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

Percentage Accurate: 95.5% → 97.9%

Time: 12.8s

Alternatives: 22

Speedup: 1.4×

• 28.3% 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: 95.5% 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: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -500000000:\\ \;\;\;\;\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -500000000.0)
   (+ (/ t (* (* z 3.0) y)) (- x (/ y (* z 3.0))))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -500000000.0) {
		tmp = (t / ((z * 3.0) * y)) + (x - (y / (z * 3.0)));
	} 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) <= (-500000000.0d0)) then
        tmp = (t / ((z * 3.0d0) * y)) + (x - (y / (z * 3.0d0)))
    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) <= -500000000.0) {
		tmp = (t / ((z * 3.0) * y)) + (x - (y / (z * 3.0)));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -500000000.0:
		tmp = (t / ((z * 3.0) * y)) + (x - (y / (z * 3.0)))
	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) <= -500000000.0)
		tmp = Float64(Float64(t / Float64(Float64(z * 3.0) * y)) + Float64(x - Float64(y / Float64(z * 3.0))));
	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) <= -500000000.0)
		tmp = (t / ((z * 3.0) * y)) + (x - (y / (z * 3.0)));
	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], -500000000.0], N[(N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] + N[(x - N[(y / N[(z * 3.0), $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 #s(literal 3 binary64)) < -5e8

   1. Initial program 98.2%

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

   if -5e8 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. associate-+r- 91.8%

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

      3. +-commutative 91.8%

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

      4. associate--l+ 91.8%

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

      5. sub-neg 91.8%

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

      6. remove-double-neg 91.8%

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

      7. distribute-frac-neg 91.8%

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

      8. distribute-neg-in 91.8%

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

      9. remove-double-neg 91.8%

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

      10. sub-neg 91.8%

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

      11. neg-mul-1 91.8%

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

      12. times-frac 98.4%

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

      13. distribute-frac-neg 98.4%

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

      14. neg-mul-1 98.4%

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

      15. *-commutative 98.4%

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

      16. associate-/l* 98.3%

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

      17. *-commutative 98.3%

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

   3. Simplified 98.3%

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

      1. metadata-eval 98.3%

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

      2. associate-/r* 98.3%

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

      3. *-commutative 98.3%

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

      4. associate-*l/ 98.4%

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

      5. *-un-lft-identity 98.4%

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

   6. Applied egg-rr 98.4%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -500000000:\\ \;\;\;\;\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -500000000:\\ \;\;\;\;\left(x + \frac{t}{z \cdot \left(3 \cdot y\right)}\right) + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -500000000.0)
   (+ (+ x (/ t (* z (* 3.0 y)))) (/ y (* z -3.0)))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -500000000.0) {
		tmp = (x + (t / (z * (3.0 * y)))) + (y / (z * -3.0));
	} 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) <= (-500000000.0d0)) then
        tmp = (x + (t / (z * (3.0d0 * y)))) + (y / (z * (-3.0d0)))
    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) <= -500000000.0) {
		tmp = (x + (t / (z * (3.0 * y)))) + (y / (z * -3.0));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -500000000.0:
		tmp = (x + (t / (z * (3.0 * y)))) + (y / (z * -3.0))
	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) <= -500000000.0)
		tmp = Float64(Float64(x + Float64(t / Float64(z * Float64(3.0 * y)))) + Float64(y / Float64(z * -3.0)));
	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) <= -500000000.0)
		tmp = (x + (t / (z * (3.0 * y)))) + (y / (z * -3.0));
	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], -500000000.0], N[(N[(x + N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(z * -3.0), $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 #s(literal 3 binary64)) < -5e8

   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. +-commutative 98.2%

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

      2. associate-+r- 98.2%

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

      3. sub-neg 98.2%

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

      4. associate-*l* 98.2%

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

      5. *-commutative 98.2%

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

      6. distribute-frac-neg2 98.2%

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

      7. distribute-rgt-neg-in 98.2%

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

      8. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

   if -5e8 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. associate-+r- 91.8%

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

      3. +-commutative 91.8%

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

      4. associate--l+ 91.8%

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

      5. sub-neg 91.8%

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

      6. remove-double-neg 91.8%

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

      7. distribute-frac-neg 91.8%

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

      8. distribute-neg-in 91.8%

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

      9. remove-double-neg 91.8%

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

      10. sub-neg 91.8%

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

      11. neg-mul-1 91.8%

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

      12. times-frac 98.4%

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

      13. distribute-frac-neg 98.4%

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

      14. neg-mul-1 98.4%

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

      15. *-commutative 98.4%

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

      16. associate-/l* 98.3%

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

      17. *-commutative 98.3%

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

   3. Simplified 98.3%

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

      1. metadata-eval 98.3%

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

      2. associate-/r* 98.3%

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

      3. *-commutative 98.3%

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

      4. associate-*l/ 98.4%

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

      5. *-un-lft-identity 98.4%

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

   6. Applied egg-rr 98.4%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -500000000:\\ \;\;\;\;\left(x + \frac{t}{z \cdot \left(3 \cdot y\right)}\right) + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 93.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1050000000 \lor \neg \left(y \leq 900000000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1050000000.0) (not (<= y 900000000000.0)))
   (- 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 <= -1050000000.0) || !(y <= 900000000000.0)) {
		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 <= (-1050000000.0d0)) .or. (.not. (y <= 900000000000.0d0))) 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 <= -1050000000.0) || !(y <= 900000000000.0)) {
		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 <= -1050000000.0) or not (y <= 900000000000.0):
		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 <= -1050000000.0) || !(y <= 900000000000.0))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1050000000.0) || ~((y <= 900000000000.0)))
		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, -1050000000.0], N[Not[LessEqual[y, 900000000000.0]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e9 or 9e11 < y

   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. +-commutative 98.1%

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

      2. associate-+r- 98.1%

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

      3. +-commutative 98.1%

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

      4. associate--l+ 98.1%

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

      5. sub-neg 98.1%

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

      6. remove-double-neg 98.1%

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

      7. distribute-frac-neg 98.1%

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

      8. distribute-neg-in 98.1%

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

      9. remove-double-neg 98.1%

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

      10. sub-neg 98.1%

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

      11. neg-mul-1 98.1%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   3. Simplified 99.6%

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

      1. metadata-eval 99.6%

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

      2. associate-/r* 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*l/ 99.8%

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

      5. *-un-lft-identity 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 94.0%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot y}}{z \cdot 3} \]
   8. Step-by-step derivation

      1. neg-mul-1 94.0%

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

   9. Simplified 94.0%

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

   if -1.05e9 < y < 9e11

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. associate-+r- 89.3%

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

      3. +-commutative 89.3%

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

      4. associate--l+ 89.3%

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

      5. sub-neg 89.3%

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

      6. remove-double-neg 89.3%

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

      7. distribute-frac-neg 89.3%

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

      8. distribute-neg-in 89.3%

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

      9. remove-double-neg 89.3%

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

      10. sub-neg 89.3%

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

      11. neg-mul-1 89.3%

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

      12. times-frac 93.8%

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

      13. distribute-frac-neg 93.8%

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

      14. neg-mul-1 93.8%

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

      15. *-commutative 93.8%

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

      16. associate-/l* 93.8%

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

      17. *-commutative 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around inf 89.9%

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

      1. *-commutative 89.9%

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

      2. associate-*l/ 92.8%

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

   7. Applied egg-rr 92.8%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1050000000 \lor \neg \left(y \leq 900000000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 90.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -850 \lor \neg \left(y \leq 410000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -850.0) (not (<= y 410000000.0)))
   (- x (/ y (* z 3.0)))
   (+ x (/ 0.3333333333333333 (* z (/ y t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -850.0) || !(y <= 410000000.0)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 / (z * (y / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-850.0d0)) .or. (.not. (y <= 410000000.0d0))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + (0.3333333333333333d0 / (z * (y / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -850.0) || !(y <= 410000000.0)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 / (z * (y / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -850.0) or not (y <= 410000000.0):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + (0.3333333333333333 / (z * (y / t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -850.0) || !(y <= 410000000.0))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(z * Float64(y / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -850.0) || ~((y <= 410000000.0)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + (0.3333333333333333 / (z * (y / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -850.0], N[Not[LessEqual[y, 410000000.0]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 / N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -850 or 4.1e8 < y

   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. +-commutative 98.1%

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

      2. associate-+r- 98.1%

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

      3. +-commutative 98.1%

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

      4. associate--l+ 98.1%

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

      5. sub-neg 98.1%

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

      6. remove-double-neg 98.1%

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

      7. distribute-frac-neg 98.1%

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

      8. distribute-neg-in 98.1%

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

      9. remove-double-neg 98.1%

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

      10. sub-neg 98.1%

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

      11. neg-mul-1 98.1%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   3. Simplified 99.6%

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

      1. metadata-eval 99.6%

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

      2. associate-/r* 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*l/ 99.8%

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

      5. *-un-lft-identity 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 94.0%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot y}}{z \cdot 3} \]
   8. Step-by-step derivation

      1. neg-mul-1 94.0%

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

   9. Simplified 94.0%

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

   if -850 < y < 4.1e8

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. associate-+r- 89.3%

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

      3. +-commutative 89.3%

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

      4. associate--l+ 89.3%

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

      5. sub-neg 89.3%

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

      6. remove-double-neg 89.3%

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

      7. distribute-frac-neg 89.3%

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

      8. distribute-neg-in 89.3%

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

      9. remove-double-neg 89.3%

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

      10. sub-neg 89.3%

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

      11. neg-mul-1 89.3%

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

      12. times-frac 93.8%

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

      13. distribute-frac-neg 93.8%

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

      14. neg-mul-1 93.8%

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

      15. *-commutative 93.8%

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

      16. associate-/l* 93.8%

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

      17. *-commutative 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around inf 89.9%

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

      1. *-commutative 89.9%

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

      2. clear-num 89.8%

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

      3. frac-times 91.4%

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

      4. metadata-eval 91.4%

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

   7. Applied egg-rr 91.4%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -850 \lor \neg \left(y \leq 410000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z \cdot \frac{y}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 89.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -28 \lor \neg \left(y \leq 42000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -28.0) (not (<= y 42000000.0)))
   (- 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 <= -28.0) || !(y <= 42000000.0)) {
		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 <= (-28.0d0)) .or. (.not. (y <= 42000000.0d0))) 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 <= -28.0) || !(y <= 42000000.0)) {
		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 <= -28.0) or not (y <= 42000000.0):
		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 <= -28.0) || !(y <= 42000000.0))
		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 <= -28.0) || ~((y <= 42000000.0)))
		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, -28.0], N[Not[LessEqual[y, 42000000.0]], $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 < -28 or 4.2e7 < y

   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. +-commutative 98.1%

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

      2. associate-+r- 98.1%

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

      3. +-commutative 98.1%

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

      4. associate--l+ 98.1%

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

      5. sub-neg 98.1%

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

      6. remove-double-neg 98.1%

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

      7. distribute-frac-neg 98.1%

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

      8. distribute-neg-in 98.1%

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

      9. remove-double-neg 98.1%

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

      10. sub-neg 98.1%

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

      11. neg-mul-1 98.1%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   3. Simplified 99.6%

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

      1. metadata-eval 99.6%

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

      2. associate-/r* 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*l/ 99.8%

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

      5. *-un-lft-identity 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 94.0%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot y}}{z \cdot 3} \]
   8. Step-by-step derivation

      1. neg-mul-1 94.0%

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

   9. Simplified 94.0%

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

   if -28 < y < 4.2e7

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. associate-+r- 89.3%

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

      3. +-commutative 89.3%

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

      4. associate--l+ 89.3%

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

      5. sub-neg 89.3%

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

      6. remove-double-neg 89.3%

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

      7. distribute-frac-neg 89.3%

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

      8. distribute-neg-in 89.3%

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

      9. remove-double-neg 89.3%

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

      10. sub-neg 89.3%

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

      11. neg-mul-1 89.3%

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

      12. times-frac 93.8%

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

      13. distribute-frac-neg 93.8%

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

      14. neg-mul-1 93.8%

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

      15. *-commutative 93.8%

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

      16. associate-/l* 93.8%

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

      17. *-commutative 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around inf 89.9%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -28 \lor \neg \left(y \leq 42000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 90.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -240000000000 \lor \neg \left(y \leq 14500000000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -240000000000.0) (not (<= y 14500000000000.0)))
   (- 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 <= -240000000000.0) || !(y <= 14500000000000.0)) {
		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 <= (-240000000000.0d0)) .or. (.not. (y <= 14500000000000.0d0))) 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 <= -240000000000.0) || !(y <= 14500000000000.0)) {
		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 <= -240000000000.0) or not (y <= 14500000000000.0):
		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 <= -240000000000.0) || !(y <= 14500000000000.0))
		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 <= -240000000000.0) || ~((y <= 14500000000000.0)))
		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, -240000000000.0], N[Not[LessEqual[y, 14500000000000.0]], $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 < -2.4e11 or 1.45e13 < y

