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

Percentage Accurate: 96.2% → 97.5%

Time: 10.9s

Alternatives: 15

Speedup: 1.0×

• 28.0% 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: 96.2% 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, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-75} \lor \neg \left(y \leq 1.6 \cdot 10^{-223}\right):\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.5e-75) (not (<= y 1.6e-223)))
   (- x (/ (- y (/ t y)) (* z 3.0)))
   (+ x (/ (/ t z) (* y 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e-75) || !(y <= 1.6e-223)) {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	} else {
		tmp = x + ((t / z) / (y * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.5d-75)) .or. (.not. (y <= 1.6d-223))) then
        tmp = x - ((y - (t / y)) / (z * 3.0d0))
    else
        tmp = x + ((t / z) / (y * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.5e-75) || !(y <= 1.6e-223)) {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	} else {
		tmp = x + ((t / z) / (y * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.5e-75) or not (y <= 1.6e-223):
		tmp = x - ((y - (t / y)) / (z * 3.0))
	else:
		tmp = x + ((t / z) / (y * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.5e-75) || !(y <= 1.6e-223))
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(t / z) / Float64(y * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.5e-75) || ~((y <= 1.6e-223)))
		tmp = x - ((y - (t / y)) / (z * 3.0));
	else
		tmp = x + ((t / z) / (y * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.5e-75], N[Not[LessEqual[y, 1.6e-223]], $MachinePrecision]], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.49999999999999989e-75 or 1.6e-223 < y

   1. Initial program 98.3%

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

      1. associate-*l* 98.3%

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

      2. *-commutative 98.3%

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

   3. Simplified 98.3%

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

      1. associate-+l- 98.3%

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

      2. *-commutative 98.3%

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

      3. associate-*l* 98.3%

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

      4. associate-/l/ 99.2%

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

      5. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

   if -2.49999999999999989e-75 < y < 1.6e-223

   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* 91.2%

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

      2. *-commutative 91.2%

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

   3. Simplified 91.2%

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

   5. Taylor expanded in y around 0 90.9%

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

      1. +-commutative 90.9%

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

      2. *-commutative 90.9%

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

      3. associate-/r* 86.1%

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

      4. associate-*l/ 86.1%

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

      5. associate-*r/ 86.1%

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

      6. associate-*l/ 99.8%

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

   7. Simplified 99.8%

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

      1. associate-/l* 91.1%

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

      2. associate-/r/ 86.1%

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

      3. metadata-eval 86.1%

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

      4. associate-/r* 86.2%

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

      5. *-commutative 86.2%

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

      6. div-inv 86.1%

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

      7. div-inv 86.1%

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

      8. *-commutative 86.1%

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

      9. times-frac 90.3%

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

   9. Applied egg-rr 90.3%

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

       1. frac-times 86.1%

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

       2. *-commutative 86.1%

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

       3. associate-*l/ 99.8%

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

       4. div-inv 99.8%

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

       5. associate-/r* 99.8%

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

       6. associate-/l/ 99.9%

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

   11. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-75} \lor \neg \left(y \leq 1.6 \cdot 10^{-223}\right):\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 96.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 2.9 \cdot 10^{+159}:\\ \;\;\;\;x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \frac{t}{z} \cdot \frac{\frac{1}{y}}{3}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 2.9e+159)
   (+ x (fma -0.3333333333333333 (/ y z) (* (/ t z) (/ (/ 1.0 y) 3.0))))
   (- x (/ (- y (/ t y)) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 2.9e+159) {
		tmp = x + fma(-0.3333333333333333, (y / z), ((t / z) * ((1.0 / y) / 3.0)));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 2.9e+159)
		tmp = Float64(x + fma(-0.3333333333333333, Float64(y / z), Float64(Float64(t / z) * Float64(Float64(1.0 / y) / 3.0))));
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 2.9e+159], N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + N[(N[(t / z), $MachinePrecision] * N[(N[(1.0 / y), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 2.90000000000000014e159

