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

Percentage Accurate: 95.8% → 97.4%

Time: 14.3s

Alternatives: 20

Speedup: 1.4×

• 28.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 95.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 97.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{z \cdot -3}\\ \mathbf{if}\;t \leq 0.0001:\\ \;\;\;\;\left(\frac{1}{z \cdot \frac{y \cdot 3}{t}} + x\right) + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ y (* z -3.0))))
   (if (<= t 0.0001)
     (+ (+ (/ 1.0 (* z (/ (* y 3.0) t))) x) t_1)
     (+ t_1 (+ x (/ t (* z (* y 3.0))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (t <= 0.0001) {
		tmp = ((1.0 / (z * ((y * 3.0) / t))) + x) + t_1;
	} else {
		tmp = t_1 + (x + (t / (z * (y * 3.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (z * (-3.0d0))
    if (t <= 0.0001d0) then
        tmp = ((1.0d0 / (z * ((y * 3.0d0) / t))) + x) + t_1
    else
        tmp = t_1 + (x + (t / (z * (y * 3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = y / (z * -3.0);
	double tmp;
	if (t <= 0.0001) {
		tmp = ((1.0 / (z * ((y * 3.0) / t))) + x) + t_1;
	} else {
		tmp = t_1 + (x + (t / (z * (y * 3.0))));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = y / (z * -3.0)
	tmp = 0
	if t <= 0.0001:
		tmp = ((1.0 / (z * ((y * 3.0) / t))) + x) + t_1
	else:
		tmp = t_1 + (x + (t / (z * (y * 3.0))))
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(y / Float64(z * -3.0))
	tmp = 0.0
	if (t <= 0.0001)
		tmp = Float64(Float64(Float64(1.0 / Float64(z * Float64(Float64(y * 3.0) / t))) + x) + t_1);
	else
		tmp = Float64(t_1 + Float64(x + Float64(t / Float64(z * Float64(y * 3.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = y / (z * -3.0);
	tmp = 0.0;
	if (t <= 0.0001)
		tmp = ((1.0 / (z * ((y * 3.0) / t))) + x) + t_1;
	else
		tmp = t_1 + (x + (t / (z * (y * 3.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, 0.0001], N[(N[(N[(1.0 / N[(z * N[(N[(y * 3.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + N[(x + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < 1.00000000000000005e-4

   1. Initial program 95.6%

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

      1. +-commutative 95.6%

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

      2. associate-+r- 95.6%

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

      3. sub-neg 95.6%

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

      4. associate-*l* 95.6%

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

      5. *-commutative 95.6%

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

      6. distribute-frac-neg2 95.6%

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

      7. distribute-rgt-neg-in 95.6%

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

      8. metadata-eval 95.6%

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

   3. Simplified 95.6%

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

      1. clear-num 95.6%

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

      2. inv-pow 95.6%

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

   6. Applied egg-rr 95.6%

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

      1. unpow-1 95.6%

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

      2. associate-/l* 98.7%

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

   8. Simplified 98.7%

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

   if 1.00000000000000005e-4 < t

   1. Initial program 98.1%

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

      1. +-commutative 98.1%

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

      2. associate-+r- 98.1%

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

      3. sub-neg 98.1%

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

      4. associate-*l* 98.1%

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

      5. *-commutative 98.1%

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

      6. distribute-frac-neg2 98.1%

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

      7. distribute-rgt-neg-in 98.1%

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

      8. metadata-eval 98.1%

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

   3. Simplified 98.1%

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

4. Final simplification 98.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 0.0001:\\ \;\;\;\;\left(\frac{1}{z \cdot \frac{y \cdot 3}{t}} + x\right) + \frac{y}{z \cdot -3}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3} + \left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\frac{y}{z \cdot -3} + \left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(0.3333333333333333 \cdot \frac{1}{z}\right) \cdot \left(\frac{t}{y} - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (* z 3.0) -1e+90)
   (+ (/ y (* z -3.0)) (+ x (/ t (* z (* y 3.0)))))
   (+ x (* (* 0.3333333333333333 (/ 1.0 z)) (- (/ t y) y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z * 3.0) <= -1e+90) {
		tmp = (y / (z * -3.0)) + (x + (t / (z * (y * 3.0))));
	} else {
		tmp = x + ((0.3333333333333333 * (1.0 / z)) * ((t / y) - 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) <= (-1d+90)) then
        tmp = (y / (z * (-3.0d0))) + (x + (t / (z * (y * 3.0d0))))
    else
        tmp = x + ((0.3333333333333333d0 * (1.0d0 / z)) * ((t / y) - 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) <= -1e+90) {
		tmp = (y / (z * -3.0)) + (x + (t / (z * (y * 3.0))));
	} else {
		tmp = x + ((0.3333333333333333 * (1.0 / z)) * ((t / y) - y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z * 3.0) <= -1e+90:
		tmp = (y / (z * -3.0)) + (x + (t / (z * (y * 3.0))))
	else:
		tmp = x + ((0.3333333333333333 * (1.0 / z)) * ((t / y) - y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(z * 3.0) <= -1e+90)
		tmp = Float64(Float64(y / Float64(z * -3.0)) + Float64(x + Float64(t / Float64(z * Float64(y * 3.0)))));
	else
		tmp = Float64(x + Float64(Float64(0.3333333333333333 * Float64(1.0 / z)) * Float64(Float64(t / y) - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z * 3.0) <= -1e+90)
		tmp = (y / (z * -3.0)) + (x + (t / (z * (y * 3.0))));
	else
		tmp = x + ((0.3333333333333333 * (1.0 / z)) * ((t / y) - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(z * 3.0), $MachinePrecision], -1e+90], N[(N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision] + N[(x + N[(t / N[(z * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(0.3333333333333333 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z 3) < -9.99999999999999966e89

   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 -9.99999999999999966e89 < (*.f64 z 3)

   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 97.5%

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

      11. distribute-frac-neg 97.5%

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

      12. neg-mul-1 97.5%

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

      13. *-commutative 97.5%

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

      14. associate-/l* 97.5%

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

      15. *-commutative 97.5%

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

   3. Simplified 97.9%

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

      1. div-inv 98.0%

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

   6. Applied egg-rr 98.0%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot 3 \leq -1 \cdot 10^{+90}:\\ \;\;\;\;\frac{y}{z \cdot -3} + \left(x + \frac{t}{z \cdot \left(y \cdot 3\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(0.3333333333333333 \cdot \frac{1}{z}\right) \cdot \left(\frac{t}{y} - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11.6:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9500000000:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{1}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.3333333333333333 \cdot \frac{-1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -11.6)
   (- x (* y (/ 0.3333333333333333 z)))
   (if (<= y 9500000000.0)
     (+ x (* 0.3333333333333333 (/ 1.0 (* y (/ z t)))))
     (+ x (* y (* 0.3333333333333333 (/ -1.0 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -11.6) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if (y <= 9500000000.0) {
		tmp = x + (0.3333333333333333 * (1.0 / (y * (z / t))));
	} else {
		tmp = x + (y * (0.3333333333333333 * (-1.0 / 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 <= (-11.6d0)) then
        tmp = x - (y * (0.3333333333333333d0 / z))
    else if (y <= 9500000000.0d0) then
        tmp = x + (0.3333333333333333d0 * (1.0d0 / (y * (z / t))))
    else
        tmp = x + (y * (0.3333333333333333d0 * ((-1.0d0) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -11.6) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if (y <= 9500000000.0) {
		tmp = x + (0.3333333333333333 * (1.0 / (y * (z / t))));
	} else {
		tmp = x + (y * (0.3333333333333333 * (-1.0 / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -11.6:
		tmp = x - (y * (0.3333333333333333 / z))
	elif y <= 9500000000.0:
		tmp = x + (0.3333333333333333 * (1.0 / (y * (z / t))))
	else:
		tmp = x + (y * (0.3333333333333333 * (-1.0 / z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -11.6)
		tmp = Float64(x - Float64(y * Float64(0.3333333333333333 / z)));
	elseif (y <= 9500000000.0)
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(1.0 / Float64(y * Float64(z / t)))));
	else
		tmp = Float64(x + Float64(y * Float64(0.3333333333333333 * Float64(-1.0 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -11.6)
		tmp = x - (y * (0.3333333333333333 / z));
	elseif (y <= 9500000000.0)
		tmp = x + (0.3333333333333333 * (1.0 / (y * (z / t))));
	else
		tmp = x + (y * (0.3333333333333333 * (-1.0 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -11.6], N[(x - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9500000000.0], N[(x + N[(0.3333333333333333 * N[(1.0 / N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(0.3333333333333333 * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -11.5999999999999996

