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

Percentage Accurate: 86.1% → 99.0%

Time: 8.8s

Alternatives: 12

Speedup: 1.3×

• 23.0% 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: 86.1% 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: 99.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.8%

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

2. Taylor expanded in t around 0 98.4%

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

   1. sub-neg 98.4%

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

   2. associate-+r+ 98.4%

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

   3. metadata-eval 98.4%

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

   4. associate-*r/ 98.4%

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

   5. +-commutative 98.4%

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

   6. associate-*r/ 98.4%

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

   7. metadata-eval 98.4%

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

   8. associate-*r/ 98.4%

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

   9. metadata-eval 98.4%

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

   10. metadata-eval 98.4%

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

4. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 2: 71.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.7 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -46000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq -0.0155 \lor \neg \left(\frac{x}{y} \leq 4.8 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.7e+69)
   (/ x y)
   (if (<= (/ x y) -46000000.0)
     (/ (+ 2.0 (/ 2.0 z)) t)
     (if (or (<= (/ x y) -0.0155) (not (<= (/ x y) 4.8e+51)))
       (- (/ x y) 2.0)
       (+ (/ 2.0 (* t z)) -2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.7e+69) {
		tmp = x / y;
	} else if ((x / y) <= -46000000.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if (((x / y) <= -0.0155) || !((x / y) <= 4.8e+51)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / (t * z)) + -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) <= (-1.7d+69)) then
        tmp = x / y
    else if ((x / y) <= (-46000000.0d0)) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    else if (((x / y) <= (-0.0155d0)) .or. (.not. ((x / y) <= 4.8d+51))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 / (t * z)) + (-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) <= -1.7e+69) {
		tmp = x / y;
	} else if ((x / y) <= -46000000.0) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else if (((x / y) <= -0.0155) || !((x / y) <= 4.8e+51)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / (t * z)) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.7e+69:
		tmp = x / y
	elif (x / y) <= -46000000.0:
		tmp = (2.0 + (2.0 / z)) / t
	elif ((x / y) <= -0.0155) or not ((x / y) <= 4.8e+51):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 / (t * z)) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.7e+69)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -46000000.0)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	elseif ((Float64(x / y) <= -0.0155) || !(Float64(x / y) <= 4.8e+51))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 / Float64(t * z)) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.7e+69)
		tmp = x / y;
	elseif ((x / y) <= -46000000.0)
		tmp = (2.0 + (2.0 / z)) / t;
	elseif (((x / y) <= -0.0155) || ~(((x / y) <= 4.8e+51)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 / (t * z)) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.7e+69], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -46000000.0], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], If[Or[LessEqual[N[(x / y), $MachinePrecision], -0.0155], N[Not[LessEqual[N[(x / y), $MachinePrecision], 4.8e+51]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -1.69999999999999993e69

   1. Initial program 78.0%

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

   2. Taylor expanded in x around inf 82.0%

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

   if -1.69999999999999993e69 < (/.f64 x y) < -4.6e7

   1. Initial program 91.5%

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

   2. Taylor expanded in t around 0 76.8%

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

      1. associate-*r/ 76.8%

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

      2. metadata-eval 76.8%

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

   4. Simplified 76.8%

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

   if -4.6e7 < (/.f64 x y) < -0.0155 or 4.7999999999999997e51 < (/.f64 x y)

   1. Initial program 90.9%

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

   2. Taylor expanded in t around inf 85.5%

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

   if -0.0155 < (/.f64 x y) < 4.7999999999999997e51

   1. Initial program 89.7%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. associate-+r+ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-*r/ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 77.8%

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

      1. *-commutative 77.8%

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

   7. Simplified 77.8%

      \[\leadsto \color{blue}{\frac{2}{z \cdot t}} + -2 \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.7 \cdot 10^{+69}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -46000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq -0.0155 \lor \neg \left(\frac{x}{y} \leq 4.8 \cdot 10^{+51}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + -2\\ \end{array} \]