   1. Initial program 96.3%

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

      1. sub-neg 96.3%

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

      2. associate-+l+ 96.3%

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

      3. remove-double-neg 96.3%

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

      4. neg-mul-1 96.3%

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

      5. *-lft-identity 96.3%

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

      6. metadata-eval 96.3%

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

      7. times-frac 96.3%

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

      8. neg-mul-1 96.3%

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

      9. neg-mul-1 96.3%

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

      10. distribute-rgt-neg-out 96.3%

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

      11. distribute-neg-frac 96.3%

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

      12. distribute-neg-out 96.3%

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

      13. neg-mul-1 96.3%

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

      14. distribute-lft-out 96.3%

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

      15. neg-mul-1 96.3%

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

      16. distribute-neg-out 96.3%

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

      17. remove-double-neg 96.3%

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

   3. Simplified 96.3%

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

      1. associate-/r* 95.5%

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

      2. div-inv 95.5%

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

      3. times-frac 99.3%

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

   6. Applied egg-rr 99.3%

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

   if 2.90000000000000014e159 < t

   1. Initial program 96.8%

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

      1. associate-*l* 96.8%

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

      2. *-commutative 96.8%

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

   3. Simplified 96.8%

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

      1. associate-+l- 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*l* 96.8%

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

      4. associate-/l/ 96.8%

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

      5. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 2.9 \cdot 10^{+159}:\\ \;\;\;\;x + \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, \frac{t}{z} \cdot \frac{\frac{1}{y}}{3}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+76}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -4e+76)
   (+ (- x (/ y (* z 3.0))) (/ t (* z (* y 3.0))))
   (- x (/ (- y (/ t y)) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -4e+76) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-4d+76)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (z * (y * 3.0d0)))
    else
        tmp = x - ((y - (t / y)) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -4e+76) {
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -4e+76:
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)))
	else:
		tmp = x - ((y - (t / y)) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -4e+76)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(z * Float64(y * 3.0))));
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -4e+76)
		tmp = (x - (y / (z * 3.0))) + (t / (z * (y * 3.0)));
	else
		tmp = x - ((y - (t / y)) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -4e+76], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -4.0000000000000002e76

   1. Initial program 99.8%

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

      1. associate-*l* 99.7%

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

      2. *-commutative 99.7%

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

   3. Simplified 99.7%

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

   if -4.0000000000000002e76 < (*.f64 z 3)

   1. Initial program 95.6%

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

      1. associate-*l* 95.6%

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

      2. *-commutative 95.6%

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

   3. Simplified 95.6%

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

      1. associate-+l- 95.6%

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

      2. *-commutative 95.6%

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

      3. associate-*l* 95.6%

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

      4. associate-/l/ 98.0%

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

      5. sub-div 98.5%

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

   6. Applied egg-rr 98.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -4 \cdot 10^{+76}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{z \cdot \left(y \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+24}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -1e+24)
   (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))
   (- x (/ (- y (/ t y)) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -1e+24) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-1d+24)) then
        tmp = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    else
        tmp = x - ((y - (t / y)) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -1e+24) {
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -1e+24:
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))
	else:
		tmp = x - ((y - (t / y)) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -1e+24)
		tmp = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))));
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / 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) <= -1e+24)
		tmp = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	else
		tmp = x - ((y - (t / y)) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -1e+24], N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -9.9999999999999998e23

   1. Initial program 99.8%

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

   if -9.9999999999999998e23 < (*.f64 z 3)

