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

Percentage Accurate: 95.4% → 99.6%

Time: 10.2s

Alternatives: 14

Speedup: 1.4×

• 28.3% 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: 95.4% 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: 99.6% accurate, 0.1× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ t (* z (* 3.0 y)))))
   (if (<= (* z 3.0) -5.0)
     (+ (+ t_1 x) (/ y (* z -3.0)))
     (if (<= (* z 3.0) 2e-10)
       (+ x (/ (- (/ t y) y) (* z 3.0)))
       (+ x (fma -0.3333333333333333 (/ y z) t_1))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = t / (z * (3.0 * y));
	double tmp;
	if ((z * 3.0) <= -5.0) {
		tmp = (t_1 + x) + (y / (z * -3.0));
	} else if ((z * 3.0) <= 2e-10) {
		tmp = x + (((t / y) - y) / (z * 3.0));
	} else {
		tmp = x + fma(-0.3333333333333333, (y / z), t_1);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(t / Float64(z * Float64(3.0 * y)))
	tmp = 0.0
	if (Float64(z * 3.0) <= -5.0)
		tmp = Float64(Float64(t_1 + x) + Float64(y / Float64(z * -3.0)));
	elseif (Float64(z * 3.0) <= 2e-10)
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	else
		tmp = Float64(x + fma(-0.3333333333333333, Float64(y / z), t_1));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * 3.0), $MachinePrecision], -5.0], N[(N[(t$95$1 + x), $MachinePrecision] + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-10], N[(x + N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-0.3333333333333333 * N[(y / z), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z #s(literal 3 binary64)) < -5

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. sub-neg 99.8%

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

      4. associate-*l* 99.9%

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

      5. *-commutative 99.9%

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

      6. distribute-frac-neg2 99.9%

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

      7. distribute-rgt-neg-in 99.9%

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

      8. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   if -5 < (*.f64 z #s(literal 3 binary64)) < 2.00000000000000007e-10

   1. Initial program 91.6%

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

      1. sub-neg 91.6%

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

      2. associate-+l+ 91.6%

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

      3. +-commutative 91.6%

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

      4. remove-double-neg 91.6%

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

      5. distribute-frac-neg 91.6%

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

      6. distribute-neg-in 91.6%

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

      7. remove-double-neg 91.6%

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

      8. sub-neg 91.6%

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

      9. neg-mul-1 91.6%

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

      10. times-frac 98.4%

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

      11. distribute-frac-neg 98.4%

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

      12. neg-mul-1 98.4%

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

      13. *-commutative 98.4%

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

      14. associate-/l* 98.4%

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

      15. *-commutative 98.4%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. div-inv 99.8%

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

      4. metadata-eval 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   if 2.00000000000000007e-10 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. associate-+l+ 99.7%

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

      3. distribute-frac-neg 99.7%

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

      4. neg-mul-1 99.7%

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

      5. *-commutative 99.7%

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

      6. times-frac 99.7%

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

      7. fma-define 99.7%

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

      8. metadata-eval 99.7%

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

      9. associate-*l* 99.8%

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

      10. *-commutative 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.9%

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

Alternative 2: 99.6% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -5.0) (not (<= (* z 3.0) 2e-10)))
   (+ (+ (/ t (* z (* 3.0 y))) x) (/ y (* z -3.0)))
   (+ x (/ (- (/ t y) y) (* z 3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -5.0) || !((z * 3.0) <= 2e-10)) {
		tmp = ((t / (z * (3.0 * y))) + x) + (y / (z * -3.0));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((z * 3.0d0) <= (-5.0d0)) .or. (.not. ((z * 3.0d0) <= 2d-10))) then
        tmp = ((t / (z * (3.0d0 * y))) + x) + (y / (z * (-3.0d0)))
    else
        tmp = x + (((t / y) - y) / (z * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -5.0) || !((z * 3.0) <= 2e-10)) {
		tmp = ((t / (z * (3.0 * y))) + x) + (y / (z * -3.0));
	} else {
		tmp = x + (((t / y) - y) / (z * 3.0));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -5.0) or not ((z * 3.0) <= 2e-10):
		tmp = ((t / (z * (3.0 * y))) + x) + (y / (z * -3.0))
	else:
		tmp = x + (((t / y) - y) / (z * 3.0))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -5.0) || !(Float64(z * 3.0) <= 2e-10))
		tmp = Float64(Float64(Float64(t / Float64(z * Float64(3.0 * y))) + x) + Float64(y / Float64(z * -3.0)));
	else
		tmp = Float64(x + Float64(Float64(Float64(t / y) - y) / Float64(z * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -5.0) || ~(((z * 3.0) <= 2e-10)))
		tmp = ((t / (z * (3.0 * y))) + x) + (y / (z * -3.0));
	else
		tmp = x + (((t / y) - y) / (z * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -5.0], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 2e-10]], $MachinePrecision]], N[(N[(N[(t / N[(z * N[(3.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 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 z #s(literal 3 binary64)) < -5 or 2.00000000000000007e-10 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. sub-neg 99.8%