Alternative 3: 92.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.2 \cdot 10^{+24} \lor \neg \left(\frac{x}{y} \leq 1.42 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5.2e+24) (not (<= (/ x y) 1.42e+35)))
   (+ (/ 2.0 (* t z)) (/ x y))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5.2e+24) || !((x / y) <= 1.42e+35)) {
		tmp = (2.0 / (t * z)) + (x / y);
	} else {
		tmp = -2.0 + ((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 (((x / y) <= (-5.2d+24)) .or. (.not. ((x / y) <= 1.42d+35))) then
        tmp = (2.0d0 / (t * z)) + (x / y)
    else
        tmp = (-2.0d0) + ((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 (((x / y) <= -5.2e+24) || !((x / y) <= 1.42e+35)) {
		tmp = (2.0 / (t * z)) + (x / y);
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5.2e+24) or not ((x / y) <= 1.42e+35):
		tmp = (2.0 / (t * z)) + (x / y)
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5.2e+24) || !(Float64(x / y) <= 1.42e+35))
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(x / y));
	else
		tmp = Float64(-2.0 + 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 (((x / y) <= -5.2e+24) || ~(((x / y) <= 1.42e+35)))
		tmp = (2.0 / (t * z)) + (x / y);
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5.2e+24], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.42e+35]], $MachinePrecision]], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.1999999999999997e24 or 1.41999999999999991e35 < (/.f64 x y)

   1. Initial program 84.9%

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

   2. Taylor expanded in z around 0 90.1%

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

   if -5.1999999999999997e24 < (/.f64 x y) < 1.41999999999999991e35

   1. Initial program 90.0%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. associate-+r+ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-*r/ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in t around 0 95.2%

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

      1. associate-*r/ 95.2%

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

      2. metadata-eval 95.2%

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

   7. Simplified 95.2%

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

4. Final simplification 93.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.2 \cdot 10^{+24} \lor \neg \left(\frac{x}{y} \leq 1.42 \cdot 10^{+35}\right):\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 4: 70.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -9.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{2}{t \cdot z} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -9.5e+77)
   (/ x y)
   (if (<= (/ x y) 4.6e+51) (+ (/ 2.0 (* t z)) -2.0) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -9.5e+77) {
		tmp = x / y;
	} else if ((x / y) <= 4.6e+51) {
		tmp = (2.0 / (t * z)) + -2.0;
	} 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 ((x / y) <= (-9.5d+77)) then
        tmp = x / y
    else if ((x / y) <= 4.6d+51) then
        tmp = (2.0d0 / (t * z)) + (-2.0d0)
    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 ((x / y) <= -9.5e+77) {
		tmp = x / y;
	} else if ((x / y) <= 4.6e+51) {
		tmp = (2.0 / (t * z)) + -2.0;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -9.5e+77:
		tmp = x / y
	elif (x / y) <= 4.6e+51:
		tmp = (2.0 / (t * z)) + -2.0
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -9.5e+77)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 4.6e+51)
		tmp = Float64(Float64(2.0 / Float64(t * z)) + -2.0);
	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 ((x / y) <= -9.5e+77)
		tmp = x / y;
	elseif ((x / y) <= 4.6e+51)
		tmp = (2.0 / (t * z)) + -2.0;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -9.5e+77], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4.6e+51], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.4999999999999998e77

   1. Initial program 79.2%

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

   2. Taylor expanded in x around inf 83.2%

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

   if -9.4999999999999998e77 < (/.f64 x y) < 4.6000000000000001e51

   1. Initial program 89.5%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. associate-+r+ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-*r/ 99.9%

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

      5. +-commutative 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around 0 75.1%

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

      1. *-commutative 75.1%

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

   7. Simplified 75.1%

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

   if 4.6000000000000001e51 < (/.f64 x y)

   1. Initial program 90.4%

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

   2. Taylor expanded in t around inf 84.6%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -9.5 \cdot 10^{+77}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{2}{t \cdot z} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 5: 65.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.00155 \lor \neg \left(\frac{x}{y} \leq 1.02 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -0.00155) (not (<= (/ x y) 1.02e-7)))
   (- (/ x y) 2.0)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -0.00155) || !((x / y) <= 1.02e-7)) {
		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 (((x / y) <= (-0.00155d0)) .or. (.not. ((x / y) <= 1.02d-7))) 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 (((x / y) <= -0.00155) || !((x / y) <= 1.02e-7)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -0.00155) or not ((x / y) <= 1.02e-7):
		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 ((Float64(x / y) <= -0.00155) || !(Float64(x / y) <= 1.02e-7))
		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 (((x / y) <= -0.00155) || ~(((x / y) <= 1.02e-7)))
		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[N[(x / y), $MachinePrecision], -0.00155], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.02e-7]], $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 (/.f64 x y) < -0.00154999999999999995 or 1.02e-7 < (/.f64 x y)

