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

Percentage Accurate: 86.8% → 99.1%

Time: 11.2s

Alternatives: 12

Speedup: 1.3×

• 24.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.3%

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

2. Taylor expanded in t around 0 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%

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

   3. metadata-eval 98.4%

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

   4. metadata-eval 98.4%

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

4. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 2: 68.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t} + \frac{x}{y}\\ t_2 := \frac{2}{t \cdot z}\\ t_3 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-300}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-258}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ 2.0 t) (/ x y)))
        (t_2 (/ 2.0 (* t z)))
        (t_3 (- (/ x y) 2.0)))
   (if (<= t -1.0)
     t_3
     (if (<= t -5.8e-247)
       t_1
       (if (<= t -1.42e-300)
         t_2
         (if (<= t 5e-258)
           (/ 2.0 t)
           (if (<= t 7.2e-156)
             t_2
             (if (<= t 1.3e-90)
               t_1
               (if (<= t 1.9e-66) t_2 (if (<= t 6.4e-17) t_1 t_3))))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) + (x / y);
	double t_2 = 2.0 / (t * z);
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.0) {
		tmp = t_3;
	} else if (t <= -5.8e-247) {
		tmp = t_1;
	} else if (t <= -1.42e-300) {
		tmp = t_2;
	} else if (t <= 5e-258) {
		tmp = 2.0 / t;
	} else if (t <= 7.2e-156) {
		tmp = t_2;
	} else if (t <= 1.3e-90) {
		tmp = t_1;
	} else if (t <= 1.9e-66) {
		tmp = t_2;
	} else if (t <= 6.4e-17) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	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) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (2.0d0 / t) + (x / y)
    t_2 = 2.0d0 / (t * z)
    t_3 = (x / y) - 2.0d0
    if (t <= (-1.0d0)) then
        tmp = t_3
    else if (t <= (-5.8d-247)) then
        tmp = t_1
    else if (t <= (-1.42d-300)) then
        tmp = t_2
    else if (t <= 5d-258) then
        tmp = 2.0d0 / t
    else if (t <= 7.2d-156) then
        tmp = t_2
    else if (t <= 1.3d-90) then
        tmp = t_1
    else if (t <= 1.9d-66) then
        tmp = t_2
    else if (t <= 6.4d-17) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) + (x / y);
	double t_2 = 2.0 / (t * z);
	double t_3 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.0) {
		tmp = t_3;
	} else if (t <= -5.8e-247) {
		tmp = t_1;
	} else if (t <= -1.42e-300) {
		tmp = t_2;
	} else if (t <= 5e-258) {
		tmp = 2.0 / t;
	} else if (t <= 7.2e-156) {
		tmp = t_2;
	} else if (t <= 1.3e-90) {
		tmp = t_1;
	} else if (t <= 1.9e-66) {
		tmp = t_2;
	} else if (t <= 6.4e-17) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / t) + (x / y)
	t_2 = 2.0 / (t * z)
	t_3 = (x / y) - 2.0
	tmp = 0
	if t <= -1.0:
		tmp = t_3
	elif t <= -5.8e-247:
		tmp = t_1
	elif t <= -1.42e-300:
		tmp = t_2
	elif t <= 5e-258:
		tmp = 2.0 / t
	elif t <= 7.2e-156:
		tmp = t_2
	elif t <= 1.3e-90:
		tmp = t_1
	elif t <= 1.9e-66:
		tmp = t_2
	elif t <= 6.4e-17:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / t) + Float64(x / y))
	t_2 = Float64(2.0 / Float64(t * z))
	t_3 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -1.0)
		tmp = t_3;
	elseif (t <= -5.8e-247)
		tmp = t_1;
	elseif (t <= -1.42e-300)
		tmp = t_2;
	elseif (t <= 5e-258)
		tmp = Float64(2.0 / t);
	elseif (t <= 7.2e-156)
		tmp = t_2;
	elseif (t <= 1.3e-90)
		tmp = t_1;
	elseif (t <= 1.9e-66)
		tmp = t_2;
	elseif (t <= 6.4e-17)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / t) + (x / y);
	t_2 = 2.0 / (t * z);
	t_3 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -1.0)
		tmp = t_3;
	elseif (t <= -5.8e-247)
		tmp = t_1;
	elseif (t <= -1.42e-300)
		tmp = t_2;
	elseif (t <= 5e-258)
		tmp = 2.0 / t;
	elseif (t <= 7.2e-156)
		tmp = t_2;
	elseif (t <= 1.3e-90)
		tmp = t_1;
	elseif (t <= 1.9e-66)
		tmp = t_2;
	elseif (t <= 6.4e-17)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -1.0], t$95$3, If[LessEqual[t, -5.8e-247], t$95$1, If[LessEqual[t, -1.42e-300], t$95$2, If[LessEqual[t, 5e-258], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 7.2e-156], t$95$2, If[LessEqual[t, 1.3e-90], t$95$1, If[LessEqual[t, 1.9e-66], t$95$2, If[LessEqual[t, 6.4e-17], t$95$1, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1 or 6.4000000000000005e-17 < t

