1. Initial program 90.7%

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

   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%

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

      2. fma-def 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in t around inf 58.6%

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

      1. associate-*r/ 58.7%

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

      2. *-commutative 58.7%

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

      3. *-commutative 58.7%

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

      4. times-frac 63.0%

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

   9. Simplified 63.0%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \lor \neg \left(y \leq 6.2 \cdot 10^{-34}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \lor \neg \left(y \leq 1.05 \cdot 10^{-33}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.2) (not (<= y 1.05e-33)))
   (- x (/ y (* z 3.0)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2) || !(y <= 1.05e-33)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (t / z) * (0.3333333333333333 / 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 <= (-4.2d0)) .or. (.not. (y <= 1.05d-33))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.2) || !(y <= 1.05e-33)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.2) or not (y <= 1.05e-33):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.2) || !(y <= 1.05e-33))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.2) || ~((y <= 1.05e-33)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.2], N[Not[LessEqual[y, 1.05e-33]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.20000000000000018 or 1.05e-33 < y

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. associate-+l- 99.8%

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

      4. *-commutative 99.8%

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

      5. associate-/r* 99.8%

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

      6. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. *-un-lft-identity 99.8%

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

      2. times-frac 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in y around inf 93.1%

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

       1. *-commutative 93.1%

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

       2. associate-/r/ 93.1%

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

       3. metadata-eval 93.1%

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

       4. associate-/l* 93.1%

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

       5. /-rgt-identity 93.1%

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

   11. Simplified 93.1%

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

   if -4.20000000000000018 < y < 1.05e-33

   1. Initial program 90.7%

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

   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%

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

      2. fma-def 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in t around inf 58.6%

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

      1. associate-*r/ 58.7%

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

      2. *-commutative 58.7%

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

      3. *-commutative 58.7%

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

      4. times-frac 63.0%

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

   9. Simplified 63.0%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \lor \neg \left(y \leq 1.05 \cdot 10^{-33}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.3:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.3)
   (+ x (/ (* y -0.3333333333333333) z))
   (if (<= y 5.8e-34)
     (* (/ t z) (/ 0.3333333333333333 y))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 5.8e-34) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.3d0)) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else if (y <= 5.8d-34) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.3) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (y <= 5.8e-34) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.3:
		tmp = x + ((y * -0.3333333333333333) / z)
	elif y <= 5.8e-34:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.3)
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	elseif (y <= 5.8e-34)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.3)
		tmp = x + ((y * -0.3333333333333333) / z);
	elseif (y <= 5.8e-34)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.3], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e-34], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.2999999999999998

   1. Initial program 99.8%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 91.0%

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

      1. *-commutative 91.0%

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

      2. associate-*l/ 91.0%

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

      3. associate-*r/ 91.0%

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

   7. Simplified 91.0%

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

      1. associate-*r/ 91.0%

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

   9. Applied egg-rr 91.0%

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

   if -2.2999999999999998 < y < 5.8000000000000004e-34

   1. Initial program 90.7%

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

   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%

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

      2. fma-def 95.8%

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

   6. Applied egg-rr 95.8%

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

   7. Taylor expanded in t around inf 58.6%

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

      1. associate-*r/ 58.7%

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

      2. *-commutative 58.7%

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

      3. *-commutative 58.7%

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

      4. times-frac 63.0%

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

   9. Simplified 63.0%

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

   if 5.8000000000000004e-34 < y

   1. Initial program 99.8%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around 0 94.9%

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

      1. *-commutative 94.9%

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

      2. associate-*l/ 94.9%

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

      3. associate-*r/ 94.9%

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

   7. Simplified 94.9%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.3:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-34}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+83} \lor \neg \left(y \leq 2.25 \cdot 10^{-20}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.4e+83) (not (<= y 2.25e-20)))
   (* -0.3333333333333333 (/ y z))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e+83) || !(y <= 2.25e-20)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.4d+83)) .or. (.not. (y <= 2.25d-20))) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e+83) || !(y <= 2.25e-20)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.4e+83) or not (y <= 2.25e-20):
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.4e+83) || !(y <= 2.25e-20))
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.4e+83) || ~((y <= 2.25e-20)))
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.4e+83], N[Not[LessEqual[y, 2.25e-20]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.4e83 or 2.2500000000000001e-20 < y

   1. Initial program 99.8%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-def 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 72.8%