   1. Initial program 95.5%

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

      1. associate-*l* 95.5%

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

      2. *-commutative 95.5%

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

   3. Simplified 95.5%

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

      1. associate-+l- 95.5%

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

      2. *-commutative 95.5%

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

      3. associate-*l* 95.5%

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

      4. associate-/l/ 97.9%

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

      5. sub-div 98.4%

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

   6. Applied egg-rr 98.4%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+24}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 96.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.25 \cdot 10^{+160}:\\ \;\;\;\;\left(x + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\right) - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t 1.25e+160)
   (-
    (+ x (/ (* (/ t z) 0.3333333333333333) y))
    (* (/ y z) 0.3333333333333333))
   (- x (/ (- y (/ t y)) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.25e+160) {
		tmp = (x + (((t / z) * 0.3333333333333333) / y)) - ((y / z) * 0.3333333333333333);
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= 1.25d+160) then
        tmp = (x + (((t / z) * 0.3333333333333333d0) / y)) - ((y / z) * 0.3333333333333333d0)
    else
        tmp = x - ((y - (t / y)) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= 1.25e+160) {
		tmp = (x + (((t / z) * 0.3333333333333333) / y)) - ((y / z) * 0.3333333333333333);
	} else {
		tmp = x - ((y - (t / y)) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= 1.25e+160:
		tmp = (x + (((t / z) * 0.3333333333333333) / y)) - ((y / z) * 0.3333333333333333)
	else:
		tmp = x - ((y - (t / y)) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= 1.25e+160)
		tmp = Float64(Float64(x + Float64(Float64(Float64(t / z) * 0.3333333333333333) / y)) - Float64(Float64(y / z) * 0.3333333333333333));
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= 1.25e+160)
		tmp = (x + (((t / z) * 0.3333333333333333) / y)) - ((y / z) * 0.3333333333333333);
	else
		tmp = x - ((y - (t / y)) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, 1.25e+160], N[(N[(x + N[(N[(N[(t / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] - N[(N[(y / z), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.25e160

   1. Initial program 96.3%

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

      1. associate-*l* 96.3%

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

      2. *-commutative 96.3%

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

   3. Simplified 96.3%

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

      1. +-commutative 96.3%

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

      2. associate-+r- 96.3%

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

      3. *-commutative 96.3%

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

      4. associate-*l* 96.3%

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

      5. associate-/r* 99.8%

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

      6. *-un-lft-identity 99.8%

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

      7. *-commutative 99.8%

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

      8. times-frac 99.3%

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

      9. metadata-eval 99.3%

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

      10. *-un-lft-identity 99.3%

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

      11. *-commutative 99.3%

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

      12. times-frac 99.3%

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

      13. metadata-eval 99.3%

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

   6. Applied egg-rr 99.3%

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

   if 1.25e160 < t

   1. Initial program 96.8%

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

      1. associate-*l* 96.8%

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

      2. *-commutative 96.8%

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

   3. Simplified 96.8%

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

      1. associate-+l- 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*l* 96.8%

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

      4. associate-/l/ 96.8%

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

      5. sub-div 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.25 \cdot 10^{+160}:\\ \;\;\;\;\left(x + \frac{\frac{t}{z} \cdot 0.3333333333333333}{y}\right) - \frac{y}{z} \cdot 0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-75} \lor \neg \left(y \leq 2 \cdot 10^{-39}\right):\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.6e-75) (not (<= y 2e-39)))
   (+ x (* (/ 0.3333333333333333 z) (- (/ t y) y)))
   (+ x (/ (/ t z) (* y 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e-75) || !(y <= 2e-39)) {
		tmp = x + ((0.3333333333333333 / z) * ((t / y) - y));
	} else {
		tmp = x + ((t / z) / (y * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.6d-75)) .or. (.not. (y <= 2d-39))) then
        tmp = x + ((0.3333333333333333d0 / z) * ((t / y) - y))
    else
        tmp = x + ((t / z) / (y * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.6e-75) || !(y <= 2e-39)) {
		tmp = x + ((0.3333333333333333 / z) * ((t / y) - y));
	} else {
		tmp = x + ((t / z) / (y * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.6e-75) or not (y <= 2e-39):
		tmp = x + ((0.3333333333333333 / z) * ((t / y) - y))
	else:
		tmp = x + ((t / z) / (y * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.6e-75) || !(y <= 2e-39))
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / z) * Float64(Float64(t / y) - y)));
	else
		tmp = Float64(x + Float64(Float64(t / z) / Float64(y * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.6e-75) || ~((y <= 2e-39)))
		tmp = x + ((0.3333333333333333 / z) * ((t / y) - y));
	else
		tmp = x + ((t / z) / (y * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.6e-75], N[Not[LessEqual[y, 2e-39]], $MachinePrecision]], N[(x + N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999988e-75 or 1.99999999999999986e-39 < y