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. associate-+l+ 98.3%

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

      3. +-commutative 98.3%

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

      4. remove-double-neg 98.3%

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

      5. distribute-frac-neg 98.3%

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

      6. distribute-neg-in 98.3%

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

      7. remove-double-neg 98.3%

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

      8. sub-neg 98.3%

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

      9. neg-mul-1 98.3%

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

      10. times-frac 98.3%

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

      11. distribute-frac-neg 98.3%

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

      12. neg-mul-1 98.3%

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

      13. *-commutative 98.3%

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

      14. associate-/l* 98.3%

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

      15. *-commutative 98.3%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 94.8%

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

      1. neg-mul-1 94.8%

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

   7. Simplified 94.8%

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

   if -11.5999999999999996 < y < 9.5e9

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. associate-+l+ 93.2%

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

      3. +-commutative 93.2%

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

      4. remove-double-neg 93.2%

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

      5. distribute-frac-neg 93.2%

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

      6. distribute-neg-in 93.2%

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

      7. remove-double-neg 93.2%

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

      8. sub-neg 93.2%

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

      9. neg-mul-1 93.2%

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

      10. times-frac 93.1%

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

      11. distribute-frac-neg 93.1%

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

      12. neg-mul-1 93.1%

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

      13. *-commutative 93.1%

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

      14. associate-/l* 93.1%

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

      15. *-commutative 93.1%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in t around inf 87.3%

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

      1. clear-num 62.2%

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

      2. inv-pow 62.2%

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

      3. *-commutative 62.2%

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

      4. *-un-lft-identity 62.2%

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

      5. times-frac 61.4%

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

      6. /-rgt-identity 61.4%

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

   7. Applied egg-rr 87.3%

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

      1. unpow-1 61.4%

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

      2. associate-*r/ 62.2%

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

      3. *-commutative 62.2%

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

      4. associate-/l* 65.8%

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

   9. Simplified 91.1%

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

   if 9.5e9 < y

   1. Initial program 99.8%

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

      1. sub-neg 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 99.8%

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

      11. distribute-frac-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-/l* 99.8%

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

      15. *-commutative 99.8%

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

   3. Simplified 99.7%

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

      1. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 99.8%

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

      1. neg-mul-1 99.7%

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

   9. Simplified 99.8%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11.6:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 9500000000:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{1}{y \cdot \frac{z}{t}}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.3333333333333333 \cdot \frac{-1}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-45} \lor \neg \left(y \leq 1.5 \cdot 10^{-150}\right):\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{1}{y \cdot \frac{z}{t}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.9e-45) (not (<= y 1.5e-150)))
   (- x (* y (/ 0.3333333333333333 z)))
   (* 0.3333333333333333 (/ 1.0 (* y (/ z t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e-45) || !(y <= 1.5e-150)) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (1.0 / (y * (z / t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-1.9d-45)) .or. (.not. (y <= 1.5d-150))) then
        tmp = x - (y * (0.3333333333333333d0 / z))
    else
        tmp = 0.3333333333333333d0 * (1.0d0 / (y * (z / t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.9e-45) || !(y <= 1.5e-150)) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (1.0 / (y * (z / t)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.9e-45) or not (y <= 1.5e-150):
		tmp = x - (y * (0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * (1.0 / (y * (z / t)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.9e-45) || !(y <= 1.5e-150))
		tmp = Float64(x - Float64(y * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(1.0 / Float64(y * Float64(z / t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.9e-45) || ~((y <= 1.5e-150)))
		tmp = x - (y * (0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * (1.0 / (y * (z / t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.9e-45], N[Not[LessEqual[y, 1.5e-150]], $MachinePrecision]], N[(x - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(1.0 / N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.89999999999999999e-45 or 1.5000000000000001e-150 < y

   1. Initial program 98.6%

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

      1. sub-neg 98.6%

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

      2. associate-+l+ 98.6%

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

      3. +-commutative 98.6%

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

      4. remove-double-neg 98.6%

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

      5. distribute-frac-neg 98.6%

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

      6. distribute-neg-in 98.6%

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

      7. remove-double-neg 98.6%

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

      8. sub-neg 98.6%

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

      9. neg-mul-1 98.6%

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

      10. times-frac 98.6%

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

      11. distribute-frac-neg 98.6%

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

      12. neg-mul-1 98.6%

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

      13. *-commutative 98.6%

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

      14. associate-/l* 98.5%

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

      15. *-commutative 98.5%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around 0 88.0%

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

      1. neg-mul-1 88.0%

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

   7. Simplified 88.0%

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

   if -1.89999999999999999e-45 < y < 1.5000000000000001e-150

   1. Initial program 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-+r- 91.5%

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

      3. sub-neg 91.5%

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

      4. associate-*l* 91.4%

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

      5. *-commutative 91.4%

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

      6. distribute-frac-neg2 91.4%

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

      7. distribute-rgt-neg-in 91.4%

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

      8. metadata-eval 91.4%

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

   3. Simplified 91.4%

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

      1. clear-num 91.4%

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

      2. inv-pow 91.4%

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

   6. Applied egg-rr 91.4%

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

      1. unpow-1 91.4%

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

      2. associate-/l* 92.3%

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

   8. Simplified 92.3%

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

   9. Taylor expanded in z around 0 70.4%

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

       1. +-commutative 70.4%

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

       2. metadata-eval 70.4%

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

       3. associate-*r* 70.4%

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

       4. neg-mul-1 70.4%

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

       5. distribute-lft-in 70.4%

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

       6. sub-neg 70.4%

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

       7. associate-*r/ 70.4%

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

   11. Simplified 70.4%

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

   12. Taylor expanded in t around inf 69.6%

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

       1. clear-num 69.6%

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

       2. inv-pow 69.6%

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

       3. *-commutative 69.6%

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

       4. *-un-lft-identity 69.6%

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

       5. times-frac 68.7%

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

       6. /-rgt-identity 68.7%

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

   14. Applied egg-rr 68.7%

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

       1. unpow-1 68.7%

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

       2. associate-*r/ 69.6%

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

       3. *-commutative 69.6%

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

       4. associate-/l* 74.8%

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

   16. Simplified 74.8%

       \[\leadsto 0.3333333333333333 \cdot \color{blue}{\frac{1}{y \cdot \frac{z}{t}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 83.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{-45} \lor \neg \left(y \leq 1.5 \cdot 10^{-150}\right):\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{1}{y \cdot \frac{z}{t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 79.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+179} \lor \neg \left(z \leq 1.56 \cdot 10^{+61}\right):\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -7.8e+179) (not (<= z 1.56e+61)))
   (- x (* y (/ 0.3333333333333333 z)))
   (* 0.3333333333333333 (/ (- (/ t y) y) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -7.8e+179) || !(z <= 1.56e+61)) {
		tmp = x - (y * (0.3333333333333333 / z));
	} 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 <= (-7.8d+179)) .or. (.not. (z <= 1.56d+61))) then
        tmp = x - (y * (0.3333333333333333d0 / z))
    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 <= -7.8e+179) || !(z <= 1.56e+61)) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else {
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -7.8e+179) or not (z <= 1.56e+61):
		tmp = x - (y * (0.3333333333333333 / z))
	else:
		tmp = 0.3333333333333333 * (((t / y) - y) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -7.8e+179) || !(z <= 1.56e+61))
		tmp = Float64(x - Float64(y * Float64(0.3333333333333333 / z)));
	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 <= -7.8e+179) || ~((z <= 1.56e+61)))
		tmp = x - (y * (0.3333333333333333 / z));
	else
		tmp = 0.3333333333333333 * (((t / y) - y) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -7.8e+179], N[Not[LessEqual[z, 1.56e+61]], $MachinePrecision]], N[(x - N[(y * N[(0.3333333333333333 / z), $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 z < -7.79999999999999947e179 or 1.56000000000000012e61 < z

