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

Percentage Accurate: 95.6% → 97.6%

Time: 9.4s

Alternatives: 11

Speedup: 1.4×

• 28.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot 3}\\ \mathbf{if}\;\left(x - t_1\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 10^{+297}:\\ \;\;\;\;x - \left(t_1 - \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - \frac{t}{y}\right) \cdot \frac{-1}{\frac{z}{-0.3333333333333333}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* z 3.0))))
   (if (<= (+ (- x t_1) (/ t (* y (* z 3.0)))) 1e+297)
     (- x (- t_1 (/ t (* z (* y 3.0)))))
     (- x (* (- y (/ t y)) (/ -1.0 (/ z -0.3333333333333333)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (z * 3.0);
	double tmp;
	if (((x - t_1) + (t / (y * (z * 3.0)))) <= 1e+297) {
		tmp = x - (t_1 - (t / (z * (y * 3.0))));
	} else {
		tmp = x - ((y - (t / y)) * (-1.0 / (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) :: t_1
    real(8) :: tmp
    t_1 = y / (z * 3.0d0)
    if (((x - t_1) + (t / (y * (z * 3.0d0)))) <= 1d+297) then
        tmp = x - (t_1 - (t / (z * (y * 3.0d0))))
    else
        tmp = x - ((y - (t / y)) * ((-1.0d0) / (z / (-0.3333333333333333d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (z * 3.0);
	double tmp;
	if (((x - t_1) + (t / (y * (z * 3.0)))) <= 1e+297) {
		tmp = x - (t_1 - (t / (z * (y * 3.0))));
	} else {
		tmp = x - ((y - (t / y)) * (-1.0 / (z / -0.3333333333333333)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (z * 3.0)
	tmp = 0
	if ((x - t_1) + (t / (y * (z * 3.0)))) <= 1e+297:
		tmp = x - (t_1 - (t / (z * (y * 3.0))))
	else:
		tmp = x - ((y - (t / y)) * (-1.0 / (z / -0.3333333333333333)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(z * 3.0))
	tmp = 0.0
	if (Float64(Float64(x - t_1) + Float64(t / Float64(y * Float64(z * 3.0)))) <= 1e+297)
		tmp = Float64(x - Float64(t_1 - Float64(t / Float64(z * Float64(y * 3.0)))));
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) * Float64(-1.0 / Float64(z / -0.3333333333333333))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (z * 3.0);
	tmp = 0.0;
	if (((x - t_1) + (t / (y * (z * 3.0)))) <= 1e+297)
		tmp = x - (t_1 - (t / (z * (y * 3.0))));
	else
		tmp = x - ((y - (t / y)) * (-1.0 / (z / -0.3333333333333333)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x - t$95$1), $MachinePrecision] + N[(t / N[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 1e+297], N[(x - N[(t$95$1 - N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[(z / -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y))) < 1e297

   1. Initial program 98.5%

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

      1. associate-+l- 98.5%

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

      2. associate-/r* 94.4%

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

      3. associate-/r* 98.5%

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

      4. associate-*l* 98.5%

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

   3. Applied egg-rr 98.5%

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

   if 1e297 < (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))

   1. Initial program 73.4%

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

      1. associate-+l- 73.4%

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

      2. sub-neg 73.4%

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

      3. sub-neg 73.4%

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

      4. distribute-neg-in 73.4%

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

      5. unsub-neg 73.4%

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

      6. neg-mul-1 73.4%

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

      7. associate-*r/ 73.4%

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

      8. associate-*l/ 73.4%

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

      9. distribute-neg-frac 73.4%

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

      10. neg-mul-1 73.4%

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

      11. times-frac 94.4%

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

      12. distribute-lft-out-- 100.0%

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

      13. *-commutative 100.0%

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

      14. associate-/r* 99.9%

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

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

   5. Applied egg-rr 100.0%

      \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]
   6. Step-by-step derivation