   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. +-commutative 98.1%

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

      2. associate-+r- 98.1%

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

      3. +-commutative 98.1%

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

      4. associate--l+ 98.1%

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

      5. sub-neg 98.1%

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

      6. remove-double-neg 98.1%

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

      7. distribute-frac-neg 98.1%

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

      8. distribute-neg-in 98.1%

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

      9. remove-double-neg 98.1%

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

      10. sub-neg 98.1%

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

      11. neg-mul-1 98.1%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   3. Simplified 99.6%

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

      1. metadata-eval 99.6%

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

      2. associate-/r* 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*l/ 99.8%

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

      5. *-un-lft-identity 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 94.0%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot y}}{z \cdot 3} \]
   8. Step-by-step derivation

      1. neg-mul-1 94.0%

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

   9. Simplified 94.0%

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

   if -2.4e11 < y < 1.45e13

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. associate-+r- 89.3%

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

      3. +-commutative 89.3%

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

      4. associate--l+ 89.3%

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

      5. sub-neg 89.3%

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

      6. remove-double-neg 89.3%

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

      7. distribute-frac-neg 89.3%

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

      8. distribute-neg-in 89.3%

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

      9. remove-double-neg 89.3%

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

      10. sub-neg 89.3%

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

      11. neg-mul-1 89.3%

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

      12. times-frac 93.8%

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

      13. distribute-frac-neg 93.8%

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

      14. neg-mul-1 93.8%

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

      15. *-commutative 93.8%

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

      16. associate-/l* 93.8%

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

      17. *-commutative 93.8%

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

   3. Simplified 93.8%

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

   5. Taylor expanded in t around inf 85.2%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -240000000000 \lor \neg \left(y \leq 14500000000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 78.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+169}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+66}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -6.5e+169)
   (+ x (/ (* y -0.3333333333333333) z))
   (if (<= x 8.2e+66)
     (* (- (/ t y) y) (/ 0.3333333333333333 z))
     (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -6.5e+169) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (x <= 8.2e+66) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} 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 (x <= (-6.5d+169)) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else if (x <= 8.2d+66) then
        tmp = ((t / y) - y) * (0.3333333333333333d0 / z)
    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 (x <= -6.5e+169) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else if (x <= 8.2e+66) {
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -6.5e+169:
		tmp = x + ((y * -0.3333333333333333) / z)
	elif x <= 8.2e+66:
		tmp = ((t / y) - y) * (0.3333333333333333 / z)
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -6.5e+169)
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	elseif (x <= 8.2e+66)
		tmp = Float64(Float64(Float64(t / y) - y) * Float64(0.3333333333333333 / z));
	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 (x <= -6.5e+169)
		tmp = x + ((y * -0.3333333333333333) / z);
	elseif (x <= 8.2e+66)
		tmp = ((t / y) - y) * (0.3333333333333333 / z);
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -6.5e+169], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e+66], N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4999999999999995e169

   1. Initial program 93.1%

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

      1. +-commutative 93.1%

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

      2. associate-+r- 93.1%

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

      3. +-commutative 93.1%

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

      4. associate--l+ 93.1%

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

      5. sub-neg 93.1%

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

      6. remove-double-neg 93.1%

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

      7. distribute-frac-neg 93.1%

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

      8. distribute-neg-in 93.1%

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

      9. remove-double-neg 93.1%

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

      10. sub-neg 93.1%

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

      11. neg-mul-1 93.1%

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

      12. times-frac 93.2%

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

      13. distribute-frac-neg 93.2%

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

      14. neg-mul-1 93.2%

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

      15. *-commutative 93.2%

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

      16. associate-/l* 93.1%

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

      17. *-commutative 93.1%

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

   3. Simplified 93.1%

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

   5. Taylor expanded in t around 0 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-*l/ 89.5%

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

   7. Simplified 89.5%

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

   if -6.4999999999999995e169 < x < 8.19999999999999989e66

   1. Initial program 92.6%

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

      1. +-commutative 92.6%

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

      2. associate-+r- 92.6%

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

      3. sub-neg 92.6%

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

      4. associate-*l* 92.7%

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

      5. *-commutative 92.7%

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

      6. distribute-frac-neg2 92.7%

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

      7. distribute-rgt-neg-in 92.7%

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

      8. metadata-eval 92.7%

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

   3. Simplified 92.7%

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

   5. Taylor expanded in z around 0 84.8%

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

      1. *-un-lft-identity 84.8%

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

      2. *-commutative 84.8%

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

      3. *-commutative 84.8%

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

      4. fma-define 84.8%

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

      5. clear-num 84.8%

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

      6. un-div-inv 84.9%

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

   7. Applied egg-rr 84.9%

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

      1. *-rgt-identity 84.9%

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

      2. fma-undefine 84.9%

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

      3. +-commutative 84.9%

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

      4. associate-/r/ 84.8%

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

      5. metadata-eval 84.8%

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

      6. associate-*r/ 84.8%

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

      7. associate-*r/ 84.8%

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

      8. metadata-eval 84.8%

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

      9. associate-*l/ 84.8%

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

      10. associate-*r/ 84.8%

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

      11. *-commutative 84.8%

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

      12. metadata-eval 84.8%

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

      13. distribute-lft-neg-in 84.8%

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

      14. distribute-rgt-neg-in 84.8%

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

      15. distribute-lft-in 84.8%

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

      16. sub-neg 84.8%

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

   9. Simplified 84.8%

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

   10. Taylor expanded in t around 0 80.8%

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

       1. *-commutative 80.8%

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

       2. *-lft-identity 80.8%

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

       3. associate-*l/ 80.8%

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

       4. associate-*r* 80.8%

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

       5. *-commutative 80.8%

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

       6. associate-/r* 84.8%

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

       7. associate-*r/ 84.8%

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

       8. *-lft-identity 84.8%

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

       9. associate-*l/ 84.8%

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

       10. distribute-lft-in 84.8%

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

       11. +-commutative 84.8%

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

       12. metadata-eval 84.8%

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

       13. distribute-lft-neg-in 84.8%

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

       14. distribute-rgt-neg-out 84.8%

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

       15. distribute-lft-out 84.8%

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

       16. sub-neg 84.8%

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

       17. associate-*r* 84.8%

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

       18. associate-*l/ 84.9%

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

       19. metadata-eval 84.9%

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

   12. Simplified 84.9%

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

   if 8.19999999999999989e66 < x

   1. Initial program 95.5%

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

      1. +-commutative 95.5%

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

      2. associate-+r- 95.5%

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

      3. +-commutative 95.5%

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

      4. associate--l+ 95.5%

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

      5. sub-neg 95.5%

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

      6. remove-double-neg 95.5%

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

      7. distribute-frac-neg 95.5%

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

      8. distribute-neg-in 95.5%

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

      9. remove-double-neg 95.5%

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

      10. sub-neg 95.5%

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

      11. neg-mul-1 95.5%

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

      12. times-frac 97.8%

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

      13. distribute-frac-neg 97.8%

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

      14. neg-mul-1 97.8%

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

      15. *-commutative 97.8%

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

      16. associate-/l* 97.8%

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

      17. *-commutative 97.8%

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

   3. Simplified 97.7%

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

      1. metadata-eval 97.7%

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

      2. associate-/r* 97.8%

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

      3. *-commutative 97.8%

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

      4. associate-*l/ 97.9%

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

      5. *-un-lft-identity 97.9%

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

   6. Applied egg-rr 97.9%

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

   7. Taylor expanded in t around 0 80.2%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot y}}{z \cdot 3} \]
   8. Step-by-step derivation

      1. neg-mul-1 80.2%

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

   9. Simplified 80.2%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+169}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+66}:\\ \;\;\;\;\left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-152} \lor \neg \left(y \leq 2000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.4e-152) (not (<= y 2000000.0)))
   (- 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 <= -3.4e-152) || !(y <= 2000000.0)) {
		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 <= (-3.4d-152)) .or. (.not. (y <= 2000000.0d0))) 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 <= -3.4e-152) || !(y <= 2000000.0)) {
		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 <= -3.4e-152) or not (y <= 2000000.0):
		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 <= -3.4e-152) || !(y <= 2000000.0))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(0.3333333333333333 * Float64(t / z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.4e-152) || ~((y <= 2000000.0)))
		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, -3.4e-152], N[Not[LessEqual[y, 2000000.0]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.3333333333333333 * N[(t / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999984e-152 or 2e6 < y

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. associate-+r- 97.7%

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

      3. +-commutative 97.7%

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

      4. associate--l+ 97.7%

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

      5. sub-neg 97.7%

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

      6. remove-double-neg 97.7%

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

      7. distribute-frac-neg 97.7%

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

      8. distribute-neg-in 97.7%

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

      9. remove-double-neg 97.7%

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

      10. sub-neg 97.7%

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

      11. neg-mul-1 97.7%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   3. Simplified 99.6%

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

      1. metadata-eval 99.6%

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

      2. associate-/r* 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-*l/ 99.8%

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

      5. *-un-lft-identity 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 86.7%

      \[\leadsto x + \frac{\color{blue}{-1 \cdot y}}{z \cdot 3} \]
   8. Step-by-step derivation

      1. neg-mul-1 86.7%

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

   9. Simplified 86.7%

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

   if -3.39999999999999984e-152 < y < 2e6

   1. Initial program 87.8%

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

      1. +-commutative 87.8%

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

      2. associate-+r- 87.8%

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

      3. sub-neg 87.8%

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

      4. associate-*l* 87.8%

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

      5. *-commutative 87.8%

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

      6. distribute-frac-neg2 87.8%

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

      7. distribute-rgt-neg-in 87.8%

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

      8. metadata-eval 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around 0 69.3%

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

   6. Taylor expanded in y around 0 66.0%

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

      1. associate-*r/ 66.0%

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

   8. Simplified 66.0%

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

      1. div-inv 65.9%

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

      2. associate-/l* 66.0%

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

      3. associate-*l* 66.0%

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

      4. metadata-eval 66.0%

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

      5. div-inv 66.1%

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

      6. times-frac 66.2%

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

      7. *-un-lft-identity 66.2%

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

      8. associate-/l/ 66.2%

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

      9. div-inv 66.1%

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

      10. metadata-eval 66.1%

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

      11. associate-/l/ 62.8%

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

   10. Applied egg-rr 62.8%

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

       1. associate-/r* 69.8%

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

       2. associate-*l/ 69.9%

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

   12. Applied egg-rr 69.9%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-152} \lor \neg \left(y \leq 2000000\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-152} \lor \neg \left(y \leq 2000000\right):\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.1e-152) (not (<= y 2000000.0)))
   (+ x (* -0.3333333333333333 (/ y z)))
   (* (/ t z) (/ 0.3333333333333333 y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e-152) || !(y <= 2000000.0)) {
		tmp = x + (-0.3333333333333333 * (y / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-3.1d-152)) .or. (.not. (y <= 2000000.0d0))) then
        tmp = x + ((-0.3333333333333333d0) * (y / z))
    else
        tmp = (t / z) * (0.3333333333333333d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.1e-152) || !(y <= 2000000.0)) {
		tmp = x + (-0.3333333333333333 * (y / z));
	} else {
		tmp = (t / z) * (0.3333333333333333 / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.1e-152) or not (y <= 2000000.0):
		tmp = x + (-0.3333333333333333 * (y / z))
	else:
		tmp = (t / z) * (0.3333333333333333 / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.1e-152) || !(y <= 2000000.0))
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(y / z)));
	else
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.1e-152) || ~((y <= 2000000.0)))
		tmp = x + (-0.3333333333333333 * (y / z));
	else
		tmp = (t / z) * (0.3333333333333333 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.1e-152], N[Not[LessEqual[y, 2000000.0]], $MachinePrecision]], N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999998e-152 or 2e6 < y

   1. Initial program 97.7%

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

      1. +-commutative 97.7%

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

      2. associate-+r- 97.7%

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

      3. +-commutative 97.7%

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

      4. associate--l+ 97.7%

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

      5. sub-neg 97.7%

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

      6. remove-double-neg 97.7%

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

      7. distribute-frac-neg 97.7%

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

      8. distribute-neg-in 97.7%

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

      9. remove-double-neg 97.7%

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

      10. sub-neg 97.7%

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

      11. neg-mul-1 97.7%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around 0 86.5%

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

   if -3.0999999999999998e-152 < y < 2e6

   1. Initial program 87.8%

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

      1. +-commutative 87.8%

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

      2. associate-+r- 87.8%

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

      3. sub-neg 87.8%

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

      4. associate-*l* 87.8%

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

      5. *-commutative 87.8%

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

      6. distribute-frac-neg2 87.8%

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

      7. distribute-rgt-neg-in 87.8%

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

      8. metadata-eval 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around 0 69.3%