   1. Initial program 98.6%

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

   3. Simplified 99.7%

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

   if -1.59999999999999988e-75 < y < 1.99999999999999986e-39

   1. Initial program 92.9%

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

      1. associate-*l* 92.9%

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

      2. *-commutative 92.9%

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

   3. Simplified 92.9%

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

   5. Taylor expanded in y around 0 92.7%

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

      1. +-commutative 92.7%

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

      2. *-commutative 92.7%

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

      3. associate-/r* 90.3%

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

      4. associate-*l/ 90.3%

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

      5. associate-*r/ 90.3%

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

      6. associate-*l/ 99.8%

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

   7. Simplified 99.8%

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

      1. associate-/l* 92.8%

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

      2. associate-/r/ 90.3%

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

      3. metadata-eval 90.3%

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

      4. associate-/r* 90.4%

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

      5. *-commutative 90.4%

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

      6. div-inv 90.3%

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

      7. div-inv 90.3%

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

      8. *-commutative 90.3%

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

      9. times-frac 91.4%

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

   9. Applied egg-rr 91.4%

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

       1. frac-times 90.3%

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

       2. *-commutative 90.3%

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

       3. associate-*l/ 99.7%

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

       4. div-inv 99.8%

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

       5. associate-/r* 99.8%

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

       6. associate-/l/ 99.9%

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

   11. Applied egg-rr 99.9%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{-75} \lor \neg \left(y \leq 2 \cdot 10^{-39}\right):\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 89.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-26} \lor \neg \left(y \leq 1.36 \cdot 10^{+69}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.4e-26) (not (<= y 1.36e+69)))
   (- x (/ y (* z 3.0)))
   (+ x (* 0.3333333333333333 (/ t (* y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e-26) || !(y <= 1.36e+69)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.4d-26)) .or. (.not. (y <= 1.36d+69))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + (0.3333333333333333d0 * (t / (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e-26) || !(y <= 1.36e+69)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.4e-26) or not (y <= 1.36e+69):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + (0.3333333333333333 * (t / (y * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.4e-26) || !(y <= 1.36e+69))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.4e-26) || ~((y <= 1.36e+69)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.4e-26], N[Not[LessEqual[y, 1.36e+69]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4000000000000001e-26 or 1.36000000000000006e69 < y

   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%

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

      2. *-commutative 99.0%

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

   3. Simplified 99.0%

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

      1. associate-+l- 99.0%

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

      2. *-commutative 99.0%

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

      3. associate-*l* 99.0%

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

      4. associate-/l/ 99.0%

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

      5. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 96.4%

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

   if -1.4000000000000001e-26 < y < 1.36000000000000006e69

   1. Initial program 93.8%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around inf 91.3%

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

4. Final simplification 93.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-26} \lor \neg \left(y \leq 1.36 \cdot 10^{+69}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-26} \lor \neg \left(y \leq 1.36 \cdot 10^{+69}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.4e-26) (not (<= y 1.36e+69)))
   (- x (/ y (* z 3.0)))
   (+ x (/ 0.3333333333333333 (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e-26) || !(y <= 1.36e+69)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (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 <= (-1.4d-26)) .or. (.not. (y <= 1.36d+69))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + (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 <= -1.4e-26) || !(y <= 1.36e+69)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.4e-26) or not (y <= 1.36e+69):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + (0.3333333333333333 / (y * (z / t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.4e-26) || !(y <= 1.36e+69))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(y * Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.4e-26) || ~((y <= 1.36e+69)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + (0.3333333333333333 / (y * (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.4e-26], N[Not[LessEqual[y, 1.36e+69]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 / N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4000000000000001e-26 or 1.36000000000000006e69 < y