      1. unpow-1 100.0%

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

   7. Simplified 100.0%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 10^{+297}:\\ \;\;\;\;x - \left(\frac{y}{z \cdot 3} - \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - \frac{t}{y}\right) \cdot \frac{-1}{\frac{z}{-0.3333333333333333}}\\ \end{array} \]

Alternative 2: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{if}\;t_1 \leq 10^{+297}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - \frac{t}{y}\right) \cdot \frac{-1}{\frac{z}{-0.3333333333333333}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))))
   (if (<= t_1 1e+297)
     t_1
     (- x (* (- y (/ t y)) (/ -1.0 (/ z -0.3333333333333333)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	double tmp;
	if (t_1 <= 1e+297) {
		tmp = t_1;
	} else {
		tmp = x - ((y - (t / y)) * (-1.0 / (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) :: t_1
    real(8) :: tmp
    t_1 = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    if (t_1 <= 1d+297) then
        tmp = t_1
    else
        tmp = x - ((y - (t / y)) * ((-1.0d0) / (z / (-0.3333333333333333d0))))
    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 / (y * (z * 3.0)));
	double tmp;
	if (t_1 <= 1e+297) {
		tmp = t_1;
	} else {
		tmp = x - ((y - (t / y)) * (-1.0 / (z / -0.3333333333333333)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)))
	tmp = 0
	if t_1 <= 1e+297:
		tmp = t_1
	else:
		tmp = x - ((y - (t / y)) * (-1.0 / (z / -0.3333333333333333)))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x - Float64(y / Float64(z * 3.0))) + Float64(t / Float64(y * Float64(z * 3.0))))
	tmp = 0.0
	if (t_1 <= 1e+297)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(y - Float64(t / y)) * Float64(-1.0 / Float64(z / -0.3333333333333333))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	tmp = 0.0;
	if (t_1 <= 1e+297)
		tmp = t_1;
	else
		tmp = x - ((y - (t / y)) * (-1.0 / (z / -0.3333333333333333)));
	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[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 1e+297], t$95$1, N[(x - N[(N[(y - N[(t / y), $MachinePrecision]), $MachinePrecision] * N[(-1.0 / N[(z / -0.3333333333333333), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y))) < 1e297

   1. Initial program 98.5%

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

   if 1e297 < (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))

   1. Initial program 73.4%

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

      1. associate-+l- 73.4%

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

      2. sub-neg 73.4%

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

      3. sub-neg 73.4%

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

      4. distribute-neg-in 73.4%

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

      5. unsub-neg 73.4%

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

      6. neg-mul-1 73.4%

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

      7. associate-*r/ 73.4%

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

      8. associate-*l/ 73.4%

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

      9. distribute-neg-frac 73.4%

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

      10. neg-mul-1 73.4%

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

      11. times-frac 94.4%

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

      12. distribute-lft-out-- 100.0%

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

      13. *-commutative 100.0%

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

      14. associate-/r* 99.9%

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

      15. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 100.0%

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

      2. inv-pow 100.0%

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

   5. Applied egg-rr 100.0%

      \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]
   6. Step-by-step derivation

      1. unpow-1 100.0%

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

   7. Simplified 100.0%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{z}{-0.3333333333333333}}} \cdot \left(y - \frac{t}{y}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 10^{+297}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \left(y - \frac{t}{y}\right) \cdot \frac{-1}{\frac{z}{-0.3333333333333333}}\\ \end{array} \]

