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

Percentage Accurate: 95.8% → 97.5%

Time: 9.2s

Alternatives: 10

Speedup: 1.4×

• 28.7% 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: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+273}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{t}{y} - y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- x (/ y (* z 3.0))) (/ t (* y (* z 3.0))))))
   (if (<= t_1 2e+273) t_1 (- x (/ (- (/ t y) y) (* z -3.0))))))

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 <= 2e+273) {
		tmp = t_1;
	} else {
		tmp = x - (((t / y) - y) / (z * -3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x - (y / (z * 3.0d0))) + (t / (y * (z * 3.0d0)))
    if (t_1 <= 2d+273) then
        tmp = t_1
    else
        tmp = x - (((t / y) - y) / (z * (-3.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	double tmp;
	if (t_1 <= 2e+273) {
		tmp = t_1;
	} else {
		tmp = x - (((t / y) - y) / (z * -3.0));
	}
	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 <= 2e+273:
		tmp = t_1
	else:
		tmp = x - (((t / y) - 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(y * Float64(z * 3.0))))
	tmp = 0.0
	if (t_1 <= 2e+273)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(Float64(t / y) - y) / Float64(z * -3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x - (y / (z * 3.0))) + (t / (y * (z * 3.0)));
	tmp = 0.0;
	if (t_1 <= 2e+273)
		tmp = t_1;
	else
		tmp = x - (((t / y) - 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[(y * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2e+273], t$95$1, N[(x - N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * -3.0), $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))) < 1.99999999999999989e273

   1. Initial program 98.8%

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

   if 1.99999999999999989e273 < (+.f64 (-.f64 x (/.f64 y (*.f64 z 3))) (/.f64 t (*.f64 (*.f64 z 3) y)))

   1. Initial program 89.4%

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

      1. sub-neg 89.4%

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

      2. distribute-frac-neg 89.4%

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

      3. associate-+l+ 89.4%

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

      4. remove-double-neg 89.4%

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

      5. distribute-frac-neg 89.4%

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

      6. unsub-neg 89.4%

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

      7. neg-mul-1 89.4%

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

      8. associate-*l/ 89.4%

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

      9. neg-mul-1 89.4%

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

      10. times-frac 99.9%

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

      11. distribute-lft-out-- 99.9%

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

      12. *-commutative 99.9%

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

      13. associate-/r* 99.9%

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

      14. 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. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

      4. div-inv 99.9%

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

      5. metadata-eval 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)} \leq 2 \cdot 10^{+273}:\\ \;\;\;\;\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{y \cdot \left(z \cdot 3\right)}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{\frac{t}{y} - y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \lor \neg \left(y \leq 5.2 \cdot 10^{+64}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -6.8) (not (<= y 5.2e+64)))
   (- x (/ y (* z 3.0)))
   (+ x (* 0.3333333333333333 (/ t (* y z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.8) || !(y <= 5.2e+64)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-6.8d0)) .or. (.not. (y <= 5.2d+64))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + (0.3333333333333333d0 * (t / (y * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -6.8) || !(y <= 5.2e+64)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -6.8) or not (y <= 5.2e+64):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + (0.3333333333333333 * (t / (y * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -6.8) || !(y <= 5.2e+64))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(y * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -6.8) || ~((y <= 5.2e+64)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + (0.3333333333333333 * (t / (y * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -6.8], N[Not[LessEqual[y, 5.2e+64]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 * N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.79999999999999982 or 5.19999999999999994e64 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. associate-+l+ 99.9%

