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

Percentage Accurate: 85.5% → 99.2%

Time: 11.2s

Alternatives: 12

Speedup: 1.1×

• 23.8% 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: 85.5% 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

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.1%

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

3. Taylor expanded in t around inf 99.5%

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

   1. sub-neg 99.5%

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

   2. metadata-eval 99.5%

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

   3. associate-*r/ 99.5%

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

   4. +-commutative 99.5%

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

   5. metadata-eval 99.5%

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

   6. associate-+l+ 99.5%

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

   7. associate-*r/ 99.5%

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

   8. metadata-eval 99.5%

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

   9. associate-*r/ 99.5%

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

   10. metadata-eval 99.5%

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

5. Simplified 99.5%

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

Alternative 2: 98.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.72 \lor \neg \left(t \leq 1\right):\\ \;\;\;\;-2 + \left(\frac{x}{y} + \frac{\frac{2}{t}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -0.72) (not (<= t 1.0)))
   (+ -2.0 (+ (/ x y) (/ (/ 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 <= -0.72) || !(t <= 1.0)) {
		tmp = -2.0 + ((x / y) + ((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 <= (-0.72d0)) .or. (.not. (t <= 1.0d0))) then
        tmp = (-2.0d0) + ((x / y) + ((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 <= -0.72) || !(t <= 1.0)) {
		tmp = -2.0 + ((x / y) + ((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 <= -0.72) or not (t <= 1.0):
		tmp = -2.0 + ((x / y) + ((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 <= -0.72) || !(t <= 1.0))
		tmp = Float64(-2.0 + Float64(Float64(x / y) + Float64(Float64(2.0 / 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 <= -0.72) || ~((t <= 1.0)))
		tmp = -2.0 + ((x / y) + ((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, -0.72], N[Not[LessEqual[t, 1.0]], $MachinePrecision]], N[(-2.0 + N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $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 < -0.71999999999999997 or 1 < t

   1. Initial program 70.1%

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

   3. Taylor expanded in t around 0 83.2%

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

      1. associate-+r+ 83.2%

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

      2. associate-*r/ 83.2%

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

      3. metadata-eval 83.2%

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

      4. sub-neg 83.2%

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

      5. metadata-eval 83.2%

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

   5. Simplified 83.2%

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

   6. Taylor expanded in z around 0 82.3%

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

   7. Taylor expanded in z around inf 99.1%

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

      1. sub-neg 99.1%

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

      2. associate-*r/ 99.1%

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

      3. metadata-eval 99.1%

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

      4. metadata-eval 99.1%

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

      5. +-commutative 99.1%

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

      6. associate-/r* 99.1%

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

      7. +-commutative 99.1%

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

   9. Simplified 99.1%

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

   if -0.71999999999999997 < t < 1

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 98.8%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.72 \lor \neg \left(t \leq 1\right):\\ \;\;\;\;-2 + \left(\frac{x}{y} + \frac{\frac{2}{t}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.16 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 \cdot \left(1 - t\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(\frac{x}{y} + \frac{\frac{2}{t}}{z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.0) (not (<= z 1.16e-5)))
   (+ (/ x y) (/ (* 2.0 (- 1.0 t)) t))
   (+ -2.0 (+ (/ x y) (/ (/ 2.0 t) z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.0) || !(z <= 1.16e-5)) {
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t);
	} else {
		tmp = -2.0 + ((x / y) + ((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 <= (-1.0d0)) .or. (.not. (z <= 1.16d-5))) then
        tmp = (x / y) + ((2.0d0 * (1.0d0 - t)) / t)
    else
        tmp = (-2.0d0) + ((x / y) + ((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 <= -1.0) || !(z <= 1.16e-5)) {
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t);
	} else {
		tmp = -2.0 + ((x / y) + ((2.0 / t) / z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.0) or not (z <= 1.16e-5):
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t)
	else:
		tmp = -2.0 + ((x / y) + ((2.0 / t) / z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.0) || !(z <= 1.16e-5))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 * Float64(1.0 - t)) / t));
	else
		tmp = Float64(-2.0 + Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.0) || ~((z <= 1.16e-5)))
		tmp = (x / y) + ((2.0 * (1.0 - t)) / t);
	else
		tmp = -2.0 + ((x / y) + ((2.0 / t) / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.0], N[Not[LessEqual[z, 1.16e-5]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 * N[(1.0 - t), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 1.1600000000000001e-5 < z