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. associate-+l+ 99.9%

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

      3. +-commutative 99.9%

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

      4. remove-double-neg 99.9%

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

      5. distribute-frac-neg 99.9%

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

      6. distribute-neg-in 99.9%

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

      7. remove-double-neg 99.9%

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

      8. sub-neg 99.9%

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

      9. neg-mul-1 99.9%

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

      10. times-frac 90.9%

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

      11. distribute-frac-neg 90.9%

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

      12. neg-mul-1 90.9%

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

      13. *-commutative 90.9%

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

      14. associate-/l* 90.8%

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

      15. *-commutative 90.8%

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

   3. Simplified 90.9%

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

   5. Taylor expanded in t around 0 84.4%

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

      1. neg-mul-1 84.4%

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

   7. Simplified 84.4%

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

   if -7.79999999999999947e179 < z < 1.56000000000000012e61

   1. Initial program 95.0%

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

      1. +-commutative 95.0%

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

      2. associate-+r- 95.0%

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

      3. sub-neg 95.0%

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

      4. associate-*l* 94.9%

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

      5. *-commutative 94.9%

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

      6. distribute-frac-neg2 94.9%

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

      7. distribute-rgt-neg-in 94.9%

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

      8. metadata-eval 94.9%

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

   3. Simplified 94.9%

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

      1. clear-num 94.9%

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

      2. inv-pow 94.9%

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

   6. Applied egg-rr 94.9%

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

      1. unpow-1 94.9%

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

      2. associate-/l* 97.8%

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

   8. Simplified 97.8%

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

   9. Taylor expanded in z around 0 86.3%

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

       1. +-commutative 86.3%

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

       2. metadata-eval 86.3%

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

       3. associate-*r* 86.3%

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

       4. neg-mul-1 86.3%

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

       5. distribute-lft-in 86.3%

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

       6. sub-neg 86.3%

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

       7. associate-*r/ 85.9%

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

   11. Simplified 85.9%

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

4. Final simplification 85.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+179} \lor \neg \left(z \leq 1.56 \cdot 10^{+61}\right):\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 89.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -20.5 \lor \neg \left(y \leq 1660000000\right):\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -20.5) (not (<= y 1660000000.0)))
   (- x (* y (/ 0.3333333333333333 z)))
   (+ x (* 0.3333333333333333 (/ t (* z y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -20.5) || !(y <= 1660000000.0)) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-20.5d0)) .or. (.not. (y <= 1660000000.0d0))) then
        tmp = x - (y * (0.3333333333333333d0 / z))
    else
        tmp = x + (0.3333333333333333d0 * (t / (z * y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -20.5) || !(y <= 1660000000.0)) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else {
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -20.5) or not (y <= 1660000000.0):
		tmp = x - (y * (0.3333333333333333 / z))
	else:
		tmp = x + (0.3333333333333333 * (t / (z * y)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -20.5) || !(y <= 1660000000.0))
		tmp = Float64(x - Float64(y * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(x + Float64(0.3333333333333333 * Float64(t / Float64(z * y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -20.5) || ~((y <= 1660000000.0)))
		tmp = x - (y * (0.3333333333333333 / z));
	else
		tmp = x + (0.3333333333333333 * (t / (z * y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -20.5], N[Not[LessEqual[y, 1660000000.0]], $MachinePrecision]], N[(x - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -20.5 or 1.66e9 < y

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. associate-+l+ 99.0%

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

      3. +-commutative 99.0%

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

      4. remove-double-neg 99.0%

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

      5. distribute-frac-neg 99.0%

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

      6. distribute-neg-in 99.0%

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

      7. remove-double-neg 99.0%

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

      8. sub-neg 99.0%

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

      9. neg-mul-1 99.0%

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

      10. times-frac 99.0%

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

      11. distribute-frac-neg 99.0%

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

      12. neg-mul-1 99.0%

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

      13. *-commutative 99.0%

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

      14. associate-/l* 99.0%

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

      15. *-commutative 99.0%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 97.1%

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

      1. neg-mul-1 97.1%

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

   7. Simplified 97.1%

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

   if -20.5 < y < 1.66e9

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. associate-+l+ 93.2%

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

      3. +-commutative 93.2%

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

      4. remove-double-neg 93.2%

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

      5. distribute-frac-neg 93.2%

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

      6. distribute-neg-in 93.2%

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

      7. remove-double-neg 93.2%

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

      8. sub-neg 93.2%

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

      9. neg-mul-1 93.2%

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

      10. times-frac 93.1%

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

      11. distribute-frac-neg 93.1%

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

      12. neg-mul-1 93.1%

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

      13. *-commutative 93.1%

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

      14. associate-/l* 93.1%

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

      15. *-commutative 93.1%

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

   3. Simplified 93.0%

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

   5. Taylor expanded in t around inf 87.3%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -20.5 \lor \neg \left(y \leq 1660000000\right):\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + 0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -12 \lor \neg \left(y \leq 720000000\right):\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -12.0) (not (<= y 720000000.0)))
   (- x (* y (/ 0.3333333333333333 z)))
   (+ x (* (/ 0.3333333333333333 y) (/ t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -12.0) || !(y <= 720000000.0)) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else {
		tmp = x + ((0.3333333333333333 / y) * (t / 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 <= (-12.0d0)) .or. (.not. (y <= 720000000.0d0))) then
        tmp = x - (y * (0.3333333333333333d0 / z))
    else
        tmp = x + ((0.3333333333333333d0 / y) * (t / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -12.0) || !(y <= 720000000.0)) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else {
		tmp = x + ((0.3333333333333333 / y) * (t / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -12.0) or not (y <= 720000000.0):
		tmp = x - (y * (0.3333333333333333 / z))
	else:
		tmp = x + ((0.3333333333333333 / y) * (t / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -12.0) || !(y <= 720000000.0))
		tmp = Float64(x - Float64(y * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / y) * Float64(t / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -12.0) || ~((y <= 720000000.0)))
		tmp = x - (y * (0.3333333333333333 / z));
	else
		tmp = x + ((0.3333333333333333 / y) * (t / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -12.0], N[Not[LessEqual[y, 720000000.0]], $MachinePrecision]], N[(x - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(0.3333333333333333 / y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -12 or 7.2e8 < y

   1. Initial program 99.0%

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

      1. sub-neg 99.0%

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

      2. associate-+l+ 99.0%

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

      3. +-commutative 99.0%

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

      4. remove-double-neg 99.0%

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

      5. distribute-frac-neg 99.0%

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

      6. distribute-neg-in 99.0%

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

      7. remove-double-neg 99.0%

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

      8. sub-neg 99.0%

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

      9. neg-mul-1 99.0%

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

      10. times-frac 99.0%

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

      11. distribute-frac-neg 99.0%

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

      12. neg-mul-1 99.0%

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

      13. *-commutative 99.0%

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

      14. associate-/l* 99.0%

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

      15. *-commutative 99.0%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in t around 0 97.1%

