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

Percentage Accurate: 95.7% → 98.0%

Time: 7.9s

Alternatives: 15

Speedup: 1.0×

• 28.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 98.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y - \frac{t}{y}\\ \mathbf{if}\;y \leq -5 \cdot 10^{-243}:\\ \;\;\;\;x - \frac{t\_1}{3 \cdot z}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-34}:\\ \;\;\;\;x - \frac{-0.3333333333333333 \cdot \frac{\mathsf{fma}\left(-y, y, t\right)}{z}}{y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{t\_1}{z}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- y (/ t y))))
   (if (<= y -5e-243)
     (- x (/ t_1 (* 3.0 z)))
     (if (<= y 2e-34)
       (- x (/ (* -0.3333333333333333 (/ (fma (- y) y t) z)) y))
       (- x (/ (/ t_1 z) 3.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y - (t / y);
	double tmp;
	if (y <= -5e-243) {
		tmp = x - (t_1 / (3.0 * z));
	} else if (y <= 2e-34) {
		tmp = x - ((-0.3333333333333333 * (fma(-y, y, t) / z)) / y);
	} else {
		tmp = x - ((t_1 / z) / 3.0);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(y - Float64(t / y))
	tmp = 0.0
	if (y <= -5e-243)
		tmp = Float64(x - Float64(t_1 / Float64(3.0 * z)));
	elseif (y <= 2e-34)
		tmp = Float64(x - Float64(Float64(-0.3333333333333333 * Float64(fma(Float64(-y), y, t) / z)) / y));
	else
		tmp = Float64(x - Float64(Float64(t_1 / z) / 3.0));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5e-243], N[(x - N[(t$95$1 / N[(3.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2e-34], N[(x - N[(N[(-0.3333333333333333 * N[(N[((-y) * y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(t$95$1 / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5e-243

   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. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/r* N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 98.9

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 98.9

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

   4. Applied rewrites 98.9%

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

   if -5e-243 < y < 1.99999999999999986e-34

   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. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/r* N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 87.7

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 87.7

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

   4. Applied rewrites 87.7%

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

   5. Taylor expanded in y around 0

      \[\leadsto x - \color{blue}{\frac{\frac{-1}{3} \cdot \frac{t}{z} + \frac{1}{3} \cdot \frac{{y}^{2}}{z}}{y}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{\frac{-1}{3} \cdot \frac{t}{z} + \frac{1}{3} \cdot \frac{{y}^{2}}{z}}{y}} \]

   7. Applied rewrites 99.7%

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

   if 1.99999999999999986e-34 < y

   1. Initial program 98.4%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 98.5

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

   4. Applied rewrites 98.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. associate--r- N/A

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

      12. lift-/.f64 N/A

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

      13. lift-/.f64 N/A

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

      14. associate-/r* N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. div-sub N/A

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

      18. lift--.f64 N/A

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

      19. lift-/.f64 N/A

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

      20. lift--.f64 99.8

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

   6. Applied rewrites 99.9%

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

Alternative 2: 97.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + t\_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot \left(y - \frac{t}{y}\right)}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (* (* z 3.0) y))))
   (if (<= (+ (- x (/ y (* z 3.0))) t_1) 2e+307)
     (+ (- x (/ (/ y z) 3.0)) t_1)
     (/ (* -0.3333333333333333 (- y (/ t y))) z))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / ((z * 3.0) * y);
	double tmp;
	if (((x - (y / (z * 3.0))) + t_1) <= 2e+307) {
		tmp = (x - ((y / z) / 3.0)) + t_1;
	} else {
		tmp = (-0.3333333333333333 * (y - (t / y))) / z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = t / ((z * 3.0d0) * y)
    if (((x - (y / (z * 3.0d0))) + t_1) <= 2d+307) then
        tmp = (x - ((y / z) / 3.0d0)) + t_1
    else
        tmp = ((-0.3333333333333333d0) * (y - (t / y))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = t / ((z * 3.0) * y);
	double tmp;
	if (((x - (y / (z * 3.0))) + t_1) <= 2e+307) {
		tmp = (x - ((y / z) / 3.0)) + t_1;
	} else {
		tmp = (-0.3333333333333333 * (y - (t / y))) / z;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = t / ((z * 3.0) * y)
	tmp = 0
	if ((x - (y / (z * 3.0))) + t_1) <= 2e+307:
		tmp = (x - ((y / z) / 3.0)) + t_1
	else:
		tmp = (-0.3333333333333333 * (y - (t / y))) / z
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(Float64(z * 3.0) * y))
	tmp = 0.0
	if (Float64(Float64(x - Float64(y / Float64(z * 3.0))) + t_1) <= 2e+307)
		tmp = Float64(Float64(x - Float64(Float64(y / z) / 3.0)) + t_1);
	else
		tmp = Float64(Float64(-0.3333333333333333 * Float64(y - Float64(t / y))) / z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = t / ((z * 3.0) * y);
	tmp = 0.0;
	if (((x - (y / (z * 3.0))) + t_1) <= 2e+307)
		tmp = (x - ((y / z) / 3.0)) + t_1;
	else
		tmp = (-0.3333333333333333 * (y - (t / y))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], 2e+307], N[(N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(-0.3333333333333333 * N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y))) < 1.99999999999999997e307

