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

Percentage Accurate: 95.3% → 97.2%

Time: 13.6s

Alternatives: 19

Speedup: 1.4×

• 27.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{-117}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -4e-117)
   (+ (- x (/ y (* z 3.0))) (/ t (* z (* 3.0 y))))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -4e-117) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	} else {
		tmp = x + (((t / y) - 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 ((z * 3.0d0) <= (-4d-117)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (z * (3.0d0 * y)))
    else
        tmp = x + (((t / y) - 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 ((z * 3.0) <= -4e-117) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -4e-117:
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)))
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -4e-117)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(z * Float64(3.0 * y))));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -4e-117)
		tmp = (x - (y / (z * 3.0))) + (t / (z * (3.0 * y)));
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -4e-117], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -4.00000000000000012e-117

   1. Initial program 99.7%

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

      1. associate-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   if -4.00000000000000012e-117 < (*.f64 z 3)

   1. Initial program 92.4%

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

      1. associate-*l* 92.3%

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

      2. *-commutative 92.3%

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

   3. Simplified 92.3%

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

      1. *-commutative 92.3%

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

      2. associate-*l* 92.4%

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

      3. associate-+l- 92.4%

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

      4. *-commutative 92.4%

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

      5. associate-/r* 96.6%

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

      6. sub-div 98.0%

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

   6. Applied egg-rr 98.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{-117}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(3 \cdot y\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 59.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{if}\;y \leq -5.9 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -75000000:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-87}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9000000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (* 0.3333333333333333 (/ t (* z y)))))
   (if (<= y -5.9e+66)
     (/ y (* z -3.0))
     (if (<= y -3.8e+32)
       x
       (if (<= y -75000000.0)
         (/ (* y -0.3333333333333333) z)
         (if (<= y 2.85e-87)
           t_1
           (if (<= y 4.6e-63)
             x
             (if (<= y 9000000000000.0)
               t_1
               (if (<= y 1.65e+161) x (* y (/ -0.3333333333333333 z)))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (z * y));
	double tmp;
	if (y <= -5.9e+66) {
		tmp = y / (z * -3.0);
	} else if (y <= -3.8e+32) {
		tmp = x;
	} else if (y <= -75000000.0) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 2.85e-87) {
		tmp = t_1;
	} else if (y <= 4.6e-63) {
		tmp = x;
	} else if (y <= 9000000000000.0) {
		tmp = t_1;
	} else if (y <= 1.65e+161) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 0.3333333333333333d0 * (t / (z * y))
    if (y <= (-5.9d+66)) then
        tmp = y / (z * (-3.0d0))
    else if (y <= (-3.8d+32)) then
        tmp = x
    else if (y <= (-75000000.0d0)) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else if (y <= 2.85d-87) then
        tmp = t_1
    else if (y <= 4.6d-63) then
        tmp = x
    else if (y <= 9000000000000.0d0) then
        tmp = t_1
    else if (y <= 1.65d+161) then
        tmp = x
    else
        tmp = y * ((-0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 0.3333333333333333 * (t / (z * y));
	double tmp;
	if (y <= -5.9e+66) {
		tmp = y / (z * -3.0);
	} else if (y <= -3.8e+32) {
		tmp = x;
	} else if (y <= -75000000.0) {
		tmp = (y * -0.3333333333333333) / z;
	} else if (y <= 2.85e-87) {
		tmp = t_1;
	} else if (y <= 4.6e-63) {
		tmp = x;
	} else if (y <= 9000000000000.0) {
		tmp = t_1;
	} else if (y <= 1.65e+161) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 0.3333333333333333 * (t / (z * y))
	tmp = 0
	if y <= -5.9e+66:
		tmp = y / (z * -3.0)
	elif y <= -3.8e+32:
		tmp = x
	elif y <= -75000000.0:
		tmp = (y * -0.3333333333333333) / z
	elif y <= 2.85e-87:
		tmp = t_1
	elif y <= 4.6e-63:
		tmp = x
	elif y <= 9000000000000.0:
		tmp = t_1
	elif y <= 1.65e+161:
		tmp = x
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(0.3333333333333333 * Float64(t / Float64(z * y)))
	tmp = 0.0
	if (y <= -5.9e+66)
		tmp = Float64(y / Float64(z * -3.0));
	elseif (y <= -3.8e+32)
		tmp = x;
	elseif (y <= -75000000.0)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	elseif (y <= 2.85e-87)
		tmp = t_1;
	elseif (y <= 4.6e-63)
		tmp = x;
	elseif (y <= 9000000000000.0)
		tmp = t_1;
	elseif (y <= 1.65e+161)
		tmp = x;
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 0.3333333333333333 * (t / (z * y));
	tmp = 0.0;
	if (y <= -5.9e+66)
		tmp = y / (z * -3.0);
	elseif (y <= -3.8e+32)
		tmp = x;
	elseif (y <= -75000000.0)
		tmp = (y * -0.3333333333333333) / z;
	elseif (y <= 2.85e-87)
		tmp = t_1;
	elseif (y <= 4.6e-63)
		tmp = x;
	elseif (y <= 9000000000000.0)
		tmp = t_1;
	elseif (y <= 1.65e+161)
		tmp = x;
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.9e+66], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.8e+32], x, If[LessEqual[y, -75000000.0], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 2.85e-87], t$95$1, If[LessEqual[y, 4.6e-63], x, If[LessEqual[y, 9000000000000.0], t$95$1, If[LessEqual[y, 1.65e+161], x, N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.89999999999999988e66