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

   6. Taylor expanded in y around 0 66.0%

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

      1. associate-*r/ 66.0%

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

   8. Simplified 66.0%

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

      1. associate-/l/ 62.9%

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

      2. *-commutative 62.9%

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

      3. times-frac 69.8%

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

   10. Applied egg-rr 69.8%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-152} \lor \neg \left(y \leq 2000000\right):\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-152}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2000000:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e-152)
   (+ x (* -0.3333333333333333 (/ y z)))
   (if (<= y 2000000.0)
     (/ (* 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 <= -3.4e-152) {
		tmp = x + (-0.3333333333333333 * (y / z));
	} else if (y <= 2000000.0) {
		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 <= (-3.4d-152)) then
        tmp = x + ((-0.3333333333333333d0) * (y / z))
    else if (y <= 2000000.0d0) 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 <= -3.4e-152) {
		tmp = x + (-0.3333333333333333 * (y / z));
	} else if (y <= 2000000.0) {
		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 <= -3.4e-152:
		tmp = x + (-0.3333333333333333 * (y / z))
	elif y <= 2000000.0:
		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 <= -3.4e-152)
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(y / z)));
	elseif (y <= 2000000.0)
		tmp = Float64(Float64(0.3333333333333333 * Float64(t / z)) / y);
	else
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e-152)
		tmp = x + (-0.3333333333333333 * (y / z));
	elseif (y <= 2000000.0)
		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, -3.4e-152], N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2000000.0], N[(N[(0.3333333333333333 * N[(t / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.39999999999999984e-152

   1. Initial program 96.5%

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

      1. +-commutative 96.5%

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

      2. associate-+r- 96.5%

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

      3. +-commutative 96.5%

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

      4. associate--l+ 96.5%

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

      5. sub-neg 96.5%

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

      6. remove-double-neg 96.5%

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

      7. distribute-frac-neg 96.5%

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

      8. distribute-neg-in 96.5%

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

      9. remove-double-neg 96.5%

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

      10. sub-neg 96.5%

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

      11. neg-mul-1 96.5%

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

      12. times-frac 99.7%

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

      13. distribute-frac-neg 99.7%

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

      14. neg-mul-1 99.7%

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

      15. *-commutative 99.7%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 80.5%

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

   if -3.39999999999999984e-152 < y < 2e6

   1. Initial program 87.8%

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

      1. +-commutative 87.8%

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

      2. associate-+r- 87.8%

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

      3. sub-neg 87.8%

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

      4. associate-*l* 87.8%

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

      5. *-commutative 87.8%

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

      6. distribute-frac-neg2 87.8%

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

      7. distribute-rgt-neg-in 87.8%

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

      8. metadata-eval 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around 0 69.3%

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

   6. Taylor expanded in y around 0 66.0%

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

      1. associate-*r/ 66.0%

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

   8. Simplified 66.0%

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

      1. div-inv 65.9%

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

      2. associate-/l* 66.0%

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

      3. associate-*l* 66.0%

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

      4. metadata-eval 66.0%

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

      5. div-inv 66.1%

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

      6. times-frac 66.2%

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

      7. *-un-lft-identity 66.2%

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

      8. associate-/l/ 66.2%

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

      9. div-inv 66.1%

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

      10. metadata-eval 66.1%

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

      11. associate-/l/ 62.8%

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

   10. Applied egg-rr 62.8%

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

       1. associate-/r* 69.8%

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

       2. associate-*l/ 69.9%

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

   12. Applied egg-rr 69.9%

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

   if 2e6 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. remove-double-neg 99.8%

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

      7. distribute-frac-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. sub-neg 99.8%

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

      11. neg-mul-1 99.8%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.6%

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

      17. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around 0 97.0%

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

      1. *-commutative 97.0%

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

      2. associate-*l/ 97.2%

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

   7. Simplified 97.2%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-152}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2000000:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 77.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-152}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 12500000000:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e-152)
   (+ x (* -0.3333333333333333 (/ y z)))
   (if (<= y 12500000000.0)
     (* (/ t z) (/ 0.3333333333333333 y))
     (+ x (/ (* y -0.3333333333333333) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-152) {
		tmp = x + (-0.3333333333333333 * (y / z));
	} else if (y <= 12500000000.0) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + ((y * -0.3333333333333333) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.4d-152)) then
        tmp = x + ((-0.3333333333333333d0) * (y / z))
    else if (y <= 12500000000.0d0) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-152) {
		tmp = x + (-0.3333333333333333 * (y / z));
	} else if (y <= 12500000000.0) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + ((y * -0.3333333333333333) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e-152:
		tmp = x + (-0.3333333333333333 * (y / z))
	elif y <= 12500000000.0:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = x + ((y * -0.3333333333333333) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e-152)
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(y / z)));
	elseif (y <= 12500000000.0)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e-152)
		tmp = x + (-0.3333333333333333 * (y / z));
	elseif (y <= 12500000000.0)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = x + ((y * -0.3333333333333333) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e-152], N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 12500000000.0], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.39999999999999984e-152

   1. Initial program 96.5%

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

      1. +-commutative 96.5%

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

      2. associate-+r- 96.5%

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

      3. +-commutative 96.5%

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

      4. associate--l+ 96.5%

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

      5. sub-neg 96.5%

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

      6. remove-double-neg 96.5%

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

      7. distribute-frac-neg 96.5%

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

      8. distribute-neg-in 96.5%

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

      9. remove-double-neg 96.5%

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

      10. sub-neg 96.5%

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

      11. neg-mul-1 96.5%

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

      12. times-frac 99.7%

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

      13. distribute-frac-neg 99.7%

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

      14. neg-mul-1 99.7%

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

      15. *-commutative 99.7%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 80.5%

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

   if -3.39999999999999984e-152 < y < 1.25e10

   1. Initial program 87.8%

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

      1. +-commutative 87.8%

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

      2. associate-+r- 87.8%

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

      3. sub-neg 87.8%

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

      4. associate-*l* 87.8%

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

      5. *-commutative 87.8%

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

      6. distribute-frac-neg2 87.8%

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

      7. distribute-rgt-neg-in 87.8%

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

      8. metadata-eval 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around 0 69.3%

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

   6. Taylor expanded in y around 0 66.0%

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

      1. associate-*r/ 66.0%

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

   8. Simplified 66.0%

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

      1. associate-/l/ 62.9%

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

      2. *-commutative 62.9%

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

      3. times-frac 69.8%

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

   10. Applied egg-rr 69.8%

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

   if 1.25e10 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. remove-double-neg 99.8%

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

      7. distribute-frac-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. sub-neg 99.8%

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

      11. neg-mul-1 99.8%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.6%

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

      17. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around 0 97.0%

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

      1. *-commutative 97.0%

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

      2. associate-*l/ 97.2%

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

   7. Simplified 97.2%

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

Alternative 12: 77.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{-152}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 2000000:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -3.4e-152)
   (+ x (* -0.3333333333333333 (/ y z)))
   (if (<= y 2000000.0)
     (* (/ t z) (/ 0.3333333333333333 y))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-152) {
		tmp = x + (-0.3333333333333333 * (y / z));
	} else if (y <= 2000000.0) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-3.4d-152)) then
        tmp = x + ((-0.3333333333333333d0) * (y / z))
    else if (y <= 2000000.0d0) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -3.4e-152) {
		tmp = x + (-0.3333333333333333 * (y / z));
	} else if (y <= 2000000.0) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -3.4e-152:
		tmp = x + (-0.3333333333333333 * (y / z))
	elif y <= 2000000.0:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -3.4e-152)
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(y / z)));
	elseif (y <= 2000000.0)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -3.4e-152)
		tmp = x + (-0.3333333333333333 * (y / z));
	elseif (y <= 2000000.0)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -3.4e-152], N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2000000.0], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.39999999999999984e-152

   1. Initial program 96.5%

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

      1. +-commutative 96.5%

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

      2. associate-+r- 96.5%

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

      3. +-commutative 96.5%

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

      4. associate--l+ 96.5%

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

      5. sub-neg 96.5%

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

      6. remove-double-neg 96.5%

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

      7. distribute-frac-neg 96.5%

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

      8. distribute-neg-in 96.5%

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

      9. remove-double-neg 96.5%

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

      10. sub-neg 96.5%

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

      11. neg-mul-1 96.5%

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

      12. times-frac 99.7%

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

      13. distribute-frac-neg 99.7%

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

      14. neg-mul-1 99.7%

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

      15. *-commutative 99.7%

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

      16. associate-/l* 99.7%

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

      17. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 80.5%

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

   if -3.39999999999999984e-152 < y < 2e6

   1. Initial program 87.8%

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

      1. +-commutative 87.8%

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

      2. associate-+r- 87.8%

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

      3. sub-neg 87.8%

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

      4. associate-*l* 87.8%

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

      5. *-commutative 87.8%

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

      6. distribute-frac-neg2 87.8%

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

      7. distribute-rgt-neg-in 87.8%

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

      8. metadata-eval 87.8%

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

   3. Simplified 87.8%

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

   5. Taylor expanded in z around 0 69.3%

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

   6. Taylor expanded in y around 0 66.0%

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

      1. associate-*r/ 66.0%

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

   8. Simplified 66.0%

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

      1. associate-/l/ 62.9%

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

      2. *-commutative 62.9%

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

      3. times-frac 69.8%

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

   10. Applied egg-rr 69.8%

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

   if 2e6 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. sub-neg 99.8%

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

      6. remove-double-neg 99.8%

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

      7. distribute-frac-neg 99.8%

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

      8. distribute-neg-in 99.8%

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

      9. remove-double-neg 99.8%

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

      10. sub-neg 99.8%

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

      11. neg-mul-1 99.8%

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

      12. times-frac 99.8%

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

      13. distribute-frac-neg 99.8%

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

      14. neg-mul-1 99.8%

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

      15. *-commutative 99.8%

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

      16. associate-/l* 99.6%

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

      17. *-commutative 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in t around 0 97.0%

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

      1. metadata-eval 97.0%

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

      2. distribute-lft-neg-in 97.0%

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

      3. associate-*r/ 97.2%

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

      4. associate-*l/ 97.0%

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

      5. *-commutative 97.0%

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

      6. distribute-rgt-neg-in 97.0%

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

      7. distribute-neg-frac 97.0%

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

      8. metadata-eval 97.0%

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

   7. Simplified 97.0%

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

Alternative 13: 63.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+16}:\\ \;\;\;\;-0.3333333333333333 \cdot \left(y \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;y \leq 460000000:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.3e+16)
   (* -0.3333333333333333 (* y (/ 1.0 z)))
   (if (<= y 460000000.0)
     (* (/ t z) (/ 0.3333333333333333 y))
     (/ (* y -0.3333333333333333) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.3e+16) {
		tmp = -0.3333333333333333 * (y * (1.0 / z));
	} else if (y <= 460000000.0) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} 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 <= (-1.3d+16)) then
        tmp = (-0.3333333333333333d0) * (y * (1.0d0 / z))
    else if (y <= 460000000.0d0) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    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 <= -1.3e+16) {
		tmp = -0.3333333333333333 * (y * (1.0 / z));
	} else if (y <= 460000000.0) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = (y * -0.3333333333333333) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.3e+16:
		tmp = -0.3333333333333333 * (y * (1.0 / z))
	elif y <= 460000000.0:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = (y * -0.3333333333333333) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.3e+16)
		tmp = Float64(-0.3333333333333333 * Float64(y * Float64(1.0 / z)));
	elseif (y <= 460000000.0)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.3e+16)
		tmp = -0.3333333333333333 * (y * (1.0 / z));
	elseif (y <= 460000000.0)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = (y * -0.3333333333333333) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.3e+16], N[(-0.3333333333333333 * N[(y * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 460000000.0], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3e16

   1. Initial program 96.7%

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

      1. +-commutative 96.7%

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

      2. associate-+r- 96.7%

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

      3. sub-neg 96.7%

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

      4. associate-*l* 96.7%

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

      5. *-commutative 96.7%

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

      6. distribute-frac-neg2 96.7%

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

      7. distribute-rgt-neg-in 96.7%

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

      8. metadata-eval 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around 0 77.2%

