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

Percentage Accurate: 95.6% → 96.1%

Time: 11.6s

Alternatives: 19

Speedup: 1.0×

• 26.8% 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: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{y}{z \cdot 3}\\ \mathbf{if}\;x \leq -3.4 \cdot 10^{-185}:\\ \;\;\;\;t\_1 + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- x (/ y (* z 3.0)))))
   (if (<= x -3.4e-185)
     (+ t_1 (/ t (* y (* z 3.0))))
     (+ t_1 (/ (* t (/ 0.3333333333333333 z)) y)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if (x <= -3.4e-185) {
		tmp = t_1 + (t / (y * (z * 3.0)));
	} else {
		tmp = t_1 + ((t * (0.3333333333333333 / z)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - (y / (z * 3.0d0))
    if (x <= (-3.4d-185)) then
        tmp = t_1 + (t / (y * (z * 3.0d0)))
    else
        tmp = t_1 + ((t * (0.3333333333333333d0 / z)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x - (y / (z * 3.0));
	double tmp;
	if (x <= -3.4e-185) {
		tmp = t_1 + (t / (y * (z * 3.0)));
	} else {
		tmp = t_1 + ((t * (0.3333333333333333 / z)) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x - (y / (z * 3.0))
	tmp = 0
	if x <= -3.4e-185:
		tmp = t_1 + (t / (y * (z * 3.0)))
	else:
		tmp = t_1 + ((t * (0.3333333333333333 / z)) / y)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x - Float64(y / Float64(z * 3.0)))
	tmp = 0.0
	if (x <= -3.4e-185)
		tmp = Float64(t_1 + Float64(t / Float64(y * Float64(z * 3.0))));
	else
		tmp = Float64(t_1 + Float64(Float64(t * Float64(0.3333333333333333 / z)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x - (y / (z * 3.0));
	tmp = 0.0;
	if (x <= -3.4e-185)
		tmp = t_1 + (t / (y * (z * 3.0)));
	else
		tmp = t_1 + ((t * (0.3333333333333333 / z)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -3.4e-185], N[(t$95$1 + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$1 + N[(N[(t * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.3999999999999998e-185

   1. Initial program 98.9%

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

   if -3.3999999999999998e-185 < x

   1. Initial program 96.4%

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

      1. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \left(\frac{\frac{t}{z \cdot 3}}{\color{blue}{y}}\right)\right) \]

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\left(\frac{t}{z \cdot 3}\right), \color{blue}{y}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\left(t \cdot \frac{1}{z \cdot 3}\right), y\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{1}{z \cdot 3}\right)\right), y\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{1}{3 \cdot z}\right)\right), y\right)\right) \]

      6. associate-/r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{\frac{1}{3}}{z}\right)\right), y\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{\frac{1}{3}}{z}\right)\right), y\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \left(\frac{\mathsf{neg}\left(\frac{-1}{3}\right)}{z}\right)\right), y\right)\right) \]

      9. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\left(\mathsf{neg}\left(\frac{-1}{3}\right)\right), z\right)\right), y\right)\right) \]

      10. metadata-eval 99.2%

          \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \mathsf{/.f64}\left(\frac{1}{3}, z\right)\right), y\right)\right) \]

   4. Applied egg-rr 99.2%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{-185}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t \cdot \frac{0.3333333333333333}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{-3}}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -9e-38)
   (+ x (/ (/ (- y (/ t y)) -3.0) z))
   (if (<= y 1.4e-62)
     (+ x (/ (* 0.3333333333333333 (/ t z)) y))
     (+ x (/ (- (/ t y) y) (* z 3.0))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-38) {
		tmp = x + (((y - (t / y)) / -3.0) / z);
	} else if (y <= 1.4e-62) {
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-9d-38)) then
        tmp = x + (((y - (t / y)) / (-3.0d0)) / z)
    else if (y <= 1.4d-62) then
        tmp = x + ((0.3333333333333333d0 * (t / z)) / y)
    else
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -9e-38) {
		tmp = x + (((y - (t / y)) / -3.0) / z);
	} else if (y <= 1.4e-62) {
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -9e-38:
		tmp = x + (((y - (t / y)) / -3.0) / z)
	elif y <= 1.4e-62:
		tmp = x + ((0.3333333333333333 * (t / z)) / y)
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -9e-38)
		tmp = Float64(x + Float64(Float64(Float64(y - Float64(t / y)) / -3.0) / z));
	elseif (y <= 1.4e-62)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 * Float64(t / z)) / y));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -9e-38)
		tmp = x + (((y - (t / y)) / -3.0) / z);
	elseif (y <= 1.4e-62)
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -9e-38], N[(x + N[(N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / -3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e-62], N[(x + N[(N[(0.3333333333333333 * N[(t / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.00000000000000018e-38

   1. Initial program 99.7%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 99.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}}\right)\right) \]

      9. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}}\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{1}{-3}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{-1}{3}\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{z}\right), \color{blue}{\frac{-1}{3}}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), z\right), \frac{-1}{3}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), z\right), \frac{-1}{3}\right)\right) \]

      15. /-lowering-/.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), z\right), \frac{-1}{3}\right)\right) \]

   6. Applied egg-rr 99.6%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{-1}{3}}{\color{blue}{z}}\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{1}{-3}}{z}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{y - \frac{t}{y}}{-3}}{z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y - \frac{t}{y}}{-3}\right), \color{blue}{z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), -3\right), z\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), -3\right), z\right)\right) \]

      7. /-lowering-/.f64 99.8%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), z\right)\right) \]

   8. Applied egg-rr 99.8%

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

   if -9.00000000000000018e-38 < y < 1.40000000000000001e-62

   1. Initial program 93.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 85.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 85.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}}\right)\right) \]

      9. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}}\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{1}{-3}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{-1}{3}\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{z}\right), \color{blue}{\frac{-1}{3}}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), z\right), \frac{-1}{3}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), z\right), \frac{-1}{3}\right)\right) \]

      15. /-lowering-/.f64 85.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), z\right), \frac{-1}{3}\right)\right) \]

   6. Applied egg-rr 85.5%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{-1}{3}}{\color{blue}{z}}\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{1}{-3}}{z}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{y - \frac{t}{y}}{-3}}{z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y - \frac{t}{y}}{-3}\right), \color{blue}{z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), -3\right), z\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), -3\right), z\right)\right) \]

      7. /-lowering-/.f64 85.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), z\right)\right) \]

   8. Applied egg-rr 85.4%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1}{3} \cdot \frac{t}{y \cdot z}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-/l/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{1}{3} \cdot \frac{\frac{t}{z}}{\color{blue}{y}}\right)\right) \]

       2. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{1}{3} \cdot \frac{t}{z}}{\color{blue}{y}}\right)\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot \frac{t}{z}\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(\frac{t}{z}\right)\right), y\right)\right) \]

       5. /-lowering-/.f64 97.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{/.f64}\left(t, z\right)\right), y\right)\right) \]

   11. Simplified 97.6%

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

   if 1.40000000000000001e-62 < y

   1. Initial program 99.9%

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

      1. associate-+l- N/A

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

      2. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \color{blue}{\left(\frac{y}{z \cdot 3} - \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{t}{y \cdot \color{blue}{\left(z \cdot 3\right)}}\right)\right) \]

      4. associate-/r* N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y}{z \cdot 3} - \frac{\frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      5. sub-div N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\color{blue}{z \cdot 3}}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