   1. Initial program 97.9%

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

      1. associate-*l* 97.9%

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

      2. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 84.3%

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

   6. Taylor expanded in t around 0 80.6%

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

      1. associate-*r/ 80.6%

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

      2. metadata-eval 80.6%

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

      3. associate-/r/ 80.7%

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

      4. associate-/r* 80.6%

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

      5. associate-/l/ 80.6%

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

      6. associate-/l* 80.6%

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

      7. *-commutative 80.6%

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

      8. associate-*r/ 80.7%

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

      9. *-rgt-identity 80.7%

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

      10. associate-/r* 80.7%

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

   8. Simplified 80.7%

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

   if -5.89999999999999988e66 < y < -3.8000000000000003e32 or 2.85e-87 < y < 4.6e-63 or 9e12 < y < 1.64999999999999999e161

   1. Initial program 97.2%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 67.9%

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

   if -3.8000000000000003e32 < y < -7.5e7

   1. Initial program 100.0%

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

      1. associate-*l* 100.0%

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

      2. *-commutative 100.0%

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

   3. Simplified 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. associate-+l- 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/r* 100.0%

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

      6. sub-div 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around inf 67.8%

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

      1. associate-*r/ 68.3%

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

   9. Simplified 68.3%

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

   if -7.5e7 < y < 2.85e-87 or 4.6e-63 < y < 9e12

   1. Initial program 93.2%

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

      1. associate-*l* 93.3%

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

      2. *-commutative 93.3%

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

   3. Simplified 93.3%

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

      1. *-commutative 93.3%

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

      2. associate-*l* 93.2%

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

      3. associate-+l- 93.3%

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

      4. *-commutative 93.3%

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

      5. associate-/r* 91.7%

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

      6. sub-div 92.5%

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

   6. Applied egg-rr 92.5%

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

   7. Taylor expanded in y around 0 63.4%

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

      1. *-commutative 63.4%

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

   9. Simplified 63.4%

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

   if 1.64999999999999999e161 < y

   1. Initial program 97.1%

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

      1. associate-*l* 97.1%

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

      2. *-commutative 97.1%

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

   3. Simplified 97.1%

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

      1. *-commutative 97.1%

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

      2. associate-*l* 97.1%

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

      3. associate-+l- 97.1%

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

      4. *-commutative 97.1%

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

      5. associate-/r* 97.1%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 91.5%

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

      1. metadata-eval 91.5%

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

      2. times-frac 91.7%

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

      3. neg-mul-1 91.7%

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

      4. *-commutative 91.7%

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

      5. distribute-frac-neg 91.7%

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

      6. *-rgt-identity 91.7%

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

      7. associate-*r/ 91.5%

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

      8. distribute-rgt-neg-in 91.5%

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

      9. distribute-neg-frac 91.5%

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

      10. metadata-eval 91.5%

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

      11. *-commutative 91.5%

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

      12. associate-/r* 91.7%

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

      13. metadata-eval 91.7%

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

   9. Simplified 91.7%

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

   10. Taylor expanded in y around inf 91.5%

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

       1. associate-*r/ 91.7%

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

       2. associate-*l/ 91.7%

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

       3. *-commutative 91.7%

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

   12. Simplified 91.7%

       \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.9 \cdot 10^{+66}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+32}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -75000000:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-87}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{-63}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9000000000000:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -41000000 \lor \neg \left(y \leq 11000000000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -41000000.0) (not (<= y 11000000000000.0)))
   (- x (/ y (* z 3.0)))
   (+ x (* (/ t y) (/ 0.3333333333333333 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -41000000.0) || !(y <= 11000000000000.0)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-41000000.0d0)) .or. (.not. (y <= 11000000000000.0d0))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + ((t / y) * (0.3333333333333333d0 / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -41000000.0) || !(y <= 11000000000000.0)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -41000000.0) or not (y <= 11000000000000.0):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + ((t / y) * (0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -41000000.0) || !(y <= 11000000000000.0))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(t / y) * Float64(0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -41000000.0) || ~((y <= 11000000000000.0)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -41000000.0], N[Not[LessEqual[y, 11000000000000.0]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1e7 or 1.1e13 < y

   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%

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

      2. *-commutative 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in t around 0 95.0%