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

      1. neg-mul-1 97.1%

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

   7. Simplified 97.1%

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

   if -12 < y < 7.2e8

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. associate-+l+ 93.2%

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

      3. +-commutative 93.2%

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

      4. remove-double-neg 93.2%

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

      5. distribute-frac-neg 93.2%

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

      6. distribute-neg-in 93.2%

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

      7. remove-double-neg 93.2%

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

      8. sub-neg 93.2%

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

      9. neg-mul-1 93.2%

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

      10. times-frac 93.1%

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

      11. distribute-frac-neg 93.1%

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

      12. neg-mul-1 93.1%

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

      13. *-commutative 93.1%

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

      14. associate-/l* 93.1%

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

      15. *-commutative 93.1%

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

   3. Simplified 93.0%

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

      1. clear-num 93.0%

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

      2. inv-pow 93.0%

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

   6. Applied egg-rr 93.0%

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

      1. unpow-1 93.0%

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

   8. Simplified 93.0%

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

   9. Taylor expanded in t around inf 87.3%

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

       1. associate-*r/ 87.3%

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

       2. times-frac 91.1%

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

   11. Simplified 91.1%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12 \lor \neg \left(y \leq 720000000\right):\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 91.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13.5:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3500000000:\\ \;\;\;\;x + \frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.3333333333333333 \cdot \frac{-1}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -13.5)
   (- x (* y (/ 0.3333333333333333 z)))
   (if (<= y 3500000000.0)
     (+ x (* (/ 0.3333333333333333 y) (/ t z)))
     (+ x (* y (* 0.3333333333333333 (/ -1.0 z)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -13.5) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if (y <= 3500000000.0) {
		tmp = x + ((0.3333333333333333 / y) * (t / z));
	} else {
		tmp = x + (y * (0.3333333333333333 * (-1.0 / 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 <= (-13.5d0)) then
        tmp = x - (y * (0.3333333333333333d0 / z))
    else if (y <= 3500000000.0d0) then
        tmp = x + ((0.3333333333333333d0 / y) * (t / z))
    else
        tmp = x + (y * (0.3333333333333333d0 * ((-1.0d0) / z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -13.5) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else if (y <= 3500000000.0) {
		tmp = x + ((0.3333333333333333 / y) * (t / z));
	} else {
		tmp = x + (y * (0.3333333333333333 * (-1.0 / z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -13.5:
		tmp = x - (y * (0.3333333333333333 / z))
	elif y <= 3500000000.0:
		tmp = x + ((0.3333333333333333 / y) * (t / z))
	else:
		tmp = x + (y * (0.3333333333333333 * (-1.0 / z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -13.5)
		tmp = Float64(x - Float64(y * Float64(0.3333333333333333 / z)));
	elseif (y <= 3500000000.0)
		tmp = Float64(x + Float64(Float64(0.3333333333333333 / y) * Float64(t / z)));
	else
		tmp = Float64(x + Float64(y * Float64(0.3333333333333333 * Float64(-1.0 / z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -13.5)
		tmp = x - (y * (0.3333333333333333 / z));
	elseif (y <= 3500000000.0)
		tmp = x + ((0.3333333333333333 / y) * (t / z));
	else
		tmp = x + (y * (0.3333333333333333 * (-1.0 / z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -13.5], N[(x - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3500000000.0], N[(x + N[(N[(0.3333333333333333 / y), $MachinePrecision] * N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(0.3333333333333333 * N[(-1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -13.5

   1. Initial program 98.3%

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

      1. sub-neg 98.3%

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

      2. associate-+l+ 98.3%

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

      3. +-commutative 98.3%

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

      4. remove-double-neg 98.3%

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

      5. distribute-frac-neg 98.3%

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

      6. distribute-neg-in 98.3%

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

      7. remove-double-neg 98.3%

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

      8. sub-neg 98.3%

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

      9. neg-mul-1 98.3%

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

      10. times-frac 98.3%

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

      11. distribute-frac-neg 98.3%

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

      12. neg-mul-1 98.3%

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

      13. *-commutative 98.3%

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

      14. associate-/l* 98.3%

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

      15. *-commutative 98.3%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in t around 0 94.8%

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

      1. neg-mul-1 94.8%

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

   7. Simplified 94.8%

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

   if -13.5 < y < 3.5e9

   1. Initial program 93.2%

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

      1. sub-neg 93.2%

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

      2. associate-+l+ 93.2%

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

      3. +-commutative 93.2%

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

      4. remove-double-neg 93.2%

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

      5. distribute-frac-neg 93.2%

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

      6. distribute-neg-in 93.2%

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

      7. remove-double-neg 93.2%

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

      8. sub-neg 93.2%

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

      9. neg-mul-1 93.2%

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

      10. times-frac 93.1%

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

      11. distribute-frac-neg 93.1%

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

      12. neg-mul-1 93.1%

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

      13. *-commutative 93.1%

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

      14. associate-/l* 93.1%

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

      15. *-commutative 93.1%

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

   3. Simplified 93.0%

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

      1. clear-num 93.0%

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

      2. inv-pow 93.0%

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

   6. Applied egg-rr 93.0%

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

      1. unpow-1 93.0%

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

   8. Simplified 93.0%

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

   9. Taylor expanded in t around inf 87.3%

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

       1. associate-*r/ 87.3%

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

       2. times-frac 91.1%

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

   11. Simplified 91.1%

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

   if 3.5e9 < y

   1. Initial program 99.8%

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

      1. sub-neg 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 99.8%

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

      11. distribute-frac-neg 99.8%

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

      12. neg-mul-1 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-/l* 99.8%

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

      15. *-commutative 99.8%

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

   3. Simplified 99.7%

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

      1. div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in t around 0 99.8%

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

      1. neg-mul-1 99.7%

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

   9. Simplified 99.8%

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

4. Final simplification 94.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13.5:\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3500000000:\\ \;\;\;\;x + \frac{0.3333333333333333}{y} \cdot \frac{t}{z}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(0.3333333333333333 \cdot \frac{-1}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-47} \lor \neg \left(y \leq 5 \cdot 10^{-150}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -1.15e-47) (not (<= y 5e-150)))
   (- x (* 0.3333333333333333 (/ y z)))
   (* 0.3333333333333333 (/ t (* z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -1.15e-47) || !(y <= 5e-150)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} 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 <= (-1.15d-47)) .or. (.not. (y <= 5d-150))) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    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 <= -1.15e-47) || !(y <= 5e-150)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = 0.3333333333333333 * (t / (z * y));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -1.15e-47) or not (y <= 5e-150):
		tmp = x - (0.3333333333333333 * (y / z))
	else:
		tmp = 0.3333333333333333 * (t / (z * y))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -1.15e-47) || !(y <= 5e-150))
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	else
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -1.15e-47) || ~((y <= 5e-150)))
		tmp = x - (0.3333333333333333 * (y / z));
	else
		tmp = 0.3333333333333333 * (t / (z * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -1.15e-47], N[Not[LessEqual[y, 5e-150]], $MachinePrecision]], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.14999999999999991e-47 or 4.9999999999999999e-150 < y

   1. Initial program 98.6%

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

   3. Taylor expanded in t around 0 87.5%

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

   if -1.14999999999999991e-47 < y < 4.9999999999999999e-150

   1. Initial program 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-+r- 91.5%

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

      3. sub-neg 91.5%

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

      4. associate-*l* 91.4%

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

      5. *-commutative 91.4%

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

      6. distribute-frac-neg2 91.4%

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

      7. distribute-rgt-neg-in 91.4%

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

      8. metadata-eval 91.4%

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

   3. Simplified 91.4%

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

      1. clear-num 91.4%

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

      2. inv-pow 91.4%

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

   6. Applied egg-rr 91.4%

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

      1. unpow-1 91.4%

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

      2. associate-/l* 92.3%

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

   8. Simplified 92.3%

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

   9. Taylor expanded in z around 0 70.4%

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

       1. +-commutative 70.4%

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

       2. metadata-eval 70.4%

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

       3. associate-*r* 70.4%

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

       4. neg-mul-1 70.4%

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

       5. distribute-lft-in 70.4%

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

       6. sub-neg 70.4%

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

       7. associate-*r/ 70.4%

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

   11. Simplified 70.4%

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

   12. Taylor expanded in t around inf 69.6%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.15 \cdot 10^{-47} \lor \neg \left(y \leq 5 \cdot 10^{-150}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-48} \lor \neg \left(y \leq 4.5 \cdot 10^{-150}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot 0.3333333333333333}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -4.6e-48) (not (<= y 4.5e-150)))
   (- x (* 0.3333333333333333 (/ y z)))
   (/ (* t 0.3333333333333333) (* z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -4.6e-48) || !(y <= 4.5e-150)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = (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 ((y <= (-4.6d-48)) .or. (.not. (y <= 4.5d-150))) then
        tmp = x - (0.3333333333333333d0 * (y / z))
    else
        tmp = (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 ((y <= -4.6e-48) || !(y <= 4.5e-150)) {
		tmp = x - (0.3333333333333333 * (y / z));
	} else {
		tmp = (t * 0.3333333333333333) / (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -4.6e-48) or not (y <= 4.5e-150):
		tmp = x - (0.3333333333333333 * (y / z))
	else:
		tmp = (t * 0.3333333333333333) / (z * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -4.6e-48) || !(y <= 4.5e-150))
		tmp = Float64(x - Float64(0.3333333333333333 * Float64(y / z)));
	else
		tmp = Float64(Float64(t * 0.3333333333333333) / Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -4.6e-48) || ~((y <= 4.5e-150)))
		tmp = x - (0.3333333333333333 * (y / z));
	else
		tmp = (t * 0.3333333333333333) / (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -4.6e-48], N[Not[LessEqual[y, 4.5e-150]], $MachinePrecision]], N[(x - N[(0.3333333333333333 * N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * 0.3333333333333333), $MachinePrecision] / N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.6000000000000001e-48 or 4.5000000000000002e-150 < y

