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

Percentage Accurate: 95.7% → 97.5%

Time: 10.7s

Alternatives: 16

Speedup: 1.4×

• 27.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 2 \cdot 10^{-94}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot \frac{\frac{0.3333333333333333}{y}}{z} - \frac{y}{z \cdot 3}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 2e-94)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ x (- (* t (/ (/ 0.3333333333333333 y) z)) (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 2e-94) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = x + ((t * ((0.3333333333333333 / y) / z)) - (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) <= 2d-94) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = x + ((t * ((0.3333333333333333d0 / y) / z)) - (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) <= 2e-94) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = x + ((t * ((0.3333333333333333 / y) / z)) - (y / (z * 3.0)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 2e-94:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = x + ((t * ((0.3333333333333333 / y) / z)) - (y / (z * 3.0)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= 2e-94)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(t * Float64(Float64(0.3333333333333333 / y) / z)) - Float64(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) <= 2e-94)
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = x + ((t * ((0.3333333333333333 / y) / z)) - (y / (z * 3.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-94], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t * N[(N[(0.3333333333333333 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < 1.9999999999999999e-94

   1. Initial program 91.1%

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

      1. associate-+l- 91.1%

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

      2. sub-neg 91.1%

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

      3. distribute-frac-neg 91.1%

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

      4. associate-/r* 94.0%

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

      5. neg-mul-1 94.0%

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

      6. *-commutative 94.0%

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

      7. times-frac 94.0%

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

      8. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in y around 0 90.9%

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

      1. +-commutative 90.9%

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

      2. metadata-eval 90.9%

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

      3. associate-/l/ 93.9%

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

      4. cancel-sign-sub-inv 93.9%

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

      5. *-commutative 93.9%

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

      6. metadata-eval 93.9%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 93.9%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 93.9%

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

      9. *-commutative 93.9%

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

      10. associate-/l/ 91.0%

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

      11. associate-/r* 98.1%

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

      12. metadata-eval 98.1%

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

      13. times-frac 98.1%

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

      14. *-rgt-identity 98.1%

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

      15. div-sub 98.6%

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

   6. Simplified 98.6%

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

   if 1.9999999999999999e-94 < (*.f64 z 3)

   1. Initial program 99.0%

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

      1. associate-+l- 99.0%

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

      2. *-commutative 99.0%

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

   3. Simplified 99.0%

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

      1. *-un-lft-identity 99.0%

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

      2. associate-*r* 98.9%

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

      3. times-frac 98.9%

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

   5. Applied egg-rr 98.9%

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

   6. Taylor expanded in y around 0 98.9%

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

      1. associate-*r/ 98.9%

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

      2. associate-*l/ 99.0%

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

      3. *-commutative 99.0%

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

      4. associate-/r* 99.0%

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

   8. Simplified 99.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 2 \cdot 10^{-94}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \left(t \cdot \frac{\frac{0.3333333333333333}{y}}{z} - \frac{y}{z \cdot 3}\right)\\ \end{array} \]

Alternative 2: 97.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 2 \cdot 10^{-94}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) 2e-94)
   (+ x (/ (- (/ t y) y) (* z 3.0)))
   (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 2e-94) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= 2d-94) then
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    else
        tmp = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= 2e-94) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= 2e-94:
		tmp = x + (((t / y) - y) / (z * 3.0))
	else:
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= 2e-94)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= 2e-94)
		tmp = x + (((t / y) - y) / (z * 3.0));
	else
		tmp = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-94], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < 1.9999999999999999e-94

   1. Initial program 91.1%

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

      1. associate-+l- 91.1%

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

      2. sub-neg 91.1%

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

      3. distribute-frac-neg 91.1%

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

      4. associate-/r* 94.0%

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

      5. neg-mul-1 94.0%

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

      6. *-commutative 94.0%

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

      7. times-frac 94.0%

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

      8. metadata-eval 94.0%

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

   3. Simplified 94.0%

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

   4. Taylor expanded in y around 0 90.9%

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

      1. +-commutative 90.9%

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

      2. metadata-eval 90.9%

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

      3. associate-/l/ 93.9%

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

      4. cancel-sign-sub-inv 93.9%

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

      5. *-commutative 93.9%

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

      6. metadata-eval 93.9%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 93.9%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 93.9%

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

      9. *-commutative 93.9%

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

      10. associate-/l/ 91.0%

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

      11. associate-/r* 98.1%

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

      12. metadata-eval 98.1%

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

      13. times-frac 98.1%

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

      14. *-rgt-identity 98.1%

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

      15. div-sub 98.6%

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

   6. Simplified 98.6%

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

   if 1.9999999999999999e-94 < (*.f64 z 3)

   1. Initial program 99.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq 2 \cdot 10^{-94}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \end{array} \]