   1. Initial program 72.3%

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

   3. Taylor expanded in z around inf 99.4%

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

      1. associate-*r/ 99.4%

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

   5. Simplified 99.4%

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

   if -1 < z < 1.1600000000000001e-5

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 89.8%

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

      1. associate-+r+ 89.8%

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

      2. associate-*r/ 89.8%

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

      3. metadata-eval 89.8%

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

      4. sub-neg 89.8%

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

      5. metadata-eval 89.8%

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

   5. Simplified 89.8%

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

   6. Taylor expanded in z around 0 88.7%

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

   7. Taylor expanded in z around inf 98.0%

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

      1. sub-neg 98.0%

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

      2. associate-*r/ 98.0%

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

      3. metadata-eval 98.0%

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

      4. metadata-eval 98.0%

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

      5. +-commutative 98.0%

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

      6. associate-/r* 98.0%

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

      7. +-commutative 98.0%

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

   9. Simplified 98.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1.16 \cdot 10^{-5}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 \cdot \left(1 - t\right)}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(\frac{x}{y} + \frac{\frac{2}{t}}{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 89.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-139} \lor \neg \left(t \leq 9.5 \cdot 10^{-47}\right):\\ \;\;\;\;-2 + \left(\frac{x}{y} + \frac{\frac{2}{t}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.4e-139) (not (<= t 9.5e-47)))
   (+ -2.0 (+ (/ x y) (/ (/ 2.0 t) z)))
   (+ (/ 2.0 (* t z)) (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.4e-139) || !(t <= 9.5e-47)) {
		tmp = -2.0 + ((x / y) + ((2.0 / t) / z));
	} else {
		tmp = (2.0 / (t * z)) + (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 ((t <= (-2.4d-139)) .or. (.not. (t <= 9.5d-47))) then
        tmp = (-2.0d0) + ((x / y) + ((2.0d0 / t) / z))
    else
        tmp = (2.0d0 / (t * z)) + (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 ((t <= -2.4e-139) || !(t <= 9.5e-47)) {
		tmp = -2.0 + ((x / y) + ((2.0 / t) / z));
	} else {
		tmp = (2.0 / (t * z)) + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.4e-139) or not (t <= 9.5e-47):
		tmp = -2.0 + ((x / y) + ((2.0 / t) / z))
	else:
		tmp = (2.0 / (t * z)) + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.4e-139) || !(t <= 9.5e-47))
		tmp = Float64(-2.0 + Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z)));
	else
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.4e-139) || ~((t <= 9.5e-47)))
		tmp = -2.0 + ((x / y) + ((2.0 / t) / z));
	else
		tmp = (2.0 / (t * z)) + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.4e-139], N[Not[LessEqual[t, 9.5e-47]], $MachinePrecision]], N[(-2.0 + N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.40000000000000015e-139 or 9.4999999999999991e-47 < t

