Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2

Percentage Accurate: 86.8% → 99.2%

Time: 11.0s

Alternatives: 12

Speedup: 1.1×

• 22.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 86.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))

C

double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = (x / y) + ((2.0d0 + ((z * 2.0d0) * (1.0d0 - t))) / (t * z))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
}

Python

def code(x, y, z, t):
	return (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z))

Julia

function code(x, y, z, t)
	return Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (x / y) + ((2.0 + ((z * 2.0) * (1.0 - t))) / (t * z));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left(\frac{2}{t} + \frac{\frac{2}{t}}{z}\right) + \left(\frac{x}{y} + -2\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (+ (/ 2.0 t) (/ (/ 2.0 t) z)) (+ (/ x y) -2.0)))

C

double code(double x, double y, double z, double t) {
	return ((2.0 / t) + ((2.0 / t) / z)) + ((x / y) + -2.0);
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    code = ((2.0d0 / t) + ((2.0d0 / t) / z)) + ((x / y) + (-2.0d0))
end function

Java

public static double code(double x, double y, double z, double t) {
	return ((2.0 / t) + ((2.0 / t) / z)) + ((x / y) + -2.0);
}

Python

def code(x, y, z, t):
	return ((2.0 / t) + ((2.0 / t) / z)) + ((x / y) + -2.0)

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(2.0 / t) + Float64(Float64(2.0 / t) / z)) + Float64(Float64(x / y) + -2.0))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = ((2.0 / t) + ((2.0 / t) / z)) + ((x / y) + -2.0);
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(2.0 / t), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] + N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 83.8%

   \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
2. Add Preprocessing

3. Taylor expanded in t around inf 99.1%

   \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2\right)} \]
4. Step-by-step derivation

   1. sub-neg 99.1%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \left(-2\right)\right)} \]

   2. metadata-eval 99.1%

      \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2 \cdot 1}}{t \cdot z}\right) + \left(-2\right)\right) \]

   3. associate-*r/ 99.1%

      \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot \frac{1}{t \cdot z}}\right) + \left(-2\right)\right) \]

   4. +-commutative 99.1%

      \[\leadsto \frac{x}{y} + \left(\color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right)} + \left(-2\right)\right) \]

   5. metadata-eval 99.1%

      \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + \color{blue}{-2}\right) \]

   6. associate-+l+ 99.1%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right)} \]

   7. associate-*r/ 99.1%

      \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

   8. metadata-eval 99.1%

      \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{2}}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

   9. associate-*r/ 99.1%

      \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\color{blue}{\frac{2 \cdot 1}{t}} + -2\right)\right) \]

   10. metadata-eval 99.1%

       \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\frac{\color{blue}{2}}{t} + -2\right)\right) \]

5. Simplified 99.1%

   \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\right)} \]

6. Taylor expanded in x around 0 99.1%

   \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \left(2 \cdot \frac{1}{t \cdot z} + \frac{x}{y}\right)\right) - 2} \]
7. Step-by-step derivation

   1. sub-neg 99.1%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \left(2 \cdot \frac{1}{t \cdot z} + \frac{x}{y}\right)\right) + \left(-2\right)} \]

   2. associate-+r+ 99.1%

      \[\leadsto \color{blue}{\left(\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) + \frac{x}{y}\right)} + \left(-2\right) \]

   3. metadata-eval 99.1%

      \[\leadsto \left(\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) + \frac{x}{y}\right) + \color{blue}{-2} \]

   4. associate-+r+ 99.1%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) + \left(\frac{x}{y} + -2\right)} \]

   5. associate-*r/ 99.1%

      \[\leadsto \left(\color{blue}{\frac{2 \cdot 1}{t}} + 2 \cdot \frac{1}{t \cdot z}\right) + \left(\frac{x}{y} + -2\right) \]

   6. metadata-eval 99.1%

      \[\leadsto \left(\frac{\color{blue}{2}}{t} + 2 \cdot \frac{1}{t \cdot z}\right) + \left(\frac{x}{y} + -2\right) \]

   7. associate-*r/ 99.1%

      \[\leadsto \left(\frac{2}{t} + \color{blue}{\frac{2 \cdot 1}{t \cdot z}}\right) + \left(\frac{x}{y} + -2\right) \]

   8. metadata-eval 99.1%

      \[\leadsto \left(\frac{2}{t} + \frac{\color{blue}{2}}{t \cdot z}\right) + \left(\frac{x}{y} + -2\right) \]

   9. +-commutative 99.1%

      \[\leadsto \color{blue}{\left(\frac{2}{t \cdot z} + \frac{2}{t}\right)} + \left(\frac{x}{y} + -2\right) \]

   10. associate-/r* 99.1%

       \[\leadsto \left(\color{blue}{\frac{\frac{2}{t}}{z}} + \frac{2}{t}\right) + \left(\frac{x}{y} + -2\right) \]

8. Simplified 99.1%

   \[\leadsto \color{blue}{\left(\frac{\frac{2}{t}}{z} + \frac{2}{t}\right) + \left(\frac{x}{y} + -2\right)} \]

9. Final simplification 99.1%

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

Alternative 2: 98.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -600000 \lor \neg \left(t \leq 10^{-20}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -600000.0) (not (<= t 1e-20)))
   (+ (/ x y) (+ -2.0 (/ 2.0 (* t z))))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -600000.0) || !(t <= 1e-20)) {
		tmp = (x / y) + (-2.0 + (2.0 / (t * z)));
	} else {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (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 ((t <= (-600000.0d0)) .or. (.not. (t <= 1d-20))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / (t * z)))
    else
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (t * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -600000.0) || !(t <= 1e-20)) {
		tmp = (x / y) + (-2.0 + (2.0 / (t * z)));
	} else {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -600000.0) or not (t <= 1e-20):
		tmp = (x / y) + (-2.0 + (2.0 / (t * z)))
	else:
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -600000.0) || !(t <= 1e-20))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / Float64(t * z))));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -600000.0) || ~((t <= 1e-20)))
		tmp = (x / y) + (-2.0 + (2.0 / (t * z)));
	else
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -600000.0], N[Not[LessEqual[t, 1e-20]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6e5 or 9.99999999999999945e-21 < t

   1. Initial program 67.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 89.0%

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. associate-+r+ 89.0%

         \[\leadsto \frac{\color{blue}{\left(2 + 2 \cdot \frac{1}{z}\right) + t \cdot \left(\frac{x}{y} - 2\right)}}{t} \]

      2. associate-*r/ 89.0%

         \[\leadsto \frac{\left(2 + \color{blue}{\frac{2 \cdot 1}{z}}\right) + t \cdot \left(\frac{x}{y} - 2\right)}{t} \]