      7. --lowering--.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\color{blue}{z} \cdot 3\right)\right)\right) \]

      8. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(z \cdot 3\right)\right)\right) \]

      9. *-lowering-*.f64 98.8%

         \[\leadsto \mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \mathsf{*.f64}\left(z, \color{blue}{3}\right)\right)\right) \]

   4. Applied egg-rr 98.8%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{\frac{y - \frac{t}{y}}{-3}}{z}\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{-62}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{t}{y} - y}{z \cdot 3}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\frac{y - \frac{t}{y}}{-3}}{z}\\ \mathbf{if}\;y \leq -9 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (/ (/ (- y (/ t y)) -3.0) z))))
   (if (<= y -9e-38)
     t_1
     (if (<= y 8e-63) (+ x (/ (* 0.3333333333333333 (/ t z)) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - (t / y)) / -3.0) / z);
	double tmp;
	if (y <= -9e-38) {
		tmp = t_1;
	} else if (y <= 8e-63) {
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	} else {
		tmp = t_1;
	}
	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 = x + (((y - (t / y)) / (-3.0d0)) / z)
    if (y <= (-9d-38)) then
        tmp = t_1
    else if (y <= 8d-63) then
        tmp = x + ((0.3333333333333333d0 * (t / z)) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (((y - (t / y)) / -3.0) / z);
	double tmp;
	if (y <= -9e-38) {
		tmp = t_1;
	} else if (y <= 8e-63) {
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (((y - (t / y)) / -3.0) / z)
	tmp = 0
	if y <= -9e-38:
		tmp = t_1
	elif y <= 8e-63:
		tmp = x + ((0.3333333333333333 * (t / z)) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(Float64(y - Float64(t / y)) / -3.0) / z))
	tmp = 0.0
	if (y <= -9e-38)
		tmp = t_1;
	elseif (y <= 8e-63)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 * Float64(t / z)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (((y - (t / y)) / -3.0) / z);
	tmp = 0.0;
	if (y <= -9e-38)
		tmp = t_1;
	elseif (y <= 8e-63)
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / -3.0), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-38], t$95$1, If[LessEqual[y, 8e-63], N[(x + N[(N[(0.3333333333333333 * N[(t / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.00000000000000018e-38 or 8.00000000000000053e-63 < y

   1. Initial program 99.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 99.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 99.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}}\right)\right) \]

      9. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}}\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{1}{-3}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{-1}{3}\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{z}\right), \color{blue}{\frac{-1}{3}}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), z\right), \frac{-1}{3}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), z\right), \frac{-1}{3}\right)\right) \]

      15. /-lowering-/.f64 99.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), z\right), \frac{-1}{3}\right)\right) \]

   6. Applied egg-rr 99.1%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{-1}{3}}{\color{blue}{z}}\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{1}{-3}}{z}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{y - \frac{t}{y}}{-3}}{z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y - \frac{t}{y}}{-3}\right), \color{blue}{z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), -3\right), z\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), -3\right), z\right)\right) \]

      7. /-lowering-/.f64 99.3%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), z\right)\right) \]

   8. Applied egg-rr 99.3%

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

   if -9.00000000000000018e-38 < y < 8.00000000000000053e-63

   1. Initial program 93.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 85.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 85.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}}\right)\right) \]

      9. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}}\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{1}{-3}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{-1}{3}\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{z}\right), \color{blue}{\frac{-1}{3}}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), z\right), \frac{-1}{3}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), z\right), \frac{-1}{3}\right)\right) \]

      15. /-lowering-/.f64 85.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), z\right), \frac{-1}{3}\right)\right) \]

   6. Applied egg-rr 85.5%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{-1}{3}}{\color{blue}{z}}\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{1}{-3}}{z}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{y - \frac{t}{y}}{-3}}{z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y - \frac{t}{y}}{-3}\right), \color{blue}{z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), -3\right), z\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), -3\right), z\right)\right) \]

      7. /-lowering-/.f64 85.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), z\right)\right) \]

   8. Applied egg-rr 85.4%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1}{3} \cdot \frac{t}{y \cdot z}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-/l/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{1}{3} \cdot \frac{\frac{t}{z}}{\color{blue}{y}}\right)\right) \]

       2. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{1}{3} \cdot \frac{t}{z}}{\color{blue}{y}}\right)\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot \frac{t}{z}\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(\frac{t}{z}\right)\right), y\right)\right) \]

       5. /-lowering-/.f64 97.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{/.f64}\left(t, z\right)\right), y\right)\right) \]

   11. Simplified 97.6%

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

Alternative 4: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{t\_1}{z} \cdot -0.3333333333333333\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + t\_1 \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- y (/ t y))))
   (if (<= y -9e-38)
     (+ x (* (/ t_1 z) -0.3333333333333333))
     (if (<= y 2.5e-60)
       (+ x (/ (* 0.3333333333333333 (/ t z)) y))
       (+ x (* t_1 (/ -0.3333333333333333 z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -9e-38) {
		tmp = x + ((t_1 / z) * -0.3333333333333333);
	} else if (y <= 2.5e-60) {
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	} else {
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y - (t / y)
    if (y <= (-9d-38)) then
        tmp = x + ((t_1 / z) * (-0.3333333333333333d0))
    else if (y <= 2.5d-60) then
        tmp = x + ((0.3333333333333333d0 * (t / z)) / y)
    else
        tmp = x + (t_1 * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -9e-38) {
		tmp = x + ((t_1 / z) * -0.3333333333333333);
	} else if (y <= 2.5e-60) {
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	} else {
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y - (t / y)
	tmp = 0
	if y <= -9e-38:
		tmp = x + ((t_1 / z) * -0.3333333333333333)
	elif y <= 2.5e-60:
		tmp = x + ((0.3333333333333333 * (t / z)) / y)
	else:
		tmp = x + (t_1 * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y - Float64(t / y))
	tmp = 0.0
	if (y <= -9e-38)
		tmp = Float64(x + Float64(Float64(t_1 / z) * -0.3333333333333333));
	elseif (y <= 2.5e-60)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 * Float64(t / z)) / y));
	else
		tmp = Float64(x + Float64(t_1 * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y - (t / y);
	tmp = 0.0;
	if (y <= -9e-38)
		tmp = x + ((t_1 / z) * -0.3333333333333333);
	elseif (y <= 2.5e-60)
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	else
		tmp = x + (t_1 * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-38], N[(x + N[(N[(t$95$1 / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-60], N[(x + N[(N[(0.3333333333333333 * N[(t / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(t$95$1 * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9.00000000000000018e-38

   1. Initial program 99.7%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 99.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}}\right)\right) \]

      9. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}}\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{1}{-3}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{-1}{3}\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{z}\right), \color{blue}{\frac{-1}{3}}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), z\right), \frac{-1}{3}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), z\right), \frac{-1}{3}\right)\right) \]

      15. /-lowering-/.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), z\right), \frac{-1}{3}\right)\right) \]

   6. Applied egg-rr 99.6%

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

   if -9.00000000000000018e-38 < y < 2.5000000000000001e-60

   1. Initial program 93.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 85.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 85.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}}\right)\right) \]

      9. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}}\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{1}{-3}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{-1}{3}\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{z}\right), \color{blue}{\frac{-1}{3}}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), z\right), \frac{-1}{3}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), z\right), \frac{-1}{3}\right)\right) \]