   1. Initial program 76.8%

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

   3. Taylor expanded in t around 0 86.9%

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

      1. associate-+r+ 86.9%

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

      2. associate-*r/ 86.9%

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

      3. metadata-eval 86.9%

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

      4. sub-neg 86.9%

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

      5. metadata-eval 86.9%

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

   5. Simplified 86.9%

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

   6. Taylor expanded in z around 0 82.0%

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

   7. Taylor expanded in z around inf 95.0%

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

      1. sub-neg 95.0%

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

      2. associate-*r/ 95.0%

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

      3. metadata-eval 95.0%

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

      4. metadata-eval 95.0%

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

      5. +-commutative 95.0%

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

      6. associate-/r* 95.0%

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

      7. +-commutative 95.0%

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

   9. Simplified 95.0%

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

   if -2.40000000000000015e-139 < t < 9.4999999999999991e-47

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 98.9%

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

   4. Taylor expanded in x around 0 90.7%

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

      1. associate-*r/ 90.7%

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

      2. metadata-eval 90.7%

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

      3. associate-*r/ 90.7%

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

      4. metadata-eval 90.7%

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

   6. Simplified 90.7%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.4 \cdot 10^{-139} \lor \neg \left(t \leq 9.5 \cdot 10^{-47}\right):\\ \;\;\;\;-2 + \left(\frac{x}{y} + \frac{\frac{2}{t}}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 63.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+45} \lor \neg \left(\frac{x}{y} \leq 10^{+83}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+45) (not (<= (/ x y) 1e+83)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+45) || !((x / y) <= 1e+83)) {
		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) <= (-5d+45)) .or. (.not. ((x / y) <= 1d+83))) 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) <= -5e+45) || !((x / y) <= 1e+83)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+45) or not ((x / y) <= 1e+83):
		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) <= -5e+45) || !(Float64(x / y) <= 1e+83))
		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) <= -5e+45) || ~(((x / y) <= 1e+83)))
		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], -5e+45], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1e+83]], $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) < -5e45 or 1.00000000000000003e83 < (/.f64 x y)

   1. Initial program 86.4%

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

   3. Taylor expanded in x around inf 72.5%

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

   if -5e45 < (/.f64 x y) < 1.00000000000000003e83

   1. Initial program 84.0%

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

   3. Taylor expanded in z around inf 69.2%

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

      1. associate-*r/ 69.2%

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

   5. Simplified 69.2%

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

   6. Taylor expanded in y around 0 44.0%

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

      1. associate-/l* 57.5%

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

   8. Simplified 57.5%

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

   9. Taylor expanded in x around 0 64.0%

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

       1. div-sub 64.0%

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

       2. *-inverses 64.0%

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

       3. sub-neg 64.0%

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

       4. metadata-eval 64.0%

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

       5. distribute-lft-in 64.0%

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

       6. associate-*r/ 64.0%

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

       7. metadata-eval 64.0%

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

       8. metadata-eval 64.0%

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

   11. Simplified 64.0%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+45} \lor \neg \left(\frac{x}{y} \leq 10^{+83}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{x + y \cdot -2}{y}\\ \mathbf{elif}\;t \leq 650000:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -2.8e-22)
   (/ (+ x (* y -2.0)) y)
   (if (<= t 650000.0) (+ (/ 2.0 (* t z)) (/ 2.0 t)) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.8e-22) {
		tmp = (x + (y * -2.0)) / y;
	} else if (t <= 650000.0) {
		tmp = (2.0 / (t * z)) + (2.0 / t);
	} else {
		tmp = (x / y) - 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 (t <= (-2.8d-22)) then
        tmp = (x + (y * (-2.0d0))) / y
    else if (t <= 650000.0d0) then
        tmp = (2.0d0 / (t * z)) + (2.0d0 / t)
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -2.8e-22) {
		tmp = (x + (y * -2.0)) / y;
	} else if (t <= 650000.0) {
		tmp = (2.0 / (t * z)) + (2.0 / t);
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -2.8e-22:
		tmp = (x + (y * -2.0)) / y
	elif t <= 650000.0:
		tmp = (2.0 / (t * z)) + (2.0 / t)
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -2.8e-22)
		tmp = Float64(Float64(x + Float64(y * -2.0)) / y);
	elseif (t <= 650000.0)
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(2.0 / t));
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -2.8e-22)
		tmp = (x + (y * -2.0)) / y;
	elseif (t <= 650000.0)
		tmp = (2.0 / (t * z)) + (2.0 / t);
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -2.8e-22], N[(N[(x + N[(y * -2.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 650000.0], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.79999999999999995e-22

   1. Initial program 71.1%

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

   3. Taylor expanded in z around inf 88.2%

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

      1. associate-*r/ 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in y around 0 77.5%

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

      1. associate-/l* 88.2%

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

   8. Simplified 88.2%

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

   9. Taylor expanded in t around inf 86.7%

      \[\leadsto \color{blue}{\frac{x + -2 \cdot y}{y}} \]
   10. Step-by-step derivation

