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

Percentage Accurate: 95.7% → 96.8%

Time: 11.5s

Alternatives: 20

Speedup: 1.4×

• 29.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot 3}\\ \mathbf{if}\;y \leq 4 \cdot 10^{-141}:\\ \;\;\;\;x + \left(\frac{t}{z} \cdot \frac{\frac{1}{y}}{3} - t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - t_1\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* z 3.0))))
   (if (<= y 4e-141)
     (+ x (- (* (/ t z) (/ (/ 1.0 y) 3.0)) t_1))
     (+ (- x t_1) (/ t (* y (* z 3.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (z * 3.0);
	double tmp;
	if (y <= 4e-141) {
		tmp = x + (((t / z) * ((1.0 / y) / 3.0)) - t_1);
	} else {
		tmp = (x - t_1) + (t / (y * (z * 3.0)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (z * 3.0d0)
    if (y <= 4d-141) then
        tmp = x + (((t / z) * ((1.0d0 / y) / 3.0d0)) - t_1)
    else
        tmp = (x - t_1) + (t / (y * (z * 3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (z * 3.0);
	double tmp;
	if (y <= 4e-141) {
		tmp = x + (((t / z) * ((1.0 / y) / 3.0)) - t_1);
	} else {
		tmp = (x - t_1) + (t / (y * (z * 3.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (z * 3.0)
	tmp = 0
	if y <= 4e-141:
		tmp = x + (((t / z) * ((1.0 / y) / 3.0)) - t_1)
	else:
		tmp = (x - t_1) + (t / (y * (z * 3.0)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(z * 3.0))
	tmp = 0.0
	if (y <= 4e-141)
		tmp = Float64(x + Float64(Float64(Float64(t / z) * Float64(Float64(1.0 / y) / 3.0)) - t_1));
	else
		tmp = Float64(Float64(x - t_1) + Float64(t / Float64(y * Float64(z * 3.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (z * 3.0);
	tmp = 0.0;
	if (y <= 4e-141)
		tmp = x + (((t / z) * ((1.0 / y) / 3.0)) - t_1);
	else
		tmp = (x - t_1) + (t / (y * (z * 3.0)));
	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, 4e-141], N[(x + N[(N[(N[(t / z), $MachinePrecision] * N[(N[(1.0 / y), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x - t$95$1), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < 4.0000000000000002e-141

   1. Initial program 95.0%

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

      1. associate-+l- 95.0%

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

      2. *-commutative 95.0%

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

   3. Simplified 95.0%

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

      1. associate-/r* 94.5%

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

      2. div-inv 94.5%

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

      3. times-frac 97.5%

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

   5. Applied egg-rr 97.5%

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

   if 4.0000000000000002e-141 < y

   1. Initial program 99.8%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{-141}:\\ \;\;\;\;x + \left(\frac{t}{z} \cdot \frac{\frac{1}{y}}{3} - \frac{y}{z \cdot 3}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \end{array} \]

Alternative 2: 59.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{if}\;y \leq -8.9 \cdot 10^{+179}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.3333333333333333 (/ t (* y z)))))
   (if (<= y -8.9e+179)
     (/ (* y -0.3333333333333333) z)
     (if (<= y -1.16e-76)
       x
       (if (<= y 7.5e-17)
         t_1
         (if (<= y 9.5e+17) x (if (<= y 5.2e+42) t_1 (/ y (* z -3.0)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (y * z));
	double tmp;
	if (y <= -8.9e+179) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -1.16e-76) {
		tmp = x;
	} else if (y <= 7.5e-17) {
		tmp = t_1;
	} else if (y <= 9.5e+17) {
		tmp = x;
	} else if (y <= 5.2e+42) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = 0.3333333333333333d0 * (t / (y * z))
    if (y <= (-8.9d+179)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= (-1.16d-76)) then
        tmp = x
    else if (y <= 7.5d-17) then
        tmp = t_1
    else if (y <= 9.5d+17) then
        tmp = x
    else if (y <= 5.2d+42) then
        tmp = t_1
    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 t_1 = 0.3333333333333333 * (t / (y * z));
	double tmp;
	if (y <= -8.9e+179) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= -1.16e-76) {
		tmp = x;
	} else if (y <= 7.5e-17) {
		tmp = t_1;
	} else if (y <= 9.5e+17) {
		tmp = x;
	} else if (y <= 5.2e+42) {
		tmp = t_1;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 * (t / (y * z))
	tmp = 0
	if y <= -8.9e+179:
		tmp = (y * -0.3333333333333333) / z
	elif y <= -1.16e-76:
		tmp = x
	elif y <= 7.5e-17:
		tmp = t_1
	elif y <= 9.5e+17:
		tmp = x
	elif y <= 5.2e+42:
		tmp = t_1
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 * Float64(t / Float64(y * z)))
	tmp = 0.0
	if (y <= -8.9e+179)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= -1.16e-76)
		tmp = x;
	elseif (y <= 7.5e-17)
		tmp = t_1;
	elseif (y <= 9.5e+17)
		tmp = x;
	elseif (y <= 5.2e+42)
		tmp = t_1;
	else
		tmp = Float64(y / Float64(z * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 * (t / (y * z));
	tmp = 0.0;
	if (y <= -8.9e+179)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= -1.16e-76)
		tmp = x;
	elseif (y <= 7.5e-17)
		tmp = t_1;
	elseif (y <= 9.5e+17)
		tmp = x;
	elseif (y <= 5.2e+42)
		tmp = t_1;
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.9e+179], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, -1.16e-76], x, If[LessEqual[y, 7.5e-17], t$95$1, If[LessEqual[y, 9.5e+17], x, If[LessEqual[y, 5.2e+42], t$95$1, N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.90000000000000036e179