Alternative 3: 79.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{-63} \lor \neg \left(z \cdot 3 \leq 8 \cdot 10^{+40}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -4e-63) (not (<= (* z 3.0) 8e+40)))
   (- x (/ y (* z 3.0)))
   (* -0.3333333333333333 (/ (- y (/ t y)) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -4e-63) || !((z * 3.0) <= 8e+40)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * 3.0d0) <= (-4d-63)) .or. (.not. ((z * 3.0d0) <= 8d+40))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (-0.3333333333333333d0) * ((y - (t / y)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -4e-63) || !((z * 3.0) <= 8e+40)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -4e-63) or not ((z * 3.0) <= 8e+40):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = -0.3333333333333333 * ((y - (t / y)) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -4e-63) || !(Float64(z * 3.0) <= 8e+40))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(-0.3333333333333333 * Float64(Float64(y - Float64(t / y)) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -4e-63) || ~(((z * 3.0) <= 8e+40)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = -0.3333333333333333 * ((y - (t / y)) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -4e-63], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 8e+40]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -4.00000000000000027e-63 or 8.00000000000000024e40 < (*.f64 z 3)

   1. Initial program 98.8%

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

      1. associate-+l- 98.8%

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

      2. sub-neg 98.8%

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

      3. distribute-frac-neg 98.8%

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

      4. associate-/r* 98.3%

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

      5. neg-mul-1 98.3%

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

      6. *-commutative 98.3%

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

      7. times-frac 98.2%

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

      8. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

   4. Taylor expanded in y around 0 98.6%

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

      1. +-commutative 98.6%

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

      2. metadata-eval 98.6%

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

      3. associate-/l/ 98.1%

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

      4. cancel-sign-sub-inv 98.1%

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

      5. *-commutative 98.1%

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

      6. metadata-eval 98.1%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 98.2%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 98.2%

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

      9. *-commutative 98.2%

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

      10. associate-/l/ 98.7%

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

      11. associate-/r* 94.2%

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

      12. metadata-eval 94.2%

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

      13. times-frac 94.2%

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

      14. *-rgt-identity 94.2%

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

      15. div-sub 94.2%

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

   6. Simplified 94.2%

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

   7. Taylor expanded in y around inf 76.6%

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

   if -4.00000000000000027e-63 < (*.f64 z 3) < 8.00000000000000024e40

   1. Initial program 88.3%

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

      1. associate-+l- 88.3%

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

      2. sub-neg 88.3%

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

      3. distribute-frac-neg 88.3%

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

      4. associate-/r* 92.0%

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

      5. neg-mul-1 92.0%

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

      6. *-commutative 92.0%

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

      7. times-frac 92.0%

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

      8. metadata-eval 92.0%

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

   3. Simplified 92.0%

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

   4. Taylor expanded in y around 0 88.3%

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

      1. +-commutative 88.3%

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

      2. metadata-eval 88.3%

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

      3. associate-/l/ 91.9%

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

      4. cancel-sign-sub-inv 91.9%

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

      5. *-commutative 91.9%

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

      6. metadata-eval 91.9%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 92.0%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 92.0%

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

      9. *-commutative 92.0%

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

      10. associate-/l/ 88.3%

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

      11. associate-/r* 98.3%

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

      12. metadata-eval 98.3%

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

      13. times-frac 98.2%

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

      14. *-rgt-identity 98.2%

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

      15. div-sub 99.0%

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

   6. Simplified 99.0%

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

   7. Taylor expanded in x around 0 93.2%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{-63} \lor \neg \left(z \cdot 3 \leq 8 \cdot 10^{+40}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y - \frac{t}{y}}{z}\\ \end{array} \]

Alternative 4: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot -3}\\ \mathbf{if}\;y \leq -3.7 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.96 \cdot 10^{-29} \lor \neg \left(y \leq 4.7 \cdot 10^{+66}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* z -3.0))))
   (if (<= y -3.7e+38)
     t_1
     (if (<= y -6.6e-14)
       x
       (if (or (<= y -1.96e-29) (not (<= y 4.7e+66)))
         t_1
         (* (/ 0.3333333333333333 y) (/ t z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (y <= -3.7e+38) {
		tmp = t_1;
	} else if (y <= -6.6e-14) {
		tmp = x;
	} else if ((y <= -1.96e-29) || !(y <= 4.7e+66)) {
		tmp = t_1;
	} else {
		tmp = (0.3333333333333333 / y) * (t / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (z * (-3.0d0))
    if (y <= (-3.7d+38)) then
        tmp = t_1
    else if (y <= (-6.6d-14)) then
        tmp = x
    else if ((y <= (-1.96d-29)) .or. (.not. (y <= 4.7d+66))) then
        tmp = t_1
    else
        tmp = (0.3333333333333333d0 / y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (y <= -3.7e+38) {
		tmp = t_1;
	} else if (y <= -6.6e-14) {
		tmp = x;
	} else if ((y <= -1.96e-29) || !(y <= 4.7e+66)) {
		tmp = t_1;
	} else {
		tmp = (0.3333333333333333 / y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (z * -3.0)
	tmp = 0
	if y <= -3.7e+38:
		tmp = t_1
	elif y <= -6.6e-14:
		tmp = x
	elif (y <= -1.96e-29) or not (y <= 4.7e+66):
		tmp = t_1
	else:
		tmp = (0.3333333333333333 / y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(z * -3.0))
	tmp = 0.0
	if (y <= -3.7e+38)
		tmp = t_1;
	elseif (y <= -6.6e-14)
		tmp = x;
	elseif ((y <= -1.96e-29) || !(y <= 4.7e+66))
		tmp = t_1;
	else
		tmp = Float64(Float64(0.3333333333333333 / y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (z * -3.0);
	tmp = 0.0;
	if (y <= -3.7e+38)
		tmp = t_1;
	elseif (y <= -6.6e-14)
		tmp = x;
	elseif ((y <= -1.96e-29) || ~((y <= 4.7e+66)))
		tmp = t_1;
	else
		tmp = (0.3333333333333333 / y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.7e+38], t$95$1, If[LessEqual[y, -6.6e-14], x, If[Or[LessEqual[y, -1.96e-29], N[Not[LessEqual[y, 4.7e+66]], $MachinePrecision]], t$95$1, N[(N[(0.3333333333333333 / y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.7000000000000001e38 or -6.5999999999999996e-14 < y < -1.95999999999999988e-29 or 4.7000000000000002e66 < y