      3. metadata-eval 89.0%

         \[\leadsto \frac{\left(2 + \frac{\color{blue}{2}}{z}\right) + t \cdot \left(\frac{x}{y} - 2\right)}{t} \]

      4. sub-neg 89.0%

         \[\leadsto \frac{\left(2 + \frac{2}{z}\right) + t \cdot \color{blue}{\left(\frac{x}{y} + \left(-2\right)\right)}}{t} \]

      5. metadata-eval 89.0%

         \[\leadsto \frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + \color{blue}{-2}\right)}{t} \]

   5. Simplified 89.0%

      \[\leadsto \color{blue}{\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}} \]

   6. Taylor expanded in z around 0 88.6%

      \[\leadsto \frac{\color{blue}{\frac{2}{z}} + t \cdot \left(\frac{x}{y} + -2\right)}{t} \]

   7. Taylor expanded in z around inf 99.5%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \frac{x}{y}\right) - 2} \]
   8. Step-by-step derivation

      1. associate-*r/ 99.5%

         \[\leadsto \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \frac{x}{y}\right) - 2 \]

      2. metadata-eval 99.5%

         \[\leadsto \left(\frac{\color{blue}{2}}{t \cdot z} + \frac{x}{y}\right) - 2 \]

      3. +-commutative 99.5%

         \[\leadsto \color{blue}{\left(\frac{x}{y} + \frac{2}{t \cdot z}\right)} - 2 \]

      4. associate--l+ 99.5%

         \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{t \cdot z} - 2\right)} \]

      5. sub-neg 99.5%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + \left(-2\right)\right)} \]

      6. metadata-eval 99.5%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \color{blue}{-2}\right) \]

      7. *-commutative 99.5%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{\color{blue}{z \cdot t}} + -2\right) \]

   9. Simplified 99.5%

      \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{z \cdot t} + -2\right)} \]

   if -6e5 < t < 9.99999999999999945e-21

   1. Initial program 98.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 98.3%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -600000 \lor \neg \left(t \leq 10^{-20}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t \cdot z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -76000000 \lor \neg \left(z \leq 1.12 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -76000000.0) (not (<= z 1.12e-8)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ x y) (+ -2.0 (/ 2.0 (* t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -76000000.0) || !(z <= 1.12e-8)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (-2.0 + (2.0 / (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 ((z <= (-76000000.0d0)) .or. (.not. (z <= 1.12d-8))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / (t * z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -76000000.0) || !(z <= 1.12e-8)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (-2.0 + (2.0 / (t * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -76000000.0) or not (z <= 1.12e-8):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (x / y) + (-2.0 + (2.0 / (t * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -76000000.0) || !(z <= 1.12e-8))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / Float64(t * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -76000000.0) || ~((z <= 1.12e-8)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = (x / y) + (-2.0 + (2.0 / (t * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -76000000.0], N[Not[LessEqual[z, 1.12e-8]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -7.6e7 or 1.11999999999999994e-8 < z

   1. Initial program 71.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2\right)} \]
   4. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \left(-2\right)\right)} \]

      2. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2 \cdot 1}}{t \cdot z}\right) + \left(-2\right)\right) \]

      3. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot \frac{1}{t \cdot z}}\right) + \left(-2\right)\right) \]

      4. +-commutative 100.0%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right)} + \left(-2\right)\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + \color{blue}{-2}\right) \]

      6. associate-+l+ 100.0%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right)} \]

      7. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      8. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{2}}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      9. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\color{blue}{\frac{2 \cdot 1}{t}} + -2\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\frac{\color{blue}{2}}{t} + -2\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\right)} \]

   6. Taylor expanded in z around inf 99.6%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) - 2} \]
   7. Step-by-step derivation

      1. sub-neg 99.6%

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) + \left(-2\right)} \]

      2. associate-*r/ 99.6%

         \[\leadsto \left(\color{blue}{\frac{2 \cdot 1}{t}} + \frac{x}{y}\right) + \left(-2\right) \]

      3. metadata-eval 99.6%

         \[\leadsto \left(\frac{\color{blue}{2}}{t} + \frac{x}{y}\right) + \left(-2\right) \]

      4. +-commutative 99.6%

         \[\leadsto \color{blue}{\left(\frac{x}{y} + \frac{2}{t}\right)} + \left(-2\right) \]

      5. metadata-eval 99.6%

         \[\leadsto \left(\frac{x}{y} + \frac{2}{t}\right) + \color{blue}{-2} \]

      6. associate-+l+ 99.6%

         \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{t} + -2\right)} \]

      7. +-commutative 99.6%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(-2 + \frac{2}{t}\right)} \]

   8. Simplified 99.6%

      \[\leadsto \color{blue}{\frac{x}{y} + \left(-2 + \frac{2}{t}\right)} \]

   if -7.6e7 < z < 1.11999999999999994e-8

   1. Initial program 98.1%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 95.0%

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. associate-+r+ 95.0%

         \[\leadsto \frac{\color{blue}{\left(2 + 2 \cdot \frac{1}{z}\right) + t \cdot \left(\frac{x}{y} - 2\right)}}{t} \]

      2. associate-*r/ 95.0%

         \[\leadsto \frac{\left(2 + \color{blue}{\frac{2 \cdot 1}{z}}\right) + t \cdot \left(\frac{x}{y} - 2\right)}{t} \]

      3. metadata-eval 95.0%

         \[\leadsto \frac{\left(2 + \frac{\color{blue}{2}}{z}\right) + t \cdot \left(\frac{x}{y} - 2\right)}{t} \]

      4. sub-neg 95.0%

         \[\leadsto \frac{\left(2 + \frac{2}{z}\right) + t \cdot \color{blue}{\left(\frac{x}{y} + \left(-2\right)\right)}}{t} \]

      5. metadata-eval 95.0%

         \[\leadsto \frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + \color{blue}{-2}\right)}{t} \]

   5. Simplified 95.0%

      \[\leadsto \color{blue}{\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}} \]

   6. Taylor expanded in z around 0 94.2%

      \[\leadsto \frac{\color{blue}{\frac{2}{z}} + t \cdot \left(\frac{x}{y} + -2\right)}{t} \]

   7. Taylor expanded in z around inf 97.3%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \frac{x}{y}\right) - 2} \]
   8. Step-by-step derivation

      1. associate-*r/ 97.3%

         \[\leadsto \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \frac{x}{y}\right) - 2 \]

      2. metadata-eval 97.3%

         \[\leadsto \left(\frac{\color{blue}{2}}{t \cdot z} + \frac{x}{y}\right) - 2 \]

      3. +-commutative 97.3%

         \[\leadsto \color{blue}{\left(\frac{x}{y} + \frac{2}{t \cdot z}\right)} - 2 \]