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

      1. *-un-lft-identity 77.2%

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

      2. *-commutative 77.2%

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

      3. *-commutative 77.2%

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

      4. fma-define 77.2%

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

      5. clear-num 77.2%

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

      6. un-div-inv 77.2%

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

   7. Applied egg-rr 77.2%

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

      1. *-rgt-identity 77.2%

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

      2. fma-undefine 77.2%

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

      3. +-commutative 77.2%

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

      4. associate-/r/ 77.2%

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

      5. metadata-eval 77.2%

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

      6. associate-*r/ 77.1%

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

      7. associate-*r/ 77.2%

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

      8. metadata-eval 77.2%

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

      9. associate-*l/ 77.2%

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

      10. associate-*r/ 77.2%

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

      11. *-commutative 77.2%

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

      12. metadata-eval 77.2%

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

      13. distribute-lft-neg-in 77.2%

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

      14. distribute-rgt-neg-in 77.2%

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

      15. distribute-lft-in 77.1%

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

      16. sub-neg 77.1%

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

   9. Simplified 77.1%

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

   10. Taylor expanded in t around 0 68.7%

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

       1. div-inv 68.7%

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

   12. Applied egg-rr 68.7%

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

   if -1.3e16 < y < 4.6e8

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. associate-+r- 89.3%

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

      3. sub-neg 89.3%

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

      4. associate-*l* 89.3%

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

      5. *-commutative 89.3%

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

      6. distribute-frac-neg2 89.3%

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

      7. distribute-rgt-neg-in 89.3%

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

      8. metadata-eval 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around 0 66.6%

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

   6. Taylor expanded in y around 0 62.6%

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

      1. associate-*r/ 62.6%

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

   8. Simplified 62.6%

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

      1. associate-/l/ 60.0%

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

      2. *-commutative 60.0%

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

      3. times-frac 65.1%

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

   10. Applied egg-rr 65.1%

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

   if 4.6e8 < y

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. sub-neg 99.8%

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

      4. associate-*l* 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-frac-neg2 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around 0 72.9%

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

      1. *-un-lft-identity 72.9%

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

      2. *-commutative 72.9%

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

      3. *-commutative 72.9%

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

      4. fma-define 72.9%

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

      5. clear-num 72.9%

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

      6. un-div-inv 72.9%

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

   7. Applied egg-rr 72.9%

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

      1. *-rgt-identity 72.9%

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

      2. fma-undefine 72.9%

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

      3. +-commutative 72.9%

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

      4. associate-/r/ 72.9%

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

      5. metadata-eval 72.9%

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

      6. associate-*r/ 72.9%

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

      7. associate-*r/ 72.9%

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

      8. metadata-eval 72.9%

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

      9. associate-*l/ 72.9%

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

      10. associate-*r/ 72.9%

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

      11. *-commutative 72.9%

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

      12. metadata-eval 72.9%

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

      13. distribute-lft-neg-in 72.9%

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

      14. distribute-rgt-neg-in 72.9%

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

      15. distribute-lft-in 72.9%

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

      16. sub-neg 72.9%

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

   9. Simplified 72.9%

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

   10. Taylor expanded in t around 0 70.3%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{+16}:\\ \;\;\;\;-0.3333333333333333 \cdot \left(y \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;y \leq 460000000:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -114:\\ \;\;\;\;-0.3333333333333333 \cdot \left(y \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;y \leq 6000000:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -114.0)
   (* -0.3333333333333333 (* y (/ 1.0 z)))
   (if (<= y 6000000.0)
     (* (/ t y) (/ 0.3333333333333333 z))
     (/ (* y -0.3333333333333333) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -114.0) {
		tmp = -0.3333333333333333 * (y * (1.0 / z));
	} else if (y <= 6000000.0) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} 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 <= (-114.0d0)) then
        tmp = (-0.3333333333333333d0) * (y * (1.0d0 / z))
    else if (y <= 6000000.0d0) then
        tmp = (t / y) * (0.3333333333333333d0 / z)
    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 <= -114.0) {
		tmp = -0.3333333333333333 * (y * (1.0 / z));
	} else if (y <= 6000000.0) {
		tmp = (t / y) * (0.3333333333333333 / z);
	} else {
		tmp = (y * -0.3333333333333333) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -114.0:
		tmp = -0.3333333333333333 * (y * (1.0 / z))
	elif y <= 6000000.0:
		tmp = (t / y) * (0.3333333333333333 / z)
	else:
		tmp = (y * -0.3333333333333333) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -114.0)
		tmp = Float64(-0.3333333333333333 * Float64(y * Float64(1.0 / z)));
	elseif (y <= 6000000.0)
		tmp = Float64(Float64(t / y) * Float64(0.3333333333333333 / z));
	else
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -114.0)
		tmp = -0.3333333333333333 * (y * (1.0 / z));
	elseif (y <= 6000000.0)
		tmp = (t / y) * (0.3333333333333333 / z);
	else
		tmp = (y * -0.3333333333333333) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -114.0], N[(-0.3333333333333333 * N[(y * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6000000.0], N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -114

   1. Initial program 96.7%

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

      1. +-commutative 96.7%

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

      2. associate-+r- 96.7%

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

      3. sub-neg 96.7%

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

      4. associate-*l* 96.7%

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

      5. *-commutative 96.7%

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

      6. distribute-frac-neg2 96.7%

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

      7. distribute-rgt-neg-in 96.7%

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

      8. metadata-eval 96.7%

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

   3. Simplified 96.7%

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

   5. Taylor expanded in z around 0 77.2%

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

      1. *-un-lft-identity 77.2%

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

      2. *-commutative 77.2%

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

      3. *-commutative 77.2%

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

      4. fma-define 77.2%

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

      5. clear-num 77.2%

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

      6. un-div-inv 77.2%

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

   7. Applied egg-rr 77.2%

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

      1. *-rgt-identity 77.2%

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

      2. fma-undefine 77.2%

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

      3. +-commutative 77.2%

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

      4. associate-/r/ 77.2%

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

      5. metadata-eval 77.2%

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

      6. associate-*r/ 77.1%

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

      7. associate-*r/ 77.2%

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

      8. metadata-eval 77.2%

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

      9. associate-*l/ 77.2%

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

      10. associate-*r/ 77.2%

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

      11. *-commutative 77.2%

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

      12. metadata-eval 77.2%

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

      13. distribute-lft-neg-in 77.2%

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

      14. distribute-rgt-neg-in 77.2%

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

      15. distribute-lft-in 77.1%

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

      16. sub-neg 77.1%

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

   9. Simplified 77.1%

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

   10. Taylor expanded in t around 0 68.7%

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

       1. div-inv 68.7%

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

   12. Applied egg-rr 68.7%

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

   if -114 < y < 6e6

   1. Initial program 89.3%

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

      1. +-commutative 89.3%

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

      2. associate-+r- 89.3%

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

      3. sub-neg 89.3%

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

      4. associate-*l* 89.3%

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

      5. *-commutative 89.3%

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

      6. distribute-frac-neg2 89.3%

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

      7. distribute-rgt-neg-in 89.3%

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

      8. metadata-eval 89.3%

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

   3. Simplified 89.3%

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

   5. Taylor expanded in z around 0 66.6%

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

   6. Taylor expanded in y around 0 62.6%

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

      1. associate-*r/ 62.6%

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

   8. Simplified 62.6%

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

      1. associate-/l/ 60.0%

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

      2. times-frac 62.7%

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

   10. Applied egg-rr 62.7%

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

   if 6e6 < y

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

      2. associate-+r- 99.8%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

      3. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) + \left(-\frac{y}{z \cdot 3}\right)} \]

      4. associate-*l* 99.8%

         \[\leadsto \left(\frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      5. *-commutative 99.8%

         \[\leadsto \left(\frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      6. distribute-frac-neg2 99.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \color{blue}{\frac{y}{-z \cdot 3}} \]

      7. distribute-rgt-neg-in 99.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{\color{blue}{z \cdot \left(-3\right)}} \]

      8. metadata-eval 99.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot \color{blue}{-3}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot -3}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 72.9%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}}{z}} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 72.9%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right)}}{z} \]

      2. *-commutative 72.9%

         \[\leadsto \frac{\color{blue}{\left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}}{z} \]

      3. *-commutative 72.9%

         \[\leadsto \frac{\left(\color{blue}{y \cdot -0.3333333333333333} + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}{z} \]

      4. fma-define 72.9%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \frac{t}{y}\right)} \cdot 1}{z} \]

      5. clear-num 72.9%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \color{blue}{\frac{1}{\frac{y}{t}}}\right) \cdot 1}{z} \]

      6. un-div-inv 72.9%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, \color{blue}{\frac{0.3333333333333333}{\frac{y}{t}}}\right) \cdot 1}{z} \]

   7. Applied egg-rr 72.9%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right) \cdot 1}}{z} \]
   8. Step-by-step derivation

      1. *-rgt-identity 72.9%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right)}}{z} \]

      2. fma-undefine 72.9%

         \[\leadsto \frac{\color{blue}{y \cdot -0.3333333333333333 + \frac{0.3333333333333333}{\frac{y}{t}}}}{z} \]

      3. +-commutative 72.9%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{\frac{y}{t}} + y \cdot -0.3333333333333333}}{z} \]

      4. associate-/r/ 72.9%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{y} \cdot t} + y \cdot -0.3333333333333333}{z} \]

      5. metadata-eval 72.9%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333 \cdot 1}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      6. associate-*r/ 72.9%

         \[\leadsto \frac{\color{blue}{\left(0.3333333333333333 \cdot \frac{1}{y}\right)} \cdot t + y \cdot -0.3333333333333333}{z} \]

      7. associate-*r/ 72.9%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot 1}{y}} \cdot t + y \cdot -0.3333333333333333}{z} \]

      8. metadata-eval 72.9%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      9. associate-*l/ 72.9%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot t}{y}} + y \cdot -0.3333333333333333}{z} \]

      10. associate-*r/ 72.9%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \frac{t}{y}} + y \cdot -0.3333333333333333}{z} \]

      11. *-commutative 72.9%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{-0.3333333333333333 \cdot y}}{z} \]

      12. metadata-eval 72.9%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333\right)} \cdot y}{z} \]

      13. distribute-lft-neg-in 72.9%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333 \cdot y\right)}}{z} \]

      14. distribute-rgt-neg-in 72.9%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{0.3333333333333333 \cdot \left(-y\right)}}{z} \]

      15. distribute-lft-in 72.9%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} + \left(-y\right)\right)}}{z} \]

      16. sub-neg 72.9%

          \[\leadsto \frac{0.3333333333333333 \cdot \color{blue}{\left(\frac{t}{y} - y\right)}}{z} \]

   9. Simplified 72.9%

      \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}}{z} \]

   10. Taylor expanded in t around 0 70.3%

       \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot y}}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -114:\\ \;\;\;\;-0.3333333333333333 \cdot \left(y \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;y \leq 6000000:\\ \;\;\;\;\frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 61.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -180:\\ \;\;\;\;-0.3333333333333333 \cdot \left(y \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;y \leq 5400000:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -180.0)
   (* -0.3333333333333333 (* y (/ 1.0 z)))
   (if (<= y 5400000.0)
     (* t (/ (/ 0.3333333333333333 z) y))
     (/ (* y -0.3333333333333333) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -180.0) {
		tmp = -0.3333333333333333 * (y * (1.0 / z));
	} else if (y <= 5400000.0) {
		tmp = t * ((0.3333333333333333 / z) / y);
	} 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 <= (-180.0d0)) then
        tmp = (-0.3333333333333333d0) * (y * (1.0d0 / z))
    else if (y <= 5400000.0d0) then
        tmp = t * ((0.3333333333333333d0 / z) / y)
    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 <= -180.0) {
		tmp = -0.3333333333333333 * (y * (1.0 / z));
	} else if (y <= 5400000.0) {
		tmp = t * ((0.3333333333333333 / z) / y);
	} else {
		tmp = (y * -0.3333333333333333) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -180.0:
		tmp = -0.3333333333333333 * (y * (1.0 / z))
	elif y <= 5400000.0:
		tmp = t * ((0.3333333333333333 / z) / y)
	else:
		tmp = (y * -0.3333333333333333) / z
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -180.0)
		tmp = Float64(-0.3333333333333333 * Float64(y * Float64(1.0 / z)));
	elseif (y <= 5400000.0)
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / z) / y));
	else
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -180.0)
		tmp = -0.3333333333333333 * (y * (1.0 / z));
	elseif (y <= 5400000.0)
		tmp = t * ((0.3333333333333333 / z) / y);
	else
		tmp = (y * -0.3333333333333333) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -180.0], N[(-0.3333333333333333 * N[(y * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5400000.0], N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -180

   1. Initial program 96.7%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. +-commutative 96.7%

         \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

      2. associate-+r- 96.7%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

      3. sub-neg 96.7%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) + \left(-\frac{y}{z \cdot 3}\right)} \]

      4. associate-*l* 96.7%

         \[\leadsto \left(\frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      5. *-commutative 96.7%

         \[\leadsto \left(\frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      6. distribute-frac-neg2 96.7%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \color{blue}{\frac{y}{-z \cdot 3}} \]

      7. distribute-rgt-neg-in 96.7%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{\color{blue}{z \cdot \left(-3\right)}} \]