   1. Initial program 97.6%

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

      1. associate-+l- 97.6%

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

      2. sub-neg 97.6%

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

      3. distribute-frac-neg 97.6%

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

      4. associate-/r* 92.5%

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

      5. neg-mul-1 92.5%

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

      6. *-commutative 92.5%

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

      7. times-frac 92.5%

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

      8. metadata-eval 92.5%

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

   3. Simplified 92.5%

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

   4. Taylor expanded in y around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. metadata-eval 97.5%

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

      3. associate-/l/ 92.4%

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

      4. cancel-sign-sub-inv 92.4%

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

      5. *-commutative 92.4%

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

      6. metadata-eval 92.4%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 92.5%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 92.5%

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

      9. *-commutative 92.5%

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

      10. associate-/l/ 97.6%

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

      11. associate-/r* 99.0%

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

      12. metadata-eval 99.0%

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

      13. times-frac 99.0%

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

      14. *-rgt-identity 99.0%

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

      15. div-sub 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around inf 95.5%

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

   8. Taylor expanded in x around 0 70.4%

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

      1. associate-*r/ 70.3%

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

      2. associate-*l/ 70.3%

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

      3. *-commutative 70.3%

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

   10. Simplified 70.3%

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

   11. Taylor expanded in y around 0 70.4%

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

       1. associate-*r/ 70.3%

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

       2. *-commutative 70.3%

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

       3. *-rgt-identity 70.3%

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

       4. associate-*r/ 70.3%

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

       5. /-rgt-identity 70.3%

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

       6. associate-/l* 70.4%

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

       7. metadata-eval 70.4%

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

       8. associate-*l/ 70.5%

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

       9. associate-*r/ 70.5%

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

       10. *-rgt-identity 70.5%

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

       11. associate-/r* 70.5%

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

   13. Simplified 70.5%

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

   if -3.7000000000000001e38 < y < -6.5999999999999996e-14

   1. Initial program 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 59.7%

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

   if -1.95999999999999988e-29 < y < 4.7000000000000002e66

   1. Initial program 89.6%

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

      1. associate-+l- 89.6%

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

      2. sub-neg 89.6%

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

      3. distribute-frac-neg 89.6%

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

      4. associate-/r* 97.4%

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

      5. neg-mul-1 97.4%

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

      6. *-commutative 97.4%

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

      7. times-frac 97.4%

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

      8. metadata-eval 97.4%

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

   3. Simplified 97.4%

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

   4. Taylor expanded in y around 0 89.4%

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

      1. +-commutative 89.4%

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

      2. metadata-eval 89.4%

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

      3. associate-/l/ 97.3%

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

      4. cancel-sign-sub-inv 97.3%

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

      5. *-commutative 97.3%

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

      6. metadata-eval 97.3%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 97.3%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 97.3%

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

      9. *-commutative 97.3%

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

      10. associate-/l/ 89.4%

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

      11. associate-/r* 93.1%

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

      12. metadata-eval 93.1%

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

      13. times-frac 93.1%

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

      14. *-rgt-identity 93.1%

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

      15. div-sub 93.1%

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

   6. Simplified 93.1%

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

   7. Taylor expanded in y around 0 57.0%

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

      1. associate-*r/ 57.1%

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

      2. associate-/r* 59.9%

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

      3. associate-*l/ 59.9%

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

      4. associate-/l* 63.5%

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

   9. Simplified 63.5%

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

       1. div-inv 63.4%

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

       2. clear-num 63.5%

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

   11. Applied egg-rr 63.5%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.7 \cdot 10^{+38}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{elif}\;y \leq -6.6 \cdot 10^{-14}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1.96 \cdot 10^{-29} \lor \neg \left(y \leq 4.7 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \end{array} \]