   1. Initial program 86.2%

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

   2. Taylor expanded in t around inf 72.5%

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

   if -0.00154999999999999995 < (/.f64 x y) < 1.02e-7

   1. Initial program 89.4%

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

   2. Taylor expanded in z around inf 59.9%

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

      1. associate-*r/ 59.9%

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

      2. sub-neg 59.9%

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

      3. distribute-rgt-in 59.9%

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

      4. metadata-eval 59.9%

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

      5. distribute-lft-neg-out 59.9%

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

      6. unsub-neg 59.9%

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

   4. Simplified 59.9%

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

   5. Taylor expanded in x around 0 59.6%

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

      1. sub-neg 59.6%

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

      2. associate-*r/ 59.6%

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

      3. metadata-eval 59.6%

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

      4. metadata-eval 59.6%

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

   7. Simplified 59.6%

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

4. Final simplification 66.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -0.00155 \lor \neg \left(\frac{x}{y} \leq 1.02 \cdot 10^{-7}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]

Alternative 6: 85.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-14} \lor \neg \left(z \leq 4.7 \cdot 10^{-49}\right):\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.6e-14) (not (<= z 4.7e-49)))
   (+ -2.0 (+ (/ 2.0 t) (/ x y)))
   (+ (/ 2.0 (* t z)) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-14) || !(z <= 4.7e-49)) {
		tmp = -2.0 + ((2.0 / t) + (x / y));
	} else {
		tmp = (2.0 / (t * z)) + -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 ((z <= (-1.6d-14)) .or. (.not. (z <= 4.7d-49))) then
        tmp = (-2.0d0) + ((2.0d0 / t) + (x / y))
    else
        tmp = (2.0d0 / (t * z)) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.6e-14) || !(z <= 4.7e-49)) {
		tmp = -2.0 + ((2.0 / t) + (x / y));
	} else {
		tmp = (2.0 / (t * z)) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.6e-14) or not (z <= 4.7e-49):
		tmp = -2.0 + ((2.0 / t) + (x / y))
	else:
		tmp = (2.0 / (t * z)) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.6e-14) || !(z <= 4.7e-49))
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) + Float64(x / y)));
	else
		tmp = Float64(Float64(2.0 / Float64(t * z)) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.6e-14) || ~((z <= 4.7e-49)))
		tmp = -2.0 + ((2.0 / t) + (x / y));
	else
		tmp = (2.0 / (t * z)) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.6e-14], N[Not[LessEqual[z, 4.7e-49]], $MachinePrecision]], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.6000000000000001e-14 or 4.70000000000000021e-49 < z

   1. Initial program 80.8%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. associate-+r+ 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-*r/ 100.0%

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

      5. +-commutative 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

      10. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 98.1%

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

      1. associate-*r/ 98.1%

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

      2. metadata-eval 98.1%

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

      3. +-commutative 98.1%

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

   7. Simplified 98.1%

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

   if -1.6000000000000001e-14 < z < 4.70000000000000021e-49

   1. Initial program 96.4%

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

   2. Taylor expanded in t around 0 96.4%

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

      1. sub-neg 96.4%

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

      2. associate-+r+ 96.4%

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

      3. metadata-eval 96.4%

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

      4. associate-*r/ 96.4%

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

      5. +-commutative 96.4%

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

      6. associate-*r/ 96.4%

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

      7. metadata-eval 96.4%

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

      8. associate-*r/ 96.4%

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

      9. metadata-eval 96.4%

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

      10. metadata-eval 96.4%

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

   4. Simplified 96.4%

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

   5. Taylor expanded in z around 0 78.7%

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

      1. *-commutative 78.7%

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

   7. Simplified 78.7%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-14} \lor \neg \left(z \leq 4.7 \cdot 10^{-49}\right):\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + -2\\ \end{array} \]