      8. metadata-eval 96.7%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot \color{blue}{-3}} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{\left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot -3}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 77.2%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}}{z}} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 77.2%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right)}}{z} \]

      2. *-commutative 77.2%

         \[\leadsto \frac{\color{blue}{\left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}}{z} \]

      3. *-commutative 77.2%

         \[\leadsto \frac{\left(\color{blue}{y \cdot -0.3333333333333333} + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}{z} \]

      4. fma-define 77.2%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \frac{t}{y}\right)} \cdot 1}{z} \]

      5. clear-num 77.2%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \color{blue}{\frac{1}{\frac{y}{t}}}\right) \cdot 1}{z} \]

      6. un-div-inv 77.2%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, \color{blue}{\frac{0.3333333333333333}{\frac{y}{t}}}\right) \cdot 1}{z} \]

   7. Applied egg-rr 77.2%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right) \cdot 1}}{z} \]
   8. Step-by-step derivation

      1. *-rgt-identity 77.2%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right)}}{z} \]

      2. fma-undefine 77.2%

         \[\leadsto \frac{\color{blue}{y \cdot -0.3333333333333333 + \frac{0.3333333333333333}{\frac{y}{t}}}}{z} \]

      3. +-commutative 77.2%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{\frac{y}{t}} + y \cdot -0.3333333333333333}}{z} \]

      4. associate-/r/ 77.2%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{y} \cdot t} + y \cdot -0.3333333333333333}{z} \]

      5. metadata-eval 77.2%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333 \cdot 1}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      6. associate-*r/ 77.1%

         \[\leadsto \frac{\color{blue}{\left(0.3333333333333333 \cdot \frac{1}{y}\right)} \cdot t + y \cdot -0.3333333333333333}{z} \]

      7. associate-*r/ 77.2%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot 1}{y}} \cdot t + y \cdot -0.3333333333333333}{z} \]

      8. metadata-eval 77.2%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      9. associate-*l/ 77.2%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot t}{y}} + y \cdot -0.3333333333333333}{z} \]

      10. associate-*r/ 77.2%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \frac{t}{y}} + y \cdot -0.3333333333333333}{z} \]

      11. *-commutative 77.2%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{-0.3333333333333333 \cdot y}}{z} \]

      12. metadata-eval 77.2%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333\right)} \cdot y}{z} \]

      13. distribute-lft-neg-in 77.2%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333 \cdot y\right)}}{z} \]

      14. distribute-rgt-neg-in 77.2%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{0.3333333333333333 \cdot \left(-y\right)}}{z} \]

      15. distribute-lft-in 77.1%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} + \left(-y\right)\right)}}{z} \]

      16. sub-neg 77.1%

          \[\leadsto \frac{0.3333333333333333 \cdot \color{blue}{\left(\frac{t}{y} - y\right)}}{z} \]

   9. Simplified 77.1%

      \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}}{z} \]

   10. Taylor expanded in t around 0 68.7%

       \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   11. Step-by-step derivation

       1. div-inv 68.7%

          \[\leadsto -0.3333333333333333 \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)} \]

   12. Applied egg-rr 68.7%

       \[\leadsto -0.3333333333333333 \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)} \]

   if -180 < y < 5.4e6

   1. Initial program 89.3%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. +-commutative 89.3%

         \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

      2. associate-+r- 89.3%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

      3. sub-neg 89.3%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) + \left(-\frac{y}{z \cdot 3}\right)} \]

      4. associate-*l* 89.3%

         \[\leadsto \left(\frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      5. *-commutative 89.3%

         \[\leadsto \left(\frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      6. distribute-frac-neg2 89.3%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \color{blue}{\frac{y}{-z \cdot 3}} \]

      7. distribute-rgt-neg-in 89.3%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{\color{blue}{z \cdot \left(-3\right)}} \]

      8. metadata-eval 89.3%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot \color{blue}{-3}} \]

   3. Simplified 89.3%

      \[\leadsto \color{blue}{\left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot -3}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 66.6%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}}{z}} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 66.6%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right)}}{z} \]

      2. *-commutative 66.6%

         \[\leadsto \frac{\color{blue}{\left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}}{z} \]

      3. *-commutative 66.6%

         \[\leadsto \frac{\left(\color{blue}{y \cdot -0.3333333333333333} + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}{z} \]

      4. fma-define 66.6%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \frac{t}{y}\right)} \cdot 1}{z} \]

      5. clear-num 66.6%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \color{blue}{\frac{1}{\frac{y}{t}}}\right) \cdot 1}{z} \]

      6. un-div-inv 66.7%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, \color{blue}{\frac{0.3333333333333333}{\frac{y}{t}}}\right) \cdot 1}{z} \]

   7. Applied egg-rr 66.7%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right) \cdot 1}}{z} \]
   8. Step-by-step derivation

      1. *-rgt-identity 66.7%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right)}}{z} \]

      2. fma-undefine 66.7%

         \[\leadsto \frac{\color{blue}{y \cdot -0.3333333333333333 + \frac{0.3333333333333333}{\frac{y}{t}}}}{z} \]

      3. +-commutative 66.7%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{\frac{y}{t}} + y \cdot -0.3333333333333333}}{z} \]

      4. associate-/r/ 66.6%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{y} \cdot t} + y \cdot -0.3333333333333333}{z} \]

      5. metadata-eval 66.6%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333 \cdot 1}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      6. associate-*r/ 66.6%

         \[\leadsto \frac{\color{blue}{\left(0.3333333333333333 \cdot \frac{1}{y}\right)} \cdot t + y \cdot -0.3333333333333333}{z} \]

      7. associate-*r/ 66.6%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot 1}{y}} \cdot t + y \cdot -0.3333333333333333}{z} \]

      8. metadata-eval 66.6%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      9. associate-*l/ 66.6%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot t}{y}} + y \cdot -0.3333333333333333}{z} \]

      10. associate-*r/ 66.6%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \frac{t}{y}} + y \cdot -0.3333333333333333}{z} \]

      11. *-commutative 66.6%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{-0.3333333333333333 \cdot y}}{z} \]

      12. metadata-eval 66.6%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333\right)} \cdot y}{z} \]

      13. distribute-lft-neg-in 66.6%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333 \cdot y\right)}}{z} \]

      14. distribute-rgt-neg-in 66.6%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{0.3333333333333333 \cdot \left(-y\right)}}{z} \]

      15. distribute-lft-in 66.6%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} + \left(-y\right)\right)}}{z} \]

      16. sub-neg 66.6%

          \[\leadsto \frac{0.3333333333333333 \cdot \color{blue}{\left(\frac{t}{y} - y\right)}}{z} \]

   9. Simplified 66.6%

      \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}}{z} \]

   10. Taylor expanded in t around 0 64.0%

       \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z} + 0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   11. Step-by-step derivation

       1. *-commutative 64.0%

          \[\leadsto \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} + 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]

       2. *-lft-identity 64.0%

          \[\leadsto \frac{\color{blue}{1 \cdot y}}{z} \cdot -0.3333333333333333 + 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]

       3. associate-*l/ 64.0%

          \[\leadsto \color{blue}{\left(\frac{1}{z} \cdot y\right)} \cdot -0.3333333333333333 + 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]

       4. associate-*r* 64.0%

          \[\leadsto \color{blue}{\frac{1}{z} \cdot \left(y \cdot -0.3333333333333333\right)} + 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]

       5. *-commutative 64.0%

          \[\leadsto \frac{1}{z} \cdot \color{blue}{\left(-0.3333333333333333 \cdot y\right)} + 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]

       6. associate-/r* 66.7%

          \[\leadsto \frac{1}{z} \cdot \left(-0.3333333333333333 \cdot y\right) + 0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{y}}{z}} \]

       7. associate-*r/ 66.6%

          \[\leadsto \frac{1}{z} \cdot \left(-0.3333333333333333 \cdot y\right) + \color{blue}{\frac{0.3333333333333333 \cdot \frac{t}{y}}{z}} \]

       8. *-lft-identity 66.6%

          \[\leadsto \frac{1}{z} \cdot \left(-0.3333333333333333 \cdot y\right) + \frac{\color{blue}{1 \cdot \left(0.3333333333333333 \cdot \frac{t}{y}\right)}}{z} \]

       9. associate-*l/ 66.6%

          \[\leadsto \frac{1}{z} \cdot \left(-0.3333333333333333 \cdot y\right) + \color{blue}{\frac{1}{z} \cdot \left(0.3333333333333333 \cdot \frac{t}{y}\right)} \]

       10. distribute-lft-in 66.6%

           \[\leadsto \color{blue}{\frac{1}{z} \cdot \left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right)} \]

       11. +-commutative 66.6%

           \[\leadsto \frac{1}{z} \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{t}{y} + -0.3333333333333333 \cdot y\right)} \]

       12. metadata-eval 66.6%

           \[\leadsto \frac{1}{z} \cdot \left(0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333\right)} \cdot y\right) \]

       13. distribute-lft-neg-in 66.6%

           \[\leadsto \frac{1}{z} \cdot \left(0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333 \cdot y\right)}\right) \]

       14. distribute-rgt-neg-out 66.6%

           \[\leadsto \frac{1}{z} \cdot \left(0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{0.3333333333333333 \cdot \left(-y\right)}\right) \]

       15. distribute-lft-out 66.6%

           \[\leadsto \frac{1}{z} \cdot \color{blue}{\left(0.3333333333333333 \cdot \left(\frac{t}{y} + \left(-y\right)\right)\right)} \]

       16. sub-neg 66.6%

           \[\leadsto \frac{1}{z} \cdot \left(0.3333333333333333 \cdot \color{blue}{\left(\frac{t}{y} - y\right)}\right) \]

       17. associate-*r* 66.6%

           \[\leadsto \color{blue}{\left(\frac{1}{z} \cdot 0.3333333333333333\right) \cdot \left(\frac{t}{y} - y\right)} \]

       18. associate-*l/ 66.7%

           \[\leadsto \color{blue}{\frac{1 \cdot 0.3333333333333333}{z}} \cdot \left(\frac{t}{y} - y\right) \]

       19. metadata-eval 66.7%

           \[\leadsto \frac{\color{blue}{0.3333333333333333}}{z} \cdot \left(\frac{t}{y} - y\right) \]

   12. Simplified 66.7%

       \[\leadsto \color{blue}{\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   13. Taylor expanded in t around inf 60.0%

       \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   14. Step-by-step derivation

       1. *-commutative 60.0%

          \[\leadsto \color{blue}{\frac{t}{y \cdot z} \cdot 0.3333333333333333} \]

       2. associate-*l/ 60.0%

          \[\leadsto \color{blue}{\frac{t \cdot 0.3333333333333333}{y \cdot z}} \]

       3. associate-*r/ 59.6%

          \[\leadsto \color{blue}{t \cdot \frac{0.3333333333333333}{y \cdot z}} \]

       4. associate-/l/ 59.6%

          \[\leadsto t \cdot \color{blue}{\frac{\frac{0.3333333333333333}{z}}{y}} \]

   15. Simplified 59.6%

       \[\leadsto \color{blue}{t \cdot \frac{\frac{0.3333333333333333}{z}}{y}} \]

   if 5.4e6 < y

   1. Initial program 99.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

      2. associate-+r- 99.8%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

      3. sub-neg 99.8%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) + \left(-\frac{y}{z \cdot 3}\right)} \]

      4. associate-*l* 99.8%

         \[\leadsto \left(\frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      5. *-commutative 99.8%

         \[\leadsto \left(\frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      6. distribute-frac-neg2 99.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \color{blue}{\frac{y}{-z \cdot 3}} \]

      7. distribute-rgt-neg-in 99.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{\color{blue}{z \cdot \left(-3\right)}} \]

      8. metadata-eval 99.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot \color{blue}{-3}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot -3}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 72.9%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}}{z}} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 72.9%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right)}}{z} \]

      2. *-commutative 72.9%

         \[\leadsto \frac{\color{blue}{\left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}}{z} \]

      3. *-commutative 72.9%

         \[\leadsto \frac{\left(\color{blue}{y \cdot -0.3333333333333333} + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}{z} \]

      4. fma-define 72.9%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \frac{t}{y}\right)} \cdot 1}{z} \]

      5. clear-num 72.9%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \color{blue}{\frac{1}{\frac{y}{t}}}\right) \cdot 1}{z} \]

      6. un-div-inv 72.9%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, \color{blue}{\frac{0.3333333333333333}{\frac{y}{t}}}\right) \cdot 1}{z} \]

   7. Applied egg-rr 72.9%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right) \cdot 1}}{z} \]
   8. Step-by-step derivation

      1. *-rgt-identity 72.9%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right)}}{z} \]

      2. fma-undefine 72.9%

         \[\leadsto \frac{\color{blue}{y \cdot -0.3333333333333333 + \frac{0.3333333333333333}{\frac{y}{t}}}}{z} \]