Alternative 5: 91.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-26} \lor \neg \left(y \leq 4.7 \cdot 10^{+66}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.5e-26) (not (<= y 4.7e+66)))
   (- x (/ y (* z 3.0)))
   (+ x (* (/ 0.3333333333333333 y) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e-26) || !(y <= 4.7e+66)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((0.3333333333333333 / y) * (t / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.5d-26)) .or. (.not. (y <= 4.7d+66))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + ((0.3333333333333333d0 / y) * (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.5e-26) || !(y <= 4.7e+66)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((0.3333333333333333 / y) * (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.5e-26) or not (y <= 4.7e+66):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + ((0.3333333333333333 / y) * (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.5e-26) || !(y <= 4.7e+66))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / y) * Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.5e-26) || ~((y <= 4.7e+66)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + ((0.3333333333333333 / y) * (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.5e-26], N[Not[LessEqual[y, 4.7e+66]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(0.3333333333333333 / y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.5e-26 or 4.7000000000000002e66 < y

   1. Initial program 98.5%

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

      1. associate-+l- 98.5%

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

      2. sub-neg 98.5%

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

      3. distribute-frac-neg 98.5%

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

      4. associate-/r* 93.0%

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

      5. neg-mul-1 93.0%

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

      6. *-commutative 93.0%

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

      7. times-frac 93.0%

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

      8. metadata-eval 93.0%

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

   3. Simplified 93.0%

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

   4. Taylor expanded in y around 0 98.4%

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

      1. +-commutative 98.4%

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

      2. metadata-eval 98.4%

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

      3. associate-/l/ 92.9%

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

      4. cancel-sign-sub-inv 92.9%

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

      5. *-commutative 92.9%

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

      6. metadata-eval 92.9%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 93.0%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 93.0%

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

      9. *-commutative 93.0%

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

      10. associate-/l/ 98.5%

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

      11. associate-/r* 99.1%

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

      12. metadata-eval 99.1%

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

      13. times-frac 99.1%

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

      14. *-rgt-identity 99.1%

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

      15. div-sub 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in y around inf 94.3%

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

   if -6.5e-26 < y < 4.7000000000000002e66

   1. Initial program 89.1%

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

   3. Simplified 93.3%

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

   4. Taylor expanded in y around 0 85.3%

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

      1. associate-*r/ 85.4%

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

      2. times-frac 91.5%

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

   6. Simplified 91.5%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-26} \lor \neg \left(y \leq 4.7 \cdot 10^{+66}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \end{array} \]

Alternative 6: 77.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-74} \lor \neg \left(y \leq 3.25 \cdot 10^{-74}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.4e-74) (not (<= y 3.25e-74)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* (/ 0.3333333333333333 y) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e-74) || !(y <= 3.25e-74)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = (0.3333333333333333 / y) * (t / 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 <= (-4.4d-74)) .or. (.not. (y <= 3.25d-74))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = (0.3333333333333333d0 / y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.4e-74) || !(y <= 3.25e-74)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = (0.3333333333333333 / y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.4e-74) or not (y <= 3.25e-74):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = (0.3333333333333333 / y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.4e-74) || !(y <= 3.25e-74))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(Float64(0.3333333333333333 / y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.4e-74) || ~((y <= 3.25e-74)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = (0.3333333333333333 / y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.4e-74], N[Not[LessEqual[y, 3.25e-74]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.3333333333333333 / y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.40000000000000021e-74 or 3.2500000000000001e-74 < y

   1. Initial program 97.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 85.9%

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

   if -4.40000000000000021e-74 < y < 3.2500000000000001e-74

   1. Initial program 87.0%

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

      1. associate-+l- 87.0%

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

      2. sub-neg 87.0%

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

      3. distribute-frac-neg 87.0%

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

      4. associate-/r* 97.5%

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

      5. neg-mul-1 97.5%

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

      6. *-commutative 97.5%

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

      7. times-frac 97.5%

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

      8. metadata-eval 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around 0 86.9%

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

      1. +-commutative 86.9%

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

      2. metadata-eval 86.9%

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

      3. associate-/l/ 97.4%

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

      4. cancel-sign-sub-inv 97.4%

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

      5. *-commutative 97.4%

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

      6. metadata-eval 97.4%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 97.4%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 97.4%

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

      9. *-commutative 97.4%

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

      10. associate-/l/ 86.9%

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

      11. associate-/r* 90.8%

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

      12. metadata-eval 90.8%

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

      13. times-frac 90.7%

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

      14. *-rgt-identity 90.7%

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

      15. div-sub 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in y around 0 60.7%

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

      1. associate-*r/ 60.8%

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

      2. associate-/r* 64.6%

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

      3. associate-*l/ 64.6%

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

      4. associate-/l* 70.4%

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

   9. Simplified 70.4%

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

       1. div-inv 70.3%

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

       2. clear-num 70.4%

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

   11. Applied egg-rr 70.4%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-74} \lor \neg \left(y \leq 3.25 \cdot 10^{-74}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \end{array} \]