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

      4. associate-*l* 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-frac-neg2 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   if -5 < (*.f64 z #s(literal 3 binary64)) < 2.00000000000000007e-10

   1. Initial program 91.6%

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

      1. sub-neg 91.6%

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

      2. associate-+l+ 91.6%

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

      3. +-commutative 91.6%

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

      4. remove-double-neg 91.6%

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

      5. distribute-frac-neg 91.6%

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

      6. distribute-neg-in 91.6%

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

      7. remove-double-neg 91.6%

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

      8. sub-neg 91.6%

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

      9. neg-mul-1 91.6%

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

      10. times-frac 98.4%

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

      11. distribute-frac-neg 98.4%

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

      12. neg-mul-1 98.4%

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

      13. *-commutative 98.4%

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

      14. associate-/l* 98.4%

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

      15. *-commutative 98.4%

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

   3. Simplified 99.8%

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

      1. *-commutative 99.8%

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

      2. clear-num 99.8%

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

      3. div-inv 99.8%

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

      4. metadata-eval 99.8%

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

      5. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

4. Final simplification 99.9%

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

Alternative 3: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+59} \lor \neg \left(z \cdot 3 \leq 0.2\right):\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (* z 3.0) -2e+59) (not (<= (* z 3.0) 0.2)))
   (+ x (* 0.3333333333333333 (/ t (* z y))))
   (* 0.3333333333333333 (/ (- (/ t y) y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -2e+59) || !((z * 3.0) <= 0.2)) {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	} else {
		tmp = 0.3333333333333333 * (((t / y) - 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 (((z * 3.0d0) <= (-2d+59)) .or. (.not. ((z * 3.0d0) <= 0.2d0))) then
        tmp = x + (0.3333333333333333d0 * (t / (z * y)))
    else
        tmp = 0.3333333333333333d0 * (((t / y) - y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((z * 3.0) <= -2e+59) || !((z * 3.0) <= 0.2)) {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	} else {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((z * 3.0) <= -2e+59) or not ((z * 3.0) <= 0.2):
		tmp = x + (0.3333333333333333 * (t / (z * y)))
	else:
		tmp = 0.3333333333333333 * (((t / y) - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(z * 3.0) <= -2e+59) || !(Float64(z * 3.0) <= 0.2))
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))));
	else
		tmp = Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((z * 3.0) <= -2e+59) || ~(((z * 3.0) <= 0.2)))
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	else
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+59], N[Not[LessEqual[N[(z * 3.0), $MachinePrecision], 0.2]], $MachinePrecision]], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z #s(literal 3 binary64)) < -1.99999999999999994e59 or 0.20000000000000001 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-frac-neg 99.8%

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

      6. distribute-neg-in 99.8%

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

      7. remove-double-neg 99.8%

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

      8. sub-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. times-frac 88.3%

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

      11. distribute-frac-neg 88.3%

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

      12. neg-mul-1 88.3%

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

      13. *-commutative 88.3%

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

      14. associate-/l* 88.3%

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

      15. *-commutative 88.3%

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

   3. Simplified 88.3%

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

   5. Taylor expanded in t around inf 84.5%

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

   if -1.99999999999999994e59 < (*.f64 z #s(literal 3 binary64)) < 0.20000000000000001