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

      1. fma-udef 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 95.4%

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

      1. associate-*r/ 95.5%

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

   8. Applied egg-rr 95.5%

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

   if -8.90000000000000036e179 < y < -1.1599999999999999e-76 or 7.49999999999999984e-17 < y < 9.5e17

   1. Initial program 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in x around inf 61.0%

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

   if -1.1599999999999999e-76 < y < 7.49999999999999984e-17 or 9.5e17 < y < 5.1999999999999998e42

   1. Initial program 94.3%

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

   3. Simplified 94.3%

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

      1. fma-udef 94.3%

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

   5. Applied egg-rr 94.3%

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

   6. Taylor expanded in y around 0 66.4%

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

   if 5.1999999999999998e42 < y

   1. Initial program 99.7%

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

   3. Simplified 99.6%

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

      1. fma-udef 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 71.7%

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

      1. associate-*r/ 71.7%

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

      2. associate-*l/ 71.7%

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

      3. *-commutative 71.7%

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

      4. clear-num 71.6%

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

      5. un-div-inv 71.7%

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

      6. div-inv 71.8%

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

      7. metadata-eval 71.8%

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

   8. Applied egg-rr 71.8%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.9 \cdot 10^{+179}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq -1.16 \cdot 10^{-76}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{-17}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+42}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]

Alternative 3: 95.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(-0.3333333333333333 \cdot \frac{y}{z} + \frac{t}{z \cdot \left(y \cdot 3\right)}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (+ (* -0.3333333333333333 (/ y z)) (/ t (* z (* y 3.0))))))

C

double code(double x, double y, double z, double t) {
	return x + ((-0.3333333333333333 * (y / z)) + (t / (z * (y * 3.0))));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (((-0.3333333333333333d0) * (y / z)) + (t / (z * (y * 3.0d0))))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((-0.3333333333333333 * (y / z)) + (t / (z * (y * 3.0))));
}

Python

def code(x, y, z, t):
	return x + ((-0.3333333333333333 * (y / z)) + (t / (z * (y * 3.0))))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(-0.3333333333333333 * Float64(y / z)) + Float64(t / Float64(z * Float64(y * 3.0)))))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((-0.3333333333333333 * (y / z)) + (t / (z * (y * 3.0))));
end

Wolfram

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

Derivation

1. Initial program 96.8%

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

3. Simplified 96.8%

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

   1. fma-udef 96.8%

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

5. Applied egg-rr 96.8%

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

6. Final simplification 96.8%

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

Alternative 4: 89.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot \left(--3\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{-3 \cdot \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.8e+72)
   (- x (* (/ y z) 0.3333333333333333))
   (if (<= y 1.8e+42)
     (+ x (/ t (* y (* z (- -3.0)))))
     (+ x (/ 1.0 (* -3.0 (/ z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e+72) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 1.8e+42) {
		tmp = x + (t / (y * (z * -(-3.0))));
	} else {
		tmp = x + (1.0 / (-3.0 * (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 <= (-6.8d+72)) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (y <= 1.8d+42) then
        tmp = x + (t / (y * (z * -(-3.0d0))))
    else
        tmp = x + (1.0d0 / ((-3.0d0) * (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 <= -6.8e+72) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 1.8e+42) {
		tmp = x + (t / (y * (z * -(-3.0))));
	} else {
		tmp = x + (1.0 / (-3.0 * (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.8e+72:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif y <= 1.8e+42:
		tmp = x + (t / (y * (z * -(-3.0))))
	else:
		tmp = x + (1.0 / (-3.0 * (z / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.8e+72)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (y <= 1.8e+42)
		tmp = Float64(x + Float64(t / Float64(y * Float64(z * Float64(-(-3.0))))));
	else
		tmp = Float64(x + Float64(1.0 / Float64(-3.0 * Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.8e+72)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (y <= 1.8e+42)
		tmp = x + (t / (y * (z * -(-3.0))));
	else
		tmp = x + (1.0 / (-3.0 * (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.8e+72], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.8e+42], N[(x + N[(t / N[(y * N[(z * (--3.0)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(-3.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.7999999999999997e72