   1. Initial program 98.6%

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

   3. Taylor expanded in t around 0 87.5%

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

   if -4.6000000000000001e-48 < y < 4.5000000000000002e-150

   1. Initial program 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-+r- 91.5%

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

      3. sub-neg 91.5%

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

      4. associate-*l* 91.4%

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

      5. *-commutative 91.4%

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

      6. distribute-frac-neg2 91.4%

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

      7. distribute-rgt-neg-in 91.4%

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

      8. metadata-eval 91.4%

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

   3. Simplified 91.4%

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

      1. clear-num 91.4%

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

      2. inv-pow 91.4%

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

   6. Applied egg-rr 91.4%

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

      1. unpow-1 91.4%

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

      2. associate-/l* 92.3%

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

   8. Simplified 92.3%

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

   9. Taylor expanded in z around 0 70.4%

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

       1. +-commutative 70.4%

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

       2. metadata-eval 70.4%

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

       3. associate-*r* 70.4%

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

       4. neg-mul-1 70.4%

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

       5. distribute-lft-in 70.4%

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

       6. sub-neg 70.4%

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

       7. associate-*r/ 70.4%

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

   11. Simplified 70.4%

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

   12. Taylor expanded in t around inf 69.6%

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

       1. associate-*r/ 69.6%

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

       2. *-commutative 69.6%

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

       3. *-commutative 69.6%

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

   14. Applied egg-rr 69.6%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-48} \lor \neg \left(y \leq 4.5 \cdot 10^{-150}\right):\\ \;\;\;\;x - 0.3333333333333333 \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot 0.3333333333333333}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-47} \lor \neg \left(y \leq 2.8 \cdot 10^{-150}\right):\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot 0.3333333333333333}{z \cdot y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -2.4e-47) (not (<= y 2.8e-150)))
   (- x (* y (/ 0.3333333333333333 z)))
   (/ (* t 0.3333333333333333) (* z y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -2.4e-47) || !(y <= 2.8e-150)) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else {
		tmp = (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 ((y <= (-2.4d-47)) .or. (.not. (y <= 2.8d-150))) then
        tmp = x - (y * (0.3333333333333333d0 / z))
    else
        tmp = (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 ((y <= -2.4e-47) || !(y <= 2.8e-150)) {
		tmp = x - (y * (0.3333333333333333 / z));
	} else {
		tmp = (t * 0.3333333333333333) / (z * y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -2.4e-47) or not (y <= 2.8e-150):
		tmp = x - (y * (0.3333333333333333 / z))
	else:
		tmp = (t * 0.3333333333333333) / (z * y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -2.4e-47) || !(y <= 2.8e-150))
		tmp = Float64(x - Float64(y * Float64(0.3333333333333333 / z)));
	else
		tmp = Float64(Float64(t * 0.3333333333333333) / Float64(z * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -2.4e-47) || ~((y <= 2.8e-150)))
		tmp = x - (y * (0.3333333333333333 / z));
	else
		tmp = (t * 0.3333333333333333) / (z * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -2.4e-47], N[Not[LessEqual[y, 2.8e-150]], $MachinePrecision]], N[(x - N[(y * N[(0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(t * 0.3333333333333333), $MachinePrecision] / N[(z * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.3999999999999999e-47 or 2.79999999999999996e-150 < y

   1. Initial program 98.6%

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

      1. sub-neg 98.6%

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

      2. associate-+l+ 98.6%

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

      3. +-commutative 98.6%

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

      4. remove-double-neg 98.6%

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

      5. distribute-frac-neg 98.6%

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

      6. distribute-neg-in 98.6%

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

      7. remove-double-neg 98.6%

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

      8. sub-neg 98.6%

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

      9. neg-mul-1 98.6%

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

      10. times-frac 98.6%

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

      11. distribute-frac-neg 98.6%

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

      12. neg-mul-1 98.6%

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

      13. *-commutative 98.6%

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

      14. associate-/l* 98.5%

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

      15. *-commutative 98.5%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in t around 0 88.0%

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

      1. neg-mul-1 88.0%

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

   7. Simplified 88.0%

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

   if -2.3999999999999999e-47 < y < 2.79999999999999996e-150

   1. Initial program 91.5%

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

      1. +-commutative 91.5%

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

      2. associate-+r- 91.5%

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

      3. sub-neg 91.5%

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

      4. associate-*l* 91.4%

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

      5. *-commutative 91.4%

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

      6. distribute-frac-neg2 91.4%

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

      7. distribute-rgt-neg-in 91.4%

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

      8. metadata-eval 91.4%

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

   3. Simplified 91.4%

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

      1. clear-num 91.4%

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

      2. inv-pow 91.4%

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

   6. Applied egg-rr 91.4%

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

      1. unpow-1 91.4%

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

      2. associate-/l* 92.3%

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

   8. Simplified 92.3%

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

   9. Taylor expanded in z around 0 70.4%

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

       1. +-commutative 70.4%

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

       2. metadata-eval 70.4%

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

       3. associate-*r* 70.4%

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

       4. neg-mul-1 70.4%

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

       5. distribute-lft-in 70.4%

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

       6. sub-neg 70.4%

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

       7. associate-*r/ 70.4%

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

   11. Simplified 70.4%

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

   12. Taylor expanded in t around inf 69.6%

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

       1. associate-*r/ 69.6%

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

       2. *-commutative 69.6%

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

       3. *-commutative 69.6%

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

   14. Applied egg-rr 69.6%

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

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.4 \cdot 10^{-47} \lor \neg \left(y \leq 2.8 \cdot 10^{-150}\right):\\ \;\;\;\;x - y \cdot \frac{0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{t \cdot 0.3333333333333333}{z \cdot y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.007:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 5200000000000:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -0.007)
   (* y (/ -0.3333333333333333 z))
   (if (<= y 5200000000000.0)
     (* 0.3333333333333333 (/ t (* z y)))
     (/ y (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.007) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 5200000000000.0) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-0.007d0)) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else if (y <= 5200000000000.0d0) then
        tmp = 0.3333333333333333d0 * (t / (z * y))
    else
        tmp = y / (z * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -0.007) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 5200000000000.0) {
		tmp = 0.3333333333333333 * (t / (z * y));
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -0.007:
		tmp = y * (-0.3333333333333333 / z)
	elif y <= 5200000000000.0:
		tmp = 0.3333333333333333 * (t / (z * y))
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -0.007)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	elseif (y <= 5200000000000.0)
		tmp = Float64(0.3333333333333333 * Float64(t / Float64(z * y)));
	else
		tmp = Float64(y / Float64(z * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -0.007)
		tmp = y * (-0.3333333333333333 / z);
	elseif (y <= 5200000000000.0)
		tmp = 0.3333333333333333 * (t / (z * y));
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -0.007], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5200000000000.0], N[(0.3333333333333333 * N[(t / N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -0.00700000000000000015