   1. Initial program 92.7%

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

   3. Taylor expanded in z around 0 93.3%

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

   4. Taylor expanded in t around 0 87.7%

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

      1. +-commutative 87.7%

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

      2. *-commutative 87.7%

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

      3. metadata-eval 87.7%

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

      4. cancel-sign-sub-inv 87.7%

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

      5. distribute-lft-out-- 87.7%

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

      6. *-commutative 87.7%

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

      7. associate-/r* 91.5%

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

      8. div-sub 92.8%

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

   6. Simplified 92.8%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+59} \lor \neg \left(z \cdot 3 \leq 0.2\right):\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 81.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+83}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{+46}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -5e+83)
   (- x (/ y (* z 3.0)))
   (if (<= (* z 3.0) 2e+46)
     (* 0.3333333333333333 (/ (- (/ t y) y) z))
     (+ x (* y (/ -0.3333333333333333 z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -5e+83) {
		tmp = x - (y / (z * 3.0));
	} else if ((z * 3.0) <= 2e+46) {
		tmp = 0.3333333333333333 * (((t / y) - y) / 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 ((z * 3.0d0) <= (-5d+83)) then
        tmp = x - (y / (z * 3.0d0))
    else if ((z * 3.0d0) <= 2d+46) then
        tmp = 0.3333333333333333d0 * (((t / y) - y) / 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 ((z * 3.0) <= -5e+83) {
		tmp = x - (y / (z * 3.0));
	} else if ((z * 3.0) <= 2e+46) {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	} else {
		tmp = x + (y * (-0.3333333333333333 / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -5e+83:
		tmp = x - (y / (z * 3.0))
	elif (z * 3.0) <= 2e+46:
		tmp = 0.3333333333333333 * (((t / y) - y) / z)
	else:
		tmp = x + (y * (-0.3333333333333333 / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -5e+83)
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	elseif (Float64(z * 3.0) <= 2e+46)
		tmp = Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z));
	else
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -5e+83)
		tmp = x - (y / (z * 3.0));
	elseif ((z * 3.0) <= 2e+46)
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	else
		tmp = x + (y * (-0.3333333333333333 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -5e+83], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 2e+46], N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z #s(literal 3 binary64)) < -5.00000000000000029e83

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 84.6%

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

      1. metadata-eval 84.6%

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

      2. times-frac 84.6%

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

      3. *-un-lft-identity 84.6%

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

      4. *-commutative 84.6%

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

   5. Applied egg-rr 84.6%

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

   if -5.00000000000000029e83 < (*.f64 z #s(literal 3 binary64)) < 2e46

   1. Initial program 93.4%

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

   3. Taylor expanded in z around 0 90.1%

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

   4. Taylor expanded in t around 0 86.2%

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

      1. +-commutative 86.2%

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

      2. *-commutative 86.2%

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

      3. metadata-eval 86.2%

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

      4. cancel-sign-sub-inv 86.2%

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

      5. distribute-lft-out-- 86.2%

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

      6. *-commutative 86.2%

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

      7. associate-/r* 88.6%

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

      8. div-sub 89.7%

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

   6. Simplified 89.7%

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

   if 2e46 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. remove-double-neg 99.7%