Alternative 7: 92.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-31} \lor \neg \left(z \leq 2.2 \cdot 10^{-33}\right):\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.2e-31) (not (<= z 2.2e-33)))
   (+ -2.0 (+ (/ 2.0 t) (/ x y)))
   (+ (/ 2.0 (* t z)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.2e-31) || !(z <= 2.2e-33)) {
		tmp = -2.0 + ((2.0 / t) + (x / y));
	} 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 <= (-3.2d-31)) .or. (.not. (z <= 2.2d-33))) then
        tmp = (-2.0d0) + ((2.0d0 / t) + (x / y))
    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 <= -3.2e-31) || !(z <= 2.2e-33)) {
		tmp = -2.0 + ((2.0 / t) + (x / y));
	} else {
		tmp = (2.0 / (t * z)) + (x / y);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.2e-31) or not (z <= 2.2e-33):
		tmp = -2.0 + ((2.0 / t) + (x / y))
	else:
		tmp = (2.0 / (t * z)) + (x / y)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.2e-31) || !(z <= 2.2e-33))
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) + Float64(x / y)));
	else
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(x / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.2e-31) || ~((z <= 2.2e-33)))
		tmp = -2.0 + ((2.0 / t) + (x / y));
	else
		tmp = (2.0 / (t * z)) + (x / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.2e-31], N[Not[LessEqual[z, 2.2e-33]], $MachinePrecision]], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.20000000000000018e-31 or 2.20000000000000005e-33 < z

   1. Initial program 80.7%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. sub-neg 100.0%

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

      2. associate-+r+ 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-*r/ 100.0%

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

      5. +-commutative 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

      10. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 98.1%

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

      1. associate-*r/ 98.1%

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

      2. metadata-eval 98.1%

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

      3. +-commutative 98.1%

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

   7. Simplified 98.1%

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

   if -3.20000000000000018e-31 < z < 2.20000000000000005e-33

   1. Initial program 96.4%

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

   2. Taylor expanded in z around 0 85.6%

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

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{-31} \lor \neg \left(z \leq 2.2 \cdot 10^{-33}\right):\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \end{array} \]

Alternative 8: 65.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.1 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.25 \cdot 10^{+35}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.1e+17)
   (/ x y)
   (if (<= (/ x y) 1.25e+35) (+ (/ 2.0 t) -2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.1e+17) {
		tmp = x / y;
	} else if ((x / y) <= 1.25e+35) {
		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) <= (-1.1d+17)) then
        tmp = x / y
    else if ((x / y) <= 1.25d+35) 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) <= -1.1e+17) {
		tmp = x / y;
	} else if ((x / y) <= 1.25e+35) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.1e+17:
		tmp = x / y
	elif (x / y) <= 1.25e+35:
		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) <= -1.1e+17)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1.25e+35)
		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) <= -1.1e+17)
		tmp = x / y;
	elseif ((x / y) <= 1.25e+35)
		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], -1.1e+17], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.25e+35], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.1e17 or 1.25000000000000005e35 < (/.f64 x y)

   1. Initial program 85.1%

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

   2. Taylor expanded in x around inf 77.5%

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

   if -1.1e17 < (/.f64 x y) < 1.25000000000000005e35

   1. Initial program 89.9%

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

   2. Taylor expanded in z around inf 59.9%

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

      1. associate-*r/ 59.9%

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

      2. sub-neg 59.9%

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

      3. distribute-rgt-in 59.9%

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

      4. metadata-eval 59.9%

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

      5. distribute-lft-neg-out 59.9%

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

      6. unsub-neg 59.9%

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

   4. Simplified 59.9%

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

   5. Taylor expanded in x around 0 55.2%

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

      1. sub-neg 55.2%

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

      2. associate-*r/ 55.2%

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

      3. metadata-eval 55.2%

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

      4. metadata-eval 55.2%

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

   7. Simplified 55.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.1 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.25 \cdot 10^{+35}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 9: 52.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1750:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.0) (/ x y) (if (<= (/ x y) 1750.0) -2.0 (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= 1750.0) {
		tmp = -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) <= (-2.0d0)) then
        tmp = x / y
    else if ((x / y) <= 1750.0d0) then
        tmp = -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) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= 1750.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2.0:
		tmp = x / y
	elif (x / y) <= 1750.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1750.0)
		tmp = -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) <= -2.0)
		tmp = x / y;
	elseif ((x / y) <= 1750.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1750.0], -2.0, N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2 or 1750 < (/.f64 x y)