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. associate-+r- 98.3%

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

      3. sub-neg 98.3%

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

      4. associate-*l* 98.3%

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

      5. *-commutative 98.3%

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

      6. distribute-frac-neg2 98.3%

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

      7. distribute-rgt-neg-in 98.3%

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

      8. metadata-eval 98.3%

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

   3. Simplified 98.3%

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

      1. clear-num 98.3%

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

      2. inv-pow 98.3%

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

   6. Applied egg-rr 98.3%

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

      1. unpow-1 98.3%

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

      2. associate-/l* 98.3%

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

   8. Simplified 98.3%

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

   9. Taylor expanded in y around inf 75.4%

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

       1. associate-*r/ 75.4%

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

       2. metadata-eval 75.4%

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

       3. associate-*r* 75.4%

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

       4. neg-mul-1 75.4%

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

       5. associate-*l/ 75.5%

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

       6. *-commutative 75.5%

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

       7. distribute-lft-neg-out 75.5%

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

       8. distribute-rgt-neg-in 75.5%

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

       9. distribute-neg-frac 75.5%

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

       10. metadata-eval 75.5%

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

   11. Simplified 75.5%

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

   if -0.00700000000000000015 < y < 5.2e12

   1. Initial program 93.1%

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

      1. +-commutative 93.1%

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

      2. associate-+r- 93.1%

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

      3. sub-neg 93.1%

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

      4. associate-*l* 93.1%

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

      5. *-commutative 93.1%

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

      6. distribute-frac-neg2 93.1%

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

      7. distribute-rgt-neg-in 93.1%

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

      8. metadata-eval 93.1%

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

   3. Simplified 93.1%

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

      1. clear-num 93.1%

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

      2. inv-pow 93.1%

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

   6. Applied egg-rr 93.1%

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

      1. unpow-1 93.1%

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

      2. associate-/l* 94.3%

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

   8. Simplified 94.3%

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

   9. Taylor expanded in z around 0 68.8%

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

       1. +-commutative 68.8%

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

       2. metadata-eval 68.8%

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

       3. associate-*r* 68.8%

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

       4. neg-mul-1 68.8%

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

       5. distribute-lft-in 68.8%

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

       6. sub-neg 68.8%

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

       7. associate-*r/ 68.9%

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

   11. Simplified 68.9%

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

   12. Taylor expanded in t around inf 63.2%

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

   if 5.2e12 < y

   1. Initial program 99.8%

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

      1. +-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. Step-by-step derivation

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. unpow-1 99.8%

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

      2. associate-/l* 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in y around inf 66.9%

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

       1. associate-*r/ 68.2%

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

       2. metadata-eval 68.2%

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

       3. associate-*r* 68.2%

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

       4. neg-mul-1 68.2%

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

       5. associate-*l/ 68.1%

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

       6. *-commutative 68.1%

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

       7. distribute-lft-neg-out 68.1%

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

       8. distribute-rgt-neg-in 68.1%

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

       9. distribute-neg-frac 68.1%

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

       10. metadata-eval 68.1%

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

   11. Simplified 68.1%

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

       1. clear-num 68.1%

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

       2. un-div-inv 68.1%

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

       3. div-inv 68.2%

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

       4. metadata-eval 68.2%

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

   13. Applied egg-rr 68.2%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.007:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 5200000000000:\\ \;\;\;\;0.3333333333333333 \cdot \frac{t}{z \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 48.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13 \lor \neg \left(y \leq 2.2 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -13.0) (not (<= y 2.2e+34))) (* (/ y z) -0.3333333333333333) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -13.0) || !(y <= 2.2e+34)) {
		tmp = (y / z) * -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((y <= (-13.0d0)) .or. (.not. (y <= 2.2d+34))) then
        tmp = (y / z) * (-0.3333333333333333d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -13.0) || !(y <= 2.2e+34)) {
		tmp = (y / z) * -0.3333333333333333;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -13.0) or not (y <= 2.2e+34):
		tmp = (y / z) * -0.3333333333333333
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -13.0) || !(y <= 2.2e+34))
		tmp = Float64(Float64(y / z) * -0.3333333333333333);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((y <= -13.0) || ~((y <= 2.2e+34)))
		tmp = (y / z) * -0.3333333333333333;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -13.0], N[Not[LessEqual[y, 2.2e+34]], $MachinePrecision]], N[(N[(y / z), $MachinePrecision] * -0.3333333333333333), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -13 or 2.2000000000000002e34 < y

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-+r- 99.0%

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

      3. sub-neg 99.0%

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

      4. associate-*l* 99.0%

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

      5. *-commutative 99.0%

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

      6. distribute-frac-neg2 99.0%

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

      7. distribute-rgt-neg-in 99.0%

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

      8. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

      1. clear-num 99.0%

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

      2. inv-pow 99.0%

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

   6. Applied egg-rr 99.0%

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

      1. unpow-1 99.0%

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

      2. associate-/l* 99.0%

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

   8. Simplified 99.0%

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

   9. Taylor expanded in y around inf 74.7%

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

   if -13 < y < 2.2000000000000002e34

   1. Initial program 93.4%

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

      1. sub-neg 93.4%

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

      2. associate-+l+ 93.4%

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

      3. +-commutative 93.4%

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

      4. remove-double-neg 93.4%

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

      5. distribute-frac-neg 93.4%

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

      6. distribute-neg-in 93.4%

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

      7. remove-double-neg 93.4%

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

      8. sub-neg 93.4%

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

      9. neg-mul-1 93.4%

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

      10. times-frac 93.3%

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

      11. distribute-frac-neg 93.3%

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

      12. neg-mul-1 93.3%

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

      13. *-commutative 93.3%

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

      14. associate-/l* 93.3%

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

      15. *-commutative 93.3%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in x around inf 30.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13 \lor \neg \left(y \leq 2.2 \cdot 10^{+34}\right):\\ \;\;\;\;\frac{y}{z} \cdot -0.3333333333333333\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 48.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -15 \lor \neg \left(y \leq 1.9 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= y -15.0) (not (<= y 1.9e+34))) (* y (/ -0.3333333333333333 z)) x))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((y <= -15.0) || !(y <= 1.9e+34)) {
		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 ((y <= (-15.0d0)) .or. (.not. (y <= 1.9d+34))) 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 ((y <= -15.0) || !(y <= 1.9e+34)) {
		tmp = y * (-0.3333333333333333 / z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (y <= -15.0) or not (y <= 1.9e+34):
		tmp = y * (-0.3333333333333333 / z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((y <= -15.0) || !(y <= 1.9e+34))
		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 ((y <= -15.0) || ~((y <= 1.9e+34)))
		tmp = y * (-0.3333333333333333 / z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[y, -15.0], N[Not[LessEqual[y, 1.9e+34]], $MachinePrecision]], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -15 or 1.9000000000000001e34 < y

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. associate-+r- 99.0%

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

      3. sub-neg 99.0%

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

      4. associate-*l* 99.0%

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

      5. *-commutative 99.0%

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

      6. distribute-frac-neg2 99.0%

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

      7. distribute-rgt-neg-in 99.0%

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

      8. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

      1. clear-num 99.0%

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

      2. inv-pow 99.0%

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

   6. Applied egg-rr 99.0%

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

      1. unpow-1 99.0%

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

      2. associate-/l* 99.0%

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

   8. Simplified 99.0%

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

   9. Taylor expanded in y around inf 74.7%

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

       1. associate-*r/ 75.3%

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

       2. metadata-eval 75.3%

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

       3. associate-*r* 75.3%

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

       4. neg-mul-1 75.3%

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

       5. associate-*l/ 75.3%

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

       6. *-commutative 75.3%

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

       7. distribute-lft-neg-out 75.3%

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

       8. distribute-rgt-neg-in 75.3%

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

       9. distribute-neg-frac 75.3%

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

       10. metadata-eval 75.3%

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

   11. Simplified 75.3%

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

   if -15 < y < 1.9000000000000001e34

   1. Initial program 93.4%

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

      1. sub-neg 93.4%

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

      2. associate-+l+ 93.4%

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

      3. +-commutative 93.4%

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

      4. remove-double-neg 93.4%

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

      5. distribute-frac-neg 93.4%

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

      6. distribute-neg-in 93.4%

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

      7. remove-double-neg 93.4%

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

      8. sub-neg 93.4%

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

      9. neg-mul-1 93.4%

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

      10. times-frac 93.3%

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

      11. distribute-frac-neg 93.3%

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

      12. neg-mul-1 93.3%

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

      13. *-commutative 93.3%

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

      14. associate-/l* 93.3%

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

      15. *-commutative 93.3%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in x around inf 30.4%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15 \lor \neg \left(y \leq 1.9 \cdot 10^{+34}\right):\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 48.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -15.5:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -15.5)
   (* y (/ -0.3333333333333333 z))
   (if (<= y 5.8e+34) x (/ -0.3333333333333333 (/ z y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -15.5) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 5.8e+34) {
		tmp = x;
	} else {
		tmp = -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 (y <= (-15.5d0)) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else if (y <= 5.8d+34) then
        tmp = x
    else
        tmp = (-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 (y <= -15.5) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 5.8e+34) {
		tmp = x;
	} else {
		tmp = -0.3333333333333333 / (z / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -15.5:
		tmp = y * (-0.3333333333333333 / z)
	elif y <= 5.8e+34:
		tmp = x
	else:
		tmp = -0.3333333333333333 / (z / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -15.5)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	elseif (y <= 5.8e+34)
		tmp = x;
	else
		tmp = Float64(-0.3333333333333333 / Float64(z / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -15.5)
		tmp = y * (-0.3333333333333333 / z);
	elseif (y <= 5.8e+34)
		tmp = x;
	else
		tmp = -0.3333333333333333 / (z / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -15.5], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.8e+34], x, N[(-0.3333333333333333 / N[(z / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -15.5