   1. Initial program 98.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 98.5

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

   4. Applied rewrites 98.5%

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

   if 1.99999999999999997e307 < (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y)))

   1. Initial program 90.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 90.5

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

   4. Applied rewrites 90.5%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. associate--r- N/A

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

      12. lift-/.f64 N/A

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

      13. lift-/.f64 N/A

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

      14. associate-/r* N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. div-sub N/A

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

      18. lift--.f64 N/A

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

      19. lift-/.f64 N/A

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

      20. lift--.f64 100.0

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

   6. Applied rewrites 100.0%

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

   7. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 99.9

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

   9. Applied rewrites 99.9%

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

   11. Applied rewrites 100.0%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \leq 2 \cdot 10^{+307}:\\ \;\;\;\;\left(x - \frac{\frac{y}{z}}{3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333 \cdot \left(y - \frac{t}{y}\right)}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 97.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\\ \mathbf{if}\;t\_1 \leq 5 \cdot 10^{+301}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{y - \frac{t}{y}}{z}}{3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y)))))
   (if (<= t_1 5e+301) t_1 (- x (/ (/ (- y (/ t y)) z) 3.0)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	double tmp;
	if (t_1 <= 5e+301) {
		tmp = t_1;
	} else {
		tmp = x - (((y - (t / y)) / z) / 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y / (z * 3.0d0))) + (t / ((z * 3.0d0) * y))
    if (t_1 <= 5d+301) then
        tmp = t_1
    else
        tmp = x - (((y - (t / y)) / z) / 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	double tmp;
	if (t_1 <= 5e+301) {
		tmp = t_1;
	} else {
		tmp = x - (((y - (t / y)) / z) / 3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y))
	tmp = 0
	if t_1 <= 5e+301:
		tmp = t_1
	else:
		tmp = x - (((y - (t / y)) / z) / 3.0)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(Float64(z * 3.0) * y)))
	tmp = 0.0
	if (t_1 <= 5e+301)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(Float64(y - Float64(t / y)) / z) / 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (y / (z * 3.0))) + (t / ((z * 3.0) * y));
	tmp = 0.0;
	if (t_1 <= 5e+301)
		tmp = t_1;
	else
		tmp = x - (((y - (t / y)) / z) / 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t / N[(N[(z * 3.0), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 5e+301], t$95$1, N[(x - N[(N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y))) < 5.0000000000000004e301

   1. Initial program 98.5%

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

   if 5.0000000000000004e301 < (+.f64 (-.f64 x (/.f64 y (*.f64 z #s(literal 3 binary64)))) (/.f64 t (*.f64 (*.f64 z #s(literal 3 binary64)) y)))

   1. Initial program 90.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 90.9

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

   4. Applied rewrites 90.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. associate--r- N/A

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

      12. lift-/.f64 N/A

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

      13. lift-/.f64 N/A

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

      14. associate-/r* N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. div-sub N/A