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

      5. distribute-frac-neg 99.7%

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

      6. distribute-neg-in 99.7%

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

      7. remove-double-neg 99.7%

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

      8. sub-neg 99.7%

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

      9. neg-mul-1 99.7%

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

      10. times-frac 89.4%

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

      11. distribute-frac-neg 89.4%

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

      12. neg-mul-1 89.4%

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

      13. *-commutative 89.4%

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

      14. associate-/l* 89.4%

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

      15. *-commutative 89.4%

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

   3. Simplified 89.4%

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

   5. Taylor expanded in t around 0 81.1%

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

      1. metadata-eval 81.1%

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

      2. distribute-lft-neg-in 81.1%

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

      3. *-commutative 81.1%

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

      4. associate-*l/ 81.1%

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

      5. associate-*r/ 81.1%

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

      6. distribute-rgt-neg-out 81.1%

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

      7. distribute-neg-frac 81.1%

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

      8. metadata-eval 81.1%

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

   7. Simplified 81.1%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -5 \cdot 10^{+83}:\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{elif}\;z \cdot 3 \leq 2 \cdot 10^{+46}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+59}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;z \cdot 3 \leq 0.2:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -2e+59)
   (+ x (* 0.3333333333333333 (/ t (* z y))))
   (if (<= (* z 3.0) 0.2)
     (* 0.3333333333333333 (/ (- (/ t y) y) z))
     (+ x (* t (/ (/ 0.3333333333333333 z) y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -2e+59) {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	} else if ((z * 3.0) <= 0.2) {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	} else {
		tmp = x + (t * ((0.3333333333333333 / z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z * 3.0d0) <= (-2d+59)) then
        tmp = x + (0.3333333333333333d0 * (t / (z * y)))
    else if ((z * 3.0d0) <= 0.2d0) then
        tmp = 0.3333333333333333d0 * (((t / y) - y) / z)
    else
        tmp = x + (t * ((0.3333333333333333d0 / z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -2e+59) {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	} else if ((z * 3.0) <= 0.2) {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	} else {
		tmp = x + (t * ((0.3333333333333333 / z) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -2e+59:
		tmp = x + (0.3333333333333333 * (t / (z * y)))
	elif (z * 3.0) <= 0.2:
		tmp = 0.3333333333333333 * (((t / y) - y) / z)
	else:
		tmp = x + (t * ((0.3333333333333333 / z) / y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -2e+59)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))));
	elseif (Float64(z * 3.0) <= 0.2)
		tmp = Float64(0.3333333333333333 * Float64(Float64(Float64(t / y) - y) / z));
	else
		tmp = Float64(x + Float64(t * Float64(Float64(0.3333333333333333 / z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -2e+59)
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	elseif ((z * 3.0) <= 0.2)
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	else
		tmp = x + (t * ((0.3333333333333333 / z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -2e+59], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(z * 3.0), $MachinePrecision], 0.2], N[(0.3333333333333333 * N[(N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], N[(x + N[(t * N[(N[(0.3333333333333333 / z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (*.f64 z #s(literal 3 binary64)) < -1.99999999999999994e59

   1. Initial program 99.8%

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

      1. sub-neg 99.8%

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

      2. associate-+l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. remove-double-neg 99.8%

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

      5. distribute-frac-neg 99.8%

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

      6. distribute-neg-in 99.8%

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

      7. remove-double-neg 99.8%

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

      8. sub-neg 99.8%

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

      9. neg-mul-1 99.8%

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

      10. times-frac 87.2%

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

      11. distribute-frac-neg 87.2%

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

      12. neg-mul-1 87.2%

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

      13. *-commutative 87.2%

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

      14. associate-/l* 87.2%

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

      15. *-commutative 87.2%

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

   3. Simplified 87.1%

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

   5. Taylor expanded in t around inf 84.0%

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

   if -1.99999999999999994e59 < (*.f64 z #s(literal 3 binary64)) < 0.20000000000000001

   1. Initial program 92.7%

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

   3. Taylor expanded in z around 0 93.3%

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

   4. Taylor expanded in t around 0 87.7%

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

      1. +-commutative 87.7%

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

      2. *-commutative 87.7%

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

      3. metadata-eval 87.7%

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

      4. cancel-sign-sub-inv 87.7%

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

      5. distribute-lft-out-- 87.7%

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

      6. *-commutative 87.7%

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

      7. associate-/r* 91.5%

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

      8. div-sub 92.8%

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

   6. Simplified 92.8%

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

   if 0.20000000000000001 < (*.f64 z #s(literal 3 binary64))

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. associate-+l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. remove-double-neg 99.7%