      4. associate--l+ 97.3%

         \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{t \cdot z} - 2\right)} \]

      5. sub-neg 97.3%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + \left(-2\right)\right)} \]

      6. metadata-eval 97.3%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \color{blue}{-2}\right) \]

      7. *-commutative 97.3%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{\color{blue}{z \cdot t}} + -2\right) \]

   9. Simplified 97.3%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -76000000 \lor \neg \left(z \leq 1.12 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t \cdot z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t} + -2\\ \mathbf{if}\;z \leq -76000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-56}:\\ \;\;\;\;-2 + \frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 105000000000:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ 2.0 t) -2.0)))
   (if (<= z -76000000.0)
     t_1
     (if (<= z 4.5e-56)
       (+ -2.0 (/ 2.0 (* t z)))
       (if (<= z 105000000000.0) (- (/ x y) 2.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) + -2.0;
	double tmp;
	if (z <= -76000000.0) {
		tmp = t_1;
	} else if (z <= 4.5e-56) {
		tmp = -2.0 + (2.0 / (t * z));
	} else if (z <= 105000000000.0) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 / t) + (-2.0d0)
    if (z <= (-76000000.0d0)) then
        tmp = t_1
    else if (z <= 4.5d-56) then
        tmp = (-2.0d0) + (2.0d0 / (t * z))
    else if (z <= 105000000000.0d0) then
        tmp = (x / y) - 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) + -2.0;
	double tmp;
	if (z <= -76000000.0) {
		tmp = t_1;
	} else if (z <= 4.5e-56) {
		tmp = -2.0 + (2.0 / (t * z));
	} else if (z <= 105000000000.0) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / t) + -2.0
	tmp = 0
	if z <= -76000000.0:
		tmp = t_1
	elif z <= 4.5e-56:
		tmp = -2.0 + (2.0 / (t * z))
	elif z <= 105000000000.0:
		tmp = (x / y) - 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / t) + -2.0)
	tmp = 0.0
	if (z <= -76000000.0)
		tmp = t_1;
	elseif (z <= 4.5e-56)
		tmp = Float64(-2.0 + Float64(2.0 / Float64(t * z)));
	elseif (z <= 105000000000.0)
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / t) + -2.0;
	tmp = 0.0;
	if (z <= -76000000.0)
		tmp = t_1;
	elseif (z <= 4.5e-56)
		tmp = -2.0 + (2.0 / (t * z));
	elseif (z <= 105000000000.0)
		tmp = (x / y) - 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[z, -76000000.0], t$95$1, If[LessEqual[z, 4.5e-56], N[(-2.0 + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 105000000000.0], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.6e7 or 1.05e11 < z

   1. Initial program 69.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2\right)} \]
   4. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \left(-2\right)\right)} \]

      2. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2 \cdot 1}}{t \cdot z}\right) + \left(-2\right)\right) \]

      3. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot \frac{1}{t \cdot z}}\right) + \left(-2\right)\right) \]

      4. +-commutative 100.0%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right)} + \left(-2\right)\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + \color{blue}{-2}\right) \]

      6. associate-+l+ 100.0%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right)} \]

      7. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      8. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{2}}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      9. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\color{blue}{\frac{2 \cdot 1}{t}} + -2\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\frac{\color{blue}{2}}{t} + -2\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\right)} \]

   6. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) - 2} \]
   7. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) + \left(-2\right)} \]

      2. associate-*r/ 99.9%

         \[\leadsto \left(\color{blue}{\frac{2 \cdot 1}{t}} + \frac{x}{y}\right) + \left(-2\right) \]

      3. metadata-eval 99.9%

         \[\leadsto \left(\frac{\color{blue}{2}}{t} + \frac{x}{y}\right) + \left(-2\right) \]

      4. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(\frac{x}{y} + \frac{2}{t}\right)} + \left(-2\right) \]

      5. metadata-eval 99.9%

         \[\leadsto \left(\frac{x}{y} + \frac{2}{t}\right) + \color{blue}{-2} \]

      6. associate-+l+ 99.9%

         \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{t} + -2\right)} \]

      7. +-commutative 99.9%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(-2 + \frac{2}{t}\right)} \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x}{y} + \left(-2 + \frac{2}{t}\right)} \]

   9. Taylor expanded in x around 0 65.5%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   10. Step-by-step derivation

       1. sub-neg 65.5%

          \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(-2\right)} \]

       2. associate-*r/ 65.5%

          \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + \left(-2\right) \]

       3. metadata-eval 65.5%

          \[\leadsto \frac{\color{blue}{2}}{t} + \left(-2\right) \]

       4. metadata-eval 65.5%

          \[\leadsto \frac{2}{t} + \color{blue}{-2} \]

   11. Simplified 65.5%

       \[\leadsto \color{blue}{\frac{2}{t} + -2} \]

   if -7.6e7 < z < 4.5000000000000001e-56

   1. Initial program 98.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 95.6%

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. associate-+r+ 95.6%

         \[\leadsto \frac{\color{blue}{\left(2 + 2 \cdot \frac{1}{z}\right) + t \cdot \left(\frac{x}{y} - 2\right)}}{t} \]

      2. associate-*r/ 95.6%

         \[\leadsto \frac{\left(2 + \color{blue}{\frac{2 \cdot 1}{z}}\right) + t \cdot \left(\frac{x}{y} - 2\right)}{t} \]

      3. metadata-eval 95.6%

         \[\leadsto \frac{\left(2 + \frac{\color{blue}{2}}{z}\right) + t \cdot \left(\frac{x}{y} - 2\right)}{t} \]

      4. sub-neg 95.6%

         \[\leadsto \frac{\left(2 + \frac{2}{z}\right) + t \cdot \color{blue}{\left(\frac{x}{y} + \left(-2\right)\right)}}{t} \]

      5. metadata-eval 95.6%

         \[\leadsto \frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + \color{blue}{-2}\right)}{t} \]

   5. Simplified 95.6%

      \[\leadsto \color{blue}{\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}} \]

   6. Taylor expanded in z around 0 95.0%

      \[\leadsto \frac{\color{blue}{\frac{2}{z}} + t \cdot \left(\frac{x}{y} + -2\right)}{t} \]

   7. Taylor expanded in z around inf 97.4%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \frac{x}{y}\right) - 2} \]
   8. Step-by-step derivation

      1. associate-*r/ 97.4%

         \[\leadsto \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \frac{x}{y}\right) - 2 \]

      2. metadata-eval 97.4%

         \[\leadsto \left(\frac{\color{blue}{2}}{t \cdot z} + \frac{x}{y}\right) - 2 \]