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

      18. lift--.f64 N/A

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

      19. lift-/.f64 N/A

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

      20. lift--.f64 99.9

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

   6. Applied rewrites 100.0%

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

Alternative 4: 97.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-243} \lor \neg \left(y \leq 9.2 \cdot 10^{-97}\right):\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{3 \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-0.3333333333333333 \cdot \frac{\mathsf{fma}\left(-y, y, t\right)}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -5e-243) (not (<= y 9.2e-97)))
   (- x (/ (- y (/ t y)) (* 3.0 z)))
   (- x (/ (* -0.3333333333333333 (/ (fma (- y) y t) z)) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -5e-243) || !(y <= 9.2e-97)) {
		tmp = x - ((y - (t / y)) / (3.0 * z));
	} else {
		tmp = x - ((-0.3333333333333333 * (fma(-y, y, t) / z)) / y);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -5e-243) || !(y <= 9.2e-97))
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(3.0 * z)));
	else
		tmp = Float64(x - Float64(Float64(-0.3333333333333333 * Float64(fma(Float64(-y), y, t) / z)) / y));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -5e-243], N[Not[LessEqual[y, 9.2e-97]], $MachinePrecision]], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(3.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(-0.3333333333333333 * N[(N[((-y) * y + t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5e-243 or 9.19999999999999976e-97 < y

   1. Initial program 96.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/r* N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 99.3

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 99.3

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

   4. Applied rewrites 99.3%

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

   if -5e-243 < y < 9.19999999999999976e-97

   1. Initial program 97.2%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/r* N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 85.0

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 85.0

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

   4. Applied rewrites 85.0%

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

   5. Taylor expanded in y around 0

      \[\leadsto x - \color{blue}{\frac{\frac{-1}{3} \cdot \frac{t}{z} + \frac{1}{3} \cdot \frac{{y}^{2}}{z}}{y}} \]
   6. Step-by-step derivation

      1. lower-/.f64 N/A

         \[\leadsto x - \color{blue}{\frac{\frac{-1}{3} \cdot \frac{t}{z} + \frac{1}{3} \cdot \frac{{y}^{2}}{z}}{y}} \]

   7. Applied rewrites 99.7%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-243} \lor \neg \left(y \leq 9.2 \cdot 10^{-97}\right):\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{3 \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-0.3333333333333333 \cdot \frac{\mathsf{fma}\left(-y, y, t\right)}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-277} \lor \neg \left(y \leq 2.45 \cdot 10^{-181}\right):\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{3 \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{-0.3333333333333333 \cdot t}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.55e-277) (not (<= y 2.45e-181)))
   (- x (/ (- y (/ t y)) (* 3.0 z)))
   (- x (/ (/ (* -0.3333333333333333 t) z) y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.55e-277) || !(y <= 2.45e-181)) {
		tmp = x - ((y - (t / y)) / (3.0 * z));
	} else {
		tmp = x - (((-0.3333333333333333 * t) / z) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.55d-277)) .or. (.not. (y <= 2.45d-181))) then
        tmp = x - ((y - (t / y)) / (3.0d0 * z))
    else
        tmp = x - ((((-0.3333333333333333d0) * t) / z) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.55e-277) || !(y <= 2.45e-181)) {
		tmp = x - ((y - (t / y)) / (3.0 * z));
	} else {
		tmp = x - (((-0.3333333333333333 * t) / z) / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.55e-277) or not (y <= 2.45e-181):
		tmp = x - ((y - (t / y)) / (3.0 * z))
	else:
		tmp = x - (((-0.3333333333333333 * t) / z) / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.55e-277) || !(y <= 2.45e-181))
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) / Float64(3.0 * z)));
	else
		tmp = Float64(x - Float64(Float64(Float64(-0.3333333333333333 * t) / z) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.55e-277) || ~((y <= 2.45e-181)))
		tmp = x - ((y - (t / y)) / (3.0 * z));
	else
		tmp = x - (((-0.3333333333333333 * t) / z) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.55e-277], N[Not[LessEqual[y, 2.45e-181]], $MachinePrecision]], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] / N[(3.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(-0.3333333333333333 * t), $MachinePrecision] / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.5499999999999999e-277 or 2.44999999999999981e-181 < y

   1. Initial program 96.8%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/r* N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 98.9

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 98.9

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

   4. Applied rewrites 98.9%

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

   if -1.5499999999999999e-277 < y < 2.44999999999999981e-181

   1. Initial program 97.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/r* N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 80.3