      15. /-lowering-/.f64 85.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), z\right), \frac{-1}{3}\right)\right) \]

   6. Applied egg-rr 85.5%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{-1}{3}}{\color{blue}{z}}\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{1}{-3}}{z}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{y - \frac{t}{y}}{-3}}{z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y - \frac{t}{y}}{-3}\right), \color{blue}{z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), -3\right), z\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), -3\right), z\right)\right) \]

      7. /-lowering-/.f64 85.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), z\right)\right) \]

   8. Applied egg-rr 85.4%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1}{3} \cdot \frac{t}{y \cdot z}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-/l/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{1}{3} \cdot \frac{\frac{t}{z}}{\color{blue}{y}}\right)\right) \]

       2. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{1}{3} \cdot \frac{t}{z}}{\color{blue}{y}}\right)\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot \frac{t}{z}\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(\frac{t}{z}\right)\right), y\right)\right) \]

       5. /-lowering-/.f64 97.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{/.f64}\left(t, z\right)\right), y\right)\right) \]

   11. Simplified 97.6%

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

   if 2.5000000000000001e-60 < y

   1. Initial program 99.9%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 98.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 98.7%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-38}:\\ \;\;\;\;x + \frac{y - \frac{t}{y}}{z} \cdot -0.3333333333333333\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-60}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -9 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (- y (/ t y)) (/ -0.3333333333333333 z)))))
   (if (<= y -9e-38)
     t_1
     (if (<= y 5.4e-63) (+ x (/ (* 0.3333333333333333 (/ t z)) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -9e-38) {
		tmp = t_1;
	} else if (y <= 5.4e-63) {
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	} else {
		tmp = t_1;
	}
	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 = x + ((y - (t / y)) * ((-0.3333333333333333d0) / z))
    if (y <= (-9d-38)) then
        tmp = t_1
    else if (y <= 5.4d-63) then
        tmp = x + ((0.3333333333333333d0 * (t / z)) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -9e-38) {
		tmp = t_1;
	} else if (y <= 5.4e-63) {
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y - (t / y)) * (-0.3333333333333333 / z))
	tmp = 0
	if y <= -9e-38:
		tmp = t_1
	elif y <= 5.4e-63:
		tmp = x + ((0.3333333333333333 * (t / z)) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y - Float64(t / y)) * Float64(-0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -9e-38)
		tmp = t_1;
	elseif (y <= 5.4e-63)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 * Float64(t / z)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y - (t / y)) * (-0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -9e-38)
		tmp = t_1;
	elseif (y <= 5.4e-63)
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -9e-38], t$95$1, If[LessEqual[y, 5.4e-63], N[(x + N[(N[(0.3333333333333333 * N[(t / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.00000000000000018e-38 or 5.4000000000000004e-63 < y

   1. Initial program 99.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 99.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 99.2%

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

   if -9.00000000000000018e-38 < y < 5.4000000000000004e-63

   1. Initial program 93.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 85.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 85.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}}\right)\right) \]

      9. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}}\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{1}{-3}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{-1}{3}\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{z}\right), \color{blue}{\frac{-1}{3}}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), z\right), \frac{-1}{3}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), z\right), \frac{-1}{3}\right)\right) \]

      15. /-lowering-/.f64 85.5%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), z\right), \frac{-1}{3}\right)\right) \]

   6. Applied egg-rr 85.5%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{-1}{3}}{\color{blue}{z}}\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{1}{-3}}{z}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{y - \frac{t}{y}}{-3}}{z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y - \frac{t}{y}}{-3}\right), \color{blue}{z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), -3\right), z\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), -3\right), z\right)\right) \]

      7. /-lowering-/.f64 85.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), z\right)\right) \]

   8. Applied egg-rr 85.4%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1}{3} \cdot \frac{t}{y \cdot z}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-/l/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{1}{3} \cdot \frac{\frac{t}{z}}{\color{blue}{y}}\right)\right) \]

       2. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{1}{3} \cdot \frac{t}{z}}{\color{blue}{y}}\right)\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot \frac{t}{z}\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(\frac{t}{z}\right)\right), y\right)\right) \]

       5. /-lowering-/.f64 97.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{/.f64}\left(t, z\right)\right), y\right)\right) \]

   11. Simplified 97.6%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{-38}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 5.4 \cdot 10^{-63}:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - \frac{t}{y}\right) \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+28}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-99}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{elif}\;y \leq 1.42 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{-0.3333333333333333}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6e+28)
   (/ (/ y -3.0) z)
   (if (<= y 6.2e-99)
     (* (/ t z) (/ 0.3333333333333333 y))
     (if (<= y 1.42e+23) x (/ y (/ z -0.3333333333333333))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e+28) {
		tmp = (y / -3.0) / z;
	} else if (y <= 6.2e-99) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else if (y <= 1.42e+23) {
		tmp = x;
	} else {
		tmp = y / (z / -0.3333333333333333);
	}
	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 <= (-6d+28)) then
        tmp = (y / (-3.0d0)) / z
    else if (y <= 6.2d-99) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else if (y <= 1.42d+23) then
        tmp = x
    else
        tmp = y / (z / (-0.3333333333333333d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6e+28) {
		tmp = (y / -3.0) / z;
	} else if (y <= 6.2e-99) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else if (y <= 1.42e+23) {
		tmp = x;
	} else {
		tmp = y / (z / -0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6e+28:
		tmp = (y / -3.0) / z
	elif y <= 6.2e-99:
		tmp = (t / z) * (0.3333333333333333 / y)
	elif y <= 1.42e+23:
		tmp = x
	else:
		tmp = y / (z / -0.3333333333333333)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6e+28)
		tmp = Float64(Float64(y / -3.0) / z);
	elseif (y <= 6.2e-99)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	elseif (y <= 1.42e+23)
		tmp = x;
	else
		tmp = Float64(y / Float64(z / -0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6e+28)
		tmp = (y / -3.0) / z;
	elseif (y <= 6.2e-99)
		tmp = (t / z) * (0.3333333333333333 / y);
	elseif (y <= 1.42e+23)
		tmp = x;
	else
		tmp = y / (z / -0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6e+28], N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[y, 6.2e-99], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.42e+23], x, N[(y / N[(z / -0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.0000000000000002e28

   1. Initial program 99.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(y \cdot \color{blue}{\left(z \cdot 3\right)}\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(\left(y \cdot z\right) \cdot \color{blue}{3}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot z\right), \color{blue}{3}\right)\right)\right) \]

      4. *-lowering-*.f64 99.7%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), 3\right)\right)\right) \]

   4. Applied egg-rr 99.7%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot y\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), z\right) \]

      4. *-lowering-*.f64 74.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{3}\right), z\right) \]

   7. Simplified 74.3%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), \color{blue}{z}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{1}{-3}\right), z\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{y}{-3}\right), z\right) \]

      4. /-lowering-/.f64 74.4%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, -3\right), z\right) \]

   9. Applied egg-rr 74.4%

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

   if -6.0000000000000002e28 < y < 6.1999999999999997e-99

   1. Initial program 94.2%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 88.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 88.0%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot t\right), \color{blue}{\left(y \cdot z\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \frac{1}{3}\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{1}{3}\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      5. *-lowering-*.f64 67.3%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{1}{3}\right), \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Simplified 67.3%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{z}\right), \color{blue}{\left(\frac{\frac{1}{3}}{y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, z\right), \left(\frac{\color{blue}{\frac{1}{3}}}{y}\right)\right) \]