      3. +-commutative 72.9%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{\frac{y}{t}} + y \cdot -0.3333333333333333}}{z} \]

      4. associate-/r/ 72.9%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{y} \cdot t} + y \cdot -0.3333333333333333}{z} \]

      5. metadata-eval 72.9%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333 \cdot 1}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      6. associate-*r/ 72.9%

         \[\leadsto \frac{\color{blue}{\left(0.3333333333333333 \cdot \frac{1}{y}\right)} \cdot t + y \cdot -0.3333333333333333}{z} \]

      7. associate-*r/ 72.9%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot 1}{y}} \cdot t + y \cdot -0.3333333333333333}{z} \]

      8. metadata-eval 72.9%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      9. associate-*l/ 72.9%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot t}{y}} + y \cdot -0.3333333333333333}{z} \]

      10. associate-*r/ 72.9%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \frac{t}{y}} + y \cdot -0.3333333333333333}{z} \]

      11. *-commutative 72.9%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{-0.3333333333333333 \cdot y}}{z} \]

      12. metadata-eval 72.9%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333\right)} \cdot y}{z} \]

      13. distribute-lft-neg-in 72.9%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333 \cdot y\right)}}{z} \]

      14. distribute-rgt-neg-in 72.9%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{0.3333333333333333 \cdot \left(-y\right)}}{z} \]

      15. distribute-lft-in 72.9%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} + \left(-y\right)\right)}}{z} \]

      16. sub-neg 72.9%

          \[\leadsto \frac{0.3333333333333333 \cdot \color{blue}{\left(\frac{t}{y} - y\right)}}{z} \]

   9. Simplified 72.9%

      \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}}{z} \]

   10. Taylor expanded in t around 0 70.3%

       \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot y}}{z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -180:\\ \;\;\;\;-0.3333333333333333 \cdot \left(y \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;y \leq 5400000:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -1.5e+81) x (if (<= x 7.2e+61) (/ (* y -0.3333333333333333) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.5e+81) {
		tmp = x;
	} else if (x <= 7.2e+61) {
		tmp = (y * -0.3333333333333333) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-1.5d+81)) then
        tmp = x
    else if (x <= 7.2d+61) then
        tmp = (y * (-0.3333333333333333d0)) / z
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -1.5e+81) {
		tmp = x;
	} else if (x <= 7.2e+61) {
		tmp = (y * -0.3333333333333333) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -1.5e+81:
		tmp = x
	elif x <= 7.2e+61:
		tmp = (y * -0.3333333333333333) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -1.5e+81)
		tmp = x;
	elseif (x <= 7.2e+61)
		tmp = Float64(Float64(y * -0.3333333333333333) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -1.5e+81)
		tmp = x;
	elseif (x <= 7.2e+61)
		tmp = (y * -0.3333333333333333) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -1.5e+81], x, If[LessEqual[x, 7.2e+61], N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.49999999999999999e81 or 7.20000000000000021e61 < x

   1. Initial program 93.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. +-commutative 93.9%

         \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

      2. associate-+r- 93.9%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

      3. +-commutative 93.9%

         \[\leadsto \color{blue}{\left(x + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} - \frac{y}{z \cdot 3} \]

      4. associate--l+ 93.9%

         \[\leadsto \color{blue}{x + \left(\frac{t}{\left(z \cdot 3\right) \cdot y} - \frac{y}{z \cdot 3}\right)} \]

      5. sub-neg 93.9%

         \[\leadsto x + \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(-\frac{y}{z \cdot 3}\right)\right)} \]

      6. remove-double-neg 93.9%

         \[\leadsto x + \left(\color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} + \left(-\frac{y}{z \cdot 3}\right)\right) \]

      7. distribute-frac-neg 93.9%

         \[\leadsto x + \left(\left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) + \left(-\frac{y}{z \cdot 3}\right)\right) \]

      8. distribute-neg-in 93.9%

         \[\leadsto x + \color{blue}{\left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \frac{y}{z \cdot 3}\right)\right)} \]

      9. remove-double-neg 93.9%

         \[\leadsto x + \left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(-\left(-\frac{y}{z \cdot 3}\right)\right)}\right)\right) \]

      10. sub-neg 93.9%

          \[\leadsto x + \left(-\color{blue}{\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)}\right) \]

      11. neg-mul-1 93.9%

          \[\leadsto x + \left(-\left(\frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

      12. times-frac 96.0%

          \[\leadsto x + \left(-\left(\color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

      13. distribute-frac-neg 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-y}{z \cdot 3}}\right)\right) \]

      14. neg-mul-1 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{-1 \cdot y}}{z \cdot 3}\right)\right) \]

      15. *-commutative 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{y \cdot -1}}{z \cdot 3}\right)\right) \]

      16. associate-/l* 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{y \cdot \frac{-1}{z \cdot 3}}\right)\right) \]

      17. *-commutative 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-1}{z \cdot 3} \cdot y}\right)\right) \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 57.7%

      \[\leadsto \color{blue}{x} \]

   if -1.49999999999999999e81 < x < 7.20000000000000021e61

   1. Initial program 92.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. +-commutative 92.8%

         \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

      2. associate-+r- 92.8%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

      3. sub-neg 92.8%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) + \left(-\frac{y}{z \cdot 3}\right)} \]

      4. associate-*l* 92.8%

         \[\leadsto \left(\frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      5. *-commutative 92.8%

         \[\leadsto \left(\frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      6. distribute-frac-neg2 92.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \color{blue}{\frac{y}{-z \cdot 3}} \]

      7. distribute-rgt-neg-in 92.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{\color{blue}{z \cdot \left(-3\right)}} \]

      8. metadata-eval 92.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot \color{blue}{-3}} \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot -3}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 88.0%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}}{z}} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 88.0%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right)}}{z} \]

      2. *-commutative 88.0%

         \[\leadsto \frac{\color{blue}{\left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}}{z} \]

      3. *-commutative 88.0%

         \[\leadsto \frac{\left(\color{blue}{y \cdot -0.3333333333333333} + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}{z} \]

      4. fma-define 88.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \frac{t}{y}\right)} \cdot 1}{z} \]

      5. clear-num 87.9%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \color{blue}{\frac{1}{\frac{y}{t}}}\right) \cdot 1}{z} \]

      6. un-div-inv 88.0%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, \color{blue}{\frac{0.3333333333333333}{\frac{y}{t}}}\right) \cdot 1}{z} \]

   7. Applied egg-rr 88.0%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right) \cdot 1}}{z} \]
   8. Step-by-step derivation

      1. *-rgt-identity 88.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right)}}{z} \]

      2. fma-undefine 88.0%

         \[\leadsto \frac{\color{blue}{y \cdot -0.3333333333333333 + \frac{0.3333333333333333}{\frac{y}{t}}}}{z} \]

      3. +-commutative 88.0%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{\frac{y}{t}} + y \cdot -0.3333333333333333}}{z} \]

      4. associate-/r/ 88.0%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{y} \cdot t} + y \cdot -0.3333333333333333}{z} \]

      5. metadata-eval 88.0%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333 \cdot 1}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      6. associate-*r/ 88.0%

         \[\leadsto \frac{\color{blue}{\left(0.3333333333333333 \cdot \frac{1}{y}\right)} \cdot t + y \cdot -0.3333333333333333}{z} \]

      7. associate-*r/ 88.0%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot 1}{y}} \cdot t + y \cdot -0.3333333333333333}{z} \]

      8. metadata-eval 88.0%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      9. associate-*l/ 88.0%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot t}{y}} + y \cdot -0.3333333333333333}{z} \]

      10. associate-*r/ 88.0%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \frac{t}{y}} + y \cdot -0.3333333333333333}{z} \]

      11. *-commutative 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{-0.3333333333333333 \cdot y}}{z} \]

      12. metadata-eval 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333\right)} \cdot y}{z} \]

      13. distribute-lft-neg-in 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333 \cdot y\right)}}{z} \]

      14. distribute-rgt-neg-in 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{0.3333333333333333 \cdot \left(-y\right)}}{z} \]

      15. distribute-lft-in 88.0%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} + \left(-y\right)\right)}}{z} \]

      16. sub-neg 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \color{blue}{\left(\frac{t}{y} - y\right)}}{z} \]

   9. Simplified 88.0%

      \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}}{z} \]

   10. Taylor expanded in t around 0 44.2%

       \[\leadsto \frac{\color{blue}{-0.3333333333333333 \cdot y}}{z} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+61}:\\ \;\;\;\;\frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+59}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.8e+81) x (if (<= x 3.1e+59) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e+81) {
		tmp = x;
	} else if (x <= 3.1e+59) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.8d+81)) then
        tmp = x
    else if (x <= 3.1d+59) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e+81) {
		tmp = x;
	} else if (x <= 3.1e+59) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.8e+81:
		tmp = x
	elif x <= 3.1e+59:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.8e+81)
		tmp = x;
	elseif (x <= 3.1e+59)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.8e+81)
		tmp = x;
	elseif (x <= 3.1e+59)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.8e+81], x, If[LessEqual[x, 3.1e+59], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999979e81 or 3.10000000000000015e59 < x

   1. Initial program 93.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. +-commutative 93.9%

         \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

      2. associate-+r- 93.9%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

      3. +-commutative 93.9%

         \[\leadsto \color{blue}{\left(x + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} - \frac{y}{z \cdot 3} \]

      4. associate--l+ 93.9%

         \[\leadsto \color{blue}{x + \left(\frac{t}{\left(z \cdot 3\right) \cdot y} - \frac{y}{z \cdot 3}\right)} \]

      5. sub-neg 93.9%

         \[\leadsto x + \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(-\frac{y}{z \cdot 3}\right)\right)} \]

      6. remove-double-neg 93.9%

         \[\leadsto x + \left(\color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} + \left(-\frac{y}{z \cdot 3}\right)\right) \]

      7. distribute-frac-neg 93.9%

         \[\leadsto x + \left(\left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) + \left(-\frac{y}{z \cdot 3}\right)\right) \]

      8. distribute-neg-in 93.9%

         \[\leadsto x + \color{blue}{\left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \frac{y}{z \cdot 3}\right)\right)} \]

      9. remove-double-neg 93.9%

         \[\leadsto x + \left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(-\left(-\frac{y}{z \cdot 3}\right)\right)}\right)\right) \]

      10. sub-neg 93.9%

          \[\leadsto x + \left(-\color{blue}{\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)}\right) \]

      11. neg-mul-1 93.9%

          \[\leadsto x + \left(-\left(\frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

      12. times-frac 96.0%

          \[\leadsto x + \left(-\left(\color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

      13. distribute-frac-neg 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-y}{z \cdot 3}}\right)\right) \]

      14. neg-mul-1 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{-1 \cdot y}}{z \cdot 3}\right)\right) \]

      15. *-commutative 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{y \cdot -1}}{z \cdot 3}\right)\right) \]

      16. associate-/l* 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{y \cdot \frac{-1}{z \cdot 3}}\right)\right) \]

      17. *-commutative 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-1}{z \cdot 3} \cdot y}\right)\right) \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 57.7%

      \[\leadsto \color{blue}{x} \]

   if -4.79999999999999979e81 < x < 3.10000000000000015e59

   1. Initial program 92.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. +-commutative 92.8%

         \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

      2. associate-+r- 92.8%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

      3. sub-neg 92.8%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) + \left(-\frac{y}{z \cdot 3}\right)} \]

      4. associate-*l* 92.8%

         \[\leadsto \left(\frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      5. *-commutative 92.8%

         \[\leadsto \left(\frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      6. distribute-frac-neg2 92.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \color{blue}{\frac{y}{-z \cdot 3}} \]

      7. distribute-rgt-neg-in 92.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{\color{blue}{z \cdot \left(-3\right)}} \]

      8. metadata-eval 92.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot \color{blue}{-3}} \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot -3}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 88.0%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}}{z}} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 88.0%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right)}}{z} \]

      2. *-commutative 88.0%

         \[\leadsto \frac{\color{blue}{\left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}}{z} \]

      3. *-commutative 88.0%

         \[\leadsto \frac{\left(\color{blue}{y \cdot -0.3333333333333333} + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}{z} \]

      4. fma-define 88.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \frac{t}{y}\right)} \cdot 1}{z} \]

      5. clear-num 87.9%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \color{blue}{\frac{1}{\frac{y}{t}}}\right) \cdot 1}{z} \]

      6. un-div-inv 88.0%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, \color{blue}{\frac{0.3333333333333333}{\frac{y}{t}}}\right) \cdot 1}{z} \]

   7. Applied egg-rr 88.0%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right) \cdot 1}}{z} \]
   8. Step-by-step derivation

      1. *-rgt-identity 88.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right)}}{z} \]