   1. Initial program 85.6%

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

   2. Taylor expanded in x around inf 72.6%

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

   if -2 < (/.f64 x y) < 1750

   1. Initial program 89.8%

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

   2. Taylor expanded in t around inf 40.1%

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

   3. Taylor expanded in x around 0 38.5%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1750:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 10: 64.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-32} \lor \neg \left(z \leq 1.65 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -8.5e-32) (not (<= z 1.65e-46)))
   (- (/ x y) 2.0)
   (/ 2.0 (* t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -8.5e-32) || !(z <= 1.65e-46)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 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 <= (-8.5d-32)) .or. (.not. (z <= 1.65d-46))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 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 <= -8.5e-32) || !(z <= 1.65e-46)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / (t * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -8.5e-32) or not (z <= 1.65e-46):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / (t * z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -8.5e-32) || !(z <= 1.65e-46))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / Float64(t * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -8.5e-32) || ~((z <= 1.65e-46)))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -8.5e-32], N[Not[LessEqual[z, 1.65e-46]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -8.5000000000000003e-32 or 1.65000000000000007e-46 < z

   1. Initial program 81.1%

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

   2. Taylor expanded in t around inf 73.2%

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

   if -8.5000000000000003e-32 < z < 1.65000000000000007e-46

   1. Initial program 96.3%

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

   2. Taylor expanded in t around 0 67.9%

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

      1. associate-*r/ 67.9%

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

      2. metadata-eval 67.9%

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

   4. Simplified 67.9%

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

   5. Taylor expanded in z around 0 67.9%

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

   6. Taylor expanded in z around 0 67.9%

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

4. Final simplification 70.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{-32} \lor \neg \left(z \leq 1.65 \cdot 10^{-46}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \]

Alternative 11: 37.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.3:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 0.96:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.3) -2.0 (if (<= t 0.96) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.3) {
		tmp = -2.0;
	} else if (t <= 0.96) {
		tmp = 2.0 / t;
	} else {
		tmp = -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 <= (-1.3d0)) then
        tmp = -2.0d0
    else if (t <= 0.96d0) then
        tmp = 2.0d0 / t
    else
        tmp = -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 <= -1.3) {
		tmp = -2.0;
	} else if (t <= 0.96) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.3:
		tmp = -2.0
	elif t <= 0.96:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.3)
		tmp = -2.0;
	elseif (t <= 0.96)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.3)
		tmp = -2.0;
	elseif (t <= 0.96)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.3], -2.0, If[LessEqual[t, 0.96], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1.30000000000000004 or 0.95999999999999996 < t

   1. Initial program 78.5%

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

   2. Taylor expanded in t around inf 82.7%

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

   3. Taylor expanded in x around 0 40.5%

      \[\leadsto \color{blue}{-2} \]

   if -1.30000000000000004 < t < 0.95999999999999996

   1. Initial program 96.7%

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

   2. Taylor expanded in t around 0 70.1%

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

      1. associate-*r/ 70.1%

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

      2. metadata-eval 70.1%

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

   4. Simplified 70.1%

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

   5. Taylor expanded in z around inf 25.3%

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

4. Final simplification 32.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.3:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 0.96:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 12: 20.2% accurate, 17.0× speedup

Math

\[\begin{array}{l} \\ -2 \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return -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
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := -2.0

Derivation

1. Initial program 87.8%

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

2. Taylor expanded in t around inf 56.4%

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

3. Taylor expanded in x around 0 21.1%

   \[\leadsto \color{blue}{-2} \]

4. Final simplification 21.1%

   \[\leadsto -2 \]

Developer target: 99.0% 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 2023293 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :herbie-target
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

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