      5. /-lowering-/.f64 69.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, z\right), \mathsf{/.f64}\left(\frac{1}{3}, \color{blue}{y}\right)\right) \]

   9. Applied egg-rr 69.6%

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

   if 6.1999999999999997e-99 < y < 1.42000000000000004e23

   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. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 94.3%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 94.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 55.9%

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

   if 1.42000000000000004e23 < y

   1. Initial program 99.9%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(y \cdot \color{blue}{\left(z \cdot 3\right)}\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(\left(y \cdot z\right) \cdot \color{blue}{3}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot z\right), \color{blue}{3}\right)\right)\right) \]

      4. *-lowering-*.f64 99.9%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), 3\right)\right)\right) \]

   4. Applied egg-rr 99.9%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot y\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), z\right) \]

      4. *-lowering-*.f64 70.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{3}\right), z\right) \]

   7. Simplified 70.0%

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

      1. metadata-eval N/A

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

      2. div-inv N/A

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

      3. associate-/l/ N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(z \cdot -3\right)}\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(z \cdot \frac{1}{\color{blue}{\frac{-1}{3}}}\right)\right) \]

      6. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\frac{z}{\color{blue}{\frac{-1}{3}}}\right)\right) \]

      7. /-lowering-/.f64 70.2%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{\frac{-1}{3}}\right)\right) \]

   9. Applied egg-rr 70.2%

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

Alternative 7: 92.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{-3} \cdot \frac{1}{z}\\ \mathbf{if}\;y \leq -4 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 31000000:\\ \;\;\;\;x + \frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (/ y -3.0) (/ 1.0 z)))))
   (if (<= y -4e+34)
     t_1
     (if (<= y 31000000.0) (+ x (/ (* 0.3333333333333333 (/ t z)) y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / -3.0) * (1.0 / z));
	double tmp;
	if (y <= -4e+34) {
		tmp = t_1;
	} else if (y <= 31000000.0) {
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	} else {
		tmp = t_1;
	}
	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 = x + ((y / (-3.0d0)) * (1.0d0 / z))
    if (y <= (-4d+34)) then
        tmp = t_1
    else if (y <= 31000000.0d0) then
        tmp = x + ((0.3333333333333333d0 * (t / z)) / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / -3.0) * (1.0 / z));
	double tmp;
	if (y <= -4e+34) {
		tmp = t_1;
	} else if (y <= 31000000.0) {
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y / -3.0) * (1.0 / z))
	tmp = 0
	if y <= -4e+34:
		tmp = t_1
	elif y <= 31000000.0:
		tmp = x + ((0.3333333333333333 * (t / z)) / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y / -3.0) * Float64(1.0 / z)))
	tmp = 0.0
	if (y <= -4e+34)
		tmp = t_1;
	elseif (y <= 31000000.0)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 * Float64(t / z)) / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y / -3.0) * (1.0 / z));
	tmp = 0.0;
	if (y <= -4e+34)
		tmp = t_1;
	elseif (y <= 31000000.0)
		tmp = x + ((0.3333333333333333 * (t / z)) / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y / -3.0), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4e+34], t$95$1, If[LessEqual[y, 31000000.0], N[(x + N[(N[(0.3333333333333333 * N[(t / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999978e34 or 3.1e7 < y

   1. Initial program 99.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 99.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\mathsf{neg}\left(3 \cdot z\right)}\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\left(\mathsf{neg}\left(3\right)\right) \cdot \color{blue}{z}}\right)\right) \]

      10. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\mathsf{neg}\left(3\right)} \cdot \color{blue}{\frac{1}{z}}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{\mathsf{neg}\left(3\right)}\right), \color{blue}{\left(\frac{1}{z}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \left(\mathsf{neg}\left(3\right)\right)\right), \left(\frac{\color{blue}{1}}{z}\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\mathsf{neg}\left(3\right)\right)\right), \left(\frac{1}{z}\right)\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(\mathsf{neg}\left(3\right)\right)\right), \left(\frac{1}{z}\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), \left(\frac{1}{z}\right)\right)\right) \]

      16. /-lowering-/.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), \mathsf{/.f64}\left(1, \color{blue}{z}\right)\right)\right) \]

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\color{blue}{y}, -3\right), \mathsf{/.f64}\left(1, z\right)\right)\right) \]
   8. Step-by-step derivation

   9. Simplified 94.4%

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

   if -3.99999999999999978e34 < y < 3.1e7

   1. Initial program 95.4%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 89.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 89.4%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}}\right)\right) \]

      9. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}}\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{1}{-3}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{-1}{3}\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{z}\right), \color{blue}{\frac{-1}{3}}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), z\right), \frac{-1}{3}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), z\right), \frac{-1}{3}\right)\right) \]

      15. /-lowering-/.f64 89.4%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), z\right), \frac{-1}{3}\right)\right) \]

   6. Applied egg-rr 89.4%

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

      1. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{-1}{3}}{\color{blue}{z}}\right)\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot \frac{1}{-3}}{z}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{y - \frac{t}{y}}{-3}}{z}\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{y - \frac{t}{y}}{-3}\right), \color{blue}{z}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), -3\right), z\right)\right) \]

      6. --lowering--.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), -3\right), z\right)\right) \]

      7. /-lowering-/.f64 89.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), z\right)\right) \]

   8. Applied egg-rr 89.4%

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

   9. Taylor expanded in y around 0

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\frac{1}{3} \cdot \frac{t}{y \cdot z}\right)}\right) \]
   10. Step-by-step derivation

       1. associate-/l/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{1}{3} \cdot \frac{\frac{t}{z}}{\color{blue}{y}}\right)\right) \]

       2. associate-*r/ N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\frac{1}{3} \cdot \frac{t}{z}}{\color{blue}{y}}\right)\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot \frac{t}{z}\right), \color{blue}{y}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \left(\frac{t}{z}\right)\right), y\right)\right) \]

       5. /-lowering-/.f64 92.0%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{/.f64}\left(\mathsf{*.f64}\left(\frac{1}{3}, \mathsf{/.f64}\left(t, z\right)\right), y\right)\right) \]

   11. Simplified 92.0%

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

Alternative 8: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{-3} \cdot \frac{1}{z}\\ \mathbf{if}\;y \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 45000000000000:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (/ y -3.0) (/ 1.0 z)))))
   (if (<= y -3.4e+42)
     t_1
     (if (<= y 45000000000000.0) (+ x (/ t (* y (* z 3.0)))) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / -3.0) * (1.0 / z));
	double tmp;
	if (y <= -3.4e+42) {
		tmp = t_1;
	} else if (y <= 45000000000000.0) {
		tmp = x + (t / (y * (z * 3.0)));
	} else {
		tmp = t_1;
	}
	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 = x + ((y / (-3.0d0)) * (1.0d0 / z))
    if (y <= (-3.4d+42)) then
        tmp = t_1
    else if (y <= 45000000000000.0d0) then
        tmp = x + (t / (y * (z * 3.0d0)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / -3.0) * (1.0 / z));
	double tmp;
	if (y <= -3.4e+42) {
		tmp = t_1;
	} else if (y <= 45000000000000.0) {
		tmp = x + (t / (y * (z * 3.0)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y / -3.0) * (1.0 / z))
	tmp = 0
	if y <= -3.4e+42:
		tmp = t_1
	elif y <= 45000000000000.0:
		tmp = x + (t / (y * (z * 3.0)))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y / -3.0) * Float64(1.0 / z)))
	tmp = 0.0
	if (y <= -3.4e+42)
		tmp = t_1;
	elseif (y <= 45000000000000.0)
		tmp = Float64(x + Float64(t / Float64(y * Float64(z * 3.0))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y / -3.0) * (1.0 / z));
	tmp = 0.0;
	if (y <= -3.4e+42)
		tmp = t_1;
	elseif (y <= 45000000000000.0)
		tmp = x + (t / (y * (z * 3.0)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y / -3.0), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.4e+42], t$95$1, If[LessEqual[y, 45000000000000.0], N[(x + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.39999999999999975e42 or 4.5e13 < y