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

      5. distribute-frac-neg 99.7%

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

      6. distribute-neg-in 99.7%

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

      7. remove-double-neg 99.7%

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

      8. sub-neg 99.7%

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

      9. neg-mul-1 99.7%

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

      10. times-frac 89.6%

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

      11. distribute-frac-neg 89.6%

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

      12. neg-mul-1 89.6%

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

      13. *-commutative 89.6%

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

      14. associate-/l* 89.6%

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

      15. *-commutative 89.6%

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

   3. Simplified 89.6%

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

      1. *-commutative 89.6%

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

      2. clear-num 89.6%

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

      3. div-inv 89.6%

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

      4. metadata-eval 89.6%

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

      5. un-div-inv 89.6%

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

   6. Applied egg-rr 89.6%

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

   7. Taylor expanded in t around inf 85.0%

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

      1. associate-*r/ 85.0%

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

      2. *-commutative 85.0%

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

      3. times-frac 74.9%

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

      4. associate-*l/ 83.2%

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

      5. associate-/l* 85.1%

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

   9. Simplified 85.1%

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

4. Final simplification 89.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -2 \cdot 10^{+59}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{elif}\;z \cdot 3 \leq 0.2:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \mathbf{else}:\\ \;\;\;\;x + t \cdot \frac{\frac{0.3333333333333333}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 58.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{if}\;y \leq -2.65 \cdot 10^{+69}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-205}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ -0.3333333333333333 (/ z y))))
   (if (<= y -2.65e+69)
     t_1
     (if (<= y -1.1e-205)
       x
       (if (<= y 3.25e-6) (* t (/ (/ 0.3333333333333333 y) z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -0.3333333333333333 / (z / y);
	double tmp;
	if (y <= -2.65e+69) {
		tmp = t_1;
	} else if (y <= -1.1e-205) {
		tmp = x;
	} else if (y <= 3.25e-6) {
		tmp = t * ((0.3333333333333333 / y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-0.3333333333333333d0) / (z / y)
    if (y <= (-2.65d+69)) then
        tmp = t_1
    else if (y <= (-1.1d-205)) then
        tmp = x
    else if (y <= 3.25d-6) then
        tmp = t * ((0.3333333333333333d0 / y) / z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -0.3333333333333333 / (z / y);
	double tmp;
	if (y <= -2.65e+69) {
		tmp = t_1;
	} else if (y <= -1.1e-205) {
		tmp = x;
	} else if (y <= 3.25e-6) {
		tmp = t * ((0.3333333333333333 / y) / z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -0.3333333333333333 / (z / y)
	tmp = 0
	if y <= -2.65e+69:
		tmp = t_1
	elif y <= -1.1e-205:
		tmp = x
	elif y <= 3.25e-6:
		tmp = t * ((0.3333333333333333 / y) / z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-0.3333333333333333 / Float64(z / y))
	tmp = 0.0
	if (y <= -2.65e+69)
		tmp = t_1;
	elseif (y <= -1.1e-205)
		tmp = x;
	elseif (y <= 3.25e-6)
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / y) / z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -0.3333333333333333 / (z / y);
	tmp = 0.0;
	if (y <= -2.65e+69)
		tmp = t_1;
	elseif (y <= -1.1e-205)
		tmp = x;
	elseif (y <= 3.25e-6)
		tmp = t * ((0.3333333333333333 / y) / z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.65e+69], t$95$1, If[LessEqual[y, -1.1e-205], x, If[LessEqual[y, 3.25e-6], N[(t * N[(N[(0.3333333333333333 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.65e69 or 3.2499999999999998e-6 < y