      3. +-commutative 97.4%

         \[\leadsto \color{blue}{\left(\frac{x}{y} + \frac{2}{t \cdot z}\right)} - 2 \]

      4. associate--l+ 97.4%

         \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{t \cdot z} - 2\right)} \]

      5. sub-neg 97.4%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + \left(-2\right)\right)} \]

      6. metadata-eval 97.4%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \color{blue}{-2}\right) \]

      7. *-commutative 97.4%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{\color{blue}{z \cdot t}} + -2\right) \]

   9. Simplified 97.4%

      \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{z \cdot t} + -2\right)} \]

   10. Taylor expanded in x around 0 78.7%

       \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} - 2} \]
   11. Step-by-step derivation

       1. sub-neg 78.7%

          \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + \left(-2\right)} \]

       2. associate-*r/ 78.7%

          \[\leadsto \color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(-2\right) \]

       3. metadata-eval 78.7%

          \[\leadsto \frac{\color{blue}{2}}{t \cdot z} + \left(-2\right) \]

       4. associate-/r* 78.7%

          \[\leadsto \color{blue}{\frac{\frac{2}{t}}{z}} + \left(-2\right) \]

       5. metadata-eval 78.7%

          \[\leadsto \frac{\frac{2}{t}}{z} + \color{blue}{-2} \]

       6. +-commutative 78.7%

          \[\leadsto \color{blue}{-2 + \frac{\frac{2}{t}}{z}} \]

       7. associate-/r* 78.7%

          \[\leadsto -2 + \color{blue}{\frac{2}{t \cdot z}} \]

   12. Simplified 78.7%

       \[\leadsto \color{blue}{-2 + \frac{2}{t \cdot z}} \]

   if 4.5000000000000001e-56 < z < 1.05e11

   1. Initial program 99.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 80.4%

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

Alternative 5: 60.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t} + -2\\ \mathbf{if}\;z \leq -2.35 \cdot 10^{-27}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-56}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;z \leq 980000000000:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ 2.0 t) -2.0)))
   (if (<= z -2.35e-27)
     t_1
     (if (<= z 2.7e-56)
       (/ 2.0 (* t z))
       (if (<= z 980000000000.0) (- (/ x y) 2.0) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) + -2.0;
	double tmp;
	if (z <= -2.35e-27) {
		tmp = t_1;
	} else if (z <= 2.7e-56) {
		tmp = 2.0 / (t * z);
	} else if (z <= 980000000000.0) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (2.0d0 / t) + (-2.0d0)
    if (z <= (-2.35d-27)) then
        tmp = t_1
    else if (z <= 2.7d-56) then
        tmp = 2.0d0 / (t * z)
    else if (z <= 980000000000.0d0) then
        tmp = (x / y) - 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) + -2.0;
	double tmp;
	if (z <= -2.35e-27) {
		tmp = t_1;
	} else if (z <= 2.7e-56) {
		tmp = 2.0 / (t * z);
	} else if (z <= 980000000000.0) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / t) + -2.0
	tmp = 0
	if z <= -2.35e-27:
		tmp = t_1
	elif z <= 2.7e-56:
		tmp = 2.0 / (t * z)
	elif z <= 980000000000.0:
		tmp = (x / y) - 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / t) + -2.0)
	tmp = 0.0
	if (z <= -2.35e-27)
		tmp = t_1;
	elseif (z <= 2.7e-56)
		tmp = Float64(2.0 / Float64(t * z));
	elseif (z <= 980000000000.0)
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / t) + -2.0;
	tmp = 0.0;
	if (z <= -2.35e-27)
		tmp = t_1;
	elseif (z <= 2.7e-56)
		tmp = 2.0 / (t * z);
	elseif (z <= 980000000000.0)
		tmp = (x / y) - 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[z, -2.35e-27], t$95$1, If[LessEqual[z, 2.7e-56], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 980000000000.0], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.35000000000000016e-27 or 9.8e11 < z

   1. Initial program 71.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2\right)} \]
   4. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \left(-2\right)\right)} \]

      2. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2 \cdot 1}}{t \cdot z}\right) + \left(-2\right)\right) \]

      3. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot \frac{1}{t \cdot z}}\right) + \left(-2\right)\right) \]

      4. +-commutative 100.0%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right)} + \left(-2\right)\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + \color{blue}{-2}\right) \]

      6. associate-+l+ 100.0%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right)} \]

      7. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      8. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{2}}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      9. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\color{blue}{\frac{2 \cdot 1}{t}} + -2\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\frac{\color{blue}{2}}{t} + -2\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\right)} \]

   6. Taylor expanded in z around inf 99.2%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) - 2} \]
   7. Step-by-step derivation

      1. sub-neg 99.2%

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) + \left(-2\right)} \]

      2. associate-*r/ 99.2%

         \[\leadsto \left(\color{blue}{\frac{2 \cdot 1}{t}} + \frac{x}{y}\right) + \left(-2\right) \]

      3. metadata-eval 99.2%

         \[\leadsto \left(\frac{\color{blue}{2}}{t} + \frac{x}{y}\right) + \left(-2\right) \]

      4. +-commutative 99.2%

         \[\leadsto \color{blue}{\left(\frac{x}{y} + \frac{2}{t}\right)} + \left(-2\right) \]

      5. metadata-eval 99.2%

         \[\leadsto \left(\frac{x}{y} + \frac{2}{t}\right) + \color{blue}{-2} \]

      6. associate-+l+ 99.2%

         \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{t} + -2\right)} \]

      7. +-commutative 99.2%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(-2 + \frac{2}{t}\right)} \]

   8. Simplified 99.2%

      \[\leadsto \color{blue}{\frac{x}{y} + \left(-2 + \frac{2}{t}\right)} \]

   9. Taylor expanded in x around 0 63.9%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   10. Step-by-step derivation

       1. sub-neg 63.9%

          \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(-2\right)} \]

       2. associate-*r/ 63.9%

          \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + \left(-2\right) \]

       3. metadata-eval 63.9%

          \[\leadsto \frac{\color{blue}{2}}{t} + \left(-2\right) \]

       4. metadata-eval 63.9%

          \[\leadsto \frac{2}{t} + \color{blue}{-2} \]