   1. Initial program 97.4%

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

      1. associate-+l- 97.4%

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

      2. *-commutative 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around 0 97.4%

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

   if -6.7999999999999997e72 < y < 1.8e42

   1. Initial program 95.6%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 86.4%

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

      1. neg-mul-1 86.4%

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

      2. distribute-neg-frac 86.4%

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

   6. Simplified 86.4%

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

      1. clear-num 86.4%

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

      2. frac-2neg 86.4%

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

      3. frac-times 88.5%

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

      4. *-un-lft-identity 88.5%

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

      5. add-sqr-sqrt 43.6%

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

      6. sqrt-unprod 51.1%

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

      7. sqr-neg 51.1%

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

      8. sqrt-unprod 17.5%

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

      9. add-sqr-sqrt 32.3%

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

      10. add-sqr-sqrt 14.8%

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

      11. sqrt-unprod 49.8%

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

      12. sqr-neg 49.8%

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

      13. sqrt-unprod 44.6%

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

      14. add-sqr-sqrt 88.5%

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

      15. div-inv 88.5%

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

      16. metadata-eval 88.5%

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

   8. Applied egg-rr 88.5%

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

   if 1.8e42 < y

   1. Initial program 99.7%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 96.1%

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

      1. div-inv 96.1%

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

   6. Applied egg-rr 96.1%

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

      1. un-div-inv 96.1%

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

      2. associate-/r/ 96.2%

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

      3. clear-num 96.1%

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

      4. div-inv 96.2%

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

      5. metadata-eval 96.2%

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

   8. Applied egg-rr 96.2%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{y} \cdot -3}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot \left(--3\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{-3 \cdot \frac{z}{y}}\\ \end{array} \]

Alternative 5: 89.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+72} \lor \neg \left(y \leq 1.1 \cdot 10^{+42}\right):\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.8e+72) (not (<= y 1.1e+42)))
   (- x (* (/ y z) 0.3333333333333333))
   (+ x (* 0.3333333333333333 (/ t (* y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.8e+72) || !(y <= 1.1e+42)) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.8d+72)) .or. (.not. (y <= 1.1d+42))) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else
        tmp = x + (0.3333333333333333d0 * (t / (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.8e+72) || !(y <= 1.1e+42)) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.8e+72) or not (y <= 1.1e+42):
		tmp = x - ((y / z) * 0.3333333333333333)
	else:
		tmp = x + (0.3333333333333333 * (t / (y * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.8e+72) || !(y <= 1.1e+42))
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.8e+72) || ~((y <= 1.1e+42)))
		tmp = x - ((y / z) * 0.3333333333333333);
	else
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.8e+72], N[Not[LessEqual[y, 1.1e+42]], $MachinePrecision]], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.7999999999999997e72 or 1.1000000000000001e42 < y

   1. Initial program 98.7%

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

      1. associate-+l- 98.7%

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

      2. *-commutative 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in t around 0 96.7%

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

   if -6.7999999999999997e72 < y < 1.1000000000000001e42

   1. Initial program 95.6%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 88.4%

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

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+72} \lor \neg \left(y \leq 1.1 \cdot 10^{+42}\right):\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 6: 79.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+95}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+64}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.45e+95)
   (- x (* (/ y z) 0.3333333333333333))
   (if (<= x 3.5e+64)
     (* -0.3333333333333333 (/ (- y (/ t y)) z))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.45e+95) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (x <= 3.5e+64) {
		tmp = -0.3333333333333333 * ((y - (t / 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 (x <= (-1.45d+95)) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (x <= 3.5d+64) then
        tmp = (-0.3333333333333333d0) * ((y - (t / 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 (x <= -1.45e+95) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (x <= 3.5e+64) {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.45e+95:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif x <= 3.5e+64:
		tmp = -0.3333333333333333 * ((y - (t / y)) / z)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.45e+95)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (x <= 3.5e+64)
		tmp = Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z));
	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 (x <= -1.45e+95)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (x <= 3.5e+64)
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.45e+95], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.5e+64], N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.45000000000000007e95