Alternative 7: 77.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-74} \lor \neg \left(y \leq 1.72 \cdot 10^{-75}\right):\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.5e-74) (not (<= y 1.72e-75)))
   (+ x (/ (* y -0.3333333333333333) z))
   (* (/ 0.3333333333333333 y) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e-74) || !(y <= 1.72e-75)) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else {
		tmp = (0.3333333333333333 / y) * (t / 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 <= (-3.5d-74)) .or. (.not. (y <= 1.72d-75))) then
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    else
        tmp = (0.3333333333333333d0 / y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5e-74) || !(y <= 1.72e-75)) {
		tmp = x + ((y * -0.3333333333333333) / z);
	} else {
		tmp = (0.3333333333333333 / y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.5e-74) or not (y <= 1.72e-75):
		tmp = x + ((y * -0.3333333333333333) / z)
	else:
		tmp = (0.3333333333333333 / y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.5e-74) || !(y <= 1.72e-75))
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	else
		tmp = Float64(Float64(0.3333333333333333 / y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.5e-74) || ~((y <= 1.72e-75)))
		tmp = x + ((y * -0.3333333333333333) / z);
	else
		tmp = (0.3333333333333333 / y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.5e-74], N[Not[LessEqual[y, 1.72e-75]], $MachinePrecision]], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(N[(0.3333333333333333 / y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.50000000000000015e-74 or 1.72e-75 < y

   1. Initial program 97.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 85.9%

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

      1. associate-*l/ 85.9%

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

   6. Applied egg-rr 85.9%

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

   if -3.50000000000000015e-74 < y < 1.72e-75

   1. Initial program 87.0%

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

      1. associate-+l- 87.0%

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

      2. sub-neg 87.0%

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

      3. distribute-frac-neg 87.0%

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

      4. associate-/r* 97.5%

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

      5. neg-mul-1 97.5%

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

      6. *-commutative 97.5%

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

      7. times-frac 97.5%

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

      8. metadata-eval 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around 0 86.9%

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

      1. +-commutative 86.9%

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

      2. metadata-eval 86.9%

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

      3. associate-/l/ 97.4%

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

      4. cancel-sign-sub-inv 97.4%

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

      5. *-commutative 97.4%

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

      6. metadata-eval 97.4%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 97.4%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 97.4%

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

      9. *-commutative 97.4%

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

      10. associate-/l/ 86.9%

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

      11. associate-/r* 90.8%

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

      12. metadata-eval 90.8%

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

      13. times-frac 90.7%

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

      14. *-rgt-identity 90.7%

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

      15. div-sub 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in y around 0 60.7%

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

      1. associate-*r/ 60.8%

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

      2. associate-/r* 64.6%

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

      3. associate-*l/ 64.6%

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

      4. associate-/l* 70.4%

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

   9. Simplified 70.4%

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

       1. div-inv 70.3%

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

       2. clear-num 70.4%

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

   11. Applied egg-rr 70.4%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{-74} \lor \neg \left(y \leq 1.72 \cdot 10^{-75}\right):\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \end{array} \]

Alternative 8: 77.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-74} \lor \neg \left(y \leq 10^{-75}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5e-74) (not (<= y 1e-75)))
   (- x (/ y (* z 3.0)))
   (* (/ 0.3333333333333333 y) (/ t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e-74) || !(y <= 1e-75)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (0.3333333333333333 / y) * (t / 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 <= (-5d-74)) .or. (.not. (y <= 1d-75))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (0.3333333333333333d0 / y) * (t / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e-74) || !(y <= 1e-75)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (0.3333333333333333 / y) * (t / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -5e-74) or not (y <= 1e-75):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = (0.3333333333333333 / y) * (t / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5e-74) || !(y <= 1e-75))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(0.3333333333333333 / y) * Float64(t / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -5e-74) || ~((y <= 1e-75)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = (0.3333333333333333 / y) * (t / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5e-74], N[Not[LessEqual[y, 1e-75]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.3333333333333333 / y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.99999999999999998e-74 or 9.9999999999999996e-76 < y

   1. Initial program 97.6%

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

      1. associate-+l- 97.6%

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

      2. sub-neg 97.6%

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

      3. distribute-frac-neg 97.6%

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

      4. associate-/r* 94.0%

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

      5. neg-mul-1 94.0%

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

      6. *-commutative 94.0%

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

      7. times-frac 93.9%

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

      8. metadata-eval 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. metadata-eval 97.5%

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

      3. associate-/l/ 93.9%

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

      4. cancel-sign-sub-inv 93.9%

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

      5. *-commutative 93.9%

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

      6. metadata-eval 93.9%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 93.9%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 93.9%

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

      9. *-commutative 93.9%

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

      10. associate-/l/ 97.6%

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

      11. associate-/r* 99.2%

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

      12. metadata-eval 99.2%

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

      13. times-frac 99.2%

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

      14. *-rgt-identity 99.2%

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

      15. div-sub 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around inf 86.1%

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

   if -4.99999999999999998e-74 < y < 9.9999999999999996e-76

   1. Initial program 87.0%

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

      1. associate-+l- 87.0%

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

      2. sub-neg 87.0%

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

      3. distribute-frac-neg 87.0%

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

      4. associate-/r* 97.5%

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

      5. neg-mul-1 97.5%

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

      6. *-commutative 97.5%

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

      7. times-frac 97.5%

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

      8. metadata-eval 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around 0 86.9%

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

      1. +-commutative 86.9%

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

      2. metadata-eval 86.9%

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

      3. associate-/l/ 97.4%

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

      4. cancel-sign-sub-inv 97.4%

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

      5. *-commutative 97.4%

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

      6. metadata-eval 97.4%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 97.4%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 97.4%