   11. Simplified 63.9%

       \[\leadsto \color{blue}{\frac{2}{t} + -2} \]

   if -2.35000000000000016e-27 < z < 2.69999999999999995e-56

   1. Initial program 97.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in z around 0 70.2%

      \[\leadsto \color{blue}{\frac{2}{t \cdot z}} \]

   if 2.69999999999999995e-56 < z < 9.8e11

   1. Initial program 99.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 80.4%

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

Alternative 6: 91.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-26} \lor \neg \left(z \leq 3.1 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.6e-26) (not (<= z 3.1e-36)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ (/ 2.0 t) z) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.6e-26) || !(z <= 3.1e-36)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = ((2.0 / t) / z) + (x / 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 <= (-4.6d-26)) .or. (.not. (z <= 3.1d-36))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = ((2.0d0 / t) / z) + (x / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.6e-26) || !(z <= 3.1e-36)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = ((2.0 / t) / z) + (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.6e-26) or not (z <= 3.1e-36):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = ((2.0 / t) / z) + (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.6e-26) || !(z <= 3.1e-36))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(Float64(2.0 / t) / z) + Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.6e-26) || ~((z <= 3.1e-36)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = ((2.0 / t) / z) + (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.6e-26], N[Not[LessEqual[z, 3.1e-36]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.60000000000000018e-26 or 3.0999999999999999e-36 < z

   1. Initial program 73.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2\right)} \]
   4. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \left(-2\right)\right)} \]

      2. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2 \cdot 1}}{t \cdot z}\right) + \left(-2\right)\right) \]

      3. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot \frac{1}{t \cdot z}}\right) + \left(-2\right)\right) \]

      4. +-commutative 100.0%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right)} + \left(-2\right)\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + \color{blue}{-2}\right) \]

      6. associate-+l+ 100.0%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right)} \]

      7. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      8. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{2}}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      9. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\color{blue}{\frac{2 \cdot 1}{t}} + -2\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\frac{\color{blue}{2}}{t} + -2\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\right)} \]

   6. Taylor expanded in z around inf 98.4%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) - 2} \]
   7. Step-by-step derivation

      1. sub-neg 98.4%

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) + \left(-2\right)} \]

      2. associate-*r/ 98.4%

         \[\leadsto \left(\color{blue}{\frac{2 \cdot 1}{t}} + \frac{x}{y}\right) + \left(-2\right) \]

      3. metadata-eval 98.4%

         \[\leadsto \left(\frac{\color{blue}{2}}{t} + \frac{x}{y}\right) + \left(-2\right) \]

      4. +-commutative 98.4%

         \[\leadsto \color{blue}{\left(\frac{x}{y} + \frac{2}{t}\right)} + \left(-2\right) \]

      5. metadata-eval 98.4%

         \[\leadsto \left(\frac{x}{y} + \frac{2}{t}\right) + \color{blue}{-2} \]

      6. associate-+l+ 98.4%

         \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{t} + -2\right)} \]

      7. +-commutative 98.4%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(-2 + \frac{2}{t}\right)} \]

   8. Simplified 98.4%

      \[\leadsto \color{blue}{\frac{x}{y} + \left(-2 + \frac{2}{t}\right)} \]

   if -4.60000000000000018e-26 < z < 3.0999999999999999e-36

   1. Initial program 97.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 97.9%

         \[\leadsto \color{blue}{\frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} + \frac{x}{y}} \]

      2. clear-num 97.8%

         \[\leadsto \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} + \color{blue}{\frac{1}{\frac{y}{x}}} \]

      3. frac-add 69.8%

         \[\leadsto \color{blue}{\frac{\left(2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)\right) \cdot \frac{y}{x} + \left(t \cdot z\right) \cdot 1}{\left(t \cdot z\right) \cdot \frac{y}{x}}} \]

      4. +-commutative 69.8%

         \[\leadsto \frac{\color{blue}{\left(\left(z \cdot 2\right) \cdot \left(1 - t\right) + 2\right)} \cdot \frac{y}{x} + \left(t \cdot z\right) \cdot 1}{\left(t \cdot z\right) \cdot \frac{y}{x}} \]

      5. associate-*l* 69.8%

         \[\leadsto \frac{\left(\color{blue}{z \cdot \left(2 \cdot \left(1 - t\right)\right)} + 2\right) \cdot \frac{y}{x} + \left(t \cdot z\right) \cdot 1}{\left(t \cdot z\right) \cdot \frac{y}{x}} \]

      6. fma-define 69.8%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(z, 2 \cdot \left(1 - t\right), 2\right)} \cdot \frac{y}{x} + \left(t \cdot z\right) \cdot 1}{\left(t \cdot z\right) \cdot \frac{y}{x}} \]

      7. *-commutative 69.8%

         \[\leadsto \frac{\mathsf{fma}\left(z, 2 \cdot \left(1 - t\right), 2\right) \cdot \frac{y}{x} + \color{blue}{1 \cdot \left(t \cdot z\right)}}{\left(t \cdot z\right) \cdot \frac{y}{x}} \]

      8. *-un-lft-identity 69.8%

         \[\leadsto \frac{\mathsf{fma}\left(z, 2 \cdot \left(1 - t\right), 2\right) \cdot \frac{y}{x} + \color{blue}{t \cdot z}}{\left(t \cdot z\right) \cdot \frac{y}{x}} \]

      9. *-commutative 69.8%

         \[\leadsto \frac{\mathsf{fma}\left(z, 2 \cdot \left(1 - t\right), 2\right) \cdot \frac{y}{x} + \color{blue}{z \cdot t}}{\left(t \cdot z\right) \cdot \frac{y}{x}} \]

      10. *-commutative 69.8%

          \[\leadsto \frac{\mathsf{fma}\left(z, 2 \cdot \left(1 - t\right), 2\right) \cdot \frac{y}{x} + z \cdot t}{\color{blue}{\left(z \cdot t\right)} \cdot \frac{y}{x}} \]

   4. Applied egg-rr 69.8%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(z, 2 \cdot \left(1 - t\right), 2\right) \cdot \frac{y}{x} + z \cdot t}{\left(z \cdot t\right) \cdot \frac{y}{x}}} \]

   5. Taylor expanded in z around 0 62.0%

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

      1. +-commutative 62.0%

         \[\leadsto \frac{\color{blue}{z \cdot t + 2 \cdot \frac{y}{x}}}{\left(z \cdot t\right) \cdot \frac{y}{x}} \]

      2. *-un-lft-identity 62.0%

         \[\leadsto \frac{\color{blue}{1 \cdot \left(z \cdot t\right)} + 2 \cdot \frac{y}{x}}{\left(z \cdot t\right) \cdot \frac{y}{x}} \]

      3. *-commutative 62.0%

         \[\leadsto \frac{1 \cdot \left(z \cdot t\right) + \color{blue}{\frac{y}{x} \cdot 2}}{\left(z \cdot t\right) \cdot \frac{y}{x}} \]

      4. *-commutative 62.0%

         \[\leadsto \frac{1 \cdot \left(z \cdot t\right) + \frac{y}{x} \cdot 2}{\color{blue}{\frac{y}{x} \cdot \left(z \cdot t\right)}} \]