   1. Initial program 98.2%

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

      1. associate-+l- 98.2%

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

      2. *-commutative 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in t around 0 77.4%

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

   if -1.45000000000000007e95 < x < 3.4999999999999999e64

   1. Initial program 96.2%

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

   3. Simplified 96.1%

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

      1. fma-udef 96.1%

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

   5. Applied egg-rr 96.1%

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

   6. Taylor expanded in z around 0 83.3%

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

      1. associate-*r/ 83.3%

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

      2. remove-double-neg 83.3%

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

      3. neg-mul-1 83.3%

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

      4. times-frac 83.3%

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

      5. metadata-eval 83.3%

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

      6. distribute-lft-in 83.3%

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

      7. *-lft-identity 83.3%

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

      8. neg-mul-1 83.3%

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

      9. times-frac 83.3%

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

      10. metadata-eval 83.3%

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

      11. neg-mul-1 83.3%

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

      12. sub-neg 83.3%

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

      13. associate-*r/ 83.4%

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

   8. Simplified 83.4%

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

   if 3.4999999999999999e64 < x

   1. Initial program 97.5%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in y around inf 85.2%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.45 \cdot 10^{+95}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{+64}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]

Alternative 7: 89.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+43}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{-3 \cdot \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.8e+72)
   (- x (* (/ y z) 0.3333333333333333))
   (if (<= y 1.05e+43)
     (+ x (* 0.3333333333333333 (/ t (* y z))))
     (+ x (/ 1.0 (* -3.0 (/ z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e+72) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 1.05e+43) {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	} else {
		tmp = x + (1.0 / (-3.0 * (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 <= (-6.8d+72)) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (y <= 1.05d+43) then
        tmp = x + (0.3333333333333333d0 * (t / (y * z)))
    else
        tmp = x + (1.0d0 / ((-3.0d0) * (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 <= -6.8e+72) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 1.05e+43) {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	} else {
		tmp = x + (1.0 / (-3.0 * (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.8e+72:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif y <= 1.05e+43:
		tmp = x + (0.3333333333333333 * (t / (y * z)))
	else:
		tmp = x + (1.0 / (-3.0 * (z / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.8e+72)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (y <= 1.05e+43)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(y * z))));
	else
		tmp = Float64(x + Float64(1.0 / Float64(-3.0 * Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.8e+72)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (y <= 1.05e+43)
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	else
		tmp = x + (1.0 / (-3.0 * (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.8e+72], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e+43], N[(x + N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(-3.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.7999999999999997e72

   1. Initial program 97.4%

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

      1. associate-+l- 97.4%

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

      2. *-commutative 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around 0 97.4%

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

   if -6.7999999999999997e72 < y < 1.05000000000000001e43

   1. Initial program 95.6%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 88.4%

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

   if 1.05000000000000001e43 < y

   1. Initial program 99.7%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 96.1%

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

      1. div-inv 96.1%

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

   6. Applied egg-rr 96.1%

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

      1. un-div-inv 96.1%

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

      2. associate-/r/ 96.2%

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

      3. clear-num 96.1%

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

      4. div-inv 96.2%

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

      5. metadata-eval 96.2%

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

   8. Applied egg-rr 96.2%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{y} \cdot -3}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+43}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{-3 \cdot \frac{z}{y}}\\ \end{array} \]

Alternative 8: 89.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{t}{3 \cdot \left(y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{-3 \cdot \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.8e+72)
   (- x (* (/ y z) 0.3333333333333333))
   (if (<= y 1.08e+43)
     (+ x (/ t (* 3.0 (* y z))))
     (+ x (/ 1.0 (* -3.0 (/ z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e+72) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 1.08e+43) {
		tmp = x + (t / (3.0 * (y * z)));
	} else {
		tmp = x + (1.0 / (-3.0 * (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 <= (-6.8d+72)) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (y <= 1.08d+43) then
        tmp = x + (t / (3.0d0 * (y * z)))
    else
        tmp = x + (1.0d0 / ((-3.0d0) * (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 <= -6.8e+72) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 1.08e+43) {
		tmp = x + (t / (3.0 * (y * z)));
	} else {
		tmp = x + (1.0 / (-3.0 * (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.8e+72:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif y <= 1.08e+43:
		tmp = x + (t / (3.0 * (y * z)))
	else:
		tmp = x + (1.0 / (-3.0 * (z / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.8e+72)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (y <= 1.08e+43)
		tmp = Float64(x + Float64(t / Float64(3.0 * Float64(y * z))));
	else
		tmp = Float64(x + Float64(1.0 / Float64(-3.0 * Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.8e+72)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (y <= 1.08e+43)
		tmp = x + (t / (3.0 * (y * z)));
	else
		tmp = x + (1.0 / (-3.0 * (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.8e+72], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.08e+43], N[(x + N[(t / N[(3.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(-3.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.7999999999999997e72