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 80.3

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

   4. Applied rewrites 80.3%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 97.6

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

   7. Applied rewrites 97.6%

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

   9. Applied rewrites 99.7%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{-277} \lor \neg \left(y \leq 2.45 \cdot 10^{-181}\right):\\ \;\;\;\;x - \frac{y - \frac{t}{y}}{3 \cdot z}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{-0.3333333333333333 \cdot t}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 91.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+73} \lor \neg \left(y \leq 6.1 \cdot 10^{+56}\right):\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.3333333333333333}{y}, \frac{t}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.9e+73) (not (<= y 6.1e+56)))
   (- x (/ (/ y z) 3.0))
   (fma (/ 0.3333333333333333 y) (/ t z) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e+73) || !(y <= 6.1e+56)) {
		tmp = x - ((y / z) / 3.0);
	} else {
		tmp = fma((0.3333333333333333 / y), (t / z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.9e+73) || !(y <= 6.1e+56))
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	else
		tmp = fma(Float64(0.3333333333333333 / y), Float64(t / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.9e+73], N[Not[LessEqual[y, 6.1e+56]], $MachinePrecision]], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], N[(N[(0.3333333333333333 / y), $MachinePrecision] * N[(t / z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000011e73 or 6.1000000000000001e56 < y

   1. Initial program 97.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 97.0

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

   4. Applied rewrites 97.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. associate--r- N/A

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

      12. lift-/.f64 N/A

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

      13. lift-/.f64 N/A

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

      14. associate-/r* N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. div-sub N/A

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

      18. lift--.f64 N/A

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

      19. lift-/.f64 N/A

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

      20. lift--.f64 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 92.4

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

   9. Applied rewrites 92.4%

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

   if -1.90000000000000011e73 < y < 6.1000000000000001e56

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0

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

      1. div-add N/A

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

      2. associate-/l* N/A

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

      3. associate-/r* N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. fp-cancel-sign-sub-inv N/A

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

      7. *-inverses N/A

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

      8. *-rgt-identity N/A

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

      9. mul-1-neg N/A

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

      10. metadata-eval N/A

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

      11. fp-cancel-sign-sub-inv N/A

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

      12. *-lft-identity N/A

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

      13. associate-*r/ N/A

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

      14. times-frac N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lower-/.f64 89.5

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

   5. Applied rewrites 89.5%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+73} \lor \neg \left(y \leq 6.1 \cdot 10^{+56}\right):\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.3333333333333333}{y}, \frac{t}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+73} \lor \neg \left(y \leq 3.6 \cdot 10^{+56}\right):\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.3333333333333333, \frac{\frac{t}{z}}{y}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.9e+73) (not (<= y 3.6e+56)))
   (- x (/ (/ y z) 3.0))
   (fma 0.3333333333333333 (/ (/ t z) y) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e+73) || !(y <= 3.6e+56)) {
		tmp = x - ((y / z) / 3.0);
	} else {
		tmp = fma(0.3333333333333333, ((t / z) / y), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.9e+73) || !(y <= 3.6e+56))
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	else
		tmp = fma(0.3333333333333333, Float64(Float64(t / z) / y), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.9e+73], N[Not[LessEqual[y, 3.6e+56]], $MachinePrecision]], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(t / z), $MachinePrecision] / y), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000011e73 or 3.59999999999999998e56 < y

   1. Initial program 97.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 97.0

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

   4. Applied rewrites 97.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. associate--r- N/A

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

      12. lift-/.f64 N/A

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

      13. lift-/.f64 N/A

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

      14. associate-/r* N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. div-sub N/A

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

      18. lift--.f64 N/A

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

      19. lift-/.f64 N/A

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

      20. lift--.f64 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 92.4

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

   9. Applied rewrites 92.4%

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

   if -1.90000000000000011e73 < y < 3.59999999999999998e56

   1. Initial program 96.9%

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

   3. Taylor expanded in y around 0

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

      1. div-add N/A

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

      2. associate-/l* N/A

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

      3. associate-/r* N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. fp-cancel-sign-sub-inv N/A