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

      4. remove-double-neg 99.9%

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

      5. distribute-frac-neg 99.9%

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

      6. unsub-neg 99.9%

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

      7. neg-mul-1 99.9%

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

      8. associate-*l/ 99.8%

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

      9. neg-mul-1 99.8%

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

      10. times-frac 99.8%

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

      11. distribute-lft-out-- 99.8%

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

      12. *-commutative 99.8%

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

      13. associate-/r* 99.7%

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

      14. 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. Add Preprocessing

   5. Taylor expanded in y around inf 97.5%

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

      1. metadata-eval 97.5%

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

      2. cancel-sign-sub-inv 97.5%

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

      3. metadata-eval 97.5%

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

      4. distribute-lft-neg-in 97.5%

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

      5. associate-*r/ 97.5%

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

      6. associate-*l/ 97.5%

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

      7. *-commutative 97.5%

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

      8. distribute-rgt-neg-in 97.5%

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

      9. distribute-neg-frac 97.5%

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

      10. metadata-eval 97.5%

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

   7. Simplified 97.5%

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

      1. clear-num 97.5%

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

      2. un-div-inv 97.6%

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

      3. div-inv 97.8%

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

      4. metadata-eval 97.8%

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

   9. Applied egg-rr 97.8%

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

   if -6.79999999999999982 < y < 5.19999999999999994e64

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. distribute-frac-neg 94.6%

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

      3. associate-+l+ 94.6%

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

      4. remove-double-neg 94.6%

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

      5. distribute-frac-neg 94.6%

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

      6. unsub-neg 94.6%

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

      7. neg-mul-1 94.6%

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

      8. associate-*l/ 94.6%

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

      9. neg-mul-1 94.6%

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

      10. times-frac 95.7%

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

      11. distribute-lft-out-- 95.7%

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

      12. *-commutative 95.7%

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

      13. associate-/r* 95.6%

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

      14. metadata-eval 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around 0 86.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \lor \neg \left(y \leq 5.2 \cdot 10^{+64}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \lor \neg \left(y \leq 5.6 \cdot 10^{+64}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -3.5) (not (<= y 5.6e+64)))
   (- x (/ y (* z 3.0)))
   (+ x (* (/ 0.3333333333333333 z) (/ t y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5) || !(y <= 5.6e+64)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((0.3333333333333333 / z) * (t / 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 <= (-3.5d0)) .or. (.not. (y <= 5.6d+64))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + ((0.3333333333333333d0 / z) * (t / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -3.5) || !(y <= 5.6e+64)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + ((0.3333333333333333 / z) * (t / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -3.5) or not (y <= 5.6e+64):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + ((0.3333333333333333 / z) * (t / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -3.5) || !(y <= 5.6e+64))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / z) * Float64(t / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -3.5) || ~((y <= 5.6e+64)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + ((0.3333333333333333 / z) * (t / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -3.5], N[Not[LessEqual[y, 5.6e+64]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(0.3333333333333333 / z), $MachinePrecision] * N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.5 or 5.60000000000000047e64 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. associate-+l+ 99.9%

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

      4. remove-double-neg 99.9%

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

      5. distribute-frac-neg 99.9%

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

      6. unsub-neg 99.9%

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

      7. neg-mul-1 99.9%

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

      8. associate-*l/ 99.8%

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

      9. neg-mul-1 99.8%

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

      10. times-frac 99.8%

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

      11. distribute-lft-out-- 99.8%

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

      12. *-commutative 99.8%

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

      13. associate-/r* 99.7%

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

      14. 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. Add Preprocessing

   5. Taylor expanded in y around inf 97.5%

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

      1. metadata-eval 97.5%

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

      2. cancel-sign-sub-inv 97.5%

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

      3. metadata-eval 97.5%

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

      4. distribute-lft-neg-in 97.5%

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

      5. associate-*r/ 97.5%

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

      6. associate-*l/ 97.5%

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

      7. *-commutative 97.5%

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

      8. distribute-rgt-neg-in 97.5%

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

      9. distribute-neg-frac 97.5%

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

      10. metadata-eval 97.5%

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

   7. Simplified 97.5%

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

      1. clear-num 97.5%

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

      2. un-div-inv 97.6%

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

      3. div-inv 97.8%

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

      4. metadata-eval 97.8%

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

   9. Applied egg-rr 97.8%

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

   if -3.5 < y < 5.60000000000000047e64

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. distribute-frac-neg 94.6%

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

      3. associate-+l+ 94.6%

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

      4. remove-double-neg 94.6%

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

      5. distribute-frac-neg 94.6%

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

      6. unsub-neg 94.6%

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

      7. neg-mul-1 94.6%

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

      8. associate-*l/ 94.6%

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

      9. neg-mul-1 94.6%

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

      10. times-frac 95.7%

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

      11. distribute-lft-out-- 95.7%

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

      12. *-commutative 95.7%

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

      13. associate-/r* 95.6%

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

      14. metadata-eval 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around 0 86.6%