   1. Initial program 97.4%

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

      1. associate-+l- 97.4%

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

      2. *-commutative 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around 0 97.4%

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

   if -6.7999999999999997e72 < y < 1.08e43

   1. Initial program 95.6%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 86.4%

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

      1. neg-mul-1 86.4%

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

      2. distribute-neg-frac 86.4%

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

   6. Simplified 86.4%

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

      1. clear-num 86.4%

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

      2. frac-2neg 86.4%

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

      3. frac-times 88.5%

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

      4. *-un-lft-identity 88.5%

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

      5. add-sqr-sqrt 43.6%

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

      6. sqrt-unprod 51.1%

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

      7. sqr-neg 51.1%

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

      8. sqrt-unprod 17.5%

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

      9. add-sqr-sqrt 32.3%

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

      10. add-sqr-sqrt 14.8%

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

      11. sqrt-unprod 49.8%

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

      12. sqr-neg 49.8%

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

      13. sqrt-unprod 44.6%

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

      14. add-sqr-sqrt 88.5%

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

      15. div-inv 88.5%

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

      16. metadata-eval 88.5%

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

   8. Applied egg-rr 88.5%

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

   9. Taylor expanded in z around 0 88.5%

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

   if 1.08e43 < y

   1. Initial program 99.7%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 96.1%

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

      1. div-inv 96.1%

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

   6. Applied egg-rr 96.1%

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

      1. un-div-inv 96.1%

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

      2. associate-/r/ 96.2%

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

      3. clear-num 96.1%

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

      4. div-inv 96.2%

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

      5. metadata-eval 96.2%

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

   8. Applied egg-rr 96.2%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{y} \cdot -3}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+72}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+43}:\\ \;\;\;\;x + \frac{t}{3 \cdot \left(y \cdot z\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{-3 \cdot \frac{z}{y}}\\ \end{array} \]

Alternative 9: 89.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{-3 \cdot \frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.4e+73)
   (- x (* (/ y z) 0.3333333333333333))
   (if (<= y 3.4e+42)
     (+ x (/ t (* z (* y 3.0))))
     (+ x (/ 1.0 (* -3.0 (/ z y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.4e+73) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 3.4e+42) {
		tmp = x + (t / (z * (y * 3.0)));
	} else {
		tmp = x + (1.0 / (-3.0 * (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 <= (-2.4d+73)) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else if (y <= 3.4d+42) then
        tmp = x + (t / (z * (y * 3.0d0)))
    else
        tmp = x + (1.0d0 / ((-3.0d0) * (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 <= -2.4e+73) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else if (y <= 3.4e+42) {
		tmp = x + (t / (z * (y * 3.0)));
	} else {
		tmp = x + (1.0 / (-3.0 * (z / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.4e+73:
		tmp = x - ((y / z) * 0.3333333333333333)
	elif y <= 3.4e+42:
		tmp = x + (t / (z * (y * 3.0)))
	else:
		tmp = x + (1.0 / (-3.0 * (z / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.4e+73)
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	elseif (y <= 3.4e+42)
		tmp = Float64(x + Float64(t / Float64(z * Float64(y * 3.0))));
	else
		tmp = Float64(x + Float64(1.0 / Float64(-3.0 * Float64(z / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.4e+73)
		tmp = x - ((y / z) * 0.3333333333333333);
	elseif (y <= 3.4e+42)
		tmp = x + (t / (z * (y * 3.0)));
	else
		tmp = x + (1.0 / (-3.0 * (z / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.4e+73], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.4e+42], N[(x + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / N[(-3.0 * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.40000000000000002e73

   1. Initial program 97.4%

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

      1. associate-+l- 97.4%

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

      2. *-commutative 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in t around 0 97.4%