      2. fma-undefine 88.0%

         \[\leadsto \frac{\color{blue}{y \cdot -0.3333333333333333 + \frac{0.3333333333333333}{\frac{y}{t}}}}{z} \]

      3. +-commutative 88.0%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{\frac{y}{t}} + y \cdot -0.3333333333333333}}{z} \]

      4. associate-/r/ 88.0%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{y} \cdot t} + y \cdot -0.3333333333333333}{z} \]

      5. metadata-eval 88.0%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333 \cdot 1}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      6. associate-*r/ 88.0%

         \[\leadsto \frac{\color{blue}{\left(0.3333333333333333 \cdot \frac{1}{y}\right)} \cdot t + y \cdot -0.3333333333333333}{z} \]

      7. associate-*r/ 88.0%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot 1}{y}} \cdot t + y \cdot -0.3333333333333333}{z} \]

      8. metadata-eval 88.0%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      9. associate-*l/ 88.0%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot t}{y}} + y \cdot -0.3333333333333333}{z} \]

      10. associate-*r/ 88.0%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \frac{t}{y}} + y \cdot -0.3333333333333333}{z} \]

      11. *-commutative 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{-0.3333333333333333 \cdot y}}{z} \]

      12. metadata-eval 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333\right)} \cdot y}{z} \]

      13. distribute-lft-neg-in 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333 \cdot y\right)}}{z} \]

      14. distribute-rgt-neg-in 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{0.3333333333333333 \cdot \left(-y\right)}}{z} \]

      15. distribute-lft-in 88.0%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} + \left(-y\right)\right)}}{z} \]

      16. sub-neg 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \color{blue}{\left(\frac{t}{y} - y\right)}}{z} \]

   9. Simplified 88.0%

      \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}}{z} \]

   10. Taylor expanded in t around 0 84.0%

       \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z} + 0.3333333333333333 \cdot \frac{t}{y \cdot z}} \]
   11. Step-by-step derivation

       1. *-commutative 84.0%

          \[\leadsto \color{blue}{\frac{y}{z} \cdot -0.3333333333333333} + 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]

       2. *-lft-identity 84.0%

          \[\leadsto \frac{\color{blue}{1 \cdot y}}{z} \cdot -0.3333333333333333 + 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]

       3. associate-*l/ 84.0%

          \[\leadsto \color{blue}{\left(\frac{1}{z} \cdot y\right)} \cdot -0.3333333333333333 + 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]

       4. associate-*r* 84.0%

          \[\leadsto \color{blue}{\frac{1}{z} \cdot \left(y \cdot -0.3333333333333333\right)} + 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]

       5. *-commutative 84.0%

          \[\leadsto \frac{1}{z} \cdot \color{blue}{\left(-0.3333333333333333 \cdot y\right)} + 0.3333333333333333 \cdot \frac{t}{y \cdot z} \]

       6. associate-/r* 88.0%

          \[\leadsto \frac{1}{z} \cdot \left(-0.3333333333333333 \cdot y\right) + 0.3333333333333333 \cdot \color{blue}{\frac{\frac{t}{y}}{z}} \]

       7. associate-*r/ 87.9%

          \[\leadsto \frac{1}{z} \cdot \left(-0.3333333333333333 \cdot y\right) + \color{blue}{\frac{0.3333333333333333 \cdot \frac{t}{y}}{z}} \]

       8. *-lft-identity 87.9%

          \[\leadsto \frac{1}{z} \cdot \left(-0.3333333333333333 \cdot y\right) + \frac{\color{blue}{1 \cdot \left(0.3333333333333333 \cdot \frac{t}{y}\right)}}{z} \]

       9. associate-*l/ 87.9%

          \[\leadsto \frac{1}{z} \cdot \left(-0.3333333333333333 \cdot y\right) + \color{blue}{\frac{1}{z} \cdot \left(0.3333333333333333 \cdot \frac{t}{y}\right)} \]

       10. distribute-lft-in 88.0%

           \[\leadsto \color{blue}{\frac{1}{z} \cdot \left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right)} \]

       11. +-commutative 88.0%

           \[\leadsto \frac{1}{z} \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{t}{y} + -0.3333333333333333 \cdot y\right)} \]

       12. metadata-eval 88.0%

           \[\leadsto \frac{1}{z} \cdot \left(0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333\right)} \cdot y\right) \]

       13. distribute-lft-neg-in 88.0%

           \[\leadsto \frac{1}{z} \cdot \left(0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333 \cdot y\right)}\right) \]

       14. distribute-rgt-neg-out 88.0%

           \[\leadsto \frac{1}{z} \cdot \left(0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{0.3333333333333333 \cdot \left(-y\right)}\right) \]

       15. distribute-lft-out 88.0%

           \[\leadsto \frac{1}{z} \cdot \color{blue}{\left(0.3333333333333333 \cdot \left(\frac{t}{y} + \left(-y\right)\right)\right)} \]

       16. sub-neg 88.0%

           \[\leadsto \frac{1}{z} \cdot \left(0.3333333333333333 \cdot \color{blue}{\left(\frac{t}{y} - y\right)}\right) \]

       17. associate-*r* 88.0%

           \[\leadsto \color{blue}{\left(\frac{1}{z} \cdot 0.3333333333333333\right) \cdot \left(\frac{t}{y} - y\right)} \]

       18. associate-*l/ 88.0%

           \[\leadsto \color{blue}{\frac{1 \cdot 0.3333333333333333}{z}} \cdot \left(\frac{t}{y} - y\right) \]

       19. metadata-eval 88.0%

           \[\leadsto \frac{\color{blue}{0.3333333333333333}}{z} \cdot \left(\frac{t}{y} - y\right) \]

   12. Simplified 88.0%

       \[\leadsto \color{blue}{\frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]

   13. Taylor expanded in t around 0 44.1%

       \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
   14. Step-by-step derivation

       1. metadata-eval 52.5%

          \[\leadsto x + \color{blue}{\left(-0.3333333333333333\right)} \cdot \frac{y}{z} \]

       2. distribute-lft-neg-in 52.5%

          \[\leadsto x + \color{blue}{\left(-0.3333333333333333 \cdot \frac{y}{z}\right)} \]

       3. associate-*r/ 52.5%

          \[\leadsto x + \left(-\color{blue}{\frac{0.3333333333333333 \cdot y}{z}}\right) \]

       4. associate-*l/ 52.5%

          \[\leadsto x + \left(-\color{blue}{\frac{0.3333333333333333}{z} \cdot y}\right) \]

       5. *-commutative 52.5%

          \[\leadsto x + \left(-\color{blue}{y \cdot \frac{0.3333333333333333}{z}}\right) \]

       6. distribute-rgt-neg-in 52.5%

          \[\leadsto x + \color{blue}{y \cdot \left(-\frac{0.3333333333333333}{z}\right)} \]

       7. distribute-neg-frac 52.5%

          \[\leadsto x + y \cdot \color{blue}{\frac{-0.3333333333333333}{z}} \]

       8. metadata-eval 52.5%

          \[\leadsto x + y \cdot \frac{\color{blue}{-0.3333333333333333}}{z} \]

   15. Simplified 44.1%

       \[\leadsto \color{blue}{y \cdot \frac{-0.3333333333333333}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 18: 48.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.8 \cdot 10^{+81}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+59}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= x -4.8e+81) x (if (<= x 2.6e+59) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e+81) {
		tmp = x;
	} else if (x <= 2.6e+59) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (x <= (-4.8d+81)) then
        tmp = x
    else if (x <= 2.6d+59) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (x <= -4.8e+81) {
		tmp = x;
	} else if (x <= 2.6e+59) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if x <= -4.8e+81:
		tmp = x
	elif x <= 2.6e+59:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (x <= -4.8e+81)
		tmp = x;
	elseif (x <= 2.6e+59)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (x <= -4.8e+81)
		tmp = x;
	elseif (x <= 2.6e+59)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[x, -4.8e+81], x, If[LessEqual[x, 2.6e+59], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.79999999999999979e81 or 2.59999999999999999e59 < x

   1. Initial program 93.9%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. +-commutative 93.9%

         \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

      2. associate-+r- 93.9%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

      3. +-commutative 93.9%

         \[\leadsto \color{blue}{\left(x + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} - \frac{y}{z \cdot 3} \]

      4. associate--l+ 93.9%

         \[\leadsto \color{blue}{x + \left(\frac{t}{\left(z \cdot 3\right) \cdot y} - \frac{y}{z \cdot 3}\right)} \]

      5. sub-neg 93.9%

         \[\leadsto x + \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(-\frac{y}{z \cdot 3}\right)\right)} \]

      6. remove-double-neg 93.9%

         \[\leadsto x + \left(\color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} + \left(-\frac{y}{z \cdot 3}\right)\right) \]

      7. distribute-frac-neg 93.9%

         \[\leadsto x + \left(\left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) + \left(-\frac{y}{z \cdot 3}\right)\right) \]

      8. distribute-neg-in 93.9%

         \[\leadsto x + \color{blue}{\left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \frac{y}{z \cdot 3}\right)\right)} \]

      9. remove-double-neg 93.9%

         \[\leadsto x + \left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(-\left(-\frac{y}{z \cdot 3}\right)\right)}\right)\right) \]

      10. sub-neg 93.9%

          \[\leadsto x + \left(-\color{blue}{\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)}\right) \]

      11. neg-mul-1 93.9%

          \[\leadsto x + \left(-\left(\frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

      12. times-frac 96.0%

          \[\leadsto x + \left(-\left(\color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

      13. distribute-frac-neg 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-y}{z \cdot 3}}\right)\right) \]

      14. neg-mul-1 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{-1 \cdot y}}{z \cdot 3}\right)\right) \]

      15. *-commutative 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{y \cdot -1}}{z \cdot 3}\right)\right) \]

      16. associate-/l* 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{y \cdot \frac{-1}{z \cdot 3}}\right)\right) \]

      17. *-commutative 96.0%

          \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-1}{z \cdot 3} \cdot y}\right)\right) \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 57.7%

      \[\leadsto \color{blue}{x} \]

   if -4.79999999999999979e81 < x < 2.59999999999999999e59

   1. Initial program 92.8%

      \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
   2. Step-by-step derivation

      1. +-commutative 92.8%

         \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

      2. associate-+r- 92.8%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

      3. sub-neg 92.8%

         \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) + \left(-\frac{y}{z \cdot 3}\right)} \]

      4. associate-*l* 92.8%

         \[\leadsto \left(\frac{t}{\color{blue}{z \cdot \left(3 \cdot y\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      5. *-commutative 92.8%

         \[\leadsto \left(\frac{t}{z \cdot \color{blue}{\left(y \cdot 3\right)}} + x\right) + \left(-\frac{y}{z \cdot 3}\right) \]

      6. distribute-frac-neg2 92.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \color{blue}{\frac{y}{-z \cdot 3}} \]

      7. distribute-rgt-neg-in 92.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{\color{blue}{z \cdot \left(-3\right)}} \]

      8. metadata-eval 92.8%

         \[\leadsto \left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot \color{blue}{-3}} \]

   3. Simplified 92.8%

      \[\leadsto \color{blue}{\left(\frac{t}{z \cdot \left(y \cdot 3\right)} + x\right) + \frac{y}{z \cdot -3}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 88.0%

      \[\leadsto \color{blue}{\frac{-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}}{z}} \]
   6. Step-by-step derivation

      1. *-un-lft-identity 88.0%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right)}}{z} \]

      2. *-commutative 88.0%

         \[\leadsto \frac{\color{blue}{\left(-0.3333333333333333 \cdot y + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}}{z} \]

      3. *-commutative 88.0%

         \[\leadsto \frac{\left(\color{blue}{y \cdot -0.3333333333333333} + 0.3333333333333333 \cdot \frac{t}{y}\right) \cdot 1}{z} \]

      4. fma-define 88.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \frac{t}{y}\right)} \cdot 1}{z} \]

      5. clear-num 87.9%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, 0.3333333333333333 \cdot \color{blue}{\frac{1}{\frac{y}{t}}}\right) \cdot 1}{z} \]

      6. un-div-inv 88.0%

         \[\leadsto \frac{\mathsf{fma}\left(y, -0.3333333333333333, \color{blue}{\frac{0.3333333333333333}{\frac{y}{t}}}\right) \cdot 1}{z} \]

   7. Applied egg-rr 88.0%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right) \cdot 1}}{z} \]
   8. Step-by-step derivation

      1. *-rgt-identity 88.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(y, -0.3333333333333333, \frac{0.3333333333333333}{\frac{y}{t}}\right)}}{z} \]

      2. fma-undefine 88.0%

         \[\leadsto \frac{\color{blue}{y \cdot -0.3333333333333333 + \frac{0.3333333333333333}{\frac{y}{t}}}}{z} \]