       1. *-commutative 86.7%

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

   11. Simplified 86.7%

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

   if -2.79999999999999995e-22 < t < 6.5e5

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 98.8%

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

   4. Taylor expanded in x around 0 84.6%

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

      1. associate-*r/ 84.6%

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

      2. metadata-eval 84.6%

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

      3. associate-*r/ 84.6%

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

      4. metadata-eval 84.6%

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

   6. Simplified 84.6%

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

   if 6.5e5 < t

   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 94.9%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.8 \cdot 10^{-22}:\\ \;\;\;\;\frac{x + y \cdot -2}{y}\\ \mathbf{elif}\;t \leq 650000:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-21} \lor \neg \left(t \leq 4600000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.1e-21) (not (<= t 4600000.0)))
   (- (/ 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 <= -3.1e-21) || !(t <= 4600000.0)) {
		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 <= (-3.1d-21)) .or. (.not. (t <= 4600000.0d0))) 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 <= -3.1e-21) || !(t <= 4600000.0)) {
		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 <= -3.1e-21) or not (t <= 4600000.0):
		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 <= -3.1e-21) || !(t <= 4600000.0))
		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 <= -3.1e-21) || ~((t <= 4600000.0)))
		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, -3.1e-21], N[Not[LessEqual[t, 4600000.0]], $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 < -3.0999999999999998e-21 or 4.6e6 < t

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf 90.2%

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

   if -3.0999999999999998e-21 < t < 4.6e6

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 84.6%

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

      1. associate-*r/ 84.6%

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

      2. metadata-eval 84.6%

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

   5. Simplified 84.6%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{-21} \lor \neg \left(t \leq 4600000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 70.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \lor \neg \left(t \leq 650000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.0) (not (<= t 650000.0)))
   (- (/ x y) 2.0)
   (+ (/ x y) (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.0) || !(t <= 650000.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (x / y) + (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 ((t <= (-1.0d0)) .or. (.not. (t <= 650000.0d0))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (x / y) + (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 ((t <= -1.0) || !(t <= 650000.0)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (x / y) + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.0) or not (t <= 650000.0):
		tmp = (x / y) - 2.0
	else:
		tmp = (x / y) + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.0) || !(t <= 650000.0))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.0) || ~((t <= 650000.0)))
		tmp = (x / y) - 2.0;
	else
		tmp = (x / y) + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.0], N[Not[LessEqual[t, 650000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 6.5e5 < t

   1. Initial program 69.9%

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

   3. Taylor expanded in t around inf 91.6%

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

   if -1 < t < 6.5e5

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 98.8%

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

   4. Taylor expanded in z around inf 59.4%

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

      1. associate-*r/ 59.4%

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

      2. metadata-eval 59.4%

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

      3. +-commutative 59.4%

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

   6. Simplified 59.4%

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

4. Final simplification 74.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \lor \neg \left(t \leq 650000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.2 \cdot 10^{-21}:\\ \;\;\;\;\frac{x + y \cdot -2}{y}\\ \mathbf{elif}\;t \leq 650000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -4.2e-21)
   (/ (+ x (* y -2.0)) y)
   (if (<= t 650000.0) (/ (+ 2.0 (/ 2.0 z)) t) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-21) {
		tmp = (x + (y * -2.0)) / y;
	} else if (t <= 650000.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = (x / y) - 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 (t <= (-4.2d-21)) then
        tmp = (x + (y * (-2.0d0))) / y
    else if (t <= 650000.0d0) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else
        tmp = (x / y) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -4.2e-21) {
		tmp = (x + (y * -2.0)) / y;
	} else if (t <= 650000.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -4.2e-21:
		tmp = (x + (y * -2.0)) / y
	elif t <= 650000.0:
		tmp = (2.0 + (2.0 / z)) / t
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -4.2e-21)
		tmp = Float64(Float64(x + Float64(y * -2.0)) / y);
	elseif (t <= 650000.0)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -4.2e-21)
		tmp = (x + (y * -2.0)) / y;
	elseif (t <= 650000.0)
		tmp = (2.0 + (2.0 / z)) / t;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -4.2e-21], N[(N[(x + N[(y * -2.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[t, 650000.0], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.20000000000000025e-21