   1. Initial program 98.2%

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

   3. Taylor expanded in z around 0 79.9%

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

   4. Taylor expanded in t around 0 71.6%

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

      1. clear-num 71.6%

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

      2. un-div-inv 71.7%

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

   6. Applied egg-rr 71.7%

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

   if -2.65e69 < y < -1.10000000000000005e-205

   1. Initial program 90.5%

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

      1. +-commutative 90.5%

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

      2. associate-+r- 90.5%

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

      3. sub-neg 90.5%

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

      4. associate-*l* 90.5%

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

      5. *-commutative 90.5%

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

      6. distribute-frac-neg2 90.5%

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

      7. distribute-rgt-neg-in 90.5%

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

      8. metadata-eval 90.5%

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

   3. Simplified 90.5%

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

   5. Taylor expanded in z around inf 46.9%

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

   if -1.10000000000000005e-205 < y < 3.2499999999999998e-6

   1. Initial program 94.4%

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

   3. Taylor expanded in z around 0 66.9%

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

   4. Taylor expanded in t around inf 66.7%

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

      1. associate-*r/ 66.6%

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

      2. *-commutative 66.6%

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

      3. associate-*r/ 66.7%

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

      4. associate-/r* 66.7%

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

   6. Simplified 66.7%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+69}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \mathbf{elif}\;y \leq -1.1 \cdot 10^{-205}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3.25 \cdot 10^{-6}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-205} \lor \neg \left(y \leq 1.35 \cdot 10^{-93}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.1e-205) (not (<= y 1.35e-93)))
   (+ x (* y (/ -0.3333333333333333 z)))
   (* t (/ (/ 0.3333333333333333 y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.1e-205) || !(y <= 1.35e-93)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = t * ((0.3333333333333333 / y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.1d-205)) .or. (.not. (y <= 1.35d-93))) then
        tmp = x + (y * ((-0.3333333333333333d0) / z))
    else
        tmp = t * ((0.3333333333333333d0 / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.1e-205) || !(y <= 1.35e-93)) {
		tmp = x + (y * (-0.3333333333333333 / z));
	} else {
		tmp = t * ((0.3333333333333333 / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.1e-205) or not (y <= 1.35e-93):
		tmp = x + (y * (-0.3333333333333333 / z))
	else:
		tmp = t * ((0.3333333333333333 / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.1e-205) || !(y <= 1.35e-93))
		tmp = Float64(x + Float64(y * Float64(-0.3333333333333333 / z)));
	else
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.1e-205) || ~((y <= 1.35e-93)))
		tmp = x + (y * (-0.3333333333333333 / z));
	else
		tmp = t * ((0.3333333333333333 / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.1e-205], N[Not[LessEqual[y, 1.35e-93]], $MachinePrecision]], N[(x + N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(0.3333333333333333 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000005e-205 or 1.3500000000000001e-93 < y

   1. Initial program 96.3%

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

      1. sub-neg 96.3%

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

      2. associate-+l+ 96.3%

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

      3. +-commutative 96.3%

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

      4. remove-double-neg 96.3%

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

      5. distribute-frac-neg 96.3%

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

      6. distribute-neg-in 96.3%

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

      7. remove-double-neg 96.3%

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

      8. sub-neg 96.3%

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

      9. neg-mul-1 96.3%

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

      10. times-frac 97.8%

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

      11. distribute-frac-neg 97.8%

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

      12. neg-mul-1 97.8%

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

      13. *-commutative 97.8%

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

      14. associate-/l* 97.8%

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

      15. *-commutative 97.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around 0 81.6%

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

      1. metadata-eval 81.6%

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

      2. distribute-lft-neg-in 81.6%

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

      3. *-commutative 81.6%

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

      4. associate-*l/ 81.6%

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

      5. associate-*r/ 81.6%

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

      6. distribute-rgt-neg-out 81.6%

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

      7. distribute-neg-frac 81.6%

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

      8. metadata-eval 81.6%

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

   7. Simplified 81.6%

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

   if -1.10000000000000005e-205 < y < 1.3500000000000001e-93

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0 68.4%

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

   4. Taylor expanded in t around inf 72.7%

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

      1. associate-*r/ 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*r/ 72.6%

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

      4. associate-/r* 72.7%

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

   6. Simplified 72.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-205} \lor \neg \left(y \leq 1.35 \cdot 10^{-93}\right):\\ \;\;\;\;x + y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-205} \lor \neg \left(y \leq 1.28 \cdot 10^{-92}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.1e-205) (not (<= y 1.28e-92)))
   (- x (/ y (* z 3.0)))
   (* t (/ (/ 0.3333333333333333 y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.1e-205) || !(y <= 1.28e-92)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = t * ((0.3333333333333333 / y) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.1d-205)) .or. (.not. (y <= 1.28d-92))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = t * ((0.3333333333333333d0 / y) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.1e-205) || !(y <= 1.28e-92)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = t * ((0.3333333333333333 / y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.1e-205) or not (y <= 1.28e-92):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = t * ((0.3333333333333333 / y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.1e-205) || !(y <= 1.28e-92))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(t * Float64(Float64(0.3333333333333333 / y) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.1e-205) || ~((y <= 1.28e-92)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = t * ((0.3333333333333333 / y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.1e-205], N[Not[LessEqual[y, 1.28e-92]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t * N[(N[(0.3333333333333333 / y), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000005e-205 or 1.2799999999999999e-92 < y