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

   if -1.4e83 < y < 2.2500000000000001e-20

   1. Initial program 92.3%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in x around inf 36.5%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+83} \lor \neg \left(y \leq 2.25 \cdot 10^{-20}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+84} \lor \neg \left(y \leq 2.7 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.85e+84) (not (<= y 2.7e-20))) (/ y (* z -3.0)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.85e+84) || !(y <= 2.7e-20)) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.85d+84)) .or. (.not. (y <= 2.7d-20))) then
        tmp = y / (z * (-3.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.85e+84) || !(y <= 2.7e-20)) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.85e+84) or not (y <= 2.7e-20):
		tmp = y / (z * -3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.85e+84) || !(y <= 2.7e-20))
		tmp = Float64(y / Float64(z * -3.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.85e+84) || ~((y <= 2.7e-20)))
		tmp = y / (z * -3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.85e+84], N[Not[LessEqual[y, 2.7e-20]], $MachinePrecision]], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1.85e84 or 2.7e-20 < y

   1. Initial program 99.8%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. fma-def 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 72.8%

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

      1. associate-*r/ 72.7%

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

      2. *-commutative 72.7%

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

      3. associate-/l* 72.8%

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

      4. div-inv 72.8%

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

      5. metadata-eval 72.8%

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

   9. Applied egg-rr 72.8%

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

   if -1.85e84 < y < 2.7e-20

   1. Initial program 92.3%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in x around inf 36.5%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.85 \cdot 10^{+84} \lor \neg \left(y \leq 2.7 \cdot 10^{-20}\right):\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+86}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.1e+86)
   (* -0.3333333333333333 (/ y z))
   (if (<= y 1.75e-20) x (/ -0.3333333333333333 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.1e+86) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 1.75e-20) {
		tmp = x;
	} else {
		tmp = -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 <= (-2.1d+86)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (y <= 1.75d-20) then
        tmp = x
    else
        tmp = (-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 <= -2.1e+86) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 1.75e-20) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.1e+86:
		tmp = -0.3333333333333333 * (y / z)
	elif y <= 1.75e-20:
		tmp = x
	else:
		tmp = -0.3333333333333333 / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.1e+86)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (y <= 1.75e-20)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.1e+86)
		tmp = -0.3333333333333333 * (y / z);
	elseif (y <= 1.75e-20)
		tmp = x;
	else
		tmp = -0.3333333333333333 / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.1e+86], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.75e-20], x, N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0999999999999999e86

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-def 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 75.5%

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

   if -2.0999999999999999e86 < y < 1.75000000000000002e-20

   1. Initial program 92.3%

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

   3. Simplified 96.5%

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

   5. Taylor expanded in x around inf 36.5%

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

   if 1.75000000000000002e-20 < y

   1. Initial program 99.8%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. fma-def 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around inf 71.1%

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

      1. clear-num 71.0%

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

      2. div-inv 71.2%

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

   9. Applied egg-rr 71.2%

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

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+86}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{-20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 95.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \frac{y - \frac{t}{y}}{3} \cdot \frac{-1}{z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (* (/ (- y (/ t y)) 3.0) (/ -1.0 z))))

C

double code(double x, double y, double z, double t) {
	return x + (((y - (t / y)) / 3.0) * (-1.0 / z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (((y - (t / y)) / 3.0d0) * ((-1.0d0) / z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + (((y - (t / y)) / 3.0) * (-1.0 / z));
}

Python

def code(x, y, z, t):
	return x + (((y - (t / y)) / 3.0) * (-1.0 / z))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(Float64(y - Float64(t / y)) / 3.0) * Float64(-1.0 / z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + (((y - (t / y)) / 3.0) * (-1.0 / z));
end

Wolfram

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

Derivation

1. Initial program 95.6%

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

   1. associate-*l* 96.0%

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

   2. *-commutative 96.0%

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

3. Simplified 96.0%

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

   1. *-commutative 96.0%

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

   2. associate-*l* 95.6%

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

   3. associate-+l- 95.6%

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

   4. *-commutative 95.6%

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

   5. associate-/r* 97.6%

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

   6. sub-div 97.6%

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

6. Applied egg-rr 97.6%

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

   1. *-un-lft-identity 97.6%

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

   2. times-frac 97.9%

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

8. Applied egg-rr 97.9%

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

9. Final simplification 97.9%

   \[\leadsto x + \frac{y - \frac{t}{y}}{3} \cdot \frac{-1}{z} \]
10. Add Preprocessing

Alternative 16: 95.6% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.6%

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

3. Simplified 97.9%

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

5. Final simplification 97.9%

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

Alternative 17: 30.3% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.6%

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

3. Simplified 97.9%

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

5. Taylor expanded in x around inf 31.0%

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

6. Final simplification 31.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024019 
(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))))