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

      1. associate-*r/ 86.6%

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

      2. *-commutative 86.6%

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

      3. times-frac 87.4%

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

   7. Simplified 87.4%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \lor \neg \left(y \leq 5.6 \cdot 10^{+64}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{z} \cdot \frac{t}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13.5 \lor \neg \left(y \leq 5.2 \cdot 10^{+64}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{z}{\frac{t}{y}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -13.5) (not (<= y 5.2e+64)))
   (- x (/ y (* z 3.0)))
   (+ x (/ 0.3333333333333333 (/ z (/ t y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -13.5) || !(y <= 5.2e+64)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 / (z / (t / 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 <= (-13.5d0)) .or. (.not. (y <= 5.2d+64))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = x + (0.3333333333333333d0 / (z / (t / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -13.5) || !(y <= 5.2e+64)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = x + (0.3333333333333333 / (z / (t / y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -13.5) or not (y <= 5.2e+64):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = x + (0.3333333333333333 / (z / (t / y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -13.5) || !(y <= 5.2e+64))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 / Float64(z / Float64(t / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -13.5) || ~((y <= 5.2e+64)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = x + (0.3333333333333333 / (z / (t / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -13.5], N[Not[LessEqual[y, 5.2e+64]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 / N[(z / N[(t / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -13.5 or 5.19999999999999994e64 < y

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-frac-neg 99.9%

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

      3. associate-+l+ 99.9%

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

      4. remove-double-neg 99.9%

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

      5. distribute-frac-neg 99.9%

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

      6. unsub-neg 99.9%

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

      7. neg-mul-1 99.9%

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

      8. associate-*l/ 99.8%

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

      9. neg-mul-1 99.8%

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

      10. times-frac 99.8%

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

      11. distribute-lft-out-- 99.8%

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

      12. *-commutative 99.8%

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

      13. associate-/r* 99.7%

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

      14. 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. Add Preprocessing

   5. Taylor expanded in y around inf 97.5%

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

      1. metadata-eval 97.5%

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

      2. cancel-sign-sub-inv 97.5%

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

      3. metadata-eval 97.5%

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

      4. distribute-lft-neg-in 97.5%

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

      5. associate-*r/ 97.5%

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

      6. associate-*l/ 97.5%

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

      7. *-commutative 97.5%

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

      8. distribute-rgt-neg-in 97.5%

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

      9. distribute-neg-frac 97.5%

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

      10. metadata-eval 97.5%

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

   7. Simplified 97.5%

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

      1. clear-num 97.5%

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

      2. un-div-inv 97.6%

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

      3. div-inv 97.8%

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

      4. metadata-eval 97.8%

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

   9. Applied egg-rr 97.8%

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

   if -13.5 < y < 5.19999999999999994e64

   1. Initial program 94.6%

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

      1. sub-neg 94.6%

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

      2. distribute-frac-neg 94.6%

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

      3. associate-+l+ 94.6%

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

      4. remove-double-neg 94.6%

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

      5. distribute-frac-neg 94.6%

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

      6. unsub-neg 94.6%

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

      7. neg-mul-1 94.6%

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

      8. associate-*l/ 94.6%

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

      9. neg-mul-1 94.6%

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

      10. times-frac 95.7%

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

      11. distribute-lft-out-- 95.7%

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

      12. *-commutative 95.7%

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

      13. associate-/r* 95.6%

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

      14. metadata-eval 95.6%

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

   3. Simplified 95.6%

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

   5. Taylor expanded in y around 0 86.6%

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

      1. associate-*r/ 86.6%

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

      2. *-commutative 86.6%

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

      3. times-frac 87.4%

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

   7. Simplified 87.4%

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

      1. associate-*l/ 87.5%

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

      2. associate-/l* 87.5%

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

   9. Applied egg-rr 87.5%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13.5 \lor \neg \left(y \leq 5.2 \cdot 10^{+64}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{\frac{z}{\frac{t}{y}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 95.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. sub-neg 96.5%