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

      1. metadata-eval 95.0%

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

      2. times-frac 95.2%

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

      3. *-un-lft-identity 95.2%

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

      4. *-commutative 95.2%

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

   7. Applied egg-rr 95.2%

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

   if -4.1e7 < y < 1.1e13

   1. Initial program 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in t around inf 87.7%

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

      1. associate-/r* 85.6%

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

      2. associate-*r/ 85.6%

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

      3. associate-*l/ 85.6%

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

      4. *-commutative 85.6%

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

   7. Simplified 85.6%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -41000000 \lor \neg \left(y \leq 11000000000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -51000000 \lor \neg \left(y \leq 3600000000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -51000000.0) (not (<= y 3600000000000.0)))
   (- x (/ y (* z 3.0)))
   (+ x (* 0.3333333333333333 (/ t (* z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -51000000.0) || !(y <= 3600000000000.0)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-51000000.0d0)) .or. (.not. (y <= 3600000000000.0d0))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + (0.3333333333333333d0 * (t / (z * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -51000000.0) || !(y <= 3600000000000.0)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -51000000.0) or not (y <= 3600000000000.0):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + (0.3333333333333333 * (t / (z * y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -51000000.0) || !(y <= 3600000000000.0))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -51000000.0) || ~((y <= 3600000000000.0)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -51000000.0], N[Not[LessEqual[y, 3600000000000.0]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1e7 or 3.6e12 < y

   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%

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

      2. *-commutative 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in t around 0 95.0%

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

      1. metadata-eval 95.0%

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

      2. times-frac 95.2%

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

      3. *-un-lft-identity 95.2%

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

      4. *-commutative 95.2%

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

   7. Applied egg-rr 95.2%

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

   if -5.1e7 < y < 3.6e12

   1. Initial program 93.0%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in y around 0 87.7%

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

      1. +-commutative 87.7%

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

   7. Simplified 87.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -51000000 \lor \neg \left(y \leq 3600000000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -64000000 \lor \neg \left(y \leq 750000000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t \cdot -0.3333333333333333}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -64000000.0) (not (<= y 750000000000.0)))
   (- x (/ y (* z 3.0)))
   (- x (/ (* t -0.3333333333333333) (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -64000000.0) || !(y <= 750000000000.0)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x - ((t * -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 <= (-64000000.0d0)) .or. (.not. (y <= 750000000000.0d0))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x - ((t * (-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 <= -64000000.0) || !(y <= 750000000000.0)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x - ((t * -0.3333333333333333) / (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -64000000.0) or not (y <= 750000000000.0):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x - ((t * -0.3333333333333333) / (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -64000000.0) || !(y <= 750000000000.0))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x - Float64(Float64(t * -0.3333333333333333) / Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -64000000.0) || ~((y <= 750000000000.0)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x - ((t * -0.3333333333333333) / (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -64000000.0], N[Not[LessEqual[y, 750000000000.0]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(t * -0.3333333333333333), $MachinePrecision] / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.4e7 or 7.5e11 < y

   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%

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

      2. *-commutative 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in t around 0 95.0%

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

      1. metadata-eval 95.0%

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

      2. times-frac 95.2%

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

      3. *-un-lft-identity 95.2%

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

      4. *-commutative 95.2%

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

   7. Applied egg-rr 95.2%

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

   if -6.4e7 < y < 7.5e11

   1. Initial program 93.0%

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

      1. associate-*l* 93.0%

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

      2. *-commutative 93.0%

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

   3. Simplified 93.0%

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

      1. *-commutative 93.0%

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

      2. associate-*l* 93.0%

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

      3. associate-+l- 93.0%

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

      4. *-commutative 93.0%

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

      5. associate-/r* 92.3%

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

      6. sub-div 93.0%

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

   6. Applied egg-rr 93.0%

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

   7. Taylor expanded in y around 0 87.7%

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

      1. associate-*r/ 87.7%

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

   9. Simplified 87.7%

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

4. Final simplification 91.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -64000000 \lor \neg \left(y \leq 750000000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{t \cdot -0.3333333333333333}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+130}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+89}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -7.6e+130)
   (+ x (* y (/ -0.3333333333333333 z)))
   (if (<= x 6.6e+89)
     (* -0.3333333333333333 (/ (- y (/ t y)) z))
     (- x (* 0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -7.6e+130) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (x <= 6.6e+89) {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	} else {
		tmp = x - (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 (x <= (-7.6d+130)) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else if (x <= 6.6d+89) then
        tmp = (-0.3333333333333333d0) * ((y - (t / y)) / z)
    else
        tmp = x - (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 (x <= -7.6e+130) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (x <= 6.6e+89) {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -7.6e+130:
		tmp = x + (y * (-0.3333333333333333 / z))
	elif x <= 6.6e+89:
		tmp = -0.3333333333333333 * ((y - (t / y)) / z)
	else:
		tmp = x - (0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -7.6e+130)
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	elseif (x <= 6.6e+89)
		tmp = Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z));
	else
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -7.6e+130)
		tmp = x + (y * (-0.3333333333333333 / z));
	elseif (x <= 6.6e+89)
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	else
		tmp = x - (0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -7.6e+130], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.6e+89], N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -7.6000000000000004e130

   1. Initial program 94.8%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t around 0 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 75.3%