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

      7. *-inverses N/A

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

      8. *-rgt-identity N/A

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

      9. mul-1-neg N/A

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

      10. metadata-eval N/A

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

      11. fp-cancel-sign-sub-inv N/A

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

      12. *-lft-identity N/A

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

      13. associate-*r/ N/A

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

      14. times-frac N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-/.f64 N/A

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

      17. lower-/.f64 89.5

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

   5. Applied rewrites 89.5%

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

   7. Applied rewrites 89.4%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+73} \lor \neg \left(y \leq 3.6 \cdot 10^{+56}\right):\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(0.3333333333333333, \frac{\frac{t}{z}}{y}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 89.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+73} \lor \neg \left(y \leq 3.6 \cdot 10^{+56}\right):\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{else}:\\ \;\;\;\;x - -0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.9e+73) (not (<= y 3.6e+56)))
   (- x (/ (/ y z) 3.0))
   (- x (* -0.3333333333333333 (/ t (* z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e+73) || !(y <= 3.6e+56)) {
		tmp = x - ((y / z) / 3.0);
	} else {
		tmp = x - (-0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.9d+73)) .or. (.not. (y <= 3.6d+56))) then
        tmp = x - ((y / z) / 3.0d0)
    else
        tmp = x - ((-0.3333333333333333d0) * (t / (z * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e+73) || !(y <= 3.6e+56)) {
		tmp = x - ((y / z) / 3.0);
	} else {
		tmp = x - (-0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.9e+73) or not (y <= 3.6e+56):
		tmp = x - ((y / z) / 3.0)
	else:
		tmp = x - (-0.3333333333333333 * (t / (z * y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.9e+73) || !(y <= 3.6e+56))
		tmp = Float64(x - Float64(Float64(y / z) / 3.0));
	else
		tmp = Float64(x - Float64(-0.3333333333333333 * Float64(t / Float64(z * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.9e+73) || ~((y <= 3.6e+56)))
		tmp = x - ((y / z) / 3.0);
	else
		tmp = x - (-0.3333333333333333 * (t / (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.9e+73], N[Not[LessEqual[y, 3.6e+56]], $MachinePrecision]], N[(x - N[(N[(y / z), $MachinePrecision] / 3.0), $MachinePrecision]), $MachinePrecision], N[(x - N[(-0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.90000000000000011e73 or 3.59999999999999998e56 < y

   1. Initial program 97.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 97.0

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

   4. Applied rewrites 97.0%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. associate--r- N/A

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

      12. lift-/.f64 N/A

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

      13. lift-/.f64 N/A

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

      14. associate-/r* N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. div-sub N/A

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

      18. lift--.f64 N/A

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

      19. lift-/.f64 N/A

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

      20. lift--.f64 99.9

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in y around inf

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

      1. lower-/.f64 92.4

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

   9. Applied rewrites 92.4%

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

   if -1.90000000000000011e73 < y < 3.59999999999999998e56

   1. Initial program 96.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/r* N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 93.1

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 93.1

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

   4. Applied rewrites 93.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 89.0

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

   7. Applied rewrites 89.0%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+73} \lor \neg \left(y \leq 3.6 \cdot 10^{+56}\right):\\ \;\;\;\;x - \frac{\frac{y}{z}}{3}\\ \mathbf{else}:\\ \;\;\;\;x - -0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 89.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+56}:\\ \;\;\;\;x - -0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.9e+73)
   (- x (/ (* 0.3333333333333333 y) z))
   (if (<= y 3.6e+56)
     (- x (* -0.3333333333333333 (/ t (* z y))))
     (fma -0.3333333333333333 (/ y z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e+73) {
		tmp = x - ((0.3333333333333333 * y) / z);
	} else if (y <= 3.6e+56) {
		tmp = x - (-0.3333333333333333 * (t / (z * y)));
	} else {
		tmp = fma(-0.3333333333333333, (y / z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.9e+73)
		tmp = Float64(x - Float64(Float64(0.3333333333333333 * y) / z));
	elseif (y <= 3.6e+56)
		tmp = Float64(x - Float64(-0.3333333333333333 * Float64(t / Float64(z * y))));
	else
		tmp = fma(-0.3333333333333333, Float64(y / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.9e+73], N[(x - N[(N[(0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+56], N[(x - N[(-0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.90000000000000011e73

   1. Initial program 95.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/r* N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 100.0

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in y around inf

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

      1. lower-*.f64 91.0

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

   9. Applied rewrites 91.0%

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

   if -1.90000000000000011e73 < y < 3.59999999999999998e56

   1. Initial program 96.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/r* N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 93.1

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 93.1

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

   4. Applied rewrites 93.1%

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

   5. Taylor expanded in y around 0

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

      1. lower-*.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. *-commutative N/A

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

      4. lower-*.f64 89.0

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

   7. Applied rewrites 89.0%

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

   if 3.59999999999999998e56 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right)} \]
   4. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. associate-*r/ N/A