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

   2. distribute-frac-neg 96.5%

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

   3. associate-+l+ 96.5%

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

   4. remove-double-neg 96.5%

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

   5. distribute-frac-neg 96.5%

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

   6. unsub-neg 96.5%

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

   7. neg-mul-1 96.5%

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

   8. associate-*l/ 96.5%

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

   9. neg-mul-1 96.5%

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

   10. times-frac 97.2%

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

   11. distribute-lft-out-- 97.2%

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

   12. *-commutative 97.2%

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

   13. associate-/r* 97.1%

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

   14. metadata-eval 97.1%

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

3. Simplified 97.1%

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

5. Final simplification 97.1%

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

Alternative 6: 95.9% 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 96.5%

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

   1. sub-neg 96.5%

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

   2. distribute-frac-neg 96.5%

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

   3. associate-+l+ 96.5%

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

   4. remove-double-neg 96.5%

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

   5. distribute-frac-neg 96.5%

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

   6. unsub-neg 96.5%

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

   7. neg-mul-1 96.5%

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

   8. associate-*l/ 96.5%

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

   9. neg-mul-1 96.5%

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

   10. times-frac 97.2%

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

   11. distribute-lft-out-- 97.2%

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

   12. *-commutative 97.2%

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

   13. associate-/r* 97.1%

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

   14. metadata-eval 97.1%

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

3. Simplified 97.1%

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

   1. associate-*l/ 97.1%

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

6. Applied egg-rr 97.1%

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

7. Final simplification 97.1%

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

Alternative 7: 95.9% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. sub-neg 96.5%

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

   2. distribute-frac-neg 96.5%

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

   3. associate-+l+ 96.5%

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

   4. remove-double-neg 96.5%

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

   5. distribute-frac-neg 96.5%

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

   6. unsub-neg 96.5%

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

   7. neg-mul-1 96.5%

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

   8. associate-*l/ 96.5%

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

   9. neg-mul-1 96.5%

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

   10. times-frac 97.2%

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

   11. distribute-lft-out-- 97.2%

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

   12. *-commutative 97.2%

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

   13. associate-/r* 97.1%

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

   14. metadata-eval 97.1%

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

3. Simplified 97.1%

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

   1. *-commutative 97.1%

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

   2. clear-num 97.1%

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

   3. un-div-inv 97.2%

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

   4. div-inv 97.3%

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

   5. metadata-eval 97.3%

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

6. Applied egg-rr 97.3%

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

7. Final simplification 97.3%

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

Alternative 8: 64.2% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

3. Taylor expanded in t around 0 60.8%

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

4. Final simplification 60.8%

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

Alternative 9: 64.3% accurate, 2.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. sub-neg 96.5%

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

   2. distribute-frac-neg 96.5%

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

   3. associate-+l+ 96.5%

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

   4. remove-double-neg 96.5%

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

   5. distribute-frac-neg 96.5%

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

   6. unsub-neg 96.5%

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

   7. neg-mul-1 96.5%

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

   8. associate-*l/ 96.5%

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

   9. neg-mul-1 96.5%

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

   10. times-frac 97.2%

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

   11. distribute-lft-out-- 97.2%

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

   12. *-commutative 97.2%

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

   13. associate-/r* 97.1%

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

   14. metadata-eval 97.1%

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

3. Simplified 97.1%

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

5. Taylor expanded in y around inf 60.8%

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

   1. metadata-eval 60.8%

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

   2. cancel-sign-sub-inv 60.8%

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

   3. metadata-eval 60.8%

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

   4. distribute-lft-neg-in 60.8%

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

   5. associate-*r/ 60.8%

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

   6. associate-*l/ 60.8%

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

   7. *-commutative 60.8%

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

   8. distribute-rgt-neg-in 60.8%

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

   9. distribute-neg-frac 60.8%

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

   10. metadata-eval 60.8%

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

7. Simplified 60.8%

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

   1. clear-num 60.8%

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

   2. un-div-inv 60.9%

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

   3. div-inv 60.9%

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

   4. metadata-eval 60.9%

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

9. Applied egg-rr 60.9%

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

10. Final simplification 60.9%

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

Alternative 10: 30.1% accurate, 15.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.5%

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

   1. sub-neg 96.5%

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

   2. distribute-frac-neg 96.5%

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

   3. associate-+l+ 96.5%

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

   4. remove-double-neg 96.5%

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

   5. distribute-frac-neg 96.5%

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

   6. unsub-neg 96.5%

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

   7. neg-mul-1 96.5%

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

   8. associate-*l/ 96.5%

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

   9. neg-mul-1 96.5%

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

   10. times-frac 97.2%

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

   11. distribute-lft-out-- 97.2%

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

   12. *-commutative 97.2%

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

   13. associate-/r* 97.1%

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

   14. metadata-eval 97.1%

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

3. Simplified 97.1%

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

5. Taylor expanded in x around inf 30.2%

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

6. Final simplification 30.2%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 95.9% 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 2024034 
(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))))