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

      3. associate-*r/ 75.4%

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

   7. Simplified 75.4%

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

   if -7.6000000000000004e130 < x < 6.59999999999999948e89

   1. Initial program 94.6%

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

      1. associate-*l* 94.6%

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

      2. *-commutative 94.6%

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

   3. Simplified 94.6%

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

      1. *-commutative 94.6%

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

      2. associate-*l* 94.6%

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

      3. associate-+l- 94.6%

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

      4. *-commutative 94.6%

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

      5. associate-/r* 95.1%

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

      6. sub-div 96.3%

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

   6. Applied egg-rr 96.3%

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

   7. Taylor expanded in x around 0 84.9%

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

   if 6.59999999999999948e89 < x

   1. Initial program 98.1%

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

      1. associate-*l* 98.1%

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

      2. *-commutative 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around 0 78.7%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+130}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{+89}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 79.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+131}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+89}:\\ \;\;\;\;\left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.8e+131)
   (+ x (* y (/ -0.3333333333333333 z)))
   (if (<= x 3.9e+89)
     (* (- y (/ t y)) (/ -0.3333333333333333 z))
     (- x (* 0.3333333333333333 (/ y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.8e+131) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (x <= 3.9e+89) {
		tmp = (y - (t / y)) * (-0.3333333333333333 / z);
	} else {
		tmp = x - (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 (x <= (-1.8d+131)) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else if (x <= 3.9d+89) then
        tmp = (y - (t / y)) * ((-0.3333333333333333d0) / z)
    else
        tmp = x - (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 (x <= -1.8e+131) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else if (x <= 3.9e+89) {
		tmp = (y - (t / y)) * (-0.3333333333333333 / z);
	} else {
		tmp = x - (0.3333333333333333 * (y / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.8e+131:
		tmp = x + (y * (-0.3333333333333333 / z))
	elif x <= 3.9e+89:
		tmp = (y - (t / y)) * (-0.3333333333333333 / z)
	else:
		tmp = x - (0.3333333333333333 * (y / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.8e+131)
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	elseif (x <= 3.9e+89)
		tmp = Float64(Float64(y - Float64(t / y)) * Float64(-0.3333333333333333 / z));
	else
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.8e+131)
		tmp = x + (y * (-0.3333333333333333 / z));
	elseif (x <= 3.9e+89)
		tmp = (y - (t / y)) * (-0.3333333333333333 / z);
	else
		tmp = x - (0.3333333333333333 * (y / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.8e+131], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.9e+89], N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.80000000000000016e131

   1. Initial program 94.8%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in t around 0 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*l/ 75.3%

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

      3. associate-*r/ 75.4%

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

   7. Simplified 75.4%

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

   if -1.80000000000000016e131 < x < 3.90000000000000011e89

   1. Initial program 94.6%

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

      1. associate-*l* 94.6%

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

      2. *-commutative 94.6%

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

   3. Simplified 94.6%

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

      1. *-commutative 94.6%

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

      2. associate-*l* 94.6%

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

      3. associate-+l- 94.6%

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

      4. *-commutative 94.6%

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

      5. associate-/r* 95.1%

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

      6. sub-div 96.3%

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

   6. Applied egg-rr 96.3%

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

   7. Taylor expanded in x around 0 84.9%

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

      1. metadata-eval 84.9%

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

      2. times-frac 85.0%

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

      3. neg-mul-1 85.0%

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

      4. *-commutative 85.0%

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

      5. distribute-frac-neg 85.0%

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

      6. *-rgt-identity 85.0%

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

      7. associate-*r/ 85.0%

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

      8. distribute-rgt-neg-in 85.0%

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

      9. distribute-neg-frac 85.0%

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

      10. metadata-eval 85.0%

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

      11. *-commutative 85.0%

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

      12. associate-/r* 85.0%

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

      13. metadata-eval 85.0%

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

   9. Simplified 85.0%

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

   if 3.90000000000000011e89 < x

   1. Initial program 98.1%

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

      1. associate-*l* 98.1%

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

      2. *-commutative 98.1%

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

   3. Simplified 98.1%

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

   5. Taylor expanded in t around 0 78.7%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+131}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+89}:\\ \;\;\;\;\left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-108} \lor \neg \left(y \leq 3.9 \cdot 10^{-89}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.3e-108) (not (<= y 3.9e-89)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* 0.3333333333333333 (/ t (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e-108) || !(y <= 3.9e-89)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.3d-108)) .or. (.not. (y <= 3.9d-89))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = 0.3333333333333333d0 * (t / (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.3e-108) || !(y <= 3.9e-89)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.3e-108) or not (y <= 3.9e-89):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * (t / (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.3e-108) || !(y <= 3.9e-89))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.3e-108) || ~((y <= 3.9e-89)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * (t / (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.3e-108], N[Not[LessEqual[y, 3.9e-89]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999992e-108 or 3.89999999999999978e-89 < y