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

      10. fp-cancel-sign-sub N/A

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

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

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

      12. associate-/l* N/A

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

      13. *-commutative N/A

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

      14. associate-/l* N/A

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

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

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

      16. *-inverses N/A

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

      17. *-rgt-identity N/A

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

      18. *-lft-identity N/A

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

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

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

      20. fp-cancel-sign-sub-inv N/A

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

      21. *-lft-identity N/A

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

      22. lower-fma.f64 N/A

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

      23. lower-/.f64 93.3

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

   5. Applied rewrites 93.3%

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

4. Final simplification 90.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+56}:\\ \;\;\;\;x - -0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 89.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.3333333333333333}{z \cdot y}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.9e+73)
   (- x (/ (* 0.3333333333333333 y) z))
   (if (<= y 3.6e+56)
     (fma (/ 0.3333333333333333 (* z y)) t x)
     (fma -0.3333333333333333 (/ y z) x))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.9e+73) {
		tmp = x - ((0.3333333333333333 * y) / z);
	} else if (y <= 3.6e+56) {
		tmp = fma((0.3333333333333333 / (z * y)), t, x);
	} else {
		tmp = fma(-0.3333333333333333, (y / z), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.9e+73)
		tmp = Float64(x - Float64(Float64(0.3333333333333333 * y) / z));
	elseif (y <= 3.6e+56)
		tmp = fma(Float64(0.3333333333333333 / Float64(z * y)), t, x);
	else
		tmp = fma(-0.3333333333333333, Float64(y / z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.9e+73], N[(x - N[(N[(0.3333333333333333 * y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+56], N[(N[(0.3333333333333333 / N[(z * y), $MachinePrecision]), $MachinePrecision] * t + x), $MachinePrecision], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.90000000000000011e73

   1. Initial program 95.3%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/r* N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 100.0

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 100.0

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

   4. Applied rewrites 100.0%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 99.8

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

   6. Applied rewrites 99.8%

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

   7. Taylor expanded in y around inf

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

      1. lower-*.f64 91.0

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

   9. Applied rewrites 91.0%

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

   if -1.90000000000000011e73 < y < 3.59999999999999998e56

   1. Initial program 96.9%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. associate-+l- N/A

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

      4. lower--.f64 N/A

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

      5. lift-/.f64 N/A

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

      6. lift-/.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. associate-/r* N/A

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

      10. sub-div N/A

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

      11. lower-/.f64 N/A

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

      12. lower--.f64 N/A

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

      13. lower-/.f64 93.1

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

      14. lift-*.f64 N/A

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

      15. *-commutative N/A

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

      16. lower-*.f64 93.1

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

   4. Applied rewrites 93.1%

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

   5. Taylor expanded in y around 0

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

      1. fp-cancel-sub-sign-inv N/A

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

      2. metadata-eval N/A

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

      3. +-commutative N/A

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

      4. div-add N/A

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

      5. associate-*r/ N/A

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

      6. associate-/r* N/A

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

      7. *-commutative N/A

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

      8. associate-*l/ N/A

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

      9. metadata-eval N/A

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

      10. associate-*r/ N/A

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

      11. associate-/l* N/A

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

      12. *-inverses N/A

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

      13. *-rgt-identity N/A

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

      14. lower-fma.f64 N/A

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

   7. Applied rewrites 88.2%

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

   9. Applied rewrites 88.2%

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

   if 3.59999999999999998e56 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right)} \]
   4. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. associate-*r/ N/A

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

      10. fp-cancel-sign-sub N/A

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

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

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

      12. associate-/l* N/A

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

      13. *-commutative N/A

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

      14. associate-/l* N/A

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

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

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

      16. *-inverses N/A

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

      17. *-rgt-identity N/A

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

      18. *-lft-identity N/A

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

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

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

      20. fp-cancel-sign-sub-inv N/A

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

      21. *-lft-identity N/A

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

      22. lower-fma.f64 N/A

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

      23. lower-/.f64 93.3

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

   5. Applied rewrites 93.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+73}:\\ \;\;\;\;x - \frac{0.3333333333333333 \cdot y}{z}\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+56}:\\ \;\;\;\;\mathsf{fma}\left(\frac{0.3333333333333333}{z \cdot y}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-60} \lor \neg \left(y \leq 6.8 \cdot 10^{-81}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z \cdot y} \cdot 0.3333333333333333\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.5e-60) (not (<= y 6.8e-81)))
   (fma -0.3333333333333333 (/ y z) x)
   (* (/ t (* z y)) 0.3333333333333333)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.5e-60) || !(y <= 6.8e-81)) {
		tmp = fma(-0.3333333333333333, (y / z), x);
	} else {
		tmp = (t / (z * y)) * 0.3333333333333333;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.5e-60) || !(y <= 6.8e-81))
		tmp = fma(-0.3333333333333333, Float64(y / z), x);
	else
		tmp = Float64(Float64(t / Float64(z * y)) * 0.3333333333333333);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.5e-60], N[Not[LessEqual[y, 6.8e-81]], $MachinePrecision]], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + x), $MachinePrecision], N[(N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision] * 0.3333333333333333), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.50000000000000001e-60 or 6.7999999999999997e-81 < y