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

   if -2.40000000000000002e73 < y < 3.39999999999999975e42

   1. Initial program 95.6%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 86.4%

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

      1. neg-mul-1 86.4%

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

      2. distribute-neg-frac 86.4%

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

   6. Simplified 86.4%

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

      1. clear-num 86.4%

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

      2. frac-2neg 86.4%

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

      3. frac-times 88.5%

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

      4. *-un-lft-identity 88.5%

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

      5. add-sqr-sqrt 43.6%

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

      6. sqrt-unprod 51.1%

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

      7. sqr-neg 51.1%

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

      8. sqrt-unprod 17.5%

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

      9. add-sqr-sqrt 32.3%

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

      10. add-sqr-sqrt 14.8%

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

      11. sqrt-unprod 49.8%

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

      12. sqr-neg 49.8%

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

      13. sqrt-unprod 44.6%

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

      14. add-sqr-sqrt 88.5%

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

      15. div-inv 88.5%

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

      16. metadata-eval 88.5%

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

   8. Applied egg-rr 88.5%

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

   9. Taylor expanded in z around 0 88.5%

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

       1. *-commutative 88.5%

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

       2. *-commutative 88.5%

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

       3. associate-*r* 88.5%

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

   11. Simplified 88.5%

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

   if 3.39999999999999975e42 < y

   1. Initial program 99.7%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 96.1%

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

      1. div-inv 96.1%

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

   6. Applied egg-rr 96.1%

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

      1. un-div-inv 96.1%

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

      2. associate-/r/ 96.2%

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

      3. clear-num 96.1%

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

      4. div-inv 96.2%

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

      5. metadata-eval 96.2%

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

   8. Applied egg-rr 96.2%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{y} \cdot -3}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{-3 \cdot \frac{z}{y}}\\ \end{array} \]

Alternative 10: 77.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-76} \lor \neg \left(y \leq 8.4 \cdot 10^{-81}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -7e-76) (not (<= y 8.4e-81)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* 0.3333333333333333 (/ t (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e-76) || !(y <= 8.4e-81)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (t / (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-7d-76)) .or. (.not. (y <= 8.4d-81))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = 0.3333333333333333d0 * (t / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -7e-76) || !(y <= 8.4e-81)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (t / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -7e-76) or not (y <= 8.4e-81):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * (t / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -7e-76) || !(y <= 8.4e-81))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -7e-76) || ~((y <= 8.4e-81)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * (t / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -7e-76], N[Not[LessEqual[y, 8.4e-81]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.99999999999999995e-76 or 8.3999999999999997e-81 < y

   1. Initial program 99.1%

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

   3. Simplified 99.0%

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

   4. Taylor expanded in y around inf 86.4%

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

   if -6.99999999999999995e-76 < y < 8.3999999999999997e-81

   1. Initial program 93.3%

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

   3. Simplified 93.3%

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

      1. fma-udef 93.3%

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

   5. Applied egg-rr 93.3%

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

   6. Taylor expanded in y around 0 69.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-76} \lor \neg \left(y \leq 8.4 \cdot 10^{-81}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 11: 77.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-77} \lor \neg \left(y \leq 6.3 \cdot 10^{-80}\right):\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.22e-77) (not (<= y 6.3e-80)))
   (- x (* (/ y z) 0.3333333333333333))
   (* 0.3333333333333333 (/ t (* y z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.22e-77) || !(y <= 6.3e-80)) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else {
		tmp = 0.3333333333333333 * (t / (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.22d-77)) .or. (.not. (y <= 6.3d-80))) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else
        tmp = 0.3333333333333333d0 * (t / (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.22e-77) || !(y <= 6.3e-80)) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else {
		tmp = 0.3333333333333333 * (t / (y * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.22e-77) or not (y <= 6.3e-80):
		tmp = x - ((y / z) * 0.3333333333333333)
	else:
		tmp = 0.3333333333333333 * (t / (y * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.22e-77) || !(y <= 6.3e-80))
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	else
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.22e-77) || ~((y <= 6.3e-80)))
		tmp = x - ((y / z) * 0.3333333333333333);
	else
		tmp = 0.3333333333333333 * (t / (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.22e-77], N[Not[LessEqual[y, 6.3e-80]], $MachinePrecision]], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.22000000000000001e-77 or 6.29999999999999966e-80 < y

   1. Initial program 99.1%

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

      1. associate-+l- 99.1%

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

      2. *-commutative 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in t around 0 86.5%

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

   if -1.22000000000000001e-77 < y < 6.29999999999999966e-80

   1. Initial program 93.3%

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

   3. Simplified 93.3%

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

      1. fma-udef 93.3%

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

   5. Applied egg-rr 93.3%

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

   6. Taylor expanded in y around 0 69.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.22 \cdot 10^{-77} \lor \neg \left(y \leq 6.3 \cdot 10^{-80}\right):\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]