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. associate-+r- 98.3%

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

      3. sub-neg 98.3%

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

      4. associate-*l* 98.3%

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

      5. *-commutative 98.3%

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

      6. distribute-frac-neg2 98.3%

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

      7. distribute-rgt-neg-in 98.3%

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

      8. metadata-eval 98.3%

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

   3. Simplified 98.3%

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

      1. clear-num 98.3%

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

      2. inv-pow 98.3%

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

   6. Applied egg-rr 98.3%

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

      1. unpow-1 98.3%

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

      2. associate-/l* 98.3%

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

   8. Simplified 98.3%

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

   9. Taylor expanded in y around inf 77.5%

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

       1. associate-*r/ 77.5%

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

       2. metadata-eval 77.5%

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

       3. associate-*r* 77.5%

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

       4. neg-mul-1 77.5%

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

       5. associate-*l/ 77.6%

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

       6. *-commutative 77.6%

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

       7. distribute-lft-neg-out 77.6%

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

       8. distribute-rgt-neg-in 77.6%

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

       9. distribute-neg-frac 77.6%

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

       10. metadata-eval 77.6%

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

   11. Simplified 77.6%

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

   if -15.5 < y < 5.8000000000000003e34

   1. Initial program 93.4%

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

      1. sub-neg 93.4%

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

      2. associate-+l+ 93.4%

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

      3. +-commutative 93.4%

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

      4. remove-double-neg 93.4%

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

      5. distribute-frac-neg 93.4%

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

      6. distribute-neg-in 93.4%

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

      7. remove-double-neg 93.4%

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

      8. sub-neg 93.4%

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

      9. neg-mul-1 93.4%

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

      10. times-frac 93.3%

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

      11. distribute-frac-neg 93.3%

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

      12. neg-mul-1 93.3%

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

      13. *-commutative 93.3%

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

      14. associate-/l* 93.3%

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

      15. *-commutative 93.3%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in x around inf 30.4%

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

   if 5.8000000000000003e34 < y

   1. Initial program 99.8%

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

      1. +-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. Step-by-step derivation

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. unpow-1 99.8%

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

      2. associate-/l* 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in y around inf 71.3%

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

       1. clear-num 71.3%

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

       2. un-div-inv 72.7%

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

   11. Applied egg-rr 72.7%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15.5:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.3333333333333333}{\frac{z}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 48.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -23.5:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= y -23.5)
   (* y (/ -0.3333333333333333 z))
   (if (<= y 3.5e+34) x (/ y (* z -3.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -23.5) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 3.5e+34) {
		tmp = x;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (y <= (-23.5d0)) then
        tmp = y * ((-0.3333333333333333d0) / z)
    else if (y <= 3.5d+34) then
        tmp = x
    else
        tmp = y / (z * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (y <= -23.5) {
		tmp = y * (-0.3333333333333333 / z);
	} else if (y <= 3.5e+34) {
		tmp = x;
	} else {
		tmp = y / (z * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if y <= -23.5:
		tmp = y * (-0.3333333333333333 / z)
	elif y <= 3.5e+34:
		tmp = x
	else:
		tmp = y / (z * -3.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (y <= -23.5)
		tmp = Float64(y * Float64(-0.3333333333333333 / z));
	elseif (y <= 3.5e+34)
		tmp = x;
	else
		tmp = Float64(y / Float64(z * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (y <= -23.5)
		tmp = y * (-0.3333333333333333 / z);
	elseif (y <= 3.5e+34)
		tmp = x;
	else
		tmp = y / (z * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[y, -23.5], N[(y * N[(-0.3333333333333333 / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+34], x, N[(y / N[(z * -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -23.5

   1. Initial program 98.3%

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

      1. +-commutative 98.3%

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

      2. associate-+r- 98.3%

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

      3. sub-neg 98.3%

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

      4. associate-*l* 98.3%

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

      5. *-commutative 98.3%

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

      6. distribute-frac-neg2 98.3%

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

      7. distribute-rgt-neg-in 98.3%

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

      8. metadata-eval 98.3%

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

   3. Simplified 98.3%

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

      1. clear-num 98.3%

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

      2. inv-pow 98.3%

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

   6. Applied egg-rr 98.3%

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

      1. unpow-1 98.3%

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

      2. associate-/l* 98.3%

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

   8. Simplified 98.3%

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

   9. Taylor expanded in y around inf 77.5%

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

       1. associate-*r/ 77.5%

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

       2. metadata-eval 77.5%

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

       3. associate-*r* 77.5%

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

       4. neg-mul-1 77.5%

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

       5. associate-*l/ 77.6%

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

       6. *-commutative 77.6%

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

       7. distribute-lft-neg-out 77.6%

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

       8. distribute-rgt-neg-in 77.6%

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

       9. distribute-neg-frac 77.6%

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

       10. metadata-eval 77.6%

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

   11. Simplified 77.6%

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

   if -23.5 < y < 3.49999999999999998e34

   1. Initial program 93.4%

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

      1. sub-neg 93.4%

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

      2. associate-+l+ 93.4%

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

      3. +-commutative 93.4%

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

      4. remove-double-neg 93.4%

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

      5. distribute-frac-neg 93.4%

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

      6. distribute-neg-in 93.4%

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

      7. remove-double-neg 93.4%

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

      8. sub-neg 93.4%

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

      9. neg-mul-1 93.4%

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

      10. times-frac 93.3%

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

      11. distribute-frac-neg 93.3%

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

      12. neg-mul-1 93.3%

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

      13. *-commutative 93.3%

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

      14. associate-/l* 93.3%

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

      15. *-commutative 93.3%

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

   3. Simplified 93.2%

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

   5. Taylor expanded in x around inf 30.4%

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

   if 3.49999999999999998e34 < y

   1. Initial program 99.8%

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

      1. +-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. Step-by-step derivation

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

   6. Applied egg-rr 99.8%

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

      1. unpow-1 99.8%

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

      2. associate-/l* 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in y around inf 71.3%

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

       1. associate-*r/ 72.7%

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

       2. metadata-eval 72.7%

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

       3. associate-*r* 72.7%

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

       4. neg-mul-1 72.7%

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

       5. associate-*l/ 72.6%

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

       6. *-commutative 72.6%

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

       7. distribute-lft-neg-out 72.6%

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

       8. distribute-rgt-neg-in 72.6%

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

       9. distribute-neg-frac 72.6%

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

       10. metadata-eval 72.6%

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

   11. Simplified 72.6%

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

       1. clear-num 72.6%

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

       2. un-div-inv 72.7%

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

       3. div-inv 72.8%

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

       4. metadata-eval 72.8%

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

   13. Applied egg-rr 72.8%

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

4. Final simplification 52.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -23.5:\\ \;\;\;\;y \cdot \frac{-0.3333333333333333}{z}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+34}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot -3}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 95.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(0.3333333333333333 \cdot \frac{1}{z}\right) \cdot \left(\frac{t}{y} - y\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ x (* (* 0.3333333333333333 (/ 1.0 z)) (- (/ t y) y))))