   1. Initial program 96.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right)} \]
   4. Step-by-step derivation

      1. fp-cancel-sub-sign-inv N/A

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

      2. +-commutative N/A

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

      3. distribute-lft-in N/A

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

      4. metadata-eval N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. associate-/l* N/A

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

      8. *-commutative N/A

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

      9. associate-*r/ N/A

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

      10. fp-cancel-sign-sub N/A

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

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

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

      12. associate-/l* N/A

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

      13. *-commutative N/A

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

      14. associate-/l* N/A

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

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

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

      16. *-inverses N/A

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

      17. *-rgt-identity N/A

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

      18. *-lft-identity N/A

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

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

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

      20. fp-cancel-sign-sub-inv N/A

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

      21. *-lft-identity N/A

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

      22. lower-fma.f64 N/A

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

      23. lower-/.f64 82.3

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

   5. Applied rewrites 82.3%

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

   if -4.50000000000000001e-60 < y < 6.7999999999999997e-81

   1. Initial program 97.2%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 73.3

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

   5. Applied rewrites 73.3%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-60} \lor \neg \left(y \leq 6.8 \cdot 10^{-81}\right):\\ \;\;\;\;\mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{t}{z \cdot y} \cdot 0.3333333333333333\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 47.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-17} \lor \neg \left(z \leq 1.65 \cdot 10^{-9}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.28e-17) (not (<= z 1.65e-9)))
   (* 1.0 x)
   (* (/ y z) -0.3333333333333333)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.28e-17) || !(z <= 1.65e-9)) {
		tmp = 1.0 * 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 ((z <= (-1.28d-17)) .or. (.not. (z <= 1.65d-9))) then
        tmp = 1.0d0 * 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 ((z <= -1.28e-17) || !(z <= 1.65e-9)) {
		tmp = 1.0 * x;
	} else {
		tmp = (y / z) * -0.3333333333333333;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.28e-17) or not (z <= 1.65e-9):
		tmp = 1.0 * x
	else:
		tmp = (y / z) * -0.3333333333333333
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.28e-17) || !(z <= 1.65e-9))
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(Float64(y / z) * -0.3333333333333333);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.28e-17) || ~((z <= 1.65e-9)))
		tmp = 1.0 * x;
	else
		tmp = (y / z) * -0.3333333333333333;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.28e-17], N[Not[LessEqual[z, 1.65e-9]], $MachinePrecision]], N[(1.0 * x), $MachinePrecision], N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.28e-17 or 1.65000000000000009e-9 < z

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 84.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 51.4%

      \[\leadsto 1 \cdot x \]

   if -1.28e-17 < z < 1.65000000000000009e-9

   1. Initial program 94.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 94.6

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

   4. Applied rewrites 94.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. associate--r- N/A

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

      12. lift-/.f64 N/A

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

      13. lift-/.f64 N/A

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

      14. associate-/r* N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. div-sub N/A

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

      18. lift--.f64 N/A

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

      19. lift-/.f64 N/A

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

      20. lift--.f64 99.8

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 50.3

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

   9. Applied rewrites 50.3%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-17} \lor \neg \left(z \leq 1.65 \cdot 10^{-9}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 47.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-17} \lor \neg \left(z \leq 1.65 \cdot 10^{-9}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.28e-17) (not (<= z 1.65e-9)))
   (* 1.0 x)
   (* y (/ -0.3333333333333333 z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.28e-17) || !(z <= 1.65e-9)) {
		tmp = 1.0 * x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.28d-17)) .or. (.not. (z <= 1.65d-9))) then
        tmp = 1.0d0 * x
    else
        tmp = y * ((-0.3333333333333333d0) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.28e-17) || !(z <= 1.65e-9)) {
		tmp = 1.0 * x;
	} else {
		tmp = y * (-0.3333333333333333 / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.28e-17) or not (z <= 1.65e-9):
		tmp = 1.0 * x
	else:
		tmp = y * (-0.3333333333333333 / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.28e-17) || !(z <= 1.65e-9))
		tmp = Float64(1.0 * x);
	else
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.28e-17) || ~((z <= 1.65e-9)))
		tmp = 1.0 * x;
	else
		tmp = y * (-0.3333333333333333 / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.28e-17], N[Not[LessEqual[z, 1.65e-9]], $MachinePrecision]], N[(1.0 * x), $MachinePrecision], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.28e-17 or 1.65000000000000009e-9 < z