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

      9. *-commutative 97.4%

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

      10. associate-/l/ 86.9%

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

      11. associate-/r* 90.8%

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

      12. metadata-eval 90.8%

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

      13. times-frac 90.7%

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

      14. *-rgt-identity 90.7%

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

      15. div-sub 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in y around 0 60.7%

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

      1. associate-*r/ 60.8%

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

      2. associate-/r* 64.6%

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

      3. associate-*l/ 64.6%

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

      4. associate-/l* 70.4%

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

   9. Simplified 70.4%

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

       1. div-inv 70.3%

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

       2. clear-num 70.4%

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

   11. Applied egg-rr 70.4%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-74} \lor \neg \left(y \leq 10^{-75}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \end{array} \]

Alternative 9: 77.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-74} \lor \neg \left(y \leq 2.45 \cdot 10^{-74}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4e-74) (not (<= y 2.45e-74)))
   (- x (/ y (* z 3.0)))
   (/ (/ 0.3333333333333333 y) (/ z t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4e-74) || !(y <= 2.45e-74)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (0.3333333333333333 / y) / (z / 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 <= (-4d-74)) .or. (.not. (y <= 2.45d-74))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (0.3333333333333333d0 / y) / (z / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4e-74) || !(y <= 2.45e-74)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (0.3333333333333333 / y) / (z / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4e-74) or not (y <= 2.45e-74):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = (0.3333333333333333 / y) / (z / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4e-74) || !(y <= 2.45e-74))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(0.3333333333333333 / y) / Float64(z / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4e-74) || ~((y <= 2.45e-74)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = (0.3333333333333333 / y) / (z / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4e-74], N[Not[LessEqual[y, 2.45e-74]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.3333333333333333 / y), $MachinePrecision] / N[(z / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999983e-74 or 2.4500000000000001e-74 < y

   1. Initial program 97.6%

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

      1. associate-+l- 97.6%

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

      2. sub-neg 97.6%

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

      3. distribute-frac-neg 97.6%

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

      4. associate-/r* 94.0%

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

      5. neg-mul-1 94.0%

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

      6. *-commutative 94.0%

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

      7. times-frac 93.9%

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

      8. metadata-eval 93.9%

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

   3. Simplified 93.9%

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

   4. Taylor expanded in y around 0 97.5%

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

      1. +-commutative 97.5%

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

      2. metadata-eval 97.5%

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

      3. associate-/l/ 93.9%

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

      4. cancel-sign-sub-inv 93.9%

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

      5. *-commutative 93.9%

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

      6. metadata-eval 93.9%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 93.9%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 93.9%

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

      9. *-commutative 93.9%

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

      10. associate-/l/ 97.6%

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

      11. associate-/r* 99.2%

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

      12. metadata-eval 99.2%

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

      13. times-frac 99.2%

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

      14. *-rgt-identity 99.2%

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

      15. div-sub 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around inf 86.1%

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

   if -3.99999999999999983e-74 < y < 2.4500000000000001e-74

   1. Initial program 87.0%

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

      1. associate-+l- 87.0%

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

      2. sub-neg 87.0%

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

      3. distribute-frac-neg 87.0%

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

      4. associate-/r* 97.5%

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

      5. neg-mul-1 97.5%

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

      6. *-commutative 97.5%

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

      7. times-frac 97.5%

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

      8. metadata-eval 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around 0 86.9%

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

      1. +-commutative 86.9%

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

      2. metadata-eval 86.9%

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

      3. associate-/l/ 97.4%

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

      4. cancel-sign-sub-inv 97.4%

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

      5. *-commutative 97.4%

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

      6. metadata-eval 97.4%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 97.4%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 97.4%

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

      9. *-commutative 97.4%

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

      10. associate-/l/ 86.9%

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

      11. associate-/r* 90.8%

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

      12. metadata-eval 90.8%

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

      13. times-frac 90.7%

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

      14. *-rgt-identity 90.7%

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

      15. div-sub 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in y around 0 60.7%

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

      1. associate-*r/ 60.8%

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

      2. associate-/r* 64.6%

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

      3. associate-*l/ 64.6%

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

      4. associate-/l* 70.4%

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

   9. Simplified 70.4%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-74} \lor \neg \left(y \leq 2.45 \cdot 10^{-74}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{0.3333333333333333}{y}}{\frac{z}{t}}\\ \end{array} \]