   1. Initial program 74.0%

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

   2. Taylor expanded in t around inf 88.4%

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

   if -1 < t < -5.8e-247 or 7.19999999999999998e-156 < t < 1.3e-90 or 1.8999999999999999e-66 < t < 6.4000000000000005e-17

   1. Initial program 98.7%

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

   2. Taylor expanded in z around inf 70.0%

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

      1. associate-*r/ 70.0%

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

      2. associate-/l* 70.0%

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

   4. Simplified 70.0%

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

   5. Taylor expanded in t around 0 69.6%

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

   if -5.8e-247 < t < -1.42e-300 or 4.9999999999999999e-258 < t < 7.19999999999999998e-156 or 1.3e-90 < t < 1.8999999999999999e-66

   1. Initial program 95.3%

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

   2. Taylor expanded in z around 0 75.4%

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

   3. Taylor expanded in x around 0 75.4%

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

   if -1.42e-300 < t < 4.9999999999999999e-258

   1. Initial program 91.9%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 69.9%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-247}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;t \leq -1.42 \cdot 10^{-300}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-258}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{-156}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-90}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-66}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 6.4 \cdot 10^{-17}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 3: 49.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.16 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -6.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq -1.55 \cdot 10^{-220}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.8 \cdot 10^{-181}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2500:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.16e+59)
   (/ x y)
   (if (<= (/ x y) -6.4e-18)
     (/ 2.0 t)
     (if (<= (/ x y) -1.55e-220)
       -2.0
       (if (<= (/ x y) 2.8e-181)
         (/ 2.0 t)
         (if (<= (/ x y) 2500.0) -2.0 (/ x y)))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.16e+59) {
		tmp = x / y;
	} else if ((x / y) <= -6.4e-18) {
		tmp = 2.0 / t;
	} else if ((x / y) <= -1.55e-220) {
		tmp = -2.0;
	} else if ((x / y) <= 2.8e-181) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2500.0) {
		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) <= (-1.16d+59)) then
        tmp = x / y
    else if ((x / y) <= (-6.4d-18)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= (-1.55d-220)) then
        tmp = -2.0d0
    else if ((x / y) <= 2.8d-181) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 2500.0d0) 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) <= -1.16e+59) {
		tmp = x / y;
	} else if ((x / y) <= -6.4e-18) {
		tmp = 2.0 / t;
	} else if ((x / y) <= -1.55e-220) {
		tmp = -2.0;
	} else if ((x / y) <= 2.8e-181) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2500.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.16e+59:
		tmp = x / y
	elif (x / y) <= -6.4e-18:
		tmp = 2.0 / t
	elif (x / y) <= -1.55e-220:
		tmp = -2.0
	elif (x / y) <= 2.8e-181:
		tmp = 2.0 / t
	elif (x / y) <= 2500.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.16e+59)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -6.4e-18)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= -1.55e-220)
		tmp = -2.0;
	elseif (Float64(x / y) <= 2.8e-181)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 2500.0)
		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) <= -1.16e+59)
		tmp = x / y;
	elseif ((x / y) <= -6.4e-18)
		tmp = 2.0 / t;
	elseif ((x / y) <= -1.55e-220)
		tmp = -2.0;
	elseif ((x / y) <= 2.8e-181)
		tmp = 2.0 / t;
	elseif ((x / y) <= 2500.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.16e+59], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -6.4e-18], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -1.55e-220], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 2.8e-181], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2500.0], -2.0, N[(x / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -1.16000000000000001e59 or 2500 < (/.f64 x y)

   1. Initial program 87.1%

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

   2. Taylor expanded in x around inf 72.7%

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

   if -1.16000000000000001e59 < (/.f64 x y) < -6.3999999999999998e-18 or -1.55000000000000006e-220 < (/.f64 x y) < 2.79999999999999986e-181