C

double code(double x, double y, double z, double t) {
	return x + ((0.3333333333333333 * (1.0 / z)) * ((t / y) - y));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x + ((0.3333333333333333d0 * (1.0d0 / z)) * ((t / y) - y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return x + ((0.3333333333333333 * (1.0 / z)) * ((t / y) - y));
}

Python

def code(x, y, z, t):
	return x + ((0.3333333333333333 * (1.0 / z)) * ((t / y) - y))

Julia

function code(x, y, z, t)
	return Float64(x + Float64(Float64(0.3333333333333333 * Float64(1.0 / z)) * Float64(Float64(t / y) - y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x + ((0.3333333333333333 * (1.0 / z)) * ((t / y) - y));
end

Wolfram

code[x_, y_, z_, t_] := N[(x + N[(N[(0.3333333333333333 * N[(1.0 / z), $MachinePrecision]), $MachinePrecision] * N[(N[(t / y), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 96.2%

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

   1. sub-neg 96.2%

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

   2. associate-+l+ 96.2%

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

   3. +-commutative 96.2%

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

   4. remove-double-neg 96.2%

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

   5. distribute-frac-neg 96.2%

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

   6. distribute-neg-in 96.2%

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

   7. remove-double-neg 96.2%

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

   8. sub-neg 96.2%

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

   9. neg-mul-1 96.2%

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

   10. times-frac 96.1%

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

   11. distribute-frac-neg 96.1%

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

   12. neg-mul-1 96.1%

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

   13. *-commutative 96.1%

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

   14. associate-/l* 96.0%

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

   15. *-commutative 96.0%

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

3. Simplified 96.4%

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

   1. div-inv 96.4%

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

6. Applied egg-rr 96.4%

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

7. Final simplification 96.4%

   \[\leadsto x + \left(0.3333333333333333 \cdot \frac{1}{z}\right) \cdot \left(\frac{t}{y} - y\right) \]
8. Add Preprocessing

Alternative 18: 95.8% accurate, 1.4× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 96.2%

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

   1. sub-neg 96.2%

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

   2. associate-+l+ 96.2%

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

   3. +-commutative 96.2%

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

   4. remove-double-neg 96.2%

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

   5. distribute-frac-neg 96.2%

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

   6. distribute-neg-in 96.2%

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

   7. remove-double-neg 96.2%

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

   8. sub-neg 96.2%

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

   9. neg-mul-1 96.2%

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

   10. times-frac 96.1%

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

   11. distribute-frac-neg 96.1%

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

   12. neg-mul-1 96.1%

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

   13. *-commutative 96.1%

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

   14. associate-/l* 96.0%

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

   15. *-commutative 96.0%

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

3. Simplified 96.4%

   \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
4. Add Preprocessing

5. Taylor expanded in z around 0 96.1%

   \[\leadsto x + \color{blue}{0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z}} \]

6. Final simplification 96.1%

   \[\leadsto x + 0.3333333333333333 \cdot \frac{\frac{t}{y} - y}{z} \]
7. Add Preprocessing

Alternative 19: 95.9% 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 96.2%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Step-by-step derivation

   1. sub-neg 96.2%

      \[\leadsto \color{blue}{\left(x + \left(-\frac{y}{z \cdot 3}\right)\right)} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. associate-+l+ 96.2%

      \[\leadsto \color{blue}{x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

   3. +-commutative 96.2%

      \[\leadsto x + \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(-\frac{y}{z \cdot 3}\right)\right)} \]

   4. remove-double-neg 96.2%

      \[\leadsto x + \left(\color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   5. distribute-frac-neg 96.2%

      \[\leadsto x + \left(\left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   6. distribute-neg-in 96.2%

      \[\leadsto x + \color{blue}{\left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \frac{y}{z \cdot 3}\right)\right)} \]

   7. remove-double-neg 96.2%

      \[\leadsto x + \left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(-\left(-\frac{y}{z \cdot 3}\right)\right)}\right)\right) \]

   8. sub-neg 96.2%

      \[\leadsto x + \left(-\color{blue}{\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)}\right) \]

   9. neg-mul-1 96.2%

      \[\leadsto x + \left(-\left(\frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   10. times-frac 96.1%

       \[\leadsto x + \left(-\left(\color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   11. distribute-frac-neg 96.1%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-y}{z \cdot 3}}\right)\right) \]

   12. neg-mul-1 96.1%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{-1 \cdot y}}{z \cdot 3}\right)\right) \]

   13. *-commutative 96.1%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{y \cdot -1}}{z \cdot 3}\right)\right) \]

   14. associate-/l* 96.0%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{y \cdot \frac{-1}{z \cdot 3}}\right)\right) \]

   15. *-commutative 96.0%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-1}{z \cdot 3} \cdot y}\right)\right) \]

3. Simplified 96.4%

   \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
4. Add Preprocessing

5. Final simplification 96.4%

   \[\leadsto x + \left(\frac{t}{y} - y\right) \cdot \frac{0.3333333333333333}{z} \]
6. Add Preprocessing

Alternative 20: 30.6% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 x)

C

double code(double x, double y, double z, double t) {
	return x;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = x
end function

Java

public static double code(double x, double y, double z, double t) {
	return x;
}

Python

def code(x, y, z, t):
	return x

Julia

function code(x, y, z, t)
	return x
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_] := x

Derivation

1. Initial program 96.2%

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y} \]
2. Step-by-step derivation

   1. sub-neg 96.2%

      \[\leadsto \color{blue}{\left(x + \left(-\frac{y}{z \cdot 3}\right)\right)} + \frac{t}{\left(z \cdot 3\right) \cdot y} \]

   2. associate-+l+ 96.2%

      \[\leadsto \color{blue}{x + \left(\left(-\frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\right)} \]

   3. +-commutative 96.2%

      \[\leadsto x + \color{blue}{\left(\frac{t}{\left(z \cdot 3\right) \cdot y} + \left(-\frac{y}{z \cdot 3}\right)\right)} \]

   4. remove-double-neg 96.2%

      \[\leadsto x + \left(\color{blue}{\left(-\left(-\frac{t}{\left(z \cdot 3\right) \cdot y}\right)\right)} + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   5. distribute-frac-neg 96.2%

      \[\leadsto x + \left(\left(-\color{blue}{\frac{-t}{\left(z \cdot 3\right) \cdot y}}\right) + \left(-\frac{y}{z \cdot 3}\right)\right) \]

   6. distribute-neg-in 96.2%

      \[\leadsto x + \color{blue}{\left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \frac{y}{z \cdot 3}\right)\right)} \]

   7. remove-double-neg 96.2%

      \[\leadsto x + \left(-\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} + \color{blue}{\left(-\left(-\frac{y}{z \cdot 3}\right)\right)}\right)\right) \]

   8. sub-neg 96.2%

      \[\leadsto x + \left(-\color{blue}{\left(\frac{-t}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)}\right) \]

   9. neg-mul-1 96.2%

      \[\leadsto x + \left(-\left(\frac{\color{blue}{-1 \cdot t}}{\left(z \cdot 3\right) \cdot y} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   10. times-frac 96.1%

       \[\leadsto x + \left(-\left(\color{blue}{\frac{-1}{z \cdot 3} \cdot \frac{t}{y}} - \left(-\frac{y}{z \cdot 3}\right)\right)\right) \]

   11. distribute-frac-neg 96.1%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-y}{z \cdot 3}}\right)\right) \]

   12. neg-mul-1 96.1%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{-1 \cdot y}}{z \cdot 3}\right)\right) \]

   13. *-commutative 96.1%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \frac{\color{blue}{y \cdot -1}}{z \cdot 3}\right)\right) \]

   14. associate-/l* 96.0%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{y \cdot \frac{-1}{z \cdot 3}}\right)\right) \]

   15. *-commutative 96.0%

       \[\leadsto x + \left(-\left(\frac{-1}{z \cdot 3} \cdot \frac{t}{y} - \color{blue}{\frac{-1}{z \cdot 3} \cdot y}\right)\right) \]

3. Simplified 96.4%

   \[\leadsto \color{blue}{x + \frac{0.3333333333333333}{z} \cdot \left(\frac{t}{y} - y\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 27.1%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 27.1%

   \[\leadsto x \]
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 2024040 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))