Alternative 3: 88.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+29}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.25e+29)
   (- x (/ y (* z 3.0)))
   (if (<= y 3.9e-12)
     (+ x (* (/ t y) (/ 0.3333333333333333 z)))
     (+ x (/ (* y -0.3333333333333333) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e+29) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 3.9e-12) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} else {
		tmp = x + ((y * -0.3333333333333333) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.25d+29)) then
        tmp = x - (y / (z * 3.0d0))
    else if (y <= 3.9d-12) then
        tmp = x + ((t / y) * (0.3333333333333333d0 / z))
    else
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.25e+29) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 3.9e-12) {
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	} else {
		tmp = x + ((y * -0.3333333333333333) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.25e+29:
		tmp = x - (y / (z * 3.0))
	elif y <= 3.9e-12:
		tmp = x + ((t / y) * (0.3333333333333333 / z))
	else:
		tmp = x + ((y * -0.3333333333333333) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.25e+29)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (y <= 3.9e-12)
		tmp = Float64(x + Float64(Float64(t / y) * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.25e+29)
		tmp = x - (y / (z * 3.0));
	elseif (y <= 3.9e-12)
		tmp = x + ((t / y) * (0.3333333333333333 / z));
	else
		tmp = x + ((y * -0.3333333333333333) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.25e+29], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.9e-12], N[(x + N[(N[(t / y), $MachinePrecision] * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e29

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 96.4%

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

      1. metadata-eval 96.4%

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

      2. times-frac 96.4%

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

      3. *-un-lft-identity 96.4%

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

      4. *-commutative 96.4%

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

   4. Applied egg-rr 96.4%

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

   if -1.25e29 < y < 3.89999999999999994e-12

   1. Initial program 91.5%

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

      1. associate-+l- 91.5%

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

      2. sub-neg 91.5%

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

      3. sub-neg 91.5%

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

      4. distribute-neg-in 91.5%

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

      5. unsub-neg 91.5%

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

      6. neg-mul-1 91.5%

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

      7. associate-*r/ 91.5%

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

      8. associate-*l/ 91.5%

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

      9. distribute-neg-frac 91.5%

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

      10. neg-mul-1 91.5%

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

      11. times-frac 93.0%

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

      12. distribute-lft-out-- 93.0%

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

      13. *-commutative 93.0%

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

      14. associate-/r* 92.9%

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

      15. metadata-eval 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-*l/ 86.1%

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

      3. times-frac 87.0%

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

   6. Simplified 87.0%

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

   if 3.89999999999999994e-12 < y

   1. Initial program 97.1%

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

      1. associate-+l- 97.1%

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

      2. sub-neg 97.1%

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

      3. sub-neg 97.1%

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

      4. distribute-neg-in 97.1%

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

      5. unsub-neg 97.1%

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

      6. neg-mul-1 97.1%

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

      7. associate-*r/ 97.1%

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

      8. associate-*l/ 97.0%

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

      9. distribute-neg-frac 97.0%

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

      10. neg-mul-1 97.0%

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

      11. times-frac 97.0%

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

      12. distribute-lft-out-- 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/r* 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 96.9%

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

      1. +-commutative 96.9%

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

      2. metadata-eval 96.9%

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

      3. cancel-sign-sub-inv 96.9%

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

      4. associate-/r* 96.9%

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

      5. associate-*r/ 96.9%

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

      6. associate-*r/ 97.1%

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

      7. div-sub 99.8%

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

      8. distribute-lft-out-- 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in t around 0 95.8%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+29}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 3.9 \cdot 10^{-12}:\\ \;\;\;\;x + \frac{t}{y} \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]

Alternative 4: 91.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+29}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -1.05e+29)
   (- x (/ y (* z 3.0)))
   (if (<= y 8.8e-11)
     (+ x (* (/ t z) (/ 0.3333333333333333 y)))
     (+ x (/ (* y -0.3333333333333333) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+29) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 8.8e-11) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + ((y * -0.3333333333333333) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-1.05d+29)) then
        tmp = x - (y / (z * 3.0d0))
    else if (y <= 8.8d-11) then
        tmp = x + ((t / z) * (0.3333333333333333d0 / y))
    else
        tmp = x + ((y * (-0.3333333333333333d0)) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -1.05e+29) {
		tmp = x - (y / (z * 3.0));
	} else if (y <= 8.8e-11) {
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	} else {
		tmp = x + ((y * -0.3333333333333333) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -1.05e+29:
		tmp = x - (y / (z * 3.0))
	elif y <= 8.8e-11:
		tmp = x + ((t / z) * (0.3333333333333333 / y))
	else:
		tmp = x + ((y * -0.3333333333333333) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -1.05e+29)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (y <= 8.8e-11)
		tmp = Float64(x + Float64(Float64(t / z) * Float64(0.3333333333333333 / y)));
	else
		tmp = Float64(x + Float64(Float64(y * -0.3333333333333333) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -1.05e+29)
		tmp = x - (y / (z * 3.0));
	elseif (y <= 8.8e-11)
		tmp = x + ((t / z) * (0.3333333333333333 / y));
	else
		tmp = x + ((y * -0.3333333333333333) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -1.05e+29], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.8e-11], N[(x + N[(N[(t / z), $MachinePrecision] * N[(0.3333333333333333 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y * -0.3333333333333333), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0500000000000001e29