   1. Initial program 97.0%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 82.3%

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

      1. *-commutative 82.3%

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

      2. associate-*l/ 82.4%

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

      3. associate-*r/ 82.4%

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

   7. Simplified 82.4%

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

   if -1.29999999999999992e-108 < y < 3.89999999999999978e-89

   1. Initial program 91.7%

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

      1. associate-*l* 91.8%

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

      2. *-commutative 91.8%

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

   3. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*l* 91.7%

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

      3. associate-+l- 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-/r* 88.1%

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

      6. sub-div 88.1%

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

   6. Applied egg-rr 88.1%

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

   7. Taylor expanded in y around 0 72.6%

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

      1. *-commutative 72.6%

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

   9. Simplified 72.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-108} \lor \neg \left(y \leq 3.9 \cdot 10^{-89}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-110} \lor \neg \left(y \leq 2.2 \cdot 10^{-89}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -8e-110) (not (<= y 2.2e-89)))
   (- x (/ y (* z 3.0)))
   (* 0.3333333333333333 (/ t (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e-110) || !(y <= 2.2e-89)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-8d-110)) .or. (.not. (y <= 2.2d-89))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = 0.3333333333333333d0 * (t / (z * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -8e-110) || !(y <= 2.2e-89)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -8e-110) or not (y <= 2.2e-89):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = 0.3333333333333333 * (t / (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -8e-110) || !(y <= 2.2e-89))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -8e-110) || ~((y <= 2.2e-89)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = 0.3333333333333333 * (t / (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -8e-110], N[Not[LessEqual[y, 2.2e-89]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.0000000000000004e-110 or 2.20000000000000012e-89 < y

   1. Initial program 97.0%

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

      1. associate-*l* 97.0%

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

      2. *-commutative 97.0%

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

   3. Simplified 97.0%

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

   5. Taylor expanded in t around 0 82.3%

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

      1. metadata-eval 82.3%

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

      2. times-frac 82.4%

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

      3. *-un-lft-identity 82.4%

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

      4. *-commutative 82.4%

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

   7. Applied egg-rr 82.4%

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

   if -8.0000000000000004e-110 < y < 2.20000000000000012e-89

   1. Initial program 91.7%

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

      1. associate-*l* 91.8%

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

      2. *-commutative 91.8%

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

   3. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*l* 91.7%

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

      3. associate-+l- 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-/r* 88.1%

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

      6. sub-div 88.1%

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

   6. Applied egg-rr 88.1%

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

   7. Taylor expanded in y around 0 72.6%

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

      1. *-commutative 72.6%

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

   9. Simplified 72.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-110} \lor \neg \left(y \leq 2.2 \cdot 10^{-89}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-108}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-87}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e-108)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 9.8e-87)
     (* 0.3333333333333333 (/ t (* z y)))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-108) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 9.8e-87) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.4d-108)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 9.8d-87) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-108) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 9.8e-87) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e-108:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 9.8e-87:
		tmp = 0.3333333333333333 * (t / (z * y))
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e-108)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 9.8e-87)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.4e-108)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 9.8e-87)
		tmp = 0.3333333333333333 * (t / (z * y));
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e-108], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.8e-87], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e-108

   1. Initial program 97.6%

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

      1. associate-*l* 97.6%

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

      2. *-commutative 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in t around 0 81.3%

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

   if -1.4e-108 < y < 9.7999999999999994e-87

   1. Initial program 91.7%

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

      1. associate-*l* 91.8%

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

      2. *-commutative 91.8%

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

   3. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*l* 91.7%

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

      3. associate-+l- 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-/r* 88.1%

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

      6. sub-div 88.1%

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

   6. Applied egg-rr 88.1%

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

   7. Taylor expanded in y around 0 72.6%

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

      1. *-commutative 72.6%

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

   9. Simplified 72.6%

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

   if 9.7999999999999994e-87 < y

   1. Initial program 96.4%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in t around 0 83.4%

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

      1. *-commutative 83.4%

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

      2. associate-*l/ 83.5%

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

      3. associate-*r/ 83.5%

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

   7. Simplified 83.5%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-108}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-87}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 75.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-110}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-87}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.8e-110)
   (- x (/ (/ y 3.0) z))
   (if (<= y 6.8e-87)
     (* 0.3333333333333333 (/ t (* z y)))
     (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-110) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 6.8e-87) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.8d-110)) then
        tmp = x - ((y / 3.0d0) / z)
    else if (y <= 6.8d-87) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.8e-110) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 6.8e-87) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.8e-110:
		tmp = x - ((y / 3.0) / z)
	elif y <= 6.8e-87:
		tmp = 0.3333333333333333 * (t / (z * y))
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.8e-110)
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	elseif (y <= 6.8e-87)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.8e-110)
		tmp = x - ((y / 3.0) / z);
	elseif (y <= 6.8e-87)
		tmp = 0.3333333333333333 * (t / (z * y));
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.8e-110], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.8e-87], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.80000000000000013e-110

   1. Initial program 97.6%

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

      1. associate-*l* 97.6%

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

      2. *-commutative 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in t around 0 81.3%