   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%

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

      2. *-commutative 99.0%

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

   3. Simplified 99.0%

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

      1. associate-+l- 99.0%

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

      2. *-commutative 99.0%

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

      3. associate-*l* 99.0%

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

      4. associate-/l/ 99.0%

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

      5. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 96.4%

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

   if -1.4000000000000001e-26 < y < 1.36000000000000006e69

   1. Initial program 93.8%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. *-commutative 91.3%

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

      3. *-commutative 91.3%

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

      4. associate-*r/ 90.2%

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

      5. *-commutative 90.2%

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

   7. Simplified 90.2%

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

      1. associate-*r/ 91.3%

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

      2. *-commutative 91.3%

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

      3. times-frac 96.8%

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

      4. div-inv 96.8%

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

      5. associate-*l* 96.7%

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

      6. *-commutative 96.7%

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

      7. div-inv 96.8%

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

      8. associate-/l* 96.8%

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

      9. div-inv 96.8%

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

      10. clear-num 96.7%

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

   9. Applied egg-rr 96.7%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-26} \lor \neg \left(y \leq 1.36 \cdot 10^{+69}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y \cdot \frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-26} \lor \neg \left(y \leq 3.8 \cdot 10^{+69}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.4e-26) (not (<= y 3.8e+69)))
   (- 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 <= -1.4e-26) || !(y <= 3.8e+69)) {
		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 <= (-1.4d-26)) .or. (.not. (y <= 3.8d+69))) 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 <= -1.4e-26) || !(y <= 3.8e+69)) {
		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 <= -1.4e-26) or not (y <= 3.8e+69):
		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 <= -1.4e-26) || !(y <= 3.8e+69))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(y / Float64(t / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.4e-26) || ~((y <= 3.8e+69)))
		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, -1.4e-26], N[Not[LessEqual[y, 3.8e+69]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 / N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4000000000000001e-26 or 3.80000000000000028e69 < y

   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%

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

      2. *-commutative 99.0%

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

   3. Simplified 99.0%

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

      1. associate-+l- 99.0%

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

      2. *-commutative 99.0%

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

      3. associate-*l* 99.0%

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

      4. associate-/l/ 99.0%

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

      5. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 96.4%

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

   if -1.4000000000000001e-26 < y < 3.80000000000000028e69

   1. Initial program 93.8%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in t around inf 91.3%

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

      1. associate-*r/ 91.3%

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

      2. *-commutative 91.3%

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

      3. *-commutative 91.3%

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

      4. associate-*r/ 90.2%

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

      5. *-commutative 90.2%

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

   7. Simplified 90.2%

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

      1. associate-*r/ 91.3%

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

      2. *-commutative 91.3%

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

      3. times-frac 96.8%

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

      4. div-inv 96.8%

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

      5. associate-*l* 96.7%

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

      6. *-commutative 96.7%

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

      7. div-inv 96.8%

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

      8. associate-/l* 96.8%

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

      9. div-inv 96.8%

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

      10. clear-num 96.7%

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

   9. Applied egg-rr 96.7%

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

       1. clear-num 96.8%

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

       2. un-div-inv 96.8%

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

   11. Applied egg-rr 96.8%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-26} \lor \neg \left(y \leq 3.8 \cdot 10^{+69}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{y}{\frac{t}{z}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 91.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-26} \lor \neg \left(y \leq 1.36 \cdot 10^{+69}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.4e-26) (not (<= y 1.36e+69)))
   (- x (/ y (* z 3.0)))
   (+ x (/ (/ t z) (* y 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e-26) || !(y <= 1.36e+69)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((t / z) / (y * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.4d-26)) .or. (.not. (y <= 1.36d+69))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + ((t / z) / (y * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.4e-26) || !(y <= 1.36e+69)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((t / z) / (y * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.4e-26) or not (y <= 1.36e+69):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + ((t / z) / (y * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.4e-26) || !(y <= 1.36e+69))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(t / z) / Float64(y * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.4e-26) || ~((y <= 1.36e+69)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + ((t / z) / (y * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.4e-26], N[Not[LessEqual[y, 1.36e+69]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.4000000000000001e-26 or 1.36000000000000006e69 < y