Alternative 10: 77.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-74}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-75}:\\ \;\;\;\;\frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -4.4e-74)
   (- x (* 0.3333333333333333 (/ y z)))
   (if (<= y 7.2e-75)
     (* (/ 0.3333333333333333 y) (/ t z))
     (+ x (/ (* y -0.3333333333333333) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e-74) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 7.2e-75) {
		tmp = (0.3333333333333333 / y) * (t / z);
	} else {
		tmp = x + ((y * -0.3333333333333333) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-4.4d-74)) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else if (y <= 7.2d-75) then
        tmp = (0.3333333333333333d0 / y) * (t / z)
    else
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -4.4e-74) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else if (y <= 7.2e-75) {
		tmp = (0.3333333333333333 / y) * (t / z);
	} else {
		tmp = x + ((y * -0.3333333333333333) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -4.4e-74:
		tmp = x - (0.3333333333333333 * (y / z))
	elif y <= 7.2e-75:
		tmp = (0.3333333333333333 / y) * (t / z)
	else:
		tmp = x + ((y * -0.3333333333333333) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -4.4e-74)
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	elseif (y <= 7.2e-75)
		tmp = Float64(Float64(0.3333333333333333 / y) * Float64(t / z));
	else
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -4.4e-74)
		tmp = x - (0.3333333333333333 * (y / z));
	elseif (y <= 7.2e-75)
		tmp = (0.3333333333333333 / y) * (t / z);
	else
		tmp = x + ((y * -0.3333333333333333) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -4.4e-74], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.2e-75], N[(N[(0.3333333333333333 / y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.40000000000000021e-74

   1. Initial program 97.0%

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

      1. associate-+l- 97.0%

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

      2. sub-neg 97.0%

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

      3. distribute-frac-neg 97.0%

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

      4. associate-/r* 94.1%

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

      5. neg-mul-1 94.1%

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

      6. *-commutative 94.1%

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

      7. times-frac 94.1%

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

      8. metadata-eval 94.1%

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

   3. Simplified 94.1%

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

   4. Taylor expanded in y around inf 88.5%

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

   if -4.40000000000000021e-74 < y < 7.2000000000000001e-75

   1. Initial program 87.0%

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

      1. associate-+l- 87.0%

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

      2. sub-neg 87.0%

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

      3. distribute-frac-neg 87.0%

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

      4. associate-/r* 97.5%

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

      5. neg-mul-1 97.5%

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

      6. *-commutative 97.5%

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

      7. times-frac 97.5%

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

      8. metadata-eval 97.5%

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

   3. Simplified 97.5%

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

   4. Taylor expanded in y around 0 86.9%

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

      1. +-commutative 86.9%

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

      2. metadata-eval 86.9%

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

      3. associate-/l/ 97.4%

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

      4. cancel-sign-sub-inv 97.4%

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

      5. *-commutative 97.4%

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

      6. metadata-eval 97.4%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 97.4%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 97.4%

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

      9. *-commutative 97.4%

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

      10. associate-/l/ 86.9%

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

      11. associate-/r* 90.8%

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

      12. metadata-eval 90.8%

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

      13. times-frac 90.7%

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

      14. *-rgt-identity 90.7%

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

      15. div-sub 90.7%

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

   6. Simplified 90.7%

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

   7. Taylor expanded in y around 0 60.7%

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

      1. associate-*r/ 60.8%

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

      2. associate-/r* 64.6%

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

      3. associate-*l/ 64.6%

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

      4. associate-/l* 70.4%

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

   9. Simplified 70.4%

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

       1. div-inv 70.3%

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

       2. clear-num 70.4%

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

   11. Applied egg-rr 70.4%

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

   if 7.2000000000000001e-75 < y

   1. Initial program 98.3%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 83.0%

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

      1. associate-*l/ 83.1%

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

   6. Applied egg-rr 83.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{-74}:\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-75}:\\ \;\;\;\;\frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]

Alternative 11: 95.7% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

3. Simplified 96.4%

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

4. Final simplification 96.4%

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

Alternative 12: 95.7% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

3. Simplified 96.4%

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

   1. associate-*l/ 96.4%

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

5. Applied egg-rr 96.4%

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

6. Final simplification 96.4%

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

Alternative 13: 95.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

   1. associate-+l- 93.8%

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

   2. sub-neg 93.8%

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

   3. distribute-frac-neg 93.8%

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

   4. associate-/r* 95.3%

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

   5. neg-mul-1 95.3%

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

   6. *-commutative 95.3%

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

   7. times-frac 95.2%

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

   8. metadata-eval 95.2%

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

3. Simplified 95.2%

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

4. Taylor expanded in y around 0 93.6%

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

   1. +-commutative 93.6%

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

   2. metadata-eval 93.6%

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

   3. associate-/l/ 95.1%

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

   4. cancel-sign-sub-inv 95.1%

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

   5. *-commutative 95.1%

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

   6. metadata-eval 95.1%

      \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

   7. times-frac 95.2%

      \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

   8. *-rgt-identity 95.2%

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

   9. *-commutative 95.2%

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

   10. associate-/l/ 93.7%

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

   11. associate-/r* 96.2%

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

   12. metadata-eval 96.2%

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

   13. times-frac 96.1%

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

   14. *-rgt-identity 96.1%

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

   15. div-sub 96.5%

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

6. Simplified 96.5%

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

7. Final simplification 96.5%

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

Alternative 14: 47.2% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-10}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.25e+136)
   x
   (if (<= z 1.06e-10) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.25e+136) {
		tmp = x;
	} else if (z <= 1.06e-10) {
		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 (z <= (-2.25d+136)) then
        tmp = x
    else if (z <= 1.06d-10) 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 (z <= -2.25e+136) {
		tmp = x;
	} else if (z <= 1.06e-10) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.25e+136:
		tmp = x
	elif z <= 1.06e-10:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.25e+136)
		tmp = x;
	elseif (z <= 1.06e-10)
		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 (z <= -2.25e+136)
		tmp = x;
	elseif (z <= 1.06e-10)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.25e+136], x, If[LessEqual[z, 1.06e-10], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.25e136 or 1.06e-10 < z