      3. +-commutative 88.0%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{\frac{y}{t}} + y \cdot -0.3333333333333333}}{z} \]

      4. associate-/r/ 88.0%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333}{y} \cdot t} + y \cdot -0.3333333333333333}{z} \]

      5. metadata-eval 88.0%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333 \cdot 1}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      6. associate-*r/ 88.0%

         \[\leadsto \frac{\color{blue}{\left(0.3333333333333333 \cdot \frac{1}{y}\right)} \cdot t + y \cdot -0.3333333333333333}{z} \]

      7. associate-*r/ 88.0%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot 1}{y}} \cdot t + y \cdot -0.3333333333333333}{z} \]

      8. metadata-eval 88.0%

         \[\leadsto \frac{\frac{\color{blue}{0.3333333333333333}}{y} \cdot t + y \cdot -0.3333333333333333}{z} \]

      9. associate-*l/ 88.0%

         \[\leadsto \frac{\color{blue}{\frac{0.3333333333333333 \cdot t}{y}} + y \cdot -0.3333333333333333}{z} \]

      10. associate-*r/ 88.0%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \frac{t}{y}} + y \cdot -0.3333333333333333}{z} \]

      11. *-commutative 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{-0.3333333333333333 \cdot y}}{z} \]

      12. metadata-eval 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333\right)} \cdot y}{z} \]

      13. distribute-lft-neg-in 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{\left(-0.3333333333333333 \cdot y\right)}}{z} \]

      14. distribute-rgt-neg-in 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \frac{t}{y} + \color{blue}{0.3333333333333333 \cdot \left(-y\right)}}{z} \]

      15. distribute-lft-in 88.0%

          \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} + \left(-y\right)\right)}}{z} \]

      16. sub-neg 88.0%

          \[\leadsto \frac{0.3333333333333333 \cdot \color{blue}{\left(\frac{t}{y} - y\right)}}{z} \]

   9. Simplified 88.0%

      \[\leadsto \frac{\color{blue}{0.3333333333333333 \cdot \left(\frac{t}{y} - y\right)}}{z} \]

   10. Taylor expanded in t around 0 44.1%

       \[\leadsto \color{blue}{-0.3333333333333333 \cdot \frac{y}{z}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 19: 96.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + \frac{\frac{t}{y} - y}{z \cdot 3} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (+ x (/ (- (/ t y) y) (* z 3.0))))

C

double code(double x, double y, double z, double t) {
	return x + (((t / y) - y) / (z * 3.0));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (((t / y) - y) / (z * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + (((t / y) - y) / (z * 3.0));
}

Python

def code(x, y, z, t):
	return x + (((t / y) - y) / (z * 3.0))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + (((t / y) - y) / (z * 3.0));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 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. +-commutative 93.2%

      \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

   2. associate-+r- 93.2%

      \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

   3. +-commutative 93.2%

      \[\leadsto \color{blue}{\left(x + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} - \frac{y}{z \cdot 3} \]

   4. associate--l+ 93.2%

      \[\leadsto \color{blue}{x + \left(\frac{t}{\left(z \cdot 3\right) \cdot y} - \frac{y}{z \cdot 3}\right)} \]

   5. sub-neg 93.2%

      \[\leadsto x + \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(-\frac{y}{z \cdot 3}\right)\right)} \]

   6. remove-double-neg 93.2%

      \[\leadsto x + \left(\color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   7. distribute-frac-neg 93.2%

      \[\leadsto x + \left(\left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   8. distribute-neg-in 93.2%

      \[\leadsto x + \color{blue}{\left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \frac{y}{z \cdot 3}\right)\right)} \]

   9. remove-double-neg 93.2%

      \[\leadsto x + \left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(-\left(-\frac{y}{z \cdot 3}\right)\right)}\right)\right) \]

   10. sub-neg 93.2%

       \[\leadsto x + \left(-\color{blue}{\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)}\right) \]

   11. neg-mul-1 93.2%

       \[\leadsto x + \left(-\left(\frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   12. times-frac 96.5%

       \[\leadsto x + \left(-\left(\color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   13. distribute-frac-neg 96.5%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-y}{z \cdot 3}}\right)\right) \]

   14. neg-mul-1 96.5%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{-1 \cdot y}}{z \cdot 3}\right)\right) \]

   15. *-commutative 96.5%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{y \cdot -1}}{z \cdot 3}\right)\right) \]

   16. associate-/l* 96.4%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{y \cdot \frac{-1}{z \cdot 3}}\right)\right) \]

   17. *-commutative 96.4%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-1}{z \cdot 3} \cdot y}\right)\right) \]

3. Simplified 96.4%

   \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. metadata-eval 96.4%

      \[\leadsto x + \frac{\color{blue}{\frac{1}{3}}}{z} \cdot \left(\frac{t}{y} - y\right) \]

   2. associate-/r* 96.4%

      \[\leadsto x + \color{blue}{\frac{1}{3 \cdot z}} \cdot \left(\frac{t}{y} - y\right) \]

   3. *-commutative 96.4%

      \[\leadsto x + \frac{1}{\color{blue}{z \cdot 3}} \cdot \left(\frac{t}{y} - y\right) \]

   4. associate-*l/ 96.5%

      \[\leadsto x + \color{blue}{\frac{1 \cdot \left(\frac{t}{y} - y\right)}{z \cdot 3}} \]

   5. *-un-lft-identity 96.5%

      \[\leadsto x + \frac{\color{blue}{\frac{t}{y} - y}}{z \cdot 3} \]

6. Applied egg-rr 96.5%

   \[\leadsto x + \color{blue}{\frac{\frac{t}{y} - y}{z \cdot 3}} \]
7. Add Preprocessing

Alternative 20: 96.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (* (- (/ t y) y) (/ 0.3333333333333333 z))))

C

double code(double x, double y, double z, double t) {
	return x + (((t / y) - y) * (0.3333333333333333 / z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (((t / y) - y) * (0.3333333333333333d0 / z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + (((t / y) - y) * (0.3333333333333333 / z));
}

Python

def code(x, y, z, t):
	return x + (((t / y) - y) * (0.3333333333333333 / z))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(Float64(t / y) - y) * Float64(0.3333333333333333 / z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + (((t / y) - y) * (0.3333333333333333 / z));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 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. +-commutative 93.2%

      \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

   2. associate-+r- 93.2%

      \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

   3. +-commutative 93.2%

      \[\leadsto \color{blue}{\left(x + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} - \frac{y}{z \cdot 3} \]

   4. associate--l+ 93.2%

      \[\leadsto \color{blue}{x + \left(\frac{t}{\left(z \cdot 3\right) \cdot y} - \frac{y}{z \cdot 3}\right)} \]

   5. sub-neg 93.2%

      \[\leadsto x + \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(-\frac{y}{z \cdot 3}\right)\right)} \]

   6. remove-double-neg 93.2%

      \[\leadsto x + \left(\color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   7. distribute-frac-neg 93.2%

      \[\leadsto x + \left(\left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   8. distribute-neg-in 93.2%

      \[\leadsto x + \color{blue}{\left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \frac{y}{z \cdot 3}\right)\right)} \]

   9. remove-double-neg 93.2%

      \[\leadsto x + \left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(-\left(-\frac{y}{z \cdot 3}\right)\right)}\right)\right) \]

   10. sub-neg 93.2%

       \[\leadsto x + \left(-\color{blue}{\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)}\right) \]

   11. neg-mul-1 93.2%

       \[\leadsto x + \left(-\left(\frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   12. times-frac 96.5%

       \[\leadsto x + \left(-\left(\color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   13. distribute-frac-neg 96.5%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-y}{z \cdot 3}}\right)\right) \]

   14. neg-mul-1 96.5%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{-1 \cdot y}}{z \cdot 3}\right)\right) \]

   15. *-commutative 96.5%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{y \cdot -1}}{z \cdot 3}\right)\right) \]

   16. associate-/l* 96.4%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{y \cdot \frac{-1}{z \cdot 3}}\right)\right) \]

   17. *-commutative 96.4%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-1}{z \cdot 3} \cdot y}\right)\right) \]

3. Simplified 96.4%

   \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
4. Add Preprocessing

5. Final simplification 96.4%

   \[\leadsto x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z} \]
6. Add Preprocessing

Alternative 21: 96.0% 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 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. +-commutative 93.2%

      \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

   2. associate-+r- 93.2%

      \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

   3. +-commutative 93.2%

      \[\leadsto \color{blue}{\left(x + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} - \frac{y}{z \cdot 3} \]

   4. associate--l+ 93.2%

      \[\leadsto \color{blue}{x + \left(\frac{t}{\left(z \cdot 3\right) \cdot y} - \frac{y}{z \cdot 3}\right)} \]

   5. sub-neg 93.2%

      \[\leadsto x + \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(-\frac{y}{z \cdot 3}\right)\right)} \]

   6. remove-double-neg 93.2%

      \[\leadsto x + \left(\color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   7. distribute-frac-neg 93.2%

      \[\leadsto x + \left(\left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   8. distribute-neg-in 93.2%

      \[\leadsto x + \color{blue}{\left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \frac{y}{z \cdot 3}\right)\right)} \]

   9. remove-double-neg 93.2%

      \[\leadsto x + \left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(-\left(-\frac{y}{z \cdot 3}\right)\right)}\right)\right) \]

   10. sub-neg 93.2%

       \[\leadsto x + \left(-\color{blue}{\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)}\right) \]

   11. neg-mul-1 93.2%

       \[\leadsto x + \left(-\left(\frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   12. times-frac 96.5%

       \[\leadsto x + \left(-\left(\color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   13. distribute-frac-neg 96.5%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-y}{z \cdot 3}}\right)\right) \]

   14. neg-mul-1 96.5%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{-1 \cdot y}}{z \cdot 3}\right)\right) \]

   15. *-commutative 96.5%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{y \cdot -1}}{z \cdot 3}\right)\right) \]

   16. associate-/l* 96.4%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{y \cdot \frac{-1}{z \cdot 3}}\right)\right) \]

   17. *-commutative 96.4%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-1}{z \cdot 3} \cdot y}\right)\right) \]

3. Simplified 96.4%

   \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 96.4%

   \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}} \]
6. Add Preprocessing

Alternative 22: 30.9% 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 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. +-commutative 93.2%

      \[\leadsto \color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(x - \frac{y}{z \cdot 3}\right)} \]

   2. associate-+r- 93.2%

      \[\leadsto \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + x\right) - \frac{y}{z \cdot 3}} \]

   3. +-commutative 93.2%

      \[\leadsto \color{blue}{\left(x + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} - \frac{y}{z \cdot 3} \]

   4. associate--l+ 93.2%

      \[\leadsto \color{blue}{x + \left(\frac{t}{\left(z \cdot 3\right) \cdot y} - \frac{y}{z \cdot 3}\right)} \]

   5. sub-neg 93.2%

      \[\leadsto x + \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(-\frac{y}{z \cdot 3}\right)\right)} \]

   6. remove-double-neg 93.2%

      \[\leadsto x + \left(\color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   7. distribute-frac-neg 93.2%

      \[\leadsto x + \left(\left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   8. distribute-neg-in 93.2%

      \[\leadsto x + \color{blue}{\left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \frac{y}{z \cdot 3}\right)\right)} \]

   9. remove-double-neg 93.2%

      \[\leadsto x + \left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(-\left(-\frac{y}{z \cdot 3}\right)\right)}\right)\right) \]

   10. sub-neg 93.2%

       \[\leadsto x + \left(-\color{blue}{\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)}\right) \]

   11. neg-mul-1 93.2%

       \[\leadsto x + \left(-\left(\frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   12. times-frac 96.5%

       \[\leadsto x + \left(-\left(\color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   13. distribute-frac-neg 96.5%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-y}{z \cdot 3}}\right)\right) \]

   14. neg-mul-1 96.5%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{-1 \cdot y}}{z \cdot 3}\right)\right) \]

   15. *-commutative 96.5%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{y \cdot -1}}{z \cdot 3}\right)\right) \]

   16. associate-/l* 96.4%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{y \cdot \frac{-1}{z \cdot 3}}\right)\right) \]

   17. *-commutative 96.4%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-1}{z \cdot 3} \cdot y}\right)\right) \]

3. Simplified 96.4%

   \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 28.0%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Developer Target 1: 96.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x - \frac{y}{z \cdot 3}\right) + \frac{\frac{t}{z \cdot 3}}{y} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y)))

C

double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x - (y / (z * 3.0d0))) + ((t / (z * 3.0d0)) / y)
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
}

Python

def code(x, y, z, t):
	return (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y)

Julia

function code(x, y, z, t)
	return Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(Float64(t / Float64(z * 3.0)) / y))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x - (y / (z * 3.0))) + ((t / (z * 3.0)) / y);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(t / N[(z * 3.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024146 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y)))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))