   1. Initial program 99.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 99.7%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\mathsf{neg}\left(3 \cdot z\right)}\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\left(\mathsf{neg}\left(3\right)\right) \cdot \color{blue}{z}}\right)\right) \]

      10. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\mathsf{neg}\left(3\right)} \cdot \color{blue}{\frac{1}{z}}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{\mathsf{neg}\left(3\right)}\right), \color{blue}{\left(\frac{1}{z}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \left(\mathsf{neg}\left(3\right)\right)\right), \left(\frac{\color{blue}{1}}{z}\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\mathsf{neg}\left(3\right)\right)\right), \left(\frac{1}{z}\right)\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(\mathsf{neg}\left(3\right)\right)\right), \left(\frac{1}{z}\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), \left(\frac{1}{z}\right)\right)\right) \]

      16. /-lowering-/.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), \mathsf{/.f64}\left(1, \color{blue}{z}\right)\right)\right) \]

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\color{blue}{y}, -3\right), \mathsf{/.f64}\left(1, z\right)\right)\right) \]
   8. Step-by-step derivation

   9. Simplified 94.4%

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

   if -3.39999999999999975e42 < y < 4.5e13

   1. Initial program 95.4%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{x}, \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 3\right), y\right)\right)\right) \]
   4. Step-by-step derivation

   5. Simplified 89.6%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;x + \frac{y}{-3} \cdot \frac{1}{z}\\ \mathbf{elif}\;y \leq 45000000000000:\\ \;\;\;\;x + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{-3} \cdot \frac{1}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{-3} \cdot \frac{1}{z}\\ \mathbf{if}\;y \leq -1.02 \cdot 10^{-28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-99}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* (/ y -3.0) (/ 1.0 z)))))
   (if (<= y -1.02e-28)
     t_1
     (if (<= y 3.5e-99) (* (/ t z) (/ 0.3333333333333333 y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / -3.0) * (1.0 / z));
	double tmp;
	if (y <= -1.02e-28) {
		tmp = t_1;
	} else if (y <= 3.5e-99) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = t_1;
	}
	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 = x + ((y / (-3.0d0)) * (1.0d0 / z))
    if (y <= (-1.02d-28)) then
        tmp = t_1
    else if (y <= 3.5d-99) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + ((y / -3.0) * (1.0 / z));
	double tmp;
	if (y <= -1.02e-28) {
		tmp = t_1;
	} else if (y <= 3.5e-99) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + ((y / -3.0) * (1.0 / z))
	tmp = 0
	if y <= -1.02e-28:
		tmp = t_1
	elif y <= 3.5e-99:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(Float64(y / -3.0) * Float64(1.0 / z)))
	tmp = 0.0
	if (y <= -1.02e-28)
		tmp = t_1;
	elseif (y <= 3.5e-99)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + ((y / -3.0) * (1.0 / z));
	tmp = 0.0;
	if (y <= -1.02e-28)
		tmp = t_1;
	elseif (y <= 3.5e-99)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(N[(y / -3.0), $MachinePrecision] * N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.02e-28], t$95$1, If[LessEqual[y, 3.5e-99], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.01999999999999997e-28 or 3.4999999999999999e-99 < y

   1. Initial program 99.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 98.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 98.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\mathsf{neg}\left(3 \cdot z\right)}\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\left(\mathsf{neg}\left(3\right)\right) \cdot \color{blue}{z}}\right)\right) \]

      10. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\mathsf{neg}\left(3\right)} \cdot \color{blue}{\frac{1}{z}}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{\mathsf{neg}\left(3\right)}\right), \color{blue}{\left(\frac{1}{z}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \left(\mathsf{neg}\left(3\right)\right)\right), \left(\frac{\color{blue}{1}}{z}\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\mathsf{neg}\left(3\right)\right)\right), \left(\frac{1}{z}\right)\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(\mathsf{neg}\left(3\right)\right)\right), \left(\frac{1}{z}\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), \left(\frac{1}{z}\right)\right)\right) \]

      16. /-lowering-/.f64 98.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), \mathsf{/.f64}\left(1, \color{blue}{z}\right)\right)\right) \]

   6. Applied egg-rr 98.6%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\color{blue}{y}, -3\right), \mathsf{/.f64}\left(1, z\right)\right)\right) \]
   8. Step-by-step derivation

   9. Simplified 84.8%

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

   if -1.01999999999999997e-28 < y < 3.4999999999999999e-99

   1. Initial program 93.3%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 86.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 86.1%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot t\right), \color{blue}{\left(y \cdot z\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \frac{1}{3}\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{1}{3}\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      5. *-lowering-*.f64 70.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{1}{3}\right), \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Simplified 70.0%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{z}\right), \color{blue}{\left(\frac{\frac{1}{3}}{y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, z\right), \left(\frac{\color{blue}{\frac{1}{3}}}{y}\right)\right) \]

      5. /-lowering-/.f64 73.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, z\right), \mathsf{/.f64}\left(\frac{1}{3}, \color{blue}{y}\right)\right) \]

   9. Applied egg-rr 73.6%

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

Alternative 10: 78.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{1}{z} \cdot \left(y \cdot -0.3333333333333333\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-99}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -2.05e-29)
   (+ x (* (/ 1.0 z) (* y -0.3333333333333333)))
   (if (<= y 6.2e-99)
     (* (/ t z) (/ 0.3333333333333333 y))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.05e-29) {
		tmp = x + ((1.0 / z) * (y * -0.3333333333333333));
	} else if (y <= 6.2e-99) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-2.05d-29)) then
        tmp = x + ((1.0d0 / z) * (y * (-0.3333333333333333d0)))
    else if (y <= 6.2d-99) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -2.05e-29) {
		tmp = x + ((1.0 / z) * (y * -0.3333333333333333));
	} else if (y <= 6.2e-99) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -2.05e-29:
		tmp = x + ((1.0 / z) * (y * -0.3333333333333333))
	elif y <= 6.2e-99:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -2.05e-29)
		tmp = Float64(x + Float64(Float64(1.0 / z) * Float64(y * -0.3333333333333333)));
	elseif (y <= 6.2e-99)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -2.05e-29)
		tmp = x + ((1.0 / z) * (y * -0.3333333333333333));
	elseif (y <= 6.2e-99)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -2.05e-29], N[(x + N[(N[(1.0 / z), $MachinePrecision] * N[(y * -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.2e-99], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.0499999999999999e-29

   1. Initial program 99.7%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 99.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

      8. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\mathsf{neg}\left(3 \cdot z\right)}\right)\right) \]