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

      1. metadata-eval 81.3%

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

      2. times-frac 81.3%

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

      3. *-un-lft-identity 81.3%

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

      4. *-commutative 81.3%

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

   7. Applied egg-rr 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-/r* 81.3%

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

   9. Simplified 81.3%

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

   if -4.80000000000000013e-110 < y < 6.7999999999999997e-87

   1. Initial program 91.7%

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

      1. associate-*l* 91.8%

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

      2. *-commutative 91.8%

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

   3. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*l* 91.7%

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

      3. associate-+l- 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-/r* 88.1%

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

      6. sub-div 88.1%

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

   6. Applied egg-rr 88.1%

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

   7. Taylor expanded in y around 0 72.6%

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

      1. *-commutative 72.6%

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

   9. Simplified 72.6%

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

   if 6.7999999999999997e-87 < y

   1. Initial program 96.4%

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

      1. associate-*l* 96.4%

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

      2. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around 0 83.4%

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

      1. metadata-eval 83.4%

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

      2. times-frac 83.6%

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

      3. *-un-lft-identity 83.6%

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

      4. *-commutative 83.6%

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

   7. Applied egg-rr 83.6%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-110}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-87}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-108}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e-108)
   (- x (/ (/ y 3.0) z))
   (if (<= y 9.5e-88) (/ t (* (* z 3.0) y)) (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-108) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 9.5e-88) {
		tmp = t / ((z * 3.0) * y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.4d-108)) then
        tmp = x - ((y / 3.0d0) / z)
    else if (y <= 9.5d-88) then
        tmp = t / ((z * 3.0d0) * y)
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-108) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 9.5e-88) {
		tmp = t / ((z * 3.0) * y);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e-108:
		tmp = x - ((y / 3.0) / z)
	elif y <= 9.5e-88:
		tmp = t / ((z * 3.0) * y)
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e-108)
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	elseif (y <= 9.5e-88)
		tmp = Float64(t / Float64(Float64(z * 3.0) * y));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.4e-108)
		tmp = x - ((y / 3.0) / z);
	elseif (y <= 9.5e-88)
		tmp = t / ((z * 3.0) * y);
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e-108], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9.5e-88], N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e-108

   1. Initial program 97.6%

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

      1. associate-*l* 97.6%

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

      2. *-commutative 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in t around 0 81.3%

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

      1. metadata-eval 81.3%

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

      2. times-frac 81.3%

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

      3. *-un-lft-identity 81.3%

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

      4. *-commutative 81.3%

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

   7. Applied egg-rr 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-/r* 81.3%

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

   9. Simplified 81.3%

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

   if -1.4e-108 < y < 9.5e-88

   1. Initial program 91.7%

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

      1. associate-*l* 91.8%

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

      2. *-commutative 91.8%

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

   3. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*l* 91.7%

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

      3. associate-+l- 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-/r* 88.1%

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

      6. sub-div 88.1%

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

   6. Applied egg-rr 88.1%

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

   7. Taylor expanded in y around 0 72.6%

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

      1. *-commutative 72.6%

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

      2. associate-/r* 69.1%

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

   9. Simplified 69.1%

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

       1. metadata-eval 69.1%

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

       2. div-inv 69.2%

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

       3. associate-/r* 69.1%

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

       4. associate-/l/ 72.7%

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

       5. *-commutative 72.7%

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

   11. Applied egg-rr 72.7%

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

   if 9.5e-88 < y

   1. Initial program 96.4%

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

      1. associate-*l* 96.4%

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

      2. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around 0 83.4%

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

      1. metadata-eval 83.4%

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

      2. times-frac 83.6%

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

      3. *-un-lft-identity 83.6%

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

      4. *-commutative 83.6%

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

   7. Applied egg-rr 83.6%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-108}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-88}:\\ \;\;\;\;\frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 78.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-108}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-89}:\\ \;\;\;\;\frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e-108)
   (- x (/ (/ y 3.0) z))
   (if (<= y 2.7e-89) (/ (/ t (* z 3.0)) y) (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-108) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 2.7e-89) {
		tmp = (t / (z * 3.0)) / y;
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.4d-108)) then
        tmp = x - ((y / 3.0d0) / z)
    else if (y <= 2.7d-89) then
        tmp = (t / (z * 3.0d0)) / y
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-108) {
		tmp = x - ((y / 3.0) / z);
	} else if (y <= 2.7e-89) {
		tmp = (t / (z * 3.0)) / y;
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e-108:
		tmp = x - ((y / 3.0) / z)
	elif y <= 2.7e-89:
		tmp = (t / (z * 3.0)) / y
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e-108)
		tmp = Float64(x - Float64(Float64(y / 3.0) / z));
	elseif (y <= 2.7e-89)
		tmp = Float64(Float64(t / Float64(z * 3.0)) / y);
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.4e-108)
		tmp = x - ((y / 3.0) / z);
	elseif (y <= 2.7e-89)
		tmp = (t / (z * 3.0)) / y;
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e-108], N[(x - N[(N[(y / 3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-89], N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e-108