      5. frac-add 86.9%

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

      6. clear-num 86.9%

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

      7. +-commutative 86.9%

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

      8. *-commutative 86.9%

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

      9. associate-/r* 87.0%

         \[\leadsto \color{blue}{\frac{\frac{2}{t}}{z}} + \frac{x}{y} \]

   7. Applied egg-rr 87.0%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{-26} \lor \neg \left(z \leq 3.1 \cdot 10^{-36}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{t}}{z} + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-25} \lor \neg \left(z \leq 4.2 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.8e-25) (not (<= z 4.2e-56)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ -2.0 (/ 2.0 (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e-25) || !(z <= 4.2e-56)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = -2.0 + (2.0 / (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 ((z <= (-5.8d-25)) .or. (.not. (z <= 4.2d-56))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (-2.0d0) + (2.0d0 / (t * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e-25) || !(z <= 4.2e-56)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = -2.0 + (2.0 / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.8e-25) or not (z <= 4.2e-56):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = -2.0 + (2.0 / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.8e-25) || !(z <= 4.2e-56))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(-2.0 + Float64(2.0 / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5.8e-25) || ~((z <= 4.2e-56)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = -2.0 + (2.0 / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.8e-25], N[Not[LessEqual[z, 4.2e-56]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.8000000000000001e-25 or 4.20000000000000012e-56 < z

   1. Initial program 74.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2\right)} \]
   4. Step-by-step derivation

      1. sub-neg 100.0%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \left(-2\right)\right)} \]

      2. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2 \cdot 1}}{t \cdot z}\right) + \left(-2\right)\right) \]

      3. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot \frac{1}{t \cdot z}}\right) + \left(-2\right)\right) \]

      4. +-commutative 100.0%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right)} + \left(-2\right)\right) \]

      5. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + \color{blue}{-2}\right) \]

      6. associate-+l+ 100.0%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right)} \]

      7. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      8. metadata-eval 100.0%

         \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{2}}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      9. associate-*r/ 100.0%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\color{blue}{\frac{2 \cdot 1}{t}} + -2\right)\right) \]

      10. metadata-eval 100.0%

          \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\frac{\color{blue}{2}}{t} + -2\right)\right) \]

   5. Simplified 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\right)} \]

   6. Taylor expanded in z around inf 97.8%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) - 2} \]
   7. Step-by-step derivation

      1. sub-neg 97.8%

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) + \left(-2\right)} \]

      2. associate-*r/ 97.8%

         \[\leadsto \left(\color{blue}{\frac{2 \cdot 1}{t}} + \frac{x}{y}\right) + \left(-2\right) \]

      3. metadata-eval 97.8%

         \[\leadsto \left(\frac{\color{blue}{2}}{t} + \frac{x}{y}\right) + \left(-2\right) \]

      4. +-commutative 97.8%

         \[\leadsto \color{blue}{\left(\frac{x}{y} + \frac{2}{t}\right)} + \left(-2\right) \]

      5. metadata-eval 97.8%

         \[\leadsto \left(\frac{x}{y} + \frac{2}{t}\right) + \color{blue}{-2} \]

      6. associate-+l+ 97.8%

         \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{t} + -2\right)} \]

      7. +-commutative 97.8%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(-2 + \frac{2}{t}\right)} \]

   8. Simplified 97.8%

      \[\leadsto \color{blue}{\frac{x}{y} + \left(-2 + \frac{2}{t}\right)} \]

   if -5.8000000000000001e-25 < z < 4.20000000000000012e-56

   1. Initial program 97.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 95.3%

      \[\leadsto \color{blue}{\frac{2 + \left(2 \cdot \frac{1}{z} + t \cdot \left(\frac{x}{y} - 2\right)\right)}{t}} \]
   4. Step-by-step derivation

      1. associate-+r+ 95.3%

         \[\leadsto \frac{\color{blue}{\left(2 + 2 \cdot \frac{1}{z}\right) + t \cdot \left(\frac{x}{y} - 2\right)}}{t} \]

      2. associate-*r/ 95.3%

         \[\leadsto \frac{\left(2 + \color{blue}{\frac{2 \cdot 1}{z}}\right) + t \cdot \left(\frac{x}{y} - 2\right)}{t} \]

      3. metadata-eval 95.3%

         \[\leadsto \frac{\left(2 + \frac{\color{blue}{2}}{z}\right) + t \cdot \left(\frac{x}{y} - 2\right)}{t} \]

      4. sub-neg 95.3%

         \[\leadsto \frac{\left(2 + \frac{2}{z}\right) + t \cdot \color{blue}{\left(\frac{x}{y} + \left(-2\right)\right)}}{t} \]

      5. metadata-eval 95.3%

         \[\leadsto \frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + \color{blue}{-2}\right)}{t} \]

   5. Simplified 95.3%

      \[\leadsto \color{blue}{\frac{\left(2 + \frac{2}{z}\right) + t \cdot \left(\frac{x}{y} + -2\right)}{t}} \]

   6. Taylor expanded in z around 0 95.3%

      \[\leadsto \frac{\color{blue}{\frac{2}{z}} + t \cdot \left(\frac{x}{y} + -2\right)}{t} \]

   7. Taylor expanded in z around inf 97.9%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \frac{x}{y}\right) - 2} \]
   8. Step-by-step derivation

      1. associate-*r/ 97.9%

         \[\leadsto \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \frac{x}{y}\right) - 2 \]

      2. metadata-eval 97.9%

         \[\leadsto \left(\frac{\color{blue}{2}}{t \cdot z} + \frac{x}{y}\right) - 2 \]

      3. +-commutative 97.9%

         \[\leadsto \color{blue}{\left(\frac{x}{y} + \frac{2}{t \cdot z}\right)} - 2 \]

      4. associate--l+ 97.9%

         \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{t \cdot z} - 2\right)} \]

      5. sub-neg 97.9%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + \left(-2\right)\right)} \]

      6. metadata-eval 97.9%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \color{blue}{-2}\right) \]

      7. *-commutative 97.9%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{\color{blue}{z \cdot t}} + -2\right) \]

   9. Simplified 97.9%

      \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{z \cdot t} + -2\right)} \]

   10. Taylor expanded in x around 0 81.6%

       \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} - 2} \]
   11. Step-by-step derivation

       1. sub-neg 81.6%

          \[\leadsto \color{blue}{2 \cdot \frac{1}{t \cdot z} + \left(-2\right)} \]

       2. associate-*r/ 81.6%

          \[\leadsto \color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(-2\right) \]

       3. metadata-eval 81.6%

          \[\leadsto \frac{\color{blue}{2}}{t \cdot z} + \left(-2\right) \]

       4. associate-/r* 81.6%

          \[\leadsto \color{blue}{\frac{\frac{2}{t}}{z}} + \left(-2\right) \]