      9. distribute-lft-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\left(\mathsf{neg}\left(3\right)\right) \cdot \color{blue}{z}}\right)\right) \]

      10. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{\mathsf{neg}\left(3\right)} \cdot \color{blue}{\frac{1}{z}}\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{\mathsf{neg}\left(3\right)}\right), \color{blue}{\left(\frac{1}{z}\right)}\right)\right) \]

      12. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), \left(\mathsf{neg}\left(3\right)\right)\right), \left(\frac{\color{blue}{1}}{z}\right)\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), \left(\mathsf{neg}\left(3\right)\right)\right), \left(\frac{1}{z}\right)\right)\right) \]

      14. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), \left(\mathsf{neg}\left(3\right)\right)\right), \left(\frac{1}{z}\right)\right)\right) \]

      15. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), \left(\frac{1}{z}\right)\right)\right) \]

      16. /-lowering-/.f64 99.7%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), -3\right), \mathsf{/.f64}\left(1, \color{blue}{z}\right)\right)\right) \]

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{-1}{3} \cdot y\right)}, \mathsf{/.f64}\left(1, z\right)\right)\right) \]
   8. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(y \cdot \frac{-1}{3}\right), \mathsf{/.f64}\left(\color{blue}{1}, z\right)\right)\right) \]

      2. *-lowering-*.f64 84.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{3}\right), \mathsf{/.f64}\left(\color{blue}{1}, z\right)\right)\right) \]

   9. Simplified 84.4%

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

   if -2.0499999999999999e-29 < y < 6.1999999999999997e-99

   1. Initial program 93.3%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 86.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 86.1%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot t\right), \color{blue}{\left(y \cdot z\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \frac{1}{3}\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{1}{3}\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      5. *-lowering-*.f64 70.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{1}{3}\right), \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Simplified 70.0%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{z}\right), \color{blue}{\left(\frac{\frac{1}{3}}{y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, z\right), \left(\frac{\color{blue}{\frac{1}{3}}}{y}\right)\right) \]

      5. /-lowering-/.f64 73.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, z\right), \mathsf{/.f64}\left(\frac{1}{3}, \color{blue}{y}\right)\right) \]

   9. Applied egg-rr 73.6%

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

   if 6.1999999999999997e-99 < y

   1. Initial program 99.9%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 97.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 97.6%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \color{blue}{y}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 85.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-29}:\\ \;\;\;\;x + \frac{1}{z} \cdot \left(y \cdot -0.3333333333333333\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-99}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 78.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-32}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-99}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -6.8e-32)
   (+ x (* -0.3333333333333333 (/ y z)))
   (if (<= y 1.15e-99)
     (* (/ t z) (/ 0.3333333333333333 y))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e-32) {
		tmp = x + (-0.3333333333333333 * (y / z));
	} else if (y <= 1.15e-99) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-6.8d-32)) then
        tmp = x + ((-0.3333333333333333d0) * (y / z))
    else if (y <= 1.15d-99) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -6.8e-32) {
		tmp = x + (-0.3333333333333333 * (y / z));
	} else if (y <= 1.15e-99) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -6.8e-32:
		tmp = x + (-0.3333333333333333 * (y / z))
	elif y <= 1.15e-99:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -6.8e-32)
		tmp = Float64(x + Float64(-0.3333333333333333 * Float64(y / z)));
	elseif (y <= 1.15e-99)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -6.8e-32)
		tmp = x + (-0.3333333333333333 * (y / z));
	elseif (y <= 1.15e-99)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -6.8e-32], N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.15e-99], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.79999999999999956e-32

   1. Initial program 99.7%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 99.6%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \color{blue}{\frac{\frac{-1}{3}}{z}}\right)\right) \]

      2. clear-num N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\color{blue}{\frac{z}{\frac{-1}{3}}}}\right)\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \color{blue}{\frac{1}{\frac{-1}{3}}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot -3}\right)\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{z \cdot \left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      6. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(y - \frac{t}{y}\right) \cdot \frac{1}{\mathsf{neg}\left(z \cdot 3\right)}\right)\right) \]

      7. associate-*r/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{\color{blue}{\mathsf{neg}\left(z \cdot 3\right)}}\right)\right) \]

      8. distribute-rgt-neg-in N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{\left(y - \frac{t}{y}\right) \cdot 1}{z \cdot \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}}\right)\right) \]

      9. times-frac N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \color{blue}{\frac{1}{\mathsf{neg}\left(3\right)}}\right)\right) \]

      10. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{1}{-3}\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y - \frac{t}{y}}{z} \cdot \frac{-1}{3}\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{y - \frac{t}{y}}{z}\right), \color{blue}{\frac{-1}{3}}\right)\right) \]

      13. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(y - \frac{t}{y}\right), z\right), \frac{-1}{3}\right)\right) \]

      14. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \left(\frac{t}{y}\right)\right), z\right), \frac{-1}{3}\right)\right) \]

      15. /-lowering-/.f64 99.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, y\right)\right), z\right), \frac{-1}{3}\right)\right) \]

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\color{blue}{\left(\frac{y}{z}\right)}, \frac{-1}{3}\right)\right) \]
   8. Step-by-step derivation

      1. /-lowering-/.f64 84.4%

         \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(y, z\right), \frac{-1}{3}\right)\right) \]

   9. Simplified 84.4%

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

   if -6.79999999999999956e-32 < y < 1.1499999999999999e-99

   1. Initial program 93.3%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 86.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 86.1%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot t\right), \color{blue}{\left(y \cdot z\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \frac{1}{3}\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{1}{3}\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      5. *-lowering-*.f64 70.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{1}{3}\right), \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Simplified 70.0%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{z}\right), \color{blue}{\left(\frac{\frac{1}{3}}{y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, z\right), \left(\frac{\color{blue}{\frac{1}{3}}}{y}\right)\right) \]

      5. /-lowering-/.f64 73.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, z\right), \mathsf{/.f64}\left(\frac{1}{3}, \color{blue}{y}\right)\right) \]

   9. Applied egg-rr 73.6%

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

   if 1.1499999999999999e-99 < y

   1. Initial program 99.9%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 97.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 97.6%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \color{blue}{y}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 85.1%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-32}:\\ \;\;\;\;x + -0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{-99}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 78.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{if}\;y \leq -2.1 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-99}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ x (* y (/ -0.3333333333333333 z)))))
   (if (<= y -2.1e-31)
     t_1
     (if (<= y 6e-99) (* (/ t z) (/ 0.3333333333333333 y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -2.1e-31) {
		tmp = t_1;
	} else if (y <= 6e-99) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = t_1;
	}
	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 = x + (y * ((-0.3333333333333333d0) / z))
    if (y <= (-2.1d-31)) then
        tmp = t_1
    else if (y <= 6d-99) then
        tmp = (t / z) * (0.3333333333333333d0 / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = x + (y * (-0.3333333333333333 / z));
	double tmp;
	if (y <= -2.1e-31) {
		tmp = t_1;
	} else if (y <= 6e-99) {
		tmp = (t / z) * (0.3333333333333333 / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = x + (y * (-0.3333333333333333 / z))
	tmp = 0
	if y <= -2.1e-31:
		tmp = t_1
	elif y <= 6e-99:
		tmp = (t / z) * (0.3333333333333333 / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)))
	tmp = 0.0
	if (y <= -2.1e-31)
		tmp = t_1;
	elseif (y <= 6e-99)
		tmp = Float64(Float64(t / z) * Float64(0.3333333333333333 / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = x + (y * (-0.3333333333333333 / z));
	tmp = 0.0;
	if (y <= -2.1e-31)
		tmp = t_1;
	elseif (y <= 6e-99)
		tmp = (t / z) * (0.3333333333333333 / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.1e-31], t$95$1, If[LessEqual[y, 6e-99], N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.09999999999999991e-31 or 6.00000000000000012e-99 < y