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 84.8%

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

   6. Taylor expanded in x around inf

      \[\leadsto 1 \cdot x \]
   7. Step-by-step derivation

   8. Applied rewrites 51.4%

      \[\leadsto 1 \cdot x \]

   if -1.28e-17 < z < 1.65000000000000009e-9

   1. Initial program 94.5%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/r* N/A

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

      4. lower-/.f64 N/A

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

      5. lower-/.f64 94.6

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

   4. Applied rewrites 94.6%

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

      1. lift-+.f64 N/A

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

      2. lift--.f64 N/A

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

      3. lift-/.f64 N/A

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

      4. lift-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. *-commutative N/A

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

      7. associate-/r* N/A

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

      8. lift-/.f64 N/A

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

      9. *-commutative N/A

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

      10. lift-*.f64 N/A

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

      11. associate--r- N/A

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

      12. lift-/.f64 N/A

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

      13. lift-/.f64 N/A

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

      14. associate-/r* N/A

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

      15. *-commutative N/A

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

      16. lift-*.f64 N/A

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

      17. div-sub N/A

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

      18. lift--.f64 N/A

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

      19. lift-/.f64 N/A

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

      20. lift--.f64 99.8

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

   6. Applied rewrites 99.9%

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

   7. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. lower-/.f64 50.3

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

   9. Applied rewrites 50.3%

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

   11. Applied rewrites 50.3%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.28 \cdot 10^{-17} \lor \neg \left(z \leq 1.65 \cdot 10^{-9}\right):\\ \;\;\;\;1 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 63.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - \frac{1}{3} \cdot \frac{1}{z}\right)} \]
4. Step-by-step derivation

   1. fp-cancel-sub-sign-inv N/A

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

   2. +-commutative N/A

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

   3. distribute-lft-in N/A

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

   4. metadata-eval N/A

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

   5. associate-*r/ N/A

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

   6. metadata-eval N/A

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

   7. associate-/l* N/A

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

   8. *-commutative N/A

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

   9. associate-*r/ N/A

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

   10. fp-cancel-sign-sub N/A

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

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

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

   12. associate-/l* N/A

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

   13. *-commutative N/A

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

   14. associate-/l* N/A

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

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

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

   16. *-inverses N/A

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

   17. *-rgt-identity N/A

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

   18. *-lft-identity N/A

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

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

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

   20. fp-cancel-sign-sub-inv N/A

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

   21. *-lft-identity N/A

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

   22. lower-fma.f64 N/A

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

   23. lower-/.f64 59.7

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

5. Applied rewrites 59.7%

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

6. Final simplification 59.7%

   \[\leadsto \mathsf{fma}\left(-0.3333333333333333, \frac{y}{z}, x\right) \]
7. Add Preprocessing

Alternative 15: 30.9% accurate, 7.3× speedup

Math

\[\begin{array}{l} \\ 1 \cdot x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (* 1.0 x))

C

double code(double x, double y, double z, double t) {
	return 1.0 * 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 = 1.0d0 * x
end function

Java

public static double code(double x, double y, double z, double t) {
	return 1.0 * x;
}

Python

def code(x, y, z, t):
	return 1.0 * x

Julia

function code(x, y, z, t)
	return Float64(1.0 * x)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 1.0 * x;
end

Wolfram

code[x_, y_, z_, t_] := N[(1.0 * x), $MachinePrecision]

Derivation

1. Initial program 96.9%

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

3. Taylor expanded in x around inf

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

   1. *-commutative N/A

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

   2. lower-*.f64 N/A

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

5. Applied rewrites 88.8%

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

6. Taylor expanded in x around inf

   \[\leadsto 1 \cdot x \]
7. Step-by-step derivation

8. Applied rewrites 29.8%

   \[\leadsto 1 \cdot x \]

9. Final simplification 29.8%

   \[\leadsto 1 \cdot x \]
10. Add Preprocessing

Developer Target 1: 96.0% accurate, 0.9× 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 2024339 
(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))))