   1. Initial program 99.1%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around inf 56.8%

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

   if -2.25e136 < z < 1.06e-10

   1. Initial program 90.2%

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

      1. associate-+l- 90.2%

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

      2. sub-neg 90.2%

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

      3. distribute-frac-neg 90.2%

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

      4. associate-/r* 93.6%

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

      5. neg-mul-1 93.6%

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

      6. *-commutative 93.6%

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

      7. times-frac 93.6%

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

      8. metadata-eval 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around 0 90.1%

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

      1. +-commutative 90.1%

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

      2. metadata-eval 90.1%

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

      3. associate-/l/ 93.5%

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

      4. cancel-sign-sub-inv 93.5%

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

      5. *-commutative 93.5%

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

      6. metadata-eval 93.5%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 93.5%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 93.5%

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

      9. *-commutative 93.5%

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

      10. associate-/l/ 90.2%

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

      11. associate-/r* 99.2%

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

      12. metadata-eval 99.2%

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

      13. times-frac 99.1%

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

      14. *-rgt-identity 99.1%

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

      15. div-sub 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around inf 47.6%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-10}:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 15: 47.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.1e+136) x (if (<= z 1.2e-5) (/ y (* z -3.0)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e+136) {
		tmp = x;
	} else if (z <= 1.2e-5) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-2.1d+136)) then
        tmp = x
    else if (z <= 1.2d-5) then
        tmp = y / (z * (-3.0d0))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.1e+136) {
		tmp = x;
	} else if (z <= 1.2e-5) {
		tmp = y / (z * -3.0);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.1e+136:
		tmp = x
	elif z <= 1.2e-5:
		tmp = y / (z * -3.0)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.1e+136)
		tmp = x;
	elseif (z <= 1.2e-5)
		tmp = Float64(y / Float64(z * -3.0));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.1e+136)
		tmp = x;
	elseif (z <= 1.2e-5)
		tmp = y / (z * -3.0);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.1e+136], x, If[LessEqual[z, 1.2e-5], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -2.0999999999999999e136 or 1.2e-5 < z

   1. Initial program 99.1%

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

   3. Simplified 91.5%

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

   4. Taylor expanded in x around inf 56.8%

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

   if -2.0999999999999999e136 < z < 1.2e-5

   1. Initial program 90.2%

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

      1. associate-+l- 90.2%

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

      2. sub-neg 90.2%

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

      3. distribute-frac-neg 90.2%

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

      4. associate-/r* 93.6%

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

      5. neg-mul-1 93.6%

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

      6. *-commutative 93.6%

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

      7. times-frac 93.6%

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

      8. metadata-eval 93.6%

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

   3. Simplified 93.6%

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

   4. Taylor expanded in y around 0 90.1%

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

      1. +-commutative 90.1%

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

      2. metadata-eval 90.1%

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

      3. associate-/l/ 93.5%

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

      4. cancel-sign-sub-inv 93.5%

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

      5. *-commutative 93.5%

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

      6. metadata-eval 93.5%

         \[\leadsto x - \left(\frac{y}{z} \cdot \color{blue}{\frac{1}{3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      7. times-frac 93.5%

         \[\leadsto x - \left(\color{blue}{\frac{y \cdot 1}{z \cdot 3}} - 0.3333333333333333 \cdot \frac{\frac{t}{z}}{y}\right) \]

      8. *-rgt-identity 93.5%

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

      9. *-commutative 93.5%

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

      10. associate-/l/ 90.2%

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

      11. associate-/r* 99.2%

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

      12. metadata-eval 99.2%

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

      13. times-frac 99.1%

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

      14. *-rgt-identity 99.1%

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

      15. div-sub 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in y around inf 59.6%

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

   8. Taylor expanded in x around 0 47.6%

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

      1. associate-*r/ 47.6%

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

      2. associate-*l/ 47.6%

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

      3. *-commutative 47.6%

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

   10. Simplified 47.6%

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

   11. Taylor expanded in y around 0 47.6%

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

       1. associate-*r/ 47.6%

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

       2. *-commutative 47.6%

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

       3. *-rgt-identity 47.6%

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

       4. associate-*r/ 47.6%

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

       5. /-rgt-identity 47.6%

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

       6. associate-/l* 47.7%

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

       7. metadata-eval 47.7%

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

       8. associate-*l/ 47.7%

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

       9. associate-*r/ 47.7%

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

       10. *-rgt-identity 47.7%

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

       11. associate-/r* 47.7%

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

   13. Simplified 47.7%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-5}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 16: 30.5% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 93.8%

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

3. Simplified 96.4%

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

4. Taylor expanded in x around inf 29.9%

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

5. Final simplification 29.9%

   \[\leadsto x \]

Developer target: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023308 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))