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

Percentage Accurate: 86.1% → 99.1%

Time: 9.1s

Alternatives: 10

Speedup: 1.3×

• 23.7% 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: 99.1% accurate, 1.1× speedup

Math

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

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(Float64(2.0 / 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[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.6%

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

2. Taylor expanded in t around 0 99.1%

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

   1. associate--l+ 99.1%

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

   2. associate-*r/ 99.1%

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

   3. metadata-eval 99.1%

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

   4. associate-/r* 99.1%

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

   5. metadata-eval 99.1%

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

   6. associate-*r/ 99.1%

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

   7. sub-neg 99.1%

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

   8. associate-*r/ 99.1%

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

   9. metadata-eval 99.1%

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

   10. metadata-eval 99.1%

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

4. Simplified 99.1%

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

5. Final simplification 99.1%

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

Alternative 2: 92.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+21} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+21) (not (<= (/ x y) 5e+41)))
   (+ (/ x y) (/ 2.0 (* t z)))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+21) || !((x / y) <= 5e+41)) {
		tmp = (x / y) + (2.0 / (t * z));
	} 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) <= (-1d+21)) .or. (.not. ((x / y) <= 5d+41))) then
        tmp = (x / y) + (2.0d0 / (t * z))
    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) <= -1e+21) || !((x / y) <= 5e+41)) {
		tmp = (x / y) + (2.0 / (t * z));
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+21) or not ((x / y) <= 5e+41):
		tmp = (x / y) + (2.0 / (t * z))
	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) <= -1e+21) || !(Float64(x / y) <= 5e+41))
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	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) <= -1e+21) || ~(((x / y) <= 5e+41)))
		tmp = (x / y) + (2.0 / (t * z));
	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], -1e+21], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+41]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $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) < -1e21 or 5.00000000000000022e41 < (/.f64 x y)

   1. Initial program 83.4%

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

   2. Taylor expanded in z around 0 88.3%

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

   if -1e21 < (/.f64 x y) < 5.00000000000000022e41

   1. Initial program 85.5%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-*r/ 99.8%

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

      7. sub-neg 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

      10. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in x around 0 99.5%

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

      1. sub-neg 99.5%

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

      2. associate-*r/ 99.5%

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

      3. metadata-eval 99.5%

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

      4. associate-*r/ 99.5%

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

      5. metadata-eval 99.5%

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

      6. metadata-eval 99.5%

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

   7. Simplified 99.6%

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

4. Final simplification 94.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+21} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 3: 62.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+43}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-28} \lor \neg \left(z \leq 1.55 \cdot 10^{-81}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -2.4e+113)
     t_1
     (if (<= z -2.4e+43)
       (/ 2.0 t)
       (if (or (<= z -3e-28) (not (<= z 1.55e-81))) t_1 (/ 2.0 (* t z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -2.4e+113) {
		tmp = t_1;
	} else if (z <= -2.4e+43) {
		tmp = 2.0 / t;
	} else if ((z <= -3e-28) || !(z <= 1.55e-81)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-2.4d+113)) then
        tmp = t_1
    else if (z <= (-2.4d+43)) then
        tmp = 2.0d0 / t
    else if ((z <= (-3d-28)) .or. (.not. (z <= 1.55d-81))) then
        tmp = t_1
    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 t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -2.4e+113) {
		tmp = t_1;
	} else if (z <= -2.4e+43) {
		tmp = 2.0 / t;
	} else if ((z <= -3e-28) || !(z <= 1.55e-81)) {
		tmp = t_1;
	} else {
		tmp = 2.0 / (t * z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -2.4e+113:
		tmp = t_1
	elif z <= -2.4e+43:
		tmp = 2.0 / t
	elif (z <= -3e-28) or not (z <= 1.55e-81):
		tmp = t_1
	else:
		tmp = 2.0 / (t * z)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -2.4e+113)
		tmp = t_1;
	elseif (z <= -2.4e+43)
		tmp = Float64(2.0 / t);
	elseif ((z <= -3e-28) || !(z <= 1.55e-81))
		tmp = t_1;
	else
		tmp = Float64(2.0 / Float64(t * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (z <= -2.4e+113)
		tmp = t_1;
	elseif (z <= -2.4e+43)
		tmp = 2.0 / t;
	elseif ((z <= -3e-28) || ~((z <= 1.55e-81)))
		tmp = t_1;
	else
		tmp = 2.0 / (t * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z, -2.4e+113], t$95$1, If[LessEqual[z, -2.4e+43], N[(2.0 / t), $MachinePrecision], If[Or[LessEqual[z, -3e-28], N[Not[LessEqual[z, 1.55e-81]], $MachinePrecision]], t$95$1, N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.39999999999999983e113 or -2.40000000000000023e43 < z < -3.00000000000000003e-28 or 1.54999999999999994e-81 < z