   1. Initial program 99.8%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 98.6%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 98.6%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \color{blue}{y}\right)\right) \]
   6. Step-by-step derivation

   7. Simplified 84.7%

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

   if -2.09999999999999991e-31 < y < 6.00000000000000012e-99

   1. Initial program 93.3%

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

      1. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 86.1%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 86.1%

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

   5. Taylor expanded in y around 0

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{1}{3} \cdot t\right), \color{blue}{\left(y \cdot z\right)}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(t \cdot \frac{1}{3}\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{1}{3}\right), \left(\color{blue}{y} \cdot z\right)\right) \]

      5. *-lowering-*.f64 70.0%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(t, \frac{1}{3}\right), \mathsf{*.f64}\left(y, \color{blue}{z}\right)\right) \]

   7. Simplified 70.0%

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

      1. *-commutative N/A

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

      2. times-frac N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{t}{z}\right), \color{blue}{\left(\frac{\frac{1}{3}}{y}\right)}\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, z\right), \left(\frac{\color{blue}{\frac{1}{3}}}{y}\right)\right) \]

      5. /-lowering-/.f64 73.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(t, z\right), \mathsf{/.f64}\left(\frac{1}{3}, \color{blue}{y}\right)\right) \]

   9. Applied egg-rr 73.6%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{-31}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{-99}:\\ \;\;\;\;\frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+124}:\\ \;\;\;\;\frac{\frac{y}{-3}}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.2e+131) x (if (<= z 3.9e+124) (/ (/ y -3.0) z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.2e+131) {
		tmp = x;
	} else if (z <= 3.9e+124) {
		tmp = (y / -3.0) / 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 <= (-1.2d+131)) then
        tmp = x
    else if (z <= 3.9d+124) then
        tmp = (y / (-3.0d0)) / 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 <= -1.2e+131) {
		tmp = x;
	} else if (z <= 3.9e+124) {
		tmp = (y / -3.0) / z;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.2e+131:
		tmp = x
	elif z <= 3.9e+124:
		tmp = (y / -3.0) / z
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.2e+131)
		tmp = x;
	elseif (z <= 3.9e+124)
		tmp = Float64(Float64(y / -3.0) / z);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.2e+131)
		tmp = x;
	elseif (z <= 3.9e+124)
		tmp = (y / -3.0) / z;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.2e+131], x, If[LessEqual[z, 3.9e+124], N[(N[(y / -3.0), $MachinePrecision] / z), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.2e131 or 3.9e124 < z

   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. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 84.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 84.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 63.7%

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

   if -1.2e131 < z < 3.9e124

   1. Initial program 96.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(y \cdot \color{blue}{\left(z \cdot 3\right)}\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(\left(y \cdot z\right) \cdot \color{blue}{3}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot z\right), \color{blue}{3}\right)\right)\right) \]

      4. *-lowering-*.f64 96.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), 3\right)\right)\right) \]

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot y\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), z\right) \]

      4. *-lowering-*.f64 45.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{3}\right), z\right) \]

   7. Simplified 45.9%

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

      1. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), \color{blue}{z}\right) \]

      2. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{1}{-3}\right), z\right) \]

      3. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{y}{-3}\right), z\right) \]

      4. /-lowering-/.f64 45.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{/.f64}\left(y, -3\right), z\right) \]

   9. Applied egg-rr 45.9%

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

Alternative 14: 47.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{+125}:\\ \;\;\;\;\frac{y}{\frac{z}{-0.3333333333333333}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.15e+131)
   x
   (if (<= z 2.5e+125) (/ y (/ z -0.3333333333333333)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.15e+131) {
		tmp = x;
	} else if (z <= 2.5e+125) {
		tmp = y / (z / -0.3333333333333333);
	} 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 <= (-1.15d+131)) then
        tmp = x
    else if (z <= 2.5d+125) then
        tmp = y / (z / (-0.3333333333333333d0))
    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 <= -1.15e+131) {
		tmp = x;
	} else if (z <= 2.5e+125) {
		tmp = y / (z / -0.3333333333333333);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.15e+131:
		tmp = x
	elif z <= 2.5e+125:
		tmp = y / (z / -0.3333333333333333)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.15e+131)
		tmp = x;
	elseif (z <= 2.5e+125)
		tmp = Float64(y / Float64(z / -0.3333333333333333));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.15e+131)
		tmp = x;
	elseif (z <= 2.5e+125)
		tmp = y / (z / -0.3333333333333333);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.15e+131], x, If[LessEqual[z, 2.5e+125], N[(y / N[(z / -0.3333333333333333), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.14999999999999996e131 or 2.49999999999999981e125 < z

   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. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 84.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 84.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 63.7%

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

   if -1.14999999999999996e131 < z < 2.49999999999999981e125

   1. Initial program 96.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(y \cdot \color{blue}{\left(z \cdot 3\right)}\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(\left(y \cdot z\right) \cdot \color{blue}{3}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot z\right), \color{blue}{3}\right)\right)\right) \]

      4. *-lowering-*.f64 96.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), 3\right)\right)\right) \]

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot y\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), z\right) \]

      4. *-lowering-*.f64 45.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{3}\right), z\right) \]

   7. Simplified 45.9%

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

      1. metadata-eval N/A

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

      2. div-inv N/A

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

      3. associate-/l/ N/A

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

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(y, \color{blue}{\left(z \cdot -3\right)}\right) \]

      5. metadata-eval N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(z \cdot \frac{1}{\color{blue}{\frac{-1}{3}}}\right)\right) \]

      6. div-inv N/A

         \[\leadsto \mathsf{/.f64}\left(y, \left(\frac{z}{\color{blue}{\frac{-1}{3}}}\right)\right) \]

      7. /-lowering-/.f64 45.9%

         \[\leadsto \mathsf{/.f64}\left(y, \mathsf{/.f64}\left(z, \color{blue}{\frac{-1}{3}}\right)\right) \]

   9. Applied egg-rr 45.9%

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

Alternative 15: 47.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+130}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+124}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -8.5e+130)
   x
   (if (<= z 2.9e+124) (/ -0.3333333333333333 (/ z y)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -8.5e+130) {
		tmp = x;
	} else if (z <= 2.9e+124) {
		tmp = -0.3333333333333333 / (z / y);
	} 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 <= (-8.5d+130)) then
        tmp = x
    else if (z <= 2.9d+124) then
        tmp = (-0.3333333333333333d0) / (z / y)
    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 <= -8.5e+130) {
		tmp = x;
	} else if (z <= 2.9e+124) {
		tmp = -0.3333333333333333 / (z / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -8.5e+130:
		tmp = x
	elif z <= 2.9e+124:
		tmp = -0.3333333333333333 / (z / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -8.5e+130)
		tmp = x;
	elseif (z <= 2.9e+124)
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -8.5e+130)
		tmp = x;
	elseif (z <= 2.9e+124)
		tmp = -0.3333333333333333 / (z / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -8.5e+130], x, If[LessEqual[z, 2.9e+124], N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -8.49999999999999965e130 or 2.90000000000000021e124 < z