       5. metadata-eval 81.6%

          \[\leadsto \frac{\frac{2}{t}}{z} + \color{blue}{-2} \]

       6. +-commutative 81.6%

          \[\leadsto \color{blue}{-2 + \frac{\frac{2}{t}}{z}} \]

       7. associate-/r* 81.6%

          \[\leadsto -2 + \color{blue}{\frac{2}{t \cdot z}} \]

   12. Simplified 81.6%

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

4. Final simplification 91.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-25} \lor \neg \left(z \leq 4.2 \cdot 10^{-56}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+29} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+29) (not (<= (/ x y) 4e+38)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+29) || !((x / y) <= 4e+38)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	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 (((x / y) <= (-1d+29)) .or. (.not. ((x / y) <= 4d+38))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+29) || !((x / y) <= 4e+38)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+29) or not ((x / y) <= 4e+38):
		tmp = x / y
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+29) || !(Float64(x / y) <= 4e+38))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e+29) || ~(((x / y) <= 4e+38)))
		tmp = x / y;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+29], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+38]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999914e28 or 3.99999999999999991e38 < (/.f64 x y)

   1. Initial program 78.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 69.3%

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

   if -9.99999999999999914e28 < (/.f64 x y) < 3.99999999999999991e38

   1. Initial program 87.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2\right)} \]
   4. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \left(-2\right)\right)} \]

      2. metadata-eval 99.9%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2 \cdot 1}}{t \cdot z}\right) + \left(-2\right)\right) \]

      3. associate-*r/ 99.9%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot \frac{1}{t \cdot z}}\right) + \left(-2\right)\right) \]

      4. +-commutative 99.9%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right)} + \left(-2\right)\right) \]

      5. metadata-eval 99.9%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + \color{blue}{-2}\right) \]

      6. associate-+l+ 99.9%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right)} \]

      7. associate-*r/ 99.9%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      8. metadata-eval 99.9%

         \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{2}}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      9. associate-*r/ 99.9%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\color{blue}{\frac{2 \cdot 1}{t}} + -2\right)\right) \]

      10. metadata-eval 99.9%

          \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\frac{\color{blue}{2}}{t} + -2\right)\right) \]

   5. Simplified 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\right)} \]

   6. Taylor expanded in z around inf 62.3%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) - 2} \]
   7. Step-by-step derivation

      1. sub-neg 62.3%

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) + \left(-2\right)} \]

      2. associate-*r/ 62.3%

         \[\leadsto \left(\color{blue}{\frac{2 \cdot 1}{t}} + \frac{x}{y}\right) + \left(-2\right) \]

      3. metadata-eval 62.3%

         \[\leadsto \left(\frac{\color{blue}{2}}{t} + \frac{x}{y}\right) + \left(-2\right) \]

      4. +-commutative 62.3%

         \[\leadsto \color{blue}{\left(\frac{x}{y} + \frac{2}{t}\right)} + \left(-2\right) \]

      5. metadata-eval 62.3%

         \[\leadsto \left(\frac{x}{y} + \frac{2}{t}\right) + \color{blue}{-2} \]

      6. associate-+l+ 62.3%

         \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{t} + -2\right)} \]

      7. +-commutative 62.3%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(-2 + \frac{2}{t}\right)} \]

   8. Simplified 62.3%

      \[\leadsto \color{blue}{\frac{x}{y} + \left(-2 + \frac{2}{t}\right)} \]

   9. Taylor expanded in x around 0 60.1%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   10. Step-by-step derivation

       1. sub-neg 60.1%

          \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(-2\right)} \]

       2. associate-*r/ 60.1%

          \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + \left(-2\right) \]

       3. metadata-eval 60.1%

          \[\leadsto \frac{\color{blue}{2}}{t} + \left(-2\right) \]

       4. metadata-eval 60.1%

          \[\leadsto \frac{2}{t} + \color{blue}{-2} \]

   11. Simplified 60.1%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+29} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2000000:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;\frac{x}{y} \leq 4 \cdot 10^{+38}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2000000.0)
   (- (/ x y) 2.0)
   (if (<= (/ x y) 4e+38) (+ (/ 2.0 t) -2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2000000.0) {
		tmp = (x / y) - 2.0;
	} else if ((x / y) <= 4e+38) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = x / 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 ((x / y) <= (-2000000.0d0)) then
        tmp = (x / y) - 2.0d0
    else if ((x / y) <= 4d+38) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2000000.0) {
		tmp = (x / y) - 2.0;
	} else if ((x / y) <= 4e+38) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2000000.0:
		tmp = (x / y) - 2.0
	elif (x / y) <= 4e+38:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2000000.0)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (Float64(x / y) <= 4e+38)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -2000000.0)
		tmp = (x / y) - 2.0;
	elseif ((x / y) <= 4e+38)
		tmp = (2.0 / t) + -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2000000.0], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4e+38], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e6

   1. Initial program 79.4%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 66.9%

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   if -2e6 < (/.f64 x y) < 3.99999999999999991e38

   1. Initial program 88.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) - 2\right)} \]
   4. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t} + \frac{2}{t \cdot z}\right) + \left(-2\right)\right)} \]

      2. metadata-eval 99.9%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \frac{\color{blue}{2 \cdot 1}}{t \cdot z}\right) + \left(-2\right)\right) \]

      3. associate-*r/ 99.9%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t} + \color{blue}{2 \cdot \frac{1}{t \cdot z}}\right) + \left(-2\right)\right) \]

      4. +-commutative 99.9%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right)} + \left(-2\right)\right) \]

      5. metadata-eval 99.9%

         \[\leadsto \frac{x}{y} + \left(\left(2 \cdot \frac{1}{t \cdot z} + 2 \cdot \frac{1}{t}\right) + \color{blue}{-2}\right) \]

      6. associate-+l+ 99.9%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(2 \cdot \frac{1}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right)} \]

      7. associate-*r/ 99.9%

         \[\leadsto \frac{x}{y} + \left(\color{blue}{\frac{2 \cdot 1}{t \cdot z}} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      8. metadata-eval 99.9%

         \[\leadsto \frac{x}{y} + \left(\frac{\color{blue}{2}}{t \cdot z} + \left(2 \cdot \frac{1}{t} + -2\right)\right) \]

      9. associate-*r/ 99.9%

         \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\color{blue}{\frac{2 \cdot 1}{t}} + -2\right)\right) \]

      10. metadata-eval 99.9%

          \[\leadsto \frac{x}{y} + \left(\frac{2}{t \cdot z} + \left(\frac{\color{blue}{2}}{t} + -2\right)\right) \]

   5. Simplified 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\frac{2}{t \cdot z} + \left(\frac{2}{t} + -2\right)\right)} \]