   1. Initial program 71.1%

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

   3. Taylor expanded in z around inf 88.2%

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

      1. associate-*r/ 88.2%

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

   5. Simplified 88.2%

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

   6. Taylor expanded in y around 0 77.5%

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

      1. associate-/l* 88.2%

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

   8. Simplified 88.2%

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

   9. Taylor expanded in t around inf 86.7%

      \[\leadsto \color{blue}{\frac{x + -2 \cdot y}{y}} \]
   10. Step-by-step derivation

       1. *-commutative 86.7%

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

   11. Simplified 86.7%

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

   if -4.20000000000000025e-21 < t < 6.5e5

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0 84.6%

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

      1. associate-*r/ 84.6%

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

      2. metadata-eval 84.6%

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

   5. Simplified 84.6%

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

   if 6.5e5 < t

   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 94.9%

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

Alternative 10: 60.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-138} \lor \neg \left(t \leq 2.9 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.5e-138) (not (<= t 2.9e-46)))
   (- (/ x y) 2.0)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.5e-138) || !(t <= 2.9e-46)) {
		tmp = (x / y) - 2.0;
	} 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 ((t <= (-3.5d-138)) .or. (.not. (t <= 2.9d-46))) then
        tmp = (x / y) - 2.0d0
    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 ((t <= -3.5e-138) || !(t <= 2.9e-46)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.5e-138) or not (t <= 2.9e-46):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.5e-138) || !(t <= 2.9e-46))
		tmp = Float64(Float64(x / y) - 2.0);
	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 ((t <= -3.5e-138) || ~((t <= 2.9e-46)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.5e-138], N[Not[LessEqual[t, 2.9e-46]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.4999999999999999e-138 or 2.90000000000000005e-46 < t

   1. Initial program 76.8%

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

   3. Taylor expanded in t around inf 79.5%

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

   if -3.4999999999999999e-138 < t < 2.90000000000000005e-46

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 60.4%

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

      1. associate-*r/ 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in y around 0 42.6%

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

      1. associate-/l* 42.7%

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

   8. Simplified 42.7%

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

   9. Taylor expanded in x around 0 50.1%

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

       1. div-sub 50.1%

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

       2. *-inverses 50.1%

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

       3. sub-neg 50.1%

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

       4. metadata-eval 50.1%

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

       5. distribute-lft-in 50.1%

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

       6. associate-*r/ 50.1%

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

       7. metadata-eval 50.1%

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

       8. metadata-eval 50.1%

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

   11. Simplified 50.1%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.5 \cdot 10^{-138} \lor \neg \left(t \leq 2.9 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 41.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-138} \lor \neg \left(t \leq 1.2 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1e-138) (not (<= t 1.2e-46))) (/ x y) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1e-138) || !(t <= 1.2e-46)) {
		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 ((t <= (-1d-138)) .or. (.not. (t <= 1.2d-46))) 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 ((t <= -1e-138) || !(t <= 1.2e-46)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1e-138) or not (t <= 1.2e-46):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1e-138) || !(t <= 1.2e-46))
		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 ((t <= -1e-138) || ~((t <= 1.2e-46)))
		tmp = x / y;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1e-138], N[Not[LessEqual[t, 1.2e-46]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.00000000000000007e-138 or 1.20000000000000007e-46 < t

   1. Initial program 76.8%

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

   3. Taylor expanded in x around inf 49.1%

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

   if -1.00000000000000007e-138 < t < 1.20000000000000007e-46

   1. Initial program 98.9%

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

   3. Taylor expanded in z around inf 60.4%

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

      1. associate-*r/ 60.4%

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

   5. Simplified 60.4%

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

   6. Taylor expanded in t around 0 50.1%

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

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \cdot 10^{-138} \lor \neg \left(t \leq 1.2 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 18.7% 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 85.1%

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

3. Taylor expanded in z around inf 75.4%

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

   1. associate-*r/ 75.4%

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

5. Simplified 75.4%

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

6. Taylor expanded in t around 0 22.9%

   \[\leadsto \color{blue}{\frac{2}{t}} \]
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 2024172 
(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))))