   1. Initial program 93.2%

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

   2. Taylor expanded in t around 0 78.6%

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

      1. associate-*r/ 78.6%

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

      2. metadata-eval 78.6%

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

   4. Simplified 78.6%

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

   5. Taylor expanded in z around inf 42.3%

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

   if -6.3999999999999998e-18 < (/.f64 x y) < -1.55000000000000006e-220 or 2.79999999999999986e-181 < (/.f64 x y) < 2500

   1. Initial program 82.4%

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

   2. Taylor expanded in t around inf 39.2%

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

   3. Taylor expanded in x around 0 39.2%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.16 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -6.4 \cdot 10^{-18}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq -1.55 \cdot 10^{-220}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 2.8 \cdot 10^{-181}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2500:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 4: 98.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.5 \lor \neg \left(\frac{x}{y} \leq 2500\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{2}{t \cdot z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.5) (not (<= (/ x y) 2500.0)))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* t z)))
   (+ -2.0 (+ (/ 2.0 t) (/ 2.0 (* t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.5) || !((x / y) <= 2500.0)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	} else {
		tmp = -2.0 + ((2.0 / t) + (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 (((x / y) <= (-2.5d0)) .or. (.not. ((x / y) <= 2500.0d0))) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (t * z))
    else
        tmp = (-2.0d0) + ((2.0d0 / t) + (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 (((x / y) <= -2.5) || !((x / y) <= 2500.0)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	} else {
		tmp = -2.0 + ((2.0 / t) + (2.0 / (t * z)));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2.5) or not ((x / y) <= 2500.0):
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z))
	else:
		tmp = -2.0 + ((2.0 / t) + (2.0 / (t * z)))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2.5) || !(Float64(x / y) <= 2500.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(t * z)));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) + Float64(2.0 / Float64(t * z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2.5) || ~(((x / y) <= 2500.0)))
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (t * z));
	else
		tmp = -2.0 + ((2.0 / t) + (2.0 / (t * z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2.5], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2500.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2.5 or 2500 < (/.f64 x y)

   1. Initial program 87.2%

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

   2. Taylor expanded in t around 0 95.8%

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

   if -2.5 < (/.f64 x y) < 2500

   1. Initial program 87.5%

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

   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%

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

      3. metadata-eval 99.9%

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

      4. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in x around 0 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*r/ 99.7%

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

      3. metadata-eval 99.7%

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

      4. associate-*r/ 99.7%

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

      5. metadata-eval 99.7%

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

   7. Simplified 99.7%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2.5 \lor \neg \left(\frac{x}{y} \leq 2500\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{2}{t \cdot z}\right)\\ \end{array} \]

Alternative 5: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -3.4 \cdot 10^{-77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-301}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-258}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (- (/ x y) 2.0)))
   (if (<= t -3.4e-77)
     t_2
     (if (<= t -1.5e-119)
       t_1
       (if (<= t -1.45e-193)
         t_2
         (if (<= t -6.2e-301)
           t_1
           (if (<= t 5.9e-258) (/ 2.0 t) (if (<= t 6.2e+18) t_1 t_2))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -3.4e-77) {
		tmp = t_2;
	} else if (t <= -1.5e-119) {
		tmp = t_1;
	} else if (t <= -1.45e-193) {
		tmp = t_2;
	} else if (t <= -6.2e-301) {
		tmp = t_1;
	} else if (t <= 5.9e-258) {
		tmp = 2.0 / t;
	} else if (t <= 6.2e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: t_2
    real(8) :: tmp
    t_1 = 2.0d0 / (t * z)
    t_2 = (x / y) - 2.0d0
    if (t <= (-3.4d-77)) then
        tmp = t_2
    else if (t <= (-1.5d-119)) then
        tmp = t_1
    else if (t <= (-1.45d-193)) then
        tmp = t_2
    else if (t <= (-6.2d-301)) then
        tmp = t_1
    else if (t <= 5.9d-258) then
        tmp = 2.0d0 / t
    else if (t <= 6.2d+18) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (t * z);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -3.4e-77) {
		tmp = t_2;
	} else if (t <= -1.5e-119) {
		tmp = t_1;
	} else if (t <= -1.45e-193) {
		tmp = t_2;
	} else if (t <= -6.2e-301) {
		tmp = t_1;
	} else if (t <= 5.9e-258) {
		tmp = 2.0 / t;
	} else if (t <= 6.2e+18) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (t * z)
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -3.4e-77:
		tmp = t_2
	elif t <= -1.5e-119:
		tmp = t_1
	elif t <= -1.45e-193:
		tmp = t_2
	elif t <= -6.2e-301:
		tmp = t_1
	elif t <= 5.9e-258:
		tmp = 2.0 / t
	elif t <= 6.2e+18:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -3.4e-77)
		tmp = t_2;
	elseif (t <= -1.5e-119)
		tmp = t_1;
	elseif (t <= -1.45e-193)
		tmp = t_2;
	elseif (t <= -6.2e-301)
		tmp = t_1;
	elseif (t <= 5.9e-258)
		tmp = Float64(2.0 / t);
	elseif (t <= 6.2e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (t * z);
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -3.4e-77)
		tmp = t_2;
	elseif (t <= -1.5e-119)
		tmp = t_1;
	elseif (t <= -1.45e-193)
		tmp = t_2;
	elseif (t <= -6.2e-301)
		tmp = t_1;
	elseif (t <= 5.9e-258)
		tmp = 2.0 / t;
	elseif (t <= 6.2e+18)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -3.4e-77], t$95$2, If[LessEqual[t, -1.5e-119], t$95$1, If[LessEqual[t, -1.45e-193], t$95$2, If[LessEqual[t, -6.2e-301], t$95$1, If[LessEqual[t, 5.9e-258], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 6.2e+18], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.39999999999999983e-77 or -1.5000000000000001e-119 < t < -1.45000000000000003e-193 or 6.2e18 < t