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 96.4%

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

      1. metadata-eval 96.4%

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

      2. times-frac 96.4%

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

      3. *-un-lft-identity 96.4%

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

      4. *-commutative 96.4%

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

   4. Applied egg-rr 96.4%

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

   if -1.0500000000000001e29 < y < 8.8000000000000006e-11

   1. Initial program 91.5%

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

      1. associate-+l- 91.5%

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

      2. sub-neg 91.5%

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

      3. sub-neg 91.5%

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

      4. distribute-neg-in 91.5%

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

      5. unsub-neg 91.5%

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

      6. neg-mul-1 91.5%

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

      7. associate-*r/ 91.5%

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

      8. associate-*l/ 91.5%

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

      9. distribute-neg-frac 91.5%

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

      10. neg-mul-1 91.5%

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

      11. times-frac 93.0%

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

      12. distribute-lft-out-- 93.0%

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

      13. *-commutative 93.0%

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

      14. associate-/r* 92.9%

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

      15. metadata-eval 92.9%

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

   3. Simplified 92.9%

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

   4. Taylor expanded in y around 0 86.0%

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

      1. *-commutative 86.0%

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

      2. associate-*l/ 86.1%

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

      3. times-frac 87.0%

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

   6. Simplified 87.0%

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

      1. frac-times 86.1%

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

   8. Applied egg-rr 86.1%

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

      1. *-commutative 86.1%

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

      2. times-frac 92.3%

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

   10. Applied egg-rr 92.3%

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

   if 8.8000000000000006e-11 < y

   1. Initial program 97.1%

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

      1. associate-+l- 97.1%

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

      2. sub-neg 97.1%

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

      3. sub-neg 97.1%

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

      4. distribute-neg-in 97.1%

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

      5. unsub-neg 97.1%

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

      6. neg-mul-1 97.1%

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

      7. associate-*r/ 97.1%

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

      8. associate-*l/ 97.0%

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

      9. distribute-neg-frac 97.0%

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

      10. neg-mul-1 97.0%

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

      11. times-frac 97.0%

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

      12. distribute-lft-out-- 99.7%

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

      13. *-commutative 99.7%

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

      14. associate-/r* 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 96.9%

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

      1. +-commutative 96.9%

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

      2. metadata-eval 96.9%

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

      3. cancel-sign-sub-inv 96.9%

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

      4. associate-/r* 96.9%

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

      5. associate-*r/ 96.9%

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

      6. associate-*r/ 97.1%

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

      7. div-sub 99.8%

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

      8. distribute-lft-out-- 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in t around 0 95.8%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+29}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{-11}:\\ \;\;\;\;x + \frac{t}{z} \cdot \frac{0.3333333333333333}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot -0.3333333333333333}{z}\\ \end{array} \]

Alternative 5: 95.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \frac{\frac{1}{\frac{y}{t}} - y}{z \cdot 3} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (/ (- (/ 1.0 (/ y t)) y) (* z 3.0))))

C

double code(double x, double y, double z, double t) {
	return x + (((1.0 / (y / t)) - y) / (z * 3.0));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + (((1.0d0 / (y / t)) - y) / (z * 3.0d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + (((1.0 / (y / t)) - y) / (z * 3.0));
}