   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%

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

      2. *-commutative 99.0%

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

   3. Simplified 99.0%

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

      1. associate-+l- 99.0%

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

      2. *-commutative 99.0%

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

      3. associate-*l* 99.0%

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

      4. associate-/l/ 99.0%

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

      5. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 96.4%

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

   if -1.4000000000000001e-26 < y < 1.36000000000000006e69

   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* 93.7%

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

      2. *-commutative 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in y around 0 91.3%

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

      1. +-commutative 91.3%

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

      2. *-commutative 91.3%

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

      3. associate-/r* 89.4%

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

      4. associate-*l/ 89.5%

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

      5. associate-*r/ 89.4%

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

      6. associate-*l/ 96.8%

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

   7. Simplified 96.8%

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

      1. associate-/l* 91.4%

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

      2. associate-/r/ 89.4%

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

      3. metadata-eval 89.4%

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

      4. associate-/r* 89.5%

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

      5. *-commutative 89.5%

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

      6. div-inv 89.5%

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

      7. div-inv 89.4%

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

      8. *-commutative 89.4%

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

      9. times-frac 90.3%

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

   9. Applied egg-rr 90.3%

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

       1. frac-times 89.4%

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

       2. *-commutative 89.4%

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

       3. associate-*l/ 96.7%

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

       4. div-inv 96.8%

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

       5. associate-/r* 96.8%

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

       6. associate-/l/ 96.8%

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

   11. Applied egg-rr 96.8%

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

4. Final simplification 96.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-26} \lor \neg \left(y \leq 1.36 \cdot 10^{+69}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 91.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-26}:\\ \;\;\;\;x + y \cdot \frac{\frac{-1}{z}}{3}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.4e-26)
   (+ x (* y (/ (/ -1.0 z) 3.0)))
   (if (<= y 1.55e+69) (+ x (/ (/ t z) (* y 3.0))) (- x (/ y (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-26) {
		tmp = x + (y * ((-1.0 / z) / 3.0));
	} else if (y <= 1.55e+69) {
		tmp = x + ((t / z) / (y * 3.0));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.4d-26)) then
        tmp = x + (y * (((-1.0d0) / z) / 3.0d0))
    else if (y <= 1.55d+69) then
        tmp = x + ((t / z) / (y * 3.0d0))
    else
        tmp = x - (y / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.4e-26) {
		tmp = x + (y * ((-1.0 / z) / 3.0));
	} else if (y <= 1.55e+69) {
		tmp = x + ((t / z) / (y * 3.0));
	} else {
		tmp = x - (y / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.4e-26:
		tmp = x + (y * ((-1.0 / z) / 3.0))
	elif y <= 1.55e+69:
		tmp = x + ((t / z) / (y * 3.0))
	else:
		tmp = x - (y / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.4e-26)
		tmp = Float64(x + Float64(y * Float64(Float64(-1.0 / z) / 3.0)));
	elseif (y <= 1.55e+69)
		tmp = Float64(x + Float64(Float64(t / z) / Float64(y * 3.0)));
	else
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.4e-26)
		tmp = x + (y * ((-1.0 / z) / 3.0));
	elseif (y <= 1.55e+69)
		tmp = x + ((t / z) / (y * 3.0));
	else
		tmp = x - (y / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.4e-26], N[(x + N[(y * N[(N[(-1.0 / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.55e+69], N[(x + N[(N[(t / z), $MachinePrecision] / N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4000000000000001e-26