   1. Initial program 74.1%

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

   2. Taylor expanded in t around inf 68.4%

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

   if -2.39999999999999983e113 < z < -2.40000000000000023e43

   1. Initial program 93.5%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/r* 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*r/ 100.0%

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

      7. sub-neg 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

      10. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

      1. sub-neg 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. +-commutative 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-+l+ 100.0%

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

      7. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in t around 0 93.9%

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

   9. Taylor expanded in x around 0 75.6%

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

   if -3.00000000000000003e-28 < z < 1.54999999999999994e-81

   1. Initial program 97.8%

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

   2. Taylor expanded in t around 0 97.8%

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

      1. associate--l+ 97.8%

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

      2. associate-*r/ 97.8%

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

      3. metadata-eval 97.8%

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

      4. associate-/r* 97.8%

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

      5. metadata-eval 97.8%

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

      6. associate-*r/ 97.8%

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

      7. sub-neg 97.8%

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

      8. associate-*r/ 97.8%

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

      9. metadata-eval 97.8%

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

      10. metadata-eval 97.8%

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

   4. Simplified 97.8%

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

   5. Taylor expanded in z around 0 68.0%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+113}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+43}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-28} \lor \neg \left(z \leq 1.55 \cdot 10^{-81}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \end{array} \]

Alternative 4: 81.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-28} \lor \neg \left(z \leq 5.4 \cdot 10^{-86}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5.8e-28) (not (<= z 5.4e-86)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5.8e-28) || !(z <= 5.4e-86)) {
		tmp = (x / y) + ((2.0 / t) + -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 ((z <= (-5.8d-28)) .or. (.not. (z <= 5.4d-86))) then
        tmp = (x / y) + ((2.0d0 / t) + (-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 ((z <= -5.8e-28) || !(z <= 5.4e-86)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5.8e-28) or not (z <= 5.4e-86):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5.8e-28) || !(z <= 5.4e-86))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -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 ((z <= -5.8e-28) || ~((z <= 5.4e-86)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5.8e-28], N[Not[LessEqual[z, 5.4e-86]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.80000000000000026e-28 or 5.39999999999999985e-86 < z

   1. Initial program 76.4%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/r* 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. sub-neg 99.9%