Alternative 12: 77.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-77} \lor \neg \left(y \leq 9.8 \cdot 10^{-80}\right):\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot 0.3333333333333333}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.5e-77) (not (<= y 9.8e-80)))
   (- x (* (/ y z) 0.3333333333333333))
   (/ (* t 0.3333333333333333) (* y z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e-77) || !(y <= 9.8e-80)) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else {
		tmp = (t * 0.3333333333333333) / (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.5d-77)) .or. (.not. (y <= 9.8d-80))) then
        tmp = x - ((y / z) * 0.3333333333333333d0)
    else
        tmp = (t * 0.3333333333333333d0) / (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e-77) || !(y <= 9.8e-80)) {
		tmp = x - ((y / z) * 0.3333333333333333);
	} else {
		tmp = (t * 0.3333333333333333) / (y * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.5e-77) or not (y <= 9.8e-80):
		tmp = x - ((y / z) * 0.3333333333333333)
	else:
		tmp = (t * 0.3333333333333333) / (y * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.5e-77) || !(y <= 9.8e-80))
		tmp = Float64(x - Float64(Float64(y / z) * 0.3333333333333333));
	else
		tmp = Float64(Float64(t * 0.3333333333333333) / Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.5e-77) || ~((y <= 9.8e-80)))
		tmp = x - ((y / z) * 0.3333333333333333);
	else
		tmp = (t * 0.3333333333333333) / (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.5e-77], N[Not[LessEqual[y, 9.8e-80]], $MachinePrecision]], N[(x - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(N[(t * 0.3333333333333333), $MachinePrecision] / N[(y * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999982e-77 or 9.79999999999999981e-80 < y

   1. Initial program 99.1%

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

      1. associate-+l- 99.1%

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

      2. *-commutative 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in t around 0 86.5%

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

   if -2.49999999999999982e-77 < y < 9.79999999999999981e-80

   1. Initial program 93.3%

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

   3. Simplified 93.3%

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

      1. fma-udef 93.3%

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

   5. Applied egg-rr 93.3%

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

      1. clear-num 2.7%

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

      2. un-div-inv 2.7%

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

   7. Applied egg-rr 93.3%

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

   8. Taylor expanded in y around 0 69.3%

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

      1. associate-*r/ 69.3%

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

   10. Simplified 69.3%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-77} \lor \neg \left(y \leq 9.8 \cdot 10^{-80}\right):\\ \;\;\;\;x - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot 0.3333333333333333}{y \cdot z}\\ \end{array} \]

Alternative 13: 96.3% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

3. Simplified 96.0%

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

4. Final simplification 96.0%

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

Alternative 14: 96.3% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

3. Simplified 96.0%

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

   1. associate-*l/ 96.0%

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

5. Applied egg-rr 96.0%

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

6. Final simplification 96.0%

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

Alternative 15: 96.3% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

   1. associate-+l- 96.8%

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

   2. *-commutative 96.8%

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

3. Simplified 96.8%

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

   1. sub-neg 96.8%

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

   2. associate-/r* 96.1%

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

   3. sub-div 96.1%

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

5. Applied egg-rr 96.1%

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

6. Final simplification 96.1%

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

Alternative 16: 45.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.9 \cdot 10^{+179} \lor \neg \left(y \leq 1150000000000\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8.9e+179) (not (<= y 1150000000000.0)))
   (* -0.3333333333333333 (/ y z))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.9e+179) || !(y <= 1150000000000.0)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-8.9d+179)) .or. (.not. (y <= 1150000000000.0d0))) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8.9e+179) || !(y <= 1150000000000.0)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8.9e+179) or not (y <= 1150000000000.0):
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8.9e+179) || !(y <= 1150000000000.0))
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8.9e+179) || ~((y <= 1150000000000.0)))
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8.9e+179], N[Not[LessEqual[y, 1150000000000.0]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -8.90000000000000036e179 or 1.15e12 < 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%

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

      1. fma-udef 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 75.9%

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

   if -8.90000000000000036e179 < y < 1.15e12

   1. Initial program 95.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in x around inf 37.2%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.9 \cdot 10^{+179} \lor \neg \left(y \leq 1150000000000\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17: 45.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.9 \cdot 10^{+179}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 110000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.9e+179)
   (* -0.3333333333333333 (/ y z))
   (if (<= y 110000000000.0) x (/ -0.3333333333333333 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.9e+179) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 110000000000.0) {
		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 <= (-8.9d+179)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (y <= 110000000000.0d0) 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 <= -8.9e+179) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 110000000000.0) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.9e+179:
		tmp = -0.3333333333333333 * (y / z)
	elif y <= 110000000000.0:
		tmp = x
	else:
		tmp = -0.3333333333333333 / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.9e+179)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (y <= 110000000000.0)
		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 <= -8.9e+179)
		tmp = -0.3333333333333333 * (y / z);
	elseif (y <= 110000000000.0)
		tmp = x;
	else
		tmp = -0.3333333333333333 / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.9e+179], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 110000000000.0], x, N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.90000000000000036e179