   1. Initial program 99.8%

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

      1. associate-*l* 99.8%

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

      2. *-commutative 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 96.9%

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

      1. metadata-eval 96.9%

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

      2. times-frac 97.0%

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

      3. *-un-lft-identity 97.0%

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

      4. *-commutative 97.0%

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

      5. clear-num 97.1%

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

   7. Applied egg-rr 97.1%

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

      1. associate-/r/ 97.0%

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

      2. associate-/r* 97.1%

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

   9. Simplified 97.1%

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

   if -1.4000000000000001e-26 < y < 1.5499999999999999e69

   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* 93.7%

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

      2. *-commutative 93.7%

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

   3. Simplified 93.7%

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

   5. Taylor expanded in y around 0 91.3%

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

      1. +-commutative 91.3%

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

      2. *-commutative 91.3%

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

      3. associate-/r* 89.4%

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

      4. associate-*l/ 89.5%

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

      5. associate-*r/ 89.4%

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

      6. associate-*l/ 96.8%

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

   7. Simplified 96.8%

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

      1. associate-/l* 91.4%

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

      2. associate-/r/ 89.4%

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

      3. metadata-eval 89.4%

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

      4. associate-/r* 89.5%

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

      5. *-commutative 89.5%

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

      6. div-inv 89.5%

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

      7. div-inv 89.4%

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

      8. *-commutative 89.4%

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

      9. times-frac 90.3%

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

   9. Applied egg-rr 90.3%

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

       1. frac-times 89.4%

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

       2. *-commutative 89.4%

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

       3. associate-*l/ 96.7%

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

       4. div-inv 96.8%

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

       5. associate-/r* 96.8%

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

       6. associate-/l/ 96.8%

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

   11. Applied egg-rr 96.8%

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

   if 1.5499999999999999e69 < y

   1. Initial program 98.2%

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

      1. associate-*l* 98.2%

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

      2. *-commutative 98.2%

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

   3. Simplified 98.2%

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

      1. associate-+l- 98.2%

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

      2. *-commutative 98.2%

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

      3. associate-*l* 98.2%

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

      4. associate-/l/ 98.2%

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

      5. sub-div 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 95.9%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{-26}:\\ \;\;\;\;x + y \cdot \frac{\frac{-1}{z}}{3}\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+69}:\\ \;\;\;\;x + \frac{\frac{t}{z}}{y \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.9% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

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) * 0.3333333333333333d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

   1. associate-*l* 96.4%

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

   2. *-commutative 96.4%

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

3. Simplified 96.4%

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

5. Taylor expanded in t around 0 66.2%

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

6. Final simplification 66.2%

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

Alternative 13: 63.9% accurate, 2.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x - (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 * (0.3333333333333333d0 / z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

   1. associate-*l* 96.4%

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

   2. *-commutative 96.4%

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

3. Simplified 96.4%

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

5. Taylor expanded in t around 0 66.2%

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

   1. clear-num 66.2%

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

   2. un-div-inv 66.2%

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

7. Applied egg-rr 66.2%

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

   1. associate-/r/ 66.2%

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

9. Applied egg-rr 66.2%

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

10. Final simplification 66.2%

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

Alternative 14: 63.9% accurate, 2.1× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z, double t) {
	return x - (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 - (y / (z * 3.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

   1. associate-*l* 96.4%

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

   2. *-commutative 96.4%

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

3. Simplified 96.4%

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

   1. associate-+l- 96.4%

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

   2. *-commutative 96.4%

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

   3. associate-*l* 96.4%

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

   4. associate-/l/ 95.7%

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

   5. sub-div 96.1%

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

6. Applied egg-rr 96.1%

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

7. Taylor expanded in y around inf 66.2%

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

8. Final simplification 66.2%

   \[\leadsto x - \frac{y}{z \cdot 3} \]
9. Add Preprocessing

Alternative 15: 30.1% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.4%

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

   1. associate-*l* 96.4%

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

   2. *-commutative 96.4%

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

3. Simplified 96.4%

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

5. Taylor expanded in x around inf 29.0%

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

6. Final simplification 29.0%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 96.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024010 
(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))))