   1. Initial program 97.6%

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

      1. associate-*l* 97.6%

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

      2. *-commutative 97.6%

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

   3. Simplified 97.6%

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

   5. Taylor expanded in t around 0 81.3%

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

      1. metadata-eval 81.3%

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

      2. times-frac 81.3%

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

      3. *-un-lft-identity 81.3%

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

      4. *-commutative 81.3%

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

   7. Applied egg-rr 81.3%

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

      1. *-commutative 81.3%

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

      2. associate-/r* 81.3%

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

   9. Simplified 81.3%

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

   if -1.4e-108 < y < 2.69999999999999988e-89

   1. Initial program 91.7%

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

      1. associate-*l* 91.8%

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

      2. *-commutative 91.8%

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

   3. Simplified 91.8%

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

      1. *-commutative 91.8%

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

      2. associate-*l* 91.7%

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

      3. associate-+l- 91.7%

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

      4. *-commutative 91.7%

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

      5. associate-/r* 88.1%

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

      6. sub-div 88.1%

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

   6. Applied egg-rr 88.1%

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

   7. Taylor expanded in y around 0 72.6%

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

      1. *-commutative 72.6%

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

      2. associate-/r* 69.1%

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

   9. Simplified 69.1%

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

       1. metadata-eval 69.1%

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

       2. div-inv 69.2%

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

       3. associate-/r* 69.1%

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

       4. associate-/l/ 72.7%

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

       5. associate-/r* 78.3%

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

   11. Applied egg-rr 78.3%

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

   if 2.69999999999999988e-89 < y

   1. Initial program 96.4%

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

      1. associate-*l* 96.4%

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

      2. *-commutative 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around 0 83.4%

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

      1. metadata-eval 83.4%

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

      2. times-frac 83.6%

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

      3. *-un-lft-identity 83.6%

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

      4. *-commutative 83.6%

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

   7. Applied egg-rr 83.6%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-108}:\\ \;\;\;\;x - \frac{\frac{y}{3}}{z}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-89}:\\ \;\;\;\;\frac{\frac{t}{z \cdot 3}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 47.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+69} \lor \neg \left(y \leq 1.65 \cdot 10^{+161}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -9.5e+69) (not (<= y 1.65e+161)))
   (* -0.3333333333333333 (/ y z))
   x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -9.5e+69) || !(y <= 1.65e+161)) {
		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 <= (-9.5d+69)) .or. (.not. (y <= 1.65d+161))) 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 <= -9.5e+69) || !(y <= 1.65e+161)) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -9.5e+69) or not (y <= 1.65e+161):
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -9.5e+69) || !(y <= 1.65e+161))
		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 <= -9.5e+69) || ~((y <= 1.65e+161)))
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -9.5e+69], N[Not[LessEqual[y, 1.65e+161]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -9.4999999999999995e69 or 1.64999999999999999e161 < y

   1. Initial program 97.6%

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

      1. associate-*l* 97.6%

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

      2. *-commutative 97.6%

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

   3. Simplified 97.6%

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

      1. *-commutative 97.6%

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

      2. associate-*l* 97.6%

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

      3. associate-+l- 97.6%

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

      4. *-commutative 97.6%

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

      5. associate-/r* 98.6%

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

      6. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 85.2%

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

   if -9.4999999999999995e69 < y < 1.64999999999999999e161

   1. Initial program 94.2%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in x around inf 36.1%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{+69} \lor \neg \left(y \leq 1.65 \cdot 10^{+161}\right):\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 47.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+68}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.8e+68)
   (* -0.3333333333333333 (/ y z))
   (if (<= y 1.65e+161) x (* y (/ -0.3333333333333333 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e+68) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 1.65e+161) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.8d+68)) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else if (y <= 1.65d+161) then
        tmp = x
    else
        tmp = y * ((-0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.8e+68) {
		tmp = -0.3333333333333333 * (y / z);
	} else if (y <= 1.65e+161) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.8e+68:
		tmp = -0.3333333333333333 * (y / z)
	elif y <= 1.65e+161:
		tmp = x
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.8e+68)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	elseif (y <= 1.65e+161)
		tmp = x;
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.8e+68)
		tmp = -0.3333333333333333 * (y / z);
	elseif (y <= 1.65e+161)
		tmp = x;
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.8e+68], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+161], x, N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.8000000000000001e68

   1. Initial program 97.9%

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

      1. associate-*l* 97.9%

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

      2. *-commutative 97.9%

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

   3. Simplified 97.9%

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

      1. *-commutative 97.9%

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

      2. associate-*l* 97.9%

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

      3. associate-+l- 97.9%

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

      4. *-commutative 97.9%

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

      5. associate-/r* 99.8%

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

      6. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 80.6%

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

   if -3.8000000000000001e68 < y < 1.64999999999999999e161

   1. Initial program 94.2%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in x around inf 36.1%

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

   if 1.64999999999999999e161 < y

   1. Initial program 97.1%

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

      1. associate-*l* 97.1%

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

      2. *-commutative 97.1%

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

   3. Simplified 97.1%

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

      1. *-commutative 97.1%

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

      2. associate-*l* 97.1%

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

      3. associate-+l- 97.1%

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

      4. *-commutative 97.1%

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

      5. associate-/r* 97.1%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 91.5%