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

      8. associate-*r/ 99.9%

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

      9. metadata-eval 99.9%

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

      10. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 93.7%

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

      1. sub-neg 93.7%

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

      2. associate-*r/ 93.7%

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

      3. metadata-eval 93.7%

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

      4. +-commutative 93.7%

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

      5. metadata-eval 93.7%

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

      6. associate-+l+ 93.7%

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

      7. +-commutative 93.7%

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

   7. Simplified 93.7%

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

   if -5.80000000000000026e-28 < z < 5.39999999999999985e-86

   1. Initial program 97.8%

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

   2. Taylor expanded in t around 0 68.4%

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

      1. associate-*r/ 68.4%

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

      2. metadata-eval 68.4%

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

   4. Simplified 68.4%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{-28} \lor \neg \left(z \leq 5.4 \cdot 10^{-86}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 5: 92.3% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-27} \lor \neg \left(z \leq 4.7 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -3.1e-27) (not (<= z 4.7e-30)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ x y) (/ 2.0 (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -3.1e-27) || !(z <= 4.7e-30)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (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 <= (-3.1d-27)) .or. (.not. (z <= 4.7d-30))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (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 <= -3.1e-27) || !(z <= 4.7e-30)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -3.1e-27) or not (z <= 4.7e-30):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (x / y) + (2.0 / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -3.1e-27) || !(z <= 4.7e-30))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -3.1e-27) || ~((z <= 4.7e-30)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = (x / y) + (2.0 / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -3.1e-27], N[Not[LessEqual[z, 4.7e-30]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -3.0999999999999998e-27 or 4.69999999999999969e-30 < z

   1. Initial program 74.1%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. associate-/r* 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*r/ 100.0%

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

      7. sub-neg 100.0%

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

      8. associate-*r/ 100.0%

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

      9. metadata-eval 100.0%

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

      10. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 97.3%

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

      1. sub-neg 97.3%

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

      2. associate-*r/ 97.3%

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

      3. metadata-eval 97.3%

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

      4. +-commutative 97.3%

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

      5. metadata-eval 97.3%

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

      6. associate-+l+ 97.3%

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

      7. +-commutative 97.3%

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

   7. Simplified 97.3%

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

   if -3.0999999999999998e-27 < z < 4.69999999999999969e-30

   1. Initial program 98.0%

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

   2. Taylor expanded in z around 0 85.4%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{-27} \lor \neg \left(z \leq 4.7 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \]

Alternative 6: 69.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -7.2 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;t \leq 40000000000:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -7.2e-24)
     t_1
     (if (<= t 5.5e-38)
       (+ (/ x y) (/ 2.0 t))
       (if (<= t 40000000000.0) (/ 2.0 (* t z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -7.2e-24) {
		tmp = t_1;
	} else if (t <= 5.5e-38) {
		tmp = (x / y) + (2.0 / t);
	} else if (t <= 40000000000.0) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (t <= (-7.2d-24)) then
        tmp = t_1
    else if (t <= 5.5d-38) then
        tmp = (x / y) + (2.0d0 / t)
    else if (t <= 40000000000.0d0) then
        tmp = 2.0d0 / (t * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -7.2e-24) {
		tmp = t_1;
	} else if (t <= 5.5e-38) {
		tmp = (x / y) + (2.0 / t);
	} else if (t <= 40000000000.0) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -7.2e-24:
		tmp = t_1
	elif t <= 5.5e-38:
		tmp = (x / y) + (2.0 / t)
	elif t <= 40000000000.0:
		tmp = 2.0 / (t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -7.2e-24)
		tmp = t_1;
	elseif (t <= 5.5e-38)
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	elseif (t <= 40000000000.0)
		tmp = Float64(2.0 / Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -7.2e-24)
		tmp = t_1;
	elseif (t <= 5.5e-38)
		tmp = (x / y) + (2.0 / t);
	elseif (t <= 40000000000.0)
		tmp = 2.0 / (t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -7.2e-24], t$95$1, If[LessEqual[t, 5.5e-38], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 40000000000.0], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -7.2000000000000002e-24 or 4e10 < t