Python

def code(x, y, z, t):
	return x + (((1.0 / (y / t)) - y) / (z * 3.0))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(Float64(1.0 / Float64(y / t)) - y) / Float64(z * 3.0)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + (((1.0 / (y / t)) - y) / (z * 3.0));
end

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. associate-+l- 95.0%

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

   2. sub-neg 95.0%

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

   3. sub-neg 95.0%

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

   4. distribute-neg-in 95.0%

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

   5. unsub-neg 95.0%

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

   6. neg-mul-1 95.0%

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

   7. associate-*r/ 95.0%

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

   8. associate-*l/ 95.0%

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

   9. distribute-neg-frac 95.0%

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

   10. neg-mul-1 95.0%

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

   11. times-frac 95.7%

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

   12. distribute-lft-out-- 96.4%

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

   13. *-commutative 96.4%

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

   14. associate-/r* 96.4%

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

   15. metadata-eval 96.4%

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

3. Simplified 96.4%

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

   1. clear-num 96.4%

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

   2. inv-pow 96.4%

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

5. Applied egg-rr 96.4%

   \[\leadsto x + \color{blue}{{\left(\frac{z}{-0.3333333333333333}\right)}^{-1}} \cdot \left(y - \frac{t}{y}\right) \]
6. Step-by-step derivation

   1. unpow-1 96.4%

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

7. Simplified 96.4%

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

   1. associate-*l/ 96.5%

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

   2. *-un-lft-identity 96.5%

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

   3. frac-2neg 96.5%

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

   4. div-inv 96.5%

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

   5. metadata-eval 96.5%

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

9. Applied egg-rr 96.5%

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

    1. neg-sub0 96.5%

       \[\leadsto x + \frac{\color{blue}{0 - \left(y - \frac{t}{y}\right)}}{-z \cdot -3} \]

    2. associate-+l- 96.5%

       \[\leadsto x + \frac{\color{blue}{\left(0 - y\right) + \frac{t}{y}}}{-z \cdot -3} \]

    3. neg-sub0 96.5%

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

    4. +-commutative 96.5%

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

    5. sub-neg 96.5%

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

    6. distribute-rgt-neg-in 96.5%

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

    7. metadata-eval 96.5%

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

11. Simplified 96.5%

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

    1. div-inv 96.5%

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

    2. fma-neg 96.5%

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

13. Applied egg-rr 96.5%

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

    1. fma-udef 96.5%

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

    2. unsub-neg 96.5%

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

15. Simplified 96.5%

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

    1. un-div-inv 96.5%

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

    2. clear-num 96.5%

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

17. Applied egg-rr 96.5%

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

18. Final simplification 96.5%

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

Alternative 6: 95.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. associate-+l- 95.0%

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

   2. sub-neg 95.0%

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

   3. sub-neg 95.0%

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

   4. distribute-neg-in 95.0%

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

   5. unsub-neg 95.0%

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

   6. neg-mul-1 95.0%

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

   7. associate-*r/ 95.0%

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

   8. associate-*l/ 95.0%

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

   9. distribute-neg-frac 95.0%

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

   10. neg-mul-1 95.0%

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

   11. times-frac 95.7%

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

   12. distribute-lft-out-- 96.4%

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

   13. *-commutative 96.4%

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

   14. associate-/r* 96.4%

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

   15. metadata-eval 96.4%

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

3. Simplified 96.4%

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

4. Final simplification 96.4%

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

Alternative 7: 95.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. associate-+l- 95.0%