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

      1. fma-udef 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 95.4%

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

   if -8.90000000000000036e179 < y < 1.1e11

   1. Initial program 95.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in x around inf 37.2%

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

   if 1.1e11 < 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%

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

      1. fma-udef 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 68.5%

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

      1. clear-num 68.6%

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

      2. un-div-inv 68.6%

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

   8. Applied egg-rr 68.6%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.9 \cdot 10^{+179}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 110000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]

Alternative 18: 45.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.9 \cdot 10^{+179}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 70000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.9e+179)
   (* -0.3333333333333333 (/ y z))
   (if (<= y 70000000000.0) x (/ y (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.9e+179) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 70000000000.0) {
		tmp = x;
	} 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 <= (-8.9d+179)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (y <= 70000000000.0d0) then
        tmp = x
    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 <= -8.9e+179) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 70000000000.0) {
		tmp = x;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.9e+179:
		tmp = -0.3333333333333333 * (y / z)
	elif y <= 70000000000.0:
		tmp = x
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.9e+179)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (y <= 70000000000.0)
		tmp = x;
	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 <= -8.9e+179)
		tmp = -0.3333333333333333 * (y / z);
	elseif (y <= 70000000000.0)
		tmp = x;
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.9e+179], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 70000000000.0], x, N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.90000000000000036e179

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

      1. fma-udef 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 95.4%

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

   if -8.90000000000000036e179 < y < 7e10

   1. Initial program 95.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in x around inf 37.2%

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

   if 7e10 < 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%

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

      1. fma-udef 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 68.5%

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

      1. associate-*r/ 68.5%

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

      2. associate-*l/ 68.4%

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

      3. *-commutative 68.4%

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

      4. clear-num 68.4%

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

      5. un-div-inv 68.5%

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

      6. div-inv 68.6%

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

      7. metadata-eval 68.6%

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

   8. Applied egg-rr 68.6%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.9 \cdot 10^{+179}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 70000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]

Alternative 19: 45.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.9 \cdot 10^{+179}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 510000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -8.9e+179)
   (/ (* y -0.3333333333333333) z)
   (if (<= y 510000000000.0) x (/ y (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -8.9e+179) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 510000000000.0) {
		tmp = x;
	} 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 <= (-8.9d+179)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= 510000000000.0d0) then
        tmp = x
    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 <= -8.9e+179) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 510000000000.0) {
		tmp = x;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -8.9e+179:
		tmp = (y * -0.3333333333333333) / z
	elif y <= 510000000000.0:
		tmp = x
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -8.9e+179)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= 510000000000.0)
		tmp = x;
	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 <= -8.9e+179)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= 510000000000.0)
		tmp = x;
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -8.9e+179], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 510000000000.0], x, N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.90000000000000036e179

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

      1. fma-udef 99.7%

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

   5. Applied egg-rr 99.7%

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

   6. Taylor expanded in y around inf 95.4%

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

      1. associate-*r/ 95.5%

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

   8. Applied egg-rr 95.5%

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

   if -8.90000000000000036e179 < y < 5.1e11

   1. Initial program 95.3%

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

   3. Simplified 94.3%

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

   4. Taylor expanded in x around inf 37.2%

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

   if 5.1e11 < 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%

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

      1. fma-udef 99.6%

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

   5. Applied egg-rr 99.6%

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

   6. Taylor expanded in y around inf 68.5%

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

      1. associate-*r/ 68.5%

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

      2. associate-*l/ 68.4%

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

      3. *-commutative 68.4%

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

      4. clear-num 68.4%

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

      5. un-div-inv 68.5%

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

      6. div-inv 68.6%

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

      7. metadata-eval 68.6%

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

   8. Applied egg-rr 68.6%

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

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.9 \cdot 10^{+179}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 510000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]

Alternative 20: 29.5% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.8%

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

3. Simplified 96.0%

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

4. Taylor expanded in x around inf 31.6%

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

5. Final simplification 31.6%

   \[\leadsto x \]

Developer target: 96.0% 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 2023306 
(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))))