   1. Initial program 68.8%

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

   2. Taylor expanded in t around inf 84.3%

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

   if -7.2000000000000002e-24 < t < 5.50000000000000005e-38

   1. Initial program 98.1%

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

   2. Taylor expanded in t around 0 98.3%

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

      1. associate--l+ 98.3%

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

      2. associate-*r/ 98.3%

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

      3. metadata-eval 98.3%

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

      4. associate-/r* 98.3%

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

      5. metadata-eval 98.3%

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

      6. associate-*r/ 98.3%

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

      7. sub-neg 98.3%

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

      8. associate-*r/ 98.3%

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

      9. metadata-eval 98.3%

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

      10. metadata-eval 98.3%

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

   4. Simplified 98.3%

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

   5. Taylor expanded in z around inf 61.9%

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

      1. sub-neg 61.9%

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

      2. associate-*r/ 61.9%

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

      3. metadata-eval 61.9%

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

      4. +-commutative 61.9%

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

      5. metadata-eval 61.9%

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

      6. associate-+l+ 61.9%

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

      7. +-commutative 61.9%

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

   7. Simplified 61.9%

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

   8. Taylor expanded in t around 0 61.9%

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

   if 5.50000000000000005e-38 < t < 4e10

   1. Initial program 99.7%

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

   2. Taylor expanded in t around 0 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. metadata-eval 99.7%

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

      4. associate-/r* 99.5%

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

      5. metadata-eval 99.5%

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

      6. associate-*r/ 99.5%

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

      7. sub-neg 99.5%

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

      8. associate-*r/ 99.5%

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

      9. metadata-eval 99.5%

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

      10. metadata-eval 99.5%

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

   4. Simplified 99.5%

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

   5. Taylor expanded in z around 0 71.3%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -7.2 \cdot 10^{-24}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-38}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;t \leq 40000000000:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 7: 46.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -8 \cdot 10^{-18} \lor \neg \left(\frac{x}{y} \leq 1.4 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -8e-18) (not (<= (/ x y) 1.4e+42))) (/ x y) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -8e-18) || !((x / y) <= 1.4e+42)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-8d-18)) .or. (.not. ((x / y) <= 1.4d+42))) then
        tmp = x / y
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -8e-18) || !((x / y) <= 1.4e+42)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -8e-18) or not ((x / y) <= 1.4e+42):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -8e-18) || !(Float64(x / y) <= 1.4e+42))
		tmp = Float64(x / y);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -8e-18) || ~(((x / y) <= 1.4e+42)))
		tmp = x / y;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -8e-18], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.4e+42]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -8.0000000000000006e-18 or 1.4e42 < (/.f64 x y)

   1. Initial program 84.3%

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

   2. Taylor expanded in x around inf 70.5%

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

   if -8.0000000000000006e-18 < (/.f64 x y) < 1.4e42

   1. Initial program 84.8%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-/r* 99.8%

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

      5. metadata-eval 99.8%

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

      6. associate-*r/ 99.8%

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

      7. sub-neg 99.8%

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

      8. associate-*r/ 99.8%

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

      9. metadata-eval 99.8%

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

      10. metadata-eval 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around inf 62.9%

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

      1. sub-neg 62.9%

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

      2. associate-*r/ 62.9%

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

      3. metadata-eval 62.9%

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

      4. +-commutative 62.9%

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

      5. metadata-eval 62.9%

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

      6. associate-+l+ 62.9%

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

      7. +-commutative 62.9%

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

   7. Simplified 62.9%

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

   8. Taylor expanded in t around 0 28.5%

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

   9. Taylor expanded in x around 0 28.3%

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

4. Final simplification 47.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -8 \cdot 10^{-18} \lor \neg \left(\frac{x}{y} \leq 1.4 \cdot 10^{+42}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]

Alternative 8: 80.5% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+33} \lor \neg \left(t \leq 36000000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2e+33) (not (<= t 36000000000.0)))
   (- (/ 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 <= -2e+33) || !(t <= 36000000000.0)) {
		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 <= (-2d+33)) .or. (.not. (t <= 36000000000.0d0))) 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 <= -2e+33) || !(t <= 36000000000.0)) {
		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 <= -2e+33) or not (t <= 36000000000.0):
		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 <= -2e+33) || !(t <= 36000000000.0))
		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 <= -2e+33) || ~((t <= 36000000000.0)))
		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, -2e+33], N[Not[LessEqual[t, 36000000000.0]], $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 < -1.9999999999999999e33 or 3.6e10 < t