   1. Initial program 96.3%

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

   3. Taylor expanded in t around 0 81.6%

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

      1. metadata-eval 81.6%

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

      2. times-frac 81.7%

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

      3. *-un-lft-identity 81.7%

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

      4. *-commutative 81.7%

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

   5. Applied egg-rr 81.7%

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

   if -1.10000000000000005e-205 < y < 1.2799999999999999e-92

   1. Initial program 92.8%

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

   3. Taylor expanded in z around 0 68.4%

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

   4. Taylor expanded in t around inf 72.7%

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

      1. associate-*r/ 72.5%

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

      2. *-commutative 72.5%

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

      3. associate-*r/ 72.6%

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

      4. associate-/r* 72.7%

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

   6. Simplified 72.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-205} \lor \neg \left(y \leq 1.28 \cdot 10^{-92}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;t \cdot \frac{\frac{0.3333333333333333}{y}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-109} \lor \neg \left(y \leq 6.2 \cdot 10^{-93}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.65e-109) (not (<= y 6.2e-93)))
   (- x (/ y (* z 3.0)))
   (/ (* 0.3333333333333333 (/ t z)) y)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.65e-109) || !(y <= 6.2e-93)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (0.3333333333333333 * (t / z)) / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-2.65d-109)) .or. (.not. (y <= 6.2d-93))) then
        tmp = x - (y / (z * 3.0d0))
    else
        tmp = (0.3333333333333333d0 * (t / z)) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.65e-109) || !(y <= 6.2e-93)) {
		tmp = x - (y / (z * 3.0));
	} else {
		tmp = (0.3333333333333333 * (t / z)) / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.65e-109) or not (y <= 6.2e-93):
		tmp = x - (y / (z * 3.0))
	else:
		tmp = (0.3333333333333333 * (t / z)) / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.65e-109) || !(y <= 6.2e-93))
		tmp = Float64(x - Float64(y / Float64(z * 3.0)));
	else
		tmp = Float64(Float64(0.3333333333333333 * Float64(t / z)) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.65e-109) || ~((y <= 6.2e-93)))
		tmp = x - (y / (z * 3.0));
	else
		tmp = (0.3333333333333333 * (t / z)) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.65e-109], N[Not[LessEqual[y, 6.2e-93]], $MachinePrecision]], N[(x - N[(y / N[(z * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.3333333333333333 * N[(t / z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6499999999999999e-109 or 6.19999999999999999e-93 < y

   1. Initial program 97.2%

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

   3. Taylor expanded in t around 0 83.7%

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

      1. metadata-eval 83.7%

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

      2. times-frac 83.8%

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

      3. *-un-lft-identity 83.8%

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

      4. *-commutative 83.8%

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

   5. Applied egg-rr 83.8%

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

   if -2.6499999999999999e-109 < y < 6.19999999999999999e-93

   1. Initial program 91.2%

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

      1. +-commutative 91.2%

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

      2. associate-+r- 91.2%

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

      3. sub-neg 91.2%

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

      4. associate-*l* 91.3%

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

      5. *-commutative 91.3%

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

      6. distribute-frac-neg2 91.3%

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

      7. distribute-rgt-neg-in 91.3%

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

      8. metadata-eval 91.3%

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

   3. Simplified 91.3%

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

   5. Taylor expanded in y around 0 94.2%

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

   6. Taylor expanded in t around inf 72.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{-109} \lor \neg \left(y \leq 6.2 \cdot 10^{-93}\right):\\ \;\;\;\;x - \frac{y}{z \cdot 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.3333333333333333 \cdot \frac{t}{z}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 47.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.28:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -6.4e+42) x (if (<= z 0.28) (* -0.3333333333333333 (/ y z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.4e+42) {
		tmp = x;
	} else if (z <= 0.28) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-6.4d+42)) then
        tmp = x
    else if (z <= 0.28d0) then
        tmp = (-0.3333333333333333d0) * (y / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -6.4e+42) {
		tmp = x;
	} else if (z <= 0.28) {
		tmp = -0.3333333333333333 * (y / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -6.4e+42:
		tmp = x
	elif z <= 0.28:
		tmp = -0.3333333333333333 * (y / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -6.4e+42)
		tmp = x;
	elseif (z <= 0.28)
		tmp = Float64(-0.3333333333333333 * Float64(y / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -6.4e+42)
		tmp = x;
	elseif (z <= 0.28)
		tmp = -0.3333333333333333 * (y / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -6.4e+42], x, If[LessEqual[z, 0.28], N[(-0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -6.40000000000000004e42 or 0.28000000000000003 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. sub-neg 99.8%

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

      4. associate-*l* 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-frac-neg2 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 58.4%