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

   2. sub-neg 95.0%

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

   3. sub-neg 95.0%

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

   4. distribute-neg-in 95.0%

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

   5. unsub-neg 95.0%

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

   6. neg-mul-1 95.0%

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

   7. associate-*r/ 95.0%

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

   8. associate-*l/ 95.0%

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

   9. distribute-neg-frac 95.0%

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

   10. neg-mul-1 95.0%

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

   11. times-frac 95.7%

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

   12. distribute-lft-out-- 96.4%

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

   13. *-commutative 96.4%

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

   14. associate-/r* 96.4%

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

   15. metadata-eval 96.4%

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

3. Simplified 96.4%

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

4. Taylor expanded in y around 0 94.9%

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

   1. +-commutative 94.9%

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

   2. metadata-eval 94.9%

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

   3. cancel-sign-sub-inv 94.9%

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

   4. associate-/r* 95.6%

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

   5. associate-*r/ 95.6%

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

   6. associate-*r/ 95.7%

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

   7. div-sub 96.5%

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

   8. distribute-lft-out-- 96.5%

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

6. Simplified 96.5%

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

7. Final simplification 96.5%

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

Alternative 8: 63.0% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. associate-+l- 95.0%

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

   2. sub-neg 95.0%

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

   3. sub-neg 95.0%

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

   4. distribute-neg-in 95.0%

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

   5. unsub-neg 95.0%

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

   6. neg-mul-1 95.0%

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

   7. associate-*r/ 95.0%

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

   8. associate-*l/ 95.0%

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

   9. distribute-neg-frac 95.0%

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

   10. neg-mul-1 95.0%

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

   11. times-frac 95.7%

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

   12. distribute-lft-out-- 96.4%

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

   13. *-commutative 96.4%

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

   14. associate-/r* 96.4%

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

   15. metadata-eval 96.4%

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

3. Simplified 96.4%

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

4. Taylor expanded in y around inf 69.1%

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

5. Final simplification 69.1%

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

Alternative 9: 63.0% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. associate-+l- 95.0%

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

   2. sub-neg 95.0%

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

   3. sub-neg 95.0%

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

   4. distribute-neg-in 95.0%

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

   5. unsub-neg 95.0%

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

   6. neg-mul-1 95.0%

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

   7. associate-*r/ 95.0%

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

   8. associate-*l/ 95.0%

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

   9. distribute-neg-frac 95.0%

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

   10. neg-mul-1 95.0%

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

   11. times-frac 95.7%

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

   12. distribute-lft-out-- 96.4%

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

   13. *-commutative 96.4%

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

   14. associate-/r* 96.4%

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

   15. metadata-eval 96.4%

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

3. Simplified 96.4%

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

4. Taylor expanded in y around 0 94.9%

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

   1. +-commutative 94.9%

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

   2. metadata-eval 94.9%

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

   3. cancel-sign-sub-inv 94.9%

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

   4. associate-/r* 95.6%

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

   5. associate-*r/ 95.6%

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

   6. associate-*r/ 95.7%

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

   7. div-sub 96.5%

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

   8. distribute-lft-out-- 96.5%

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

6. Simplified 96.5%

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

7. Taylor expanded in t around 0 69.1%

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

8. Final simplification 69.1%

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

Alternative 10: 63.0% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

2. Taylor expanded in t around 0 69.1%

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

   1. metadata-eval 69.1%

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

   2. times-frac 69.1%

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

   3. *-un-lft-identity 69.1%

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

   4. *-commutative 69.1%

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

4. Applied egg-rr 69.1%

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

5. Final simplification 69.1%

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

Alternative 11: 30.5% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.0%

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

   1. associate-+l- 95.0%

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

   2. sub-neg 95.0%

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

   3. sub-neg 95.0%

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

   4. distribute-neg-in 95.0%

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

   5. unsub-neg 95.0%

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

   6. neg-mul-1 95.0%

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

   7. associate-*r/ 95.0%

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

   8. associate-*l/ 95.0%

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

   9. distribute-neg-frac 95.0%

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

   10. neg-mul-1 95.0%

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

   11. times-frac 95.7%

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

   12. distribute-lft-out-- 96.4%

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

   13. *-commutative 96.4%

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

   14. associate-/r* 96.4%

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

   15. metadata-eval 96.4%

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

3. Simplified 96.4%

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

4. Taylor expanded in x around inf 32.6%

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

5. Final simplification 32.6%

   \[\leadsto x \]

Developer target: 95.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023208 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))