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

      1. metadata-eval 91.5%

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

      2. times-frac 91.7%

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

      3. neg-mul-1 91.7%

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

      4. *-commutative 91.7%

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

      5. distribute-frac-neg 91.7%

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

      6. *-rgt-identity 91.7%

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

      7. associate-*r/ 91.5%

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

      8. distribute-rgt-neg-in 91.5%

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

      9. distribute-neg-frac 91.5%

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

      10. metadata-eval 91.5%

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

      11. *-commutative 91.5%

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

      12. associate-/r* 91.7%

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

      13. metadata-eval 91.7%

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

   9. Simplified 91.7%

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

   10. Taylor expanded in y around inf 91.5%

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

       1. associate-*r/ 91.7%

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

       2. associate-*l/ 91.7%

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

       3. *-commutative 91.7%

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

   12. Simplified 91.7%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+68}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 47.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+67}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.08e+67)
   (/ y (* z -3.0))
   (if (<= y 1.65e+161) x (* y (/ -0.3333333333333333 z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.08e+67) {
		tmp = y / (z * -3.0);
	} else if (y <= 1.65e+161) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.08d+67)) then
        tmp = y / (z * (-3.0d0))
    else if (y <= 1.65d+161) then
        tmp = x
    else
        tmp = y * ((-0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.08e+67) {
		tmp = y / (z * -3.0);
	} else if (y <= 1.65e+161) {
		tmp = x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.08e+67:
		tmp = y / (z * -3.0)
	elif y <= 1.65e+161:
		tmp = x
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.08e+67)
		tmp = Float64(y / Float64(z * -3.0));
	elseif (y <= 1.65e+161)
		tmp = x;
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.08e+67)
		tmp = y / (z * -3.0);
	elseif (y <= 1.65e+161)
		tmp = x;
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.08e+67], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+161], x, N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.08e67

   1. Initial program 97.9%

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

      1. associate-*l* 97.9%

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

      2. *-commutative 97.9%

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

   3. Simplified 97.9%

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

   5. Taylor expanded in z around 0 84.3%

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

   6. Taylor expanded in t around 0 80.6%

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

      1. associate-*r/ 80.6%

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

      2. metadata-eval 80.6%

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

      3. associate-/r/ 80.7%

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

      4. associate-/r* 80.6%

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

      5. associate-/l/ 80.6%

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

      6. associate-/l* 80.6%

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

      7. *-commutative 80.6%

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

      8. associate-*r/ 80.7%

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

      9. *-rgt-identity 80.7%

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

      10. associate-/r* 80.7%

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

   8. Simplified 80.7%

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

   if -1.08e67 < y < 1.64999999999999999e161

   1. Initial program 94.2%

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

   3. Simplified 94.3%

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

   5. Taylor expanded in x around inf 36.1%

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

   if 1.64999999999999999e161 < y

   1. Initial program 97.1%

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

      1. associate-*l* 97.1%

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

      2. *-commutative 97.1%

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

   3. Simplified 97.1%

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

      1. *-commutative 97.1%

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

      2. associate-*l* 97.1%

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

      3. associate-+l- 97.1%

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

      4. *-commutative 97.1%

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

      5. associate-/r* 97.1%

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

      6. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around 0 91.5%

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

      1. metadata-eval 91.5%

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

      2. times-frac 91.7%

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

      3. neg-mul-1 91.7%

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

      4. *-commutative 91.7%

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

      5. distribute-frac-neg 91.7%

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

      6. *-rgt-identity 91.7%

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

      7. associate-*r/ 91.5%

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

      8. distribute-rgt-neg-in 91.5%

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

      9. distribute-neg-frac 91.5%

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

      10. metadata-eval 91.5%

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

      11. *-commutative 91.5%

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

      12. associate-/r* 91.7%

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

      13. metadata-eval 91.7%

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

   9. Simplified 91.7%

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

   10. Taylor expanded in y around inf 91.5%

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

       1. associate-*r/ 91.7%

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

       2. associate-*l/ 91.7%

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

       3. *-commutative 91.7%

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

   12. Simplified 91.7%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.08 \cdot 10^{+67}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+161}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 95.7% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

3. Simplified 96.1%

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

5. Taylor expanded in z around 0 96.0%

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

6. Final simplification 96.0%

   \[\leadsto x + 0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z} \]
7. Add Preprocessing

Alternative 18: 95.7% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

3. Simplified 96.1%

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

5. Final simplification 96.1%

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

Alternative 19: 31.3% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.3%

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

3. Simplified 96.1%

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

5. Taylor expanded in x around inf 28.6%

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

6. Final simplification 28.6%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.4% 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 2024027 
(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))))