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

   if -6.40000000000000004e42 < z < 0.28000000000000003

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 0 93.2%

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

   4. Taylor expanded in t around 0 55.7%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.4 \cdot 10^{+42}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.28:\\ \;\;\;\;-0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -5.2e+47) x (if (<= z 0.6) (* y (/ -0.3333333333333333 z)) x)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+47) {
		tmp = x;
	} else if (z <= 0.6) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (z <= (-5.2d+47)) then
        tmp = x
    else if (z <= 0.6d0) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -5.2e+47) {
		tmp = x;
	} else if (z <= 0.6) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -5.2e+47:
		tmp = x
	elif z <= 0.6:
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -5.2e+47)
		tmp = x;
	elseif (z <= 0.6)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -5.2e+47)
		tmp = x;
	elseif (z <= 0.6)
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -5.2e+47], x, If[LessEqual[z, 0.6], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if z < -5.20000000000000007e47 or 0.599999999999999978 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-+r- 99.8%

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

      3. sub-neg 99.8%

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

      4. associate-*l* 99.8%

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

      5. *-commutative 99.8%

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

      6. distribute-frac-neg2 99.8%

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

      7. distribute-rgt-neg-in 99.8%

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

      8. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 58.4%

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

   if -5.20000000000000007e47 < z < 0.599999999999999978

   1. Initial program 92.5%

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

   3. Taylor expanded in z around 0 93.2%

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

   4. Taylor expanded in t around 0 87.5%

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

      1. +-commutative 87.5%

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

      2. *-commutative 87.5%

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

      3. metadata-eval 87.5%

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

      4. cancel-sign-sub-inv 87.5%

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

      5. distribute-lft-out-- 87.5%

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

      6. *-commutative 87.5%

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

      7. associate-/r* 91.4%

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

      8. div-sub 92.7%

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

   6. Simplified 92.7%

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

   7. Taylor expanded in t around 0 55.7%

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

      1. *-commutative 55.7%

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

      2. associate-*l/ 55.7%

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

      3. associate-*r/ 55.7%

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

   9. Simplified 55.7%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 95.7% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 95.4%

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

   1. sub-neg 95.4%

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

   2. associate-+l+ 95.4%

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

   3. +-commutative 95.4%

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

   4. remove-double-neg 95.4%

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

   5. distribute-frac-neg 95.4%

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

   6. distribute-neg-in 95.4%

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

   7. remove-double-neg 95.4%

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

   8. sub-neg 95.4%

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

   9. neg-mul-1 95.4%

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

   10. times-frac 94.3%

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

   11. distribute-frac-neg 94.3%

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

   12. neg-mul-1 94.3%

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

   13. *-commutative 94.3%

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

   14. associate-/l* 94.3%

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

   15. *-commutative 94.3%

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

3. Simplified 95.0%

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

5. Final simplification 95.0%

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

Alternative 13: 95.8% 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 95.4%

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

   1. sub-neg 95.4%

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

   2. associate-+l+ 95.4%

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

   3. +-commutative 95.4%

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

   4. remove-double-neg 95.4%

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

   5. distribute-frac-neg 95.4%

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

   6. distribute-neg-in 95.4%

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

   7. remove-double-neg 95.4%

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

   8. sub-neg 95.4%

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

   9. neg-mul-1 95.4%

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

   10. times-frac 94.3%

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

   11. distribute-frac-neg 94.3%

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

   12. neg-mul-1 94.3%

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

   13. *-commutative 94.3%

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

   14. associate-/l* 94.3%

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

   15. *-commutative 94.3%

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

3. Simplified 95.0%

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

   1. *-commutative 95.0%

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

   2. clear-num 95.1%

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

   3. div-inv 95.1%

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

   4. metadata-eval 95.1%

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

   5. un-div-inv 95.1%

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

6. Applied egg-rr 95.1%

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

7. Final simplification 95.1%

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

Alternative 14: 29.7% 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 95.4%

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

   1. +-commutative 95.4%

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

   2. associate-+r- 95.4%

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

   3. sub-neg 95.4%

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

   4. associate-*l* 95.4%

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

   5. *-commutative 95.4%

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

   6. distribute-frac-neg2 95.4%

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

   7. distribute-rgt-neg-in 95.4%

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

   8. metadata-eval 95.4%

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

3. Simplified 95.4%

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

5. Taylor expanded in z around inf 28.1%

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

6. Final simplification 28.1%

   \[\leadsto x \]
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 2024082 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

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

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