   6. Taylor expanded in z around inf 61.9%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) - 2} \]
   7. Step-by-step derivation

      1. sub-neg 61.9%

         \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + \frac{x}{y}\right) + \left(-2\right)} \]

      2. associate-*r/ 61.9%

         \[\leadsto \left(\color{blue}{\frac{2 \cdot 1}{t}} + \frac{x}{y}\right) + \left(-2\right) \]

      3. metadata-eval 61.9%

         \[\leadsto \left(\frac{\color{blue}{2}}{t} + \frac{x}{y}\right) + \left(-2\right) \]

      4. +-commutative 61.9%

         \[\leadsto \color{blue}{\left(\frac{x}{y} + \frac{2}{t}\right)} + \left(-2\right) \]

      5. metadata-eval 61.9%

         \[\leadsto \left(\frac{x}{y} + \frac{2}{t}\right) + \color{blue}{-2} \]

      6. associate-+l+ 61.9%

         \[\leadsto \color{blue}{\frac{x}{y} + \left(\frac{2}{t} + -2\right)} \]

      7. +-commutative 61.9%

         \[\leadsto \frac{x}{y} + \color{blue}{\left(-2 + \frac{2}{t}\right)} \]

   8. Simplified 61.9%

      \[\leadsto \color{blue}{\frac{x}{y} + \left(-2 + \frac{2}{t}\right)} \]

   9. Taylor expanded in x around 0 60.9%

      \[\leadsto \color{blue}{2 \cdot \frac{1}{t} - 2} \]
   10. Step-by-step derivation

       1. sub-neg 60.9%

          \[\leadsto \color{blue}{2 \cdot \frac{1}{t} + \left(-2\right)} \]

       2. associate-*r/ 60.9%

          \[\leadsto \color{blue}{\frac{2 \cdot 1}{t}} + \left(-2\right) \]

       3. metadata-eval 60.9%

          \[\leadsto \frac{\color{blue}{2}}{t} + \left(-2\right) \]

       4. metadata-eval 60.9%

          \[\leadsto \frac{2}{t} + \color{blue}{-2} \]

   11. Simplified 60.9%

       \[\leadsto \color{blue}{\frac{2}{t} + -2} \]

   if 3.99999999999999991e38 < (/.f64 x y)

   1. Initial program 74.5%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 70.4%

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

Alternative 10: 80.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -18.5 \lor \neg \left(t \leq 380\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -18.5) (not (<= t 380.0)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -18.5) || !(t <= 380.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / 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 ((t <= (-18.5d0)) .or. (.not. (t <= 380.0d0))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -18.5) || !(t <= 380.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -18.5) or not (t <= 380.0):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -18.5) || !(t <= 380.0))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -18.5) || ~((t <= 380.0)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -18.5], N[Not[LessEqual[t, 380.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -18.5 or 380 < t

   1. Initial program 67.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around inf 81.9%

      \[\leadsto \color{blue}{\frac{x}{y} - 2} \]

   if -18.5 < t < 380

   1. Initial program 98.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 84.3%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 84.3%

         \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

      2. metadata-eval 84.3%

         \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

   5. Simplified 84.3%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -18.5 \lor \neg \left(t \leq 380\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 47.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+29} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+29) (not (<= (/ x y) 4e+38))) (/ x y) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+29) || !((x / y) <= 4e+38)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / 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 (((x / y) <= (-1d+29)) .or. (.not. ((x / y) <= 4d+38))) then
        tmp = x / y
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+29) || !((x / y) <= 4e+38)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+29) or not ((x / y) <= 4e+38):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+29) || !(Float64(x / y) <= 4e+38))
		tmp = Float64(x / y);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e+29) || ~(((x / y) <= 4e+38)))
		tmp = x / y;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+29], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4e+38]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999914e28 or 3.99999999999999991e38 < (/.f64 x y)

   1. Initial program 78.0%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 69.3%

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

   if -9.99999999999999914e28 < (/.f64 x y) < 3.99999999999999991e38

   1. Initial program 87.9%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   2. Add Preprocessing

   3. Taylor expanded in t around 0 67.3%

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   4. Step-by-step derivation

      1. associate-*r/ 67.3%

         \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

      2. metadata-eval 67.3%

         \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

   5. Simplified 67.3%

      \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]

   6. Taylor expanded in z around inf 30.9%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+29} \lor \neg \left(\frac{x}{y} \leq 4 \cdot 10^{+38}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 19.8% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \frac{2}{t} \end{array} \]

FPCore

(FPCore (x y z t) :precision binary64 (/ 2.0 t))

C

double code(double x, double y, double z, double t) {
	return 2.0 / t;
}

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 = 2.0d0 / t
end function

Java

public static double code(double x, double y, double z, double t) {
	return 2.0 / t;
}

Python

def code(x, y, z, t):
	return 2.0 / t

Julia

function code(x, y, z, t)
	return Float64(2.0 / t)
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = 2.0 / t;
end

Wolfram

code[x_, y_, z_, t_] := N[(2.0 / t), $MachinePrecision]

Derivation

1. Initial program 83.8%

   \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
2. Add Preprocessing

3. Taylor expanded in t around 0 52.8%

   \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
4. Step-by-step derivation

   1. associate-*r/ 52.8%

      \[\leadsto \frac{2 + \color{blue}{\frac{2 \cdot 1}{z}}}{t} \]

   2. metadata-eval 52.8%

      \[\leadsto \frac{2 + \frac{\color{blue}{2}}{z}}{t} \]

5. Simplified 52.8%

   \[\leadsto \color{blue}{\frac{2 + \frac{2}{z}}{t}} \]

6. Taylor expanded in z around inf 24.3%

   \[\leadsto \color{blue}{\frac{2}{t}} \]
7. Add Preprocessing

Developer Target 1: 99.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{2}{z} + 2}{t} - \left(2 - \frac{x}{y}\right) \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / 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 = (((2.0d0 / z) + 2.0d0) / t) - (2.0d0 - (x / y))
end function

Java

public static double code(double x, double y, double z, double t) {
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
}

Python

def code(x, y, z, t):
	return (((2.0 / z) + 2.0) / t) - (2.0 - (x / y))

Julia

function code(x, y, z, t)
	return Float64(Float64(Float64(Float64(2.0 / z) + 2.0) / t) - Float64(2.0 - Float64(x / y)))
end

MATLAB

function tmp = code(x, y, z, t)
	tmp = (((2.0 / z) + 2.0) / t) - (2.0 - (x / y));
end

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(N[(2.0 / z), $MachinePrecision] + 2.0), $MachinePrecision] / t), $MachinePrecision] - N[(2.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024170 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))