   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. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 84.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 84.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 63.7%

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

   if -8.49999999999999965e130 < z < 2.90000000000000021e124

   1. Initial program 96.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(y \cdot \color{blue}{\left(z \cdot 3\right)}\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(\left(y \cdot z\right) \cdot \color{blue}{3}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot z\right), \color{blue}{3}\right)\right)\right) \]

      4. *-lowering-*.f64 96.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), 3\right)\right)\right) \]

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot y\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), z\right) \]

      4. *-lowering-*.f64 45.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{3}\right), z\right) \]

   7. Simplified 45.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 45.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), y\right) \]

   9. Applied egg-rr 45.8%

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

       1. associate-*l/ N/A

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

       2. associate-/l* N/A

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

       3. clear-num N/A

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

       4. div-inv N/A

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

       5. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\frac{-1}{3}, \color{blue}{\left(\frac{z}{y}\right)}\right) \]

       6. /-lowering-/.f64 45.9%

          \[\leadsto \mathsf{/.f64}\left(\frac{-1}{3}, \mathsf{/.f64}\left(z, \color{blue}{y}\right)\right) \]

   11. Applied egg-rr 45.9%

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

Alternative 16: 47.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+124}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -1.05e+131)
   x
   (if (<= z 4.5e+124) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+131) {
		tmp = x;
	} else if (z <= 4.5e+124) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-1.05d+131)) then
        tmp = x
    else if (z <= 4.5d+124) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -1.05e+131) {
		tmp = x;
	} else if (z <= 4.5e+124) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -1.05e+131:
		tmp = x
	elif z <= 4.5e+124:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -1.05e+131)
		tmp = x;
	elseif (z <= 4.5e+124)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -1.05e+131)
		tmp = x;
	elseif (z <= 4.5e+124)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -1.05e+131], x, If[LessEqual[z, 4.5e+124], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -1.04999999999999993e131 or 4.5000000000000004e124 < z

   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. sub-neg N/A

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

      2. associate-+l+ N/A

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

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

      4. remove-double-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

      5. unsub-neg N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      8. associate-*l/ N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      9. associate-/l* N/A

         \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

      11. distribute-neg-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

      12. neg-mul-1 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

      13. times-frac N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

      14. distribute-lft-out-- N/A

          \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      15. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

      16. *-commutative N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      17. associate-/r* N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      18. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

      20. --lowering--.f64 N/A

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

      21. /-lowering-/.f64 84.2%

          \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

   3. Simplified 84.2%

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

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{x} \]
   6. Step-by-step derivation

   7. Simplified 63.7%

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

   if -1.04999999999999993e131 < z < 4.5000000000000004e124

   1. Initial program 96.2%

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

      1. *-commutative N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(y \cdot \color{blue}{\left(z \cdot 3\right)}\right)\right)\right) \]

      2. associate-*r* N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(\left(y \cdot z\right) \cdot \color{blue}{3}\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot z\right), \color{blue}{3}\right)\right)\right) \]

      4. *-lowering-*.f64 96.2%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), 3\right)\right)\right) \]

   4. Applied egg-rr 96.2%

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

   5. Taylor expanded in y around inf

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

      1. associate-*r/ N/A

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

      2. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\left(\frac{-1}{3} \cdot y\right), \color{blue}{z}\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{/.f64}\left(\left(y \cdot \frac{-1}{3}\right), z\right) \]

      4. *-lowering-*.f64 45.9%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, \frac{-1}{3}\right), z\right) \]

   7. Simplified 45.9%

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

      1. associate-/l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \color{blue}{y}\right) \]

      4. /-lowering-/.f64 45.8%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), y\right) \]

   9. Applied egg-rr 45.8%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.05 \cdot 10^{+131}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+124}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

3. Final simplification 97.3%

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

Alternative 18: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.3%

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

   1. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(y \cdot \color{blue}{\left(z \cdot 3\right)}\right)\right)\right) \]

   2. associate-*r* N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \left(\left(y \cdot z\right) \cdot \color{blue}{3}\right)\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\left(y \cdot z\right), \color{blue}{3}\right)\right)\right) \]

   4. *-lowering-*.f64 97.3%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{\_.f64}\left(x, \mathsf{/.f64}\left(y, \mathsf{*.f64}\left(z, 3\right)\right)\right), \mathsf{/.f64}\left(t, \mathsf{*.f64}\left(\mathsf{*.f64}\left(y, z\right), 3\right)\right)\right) \]

4. Applied egg-rr 97.3%

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

5. Final simplification 97.3%

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

Alternative 19: 31.1% 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 97.3%

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

   1. sub-neg N/A

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

   2. associate-+l+ N/A

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

   3. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \color{blue}{\left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)}\right) \]

   4. remove-double-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)\right)\right)\right)\right) \]

   5. unsub-neg N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\left(\mathsf{neg}\left(\frac{y}{z \cdot 3}\right)\right) - \color{blue}{\left(\mathsf{neg}\left(\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)}\right)\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(-1 \cdot \frac{y}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y}{z \cdot 3} \cdot -1 - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   8. associate-*l/ N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{y \cdot -1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   9. associate-/l* N/A

      \[\leadsto \mathsf{+.f64}\left(x, \left(y \cdot \frac{-1}{z \cdot 3} - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \left(\mathsf{neg}\left(\color{blue}{\frac{t}{\left(z \cdot 3\right) \cdot y}}\right)\right)\right)\right) \]

   11. distribute-neg-frac N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{\mathsf{neg}\left(t\right)}{\color{blue}{\left(z \cdot 3\right) \cdot y}}\right)\right) \]

   12. neg-mul-1 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1 \cdot t}{\color{blue}{\left(z \cdot 3\right)} \cdot y}\right)\right) \]

   13. times-frac N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot y - \frac{-1}{z \cdot 3} \cdot \color{blue}{\frac{t}{y}}\right)\right) \]

   14. distribute-lft-out-- N/A

       \[\leadsto \mathsf{+.f64}\left(x, \left(\frac{-1}{z \cdot 3} \cdot \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

   15. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{z \cdot 3}\right), \color{blue}{\left(y - \frac{t}{y}\right)}\right)\right) \]

   16. *-commutative N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{-1}{3 \cdot z}\right), \left(y - \frac{t}{y}\right)\right)\right) \]

   17. associate-/r* N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\left(\frac{\frac{-1}{3}}{z}\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

   18. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\left(\frac{-1}{3}\right), z\right), \left(\color{blue}{y} - \frac{t}{y}\right)\right)\right) \]

   19. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \left(y - \frac{t}{y}\right)\right)\right) \]

   20. --lowering--.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \color{blue}{\left(\frac{t}{y}\right)}\right)\right)\right) \]

   21. /-lowering-/.f64 93.8%

       \[\leadsto \mathsf{+.f64}\left(x, \mathsf{*.f64}\left(\mathsf{/.f64}\left(\frac{-1}{3}, z\right), \mathsf{\_.f64}\left(y, \mathsf{/.f64}\left(t, \color{blue}{y}\right)\right)\right)\right) \]

3. Simplified 93.8%

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

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{x} \]
6. Step-by-step derivation

7. Simplified 29.1%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 96.6% 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 2024155 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y)))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))