   1. Initial program 66.3%

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

   2. Taylor expanded in t around inf 88.3%

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

   if -1.9999999999999999e33 < t < 3.6e10

   1. Initial program 98.3%

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

   2. Taylor expanded in t around 0 77.7%

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

      1. associate-*r/ 77.7%

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

      2. metadata-eval 77.7%

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

   4. Simplified 77.7%

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

4. Final simplification 82.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2 \cdot 10^{+33} \lor \neg \left(t \leq 36000000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 9: 60.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-94} \lor \neg \left(t \leq 1.35 \cdot 10^{-149}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -4.1e-94) (not (<= t 1.35e-149))) (- (/ x y) 2.0) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -4.1e-94) || !(t <= 1.35e-149)) {
		tmp = (x / y) - 2.0;
	} 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 <= (-4.1d-94)) .or. (.not. (t <= 1.35d-149))) then
        tmp = (x / y) - 2.0d0
    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 <= -4.1e-94) || !(t <= 1.35e-149)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -4.1e-94) or not (t <= 1.35e-149):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -4.1e-94) || !(t <= 1.35e-149))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -4.1e-94) || ~((t <= 1.35e-149)))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -4.1e-94], N[Not[LessEqual[t, 1.35e-149]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -4.10000000000000001e-94 or 1.35000000000000007e-149 < t

   1. Initial program 77.7%

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

   2. Taylor expanded in t around inf 72.1%

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

   if -4.10000000000000001e-94 < t < 1.35000000000000007e-149

   1. Initial program 98.5%

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

   2. Taylor expanded in t around 0 98.8%

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

      1. associate--l+ 98.8%

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

      2. associate-*r/ 98.8%

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

      3. metadata-eval 98.8%

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

      4. associate-/r* 98.7%

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

      5. metadata-eval 98.7%

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

      6. associate-*r/ 98.7%

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

      7. sub-neg 98.7%

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

      8. associate-*r/ 98.7%

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

      9. metadata-eval 98.7%

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

      10. metadata-eval 98.7%

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

   4. Simplified 98.7%

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

   5. Taylor expanded in z around inf 57.9%

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

      1. sub-neg 57.9%

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

      2. associate-*r/ 57.9%

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

      3. metadata-eval 57.9%

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

      4. +-commutative 57.9%

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

      5. metadata-eval 57.9%

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

      6. associate-+l+ 57.9%

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

      7. +-commutative 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in t around 0 57.9%

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

   9. Taylor expanded in x around 0 46.4%

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

4. Final simplification 63.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.1 \cdot 10^{-94} \lor \neg \left(t \leq 1.35 \cdot 10^{-149}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]

Alternative 10: 19.6% 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 84.6%

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

2. Taylor expanded in t around 0 99.1%

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

   1. associate--l+ 99.1%

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

   2. associate-*r/ 99.1%

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

   3. metadata-eval 99.1%

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

   4. associate-/r* 99.1%

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

   5. metadata-eval 99.1%

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

   6. associate-*r/ 99.1%

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

   7. sub-neg 99.1%

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

   8. associate-*r/ 99.1%

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

   9. metadata-eval 99.1%

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

   10. metadata-eval 99.1%

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

4. Simplified 99.1%

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

5. Taylor expanded in z around inf 71.2%

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

   1. sub-neg 71.2%

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

   2. associate-*r/ 71.2%

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

   3. metadata-eval 71.2%

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

   4. +-commutative 71.2%

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

   5. metadata-eval 71.2%

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

   6. associate-+l+ 71.2%

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

   7. +-commutative 71.2%

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

7. Simplified 71.2%

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

8. Taylor expanded in t around 0 51.6%

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

9. Taylor expanded in x around 0 21.0%

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

10. Final simplification 21.0%

    \[\leadsto \frac{2}{t} \]

Developer target: 99.1% 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 2023318 
(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))))