   1. Initial program 80.1%

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

   2. Taylor expanded in t around inf 82.4%

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

   if -3.39999999999999983e-77 < t < -1.5000000000000001e-119 or -1.45000000000000003e-193 < t < -6.20000000000000029e-301 or 5.8999999999999997e-258 < t < 6.2e18

   1. Initial program 96.8%

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

   2. Taylor expanded in z around 0 69.0%

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

   3. Taylor expanded in x around 0 59.0%

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

   if -6.20000000000000029e-301 < t < 5.8999999999999997e-258

   1. Initial program 91.9%

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

   2. Taylor expanded in t around 0 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 69.9%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.4 \cdot 10^{-77}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-119}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-193}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-301}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{elif}\;t \leq 5.9 \cdot 10^{-258}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 6: 79.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := -2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \mathbf{if}\;t \leq -5.5 \cdot 10^{-77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-193}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+18}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)) (t_2 (+ -2.0 (+ (/ 2.0 t) (/ x y)))))
   (if (<= t -5.5e-77)
     t_2
     (if (<= t -7.2e-115)
       t_1
       (if (<= t -1.05e-193) t_2 (if (<= t 6.2e+18) t_1 (- (/ x y) 2.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = -2.0 + ((2.0 / t) + (x / y));
	double tmp;
	if (t <= -5.5e-77) {
		tmp = t_2;
	} else if (t <= -7.2e-115) {
		tmp = t_1;
	} else if (t <= -1.05e-193) {
		tmp = t_2;
	} else if (t <= 6.2e+18) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (2.0d0 + (2.0d0 / z)) / t
    t_2 = (-2.0d0) + ((2.0d0 / t) + (x / y))
    if (t <= (-5.5d-77)) then
        tmp = t_2
    else if (t <= (-7.2d-115)) then
        tmp = t_1
    else if (t <= (-1.05d-193)) then
        tmp = t_2
    else if (t <= 6.2d+18) then
        tmp = t_1
    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 t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = -2.0 + ((2.0 / t) + (x / y));
	double tmp;
	if (t <= -5.5e-77) {
		tmp = t_2;
	} else if (t <= -7.2e-115) {
		tmp = t_1;
	} else if (t <= -1.05e-193) {
		tmp = t_2;
	} else if (t <= 6.2e+18) {
		tmp = t_1;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = -2.0 + ((2.0 / t) + (x / y))
	tmp = 0
	if t <= -5.5e-77:
		tmp = t_2
	elif t <= -7.2e-115:
		tmp = t_1
	elif t <= -1.05e-193:
		tmp = t_2
	elif t <= 6.2e+18:
		tmp = t_1
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	t_2 = Float64(-2.0 + Float64(Float64(2.0 / t) + Float64(x / y)))
	tmp = 0.0
	if (t <= -5.5e-77)
		tmp = t_2;
	elseif (t <= -7.2e-115)
		tmp = t_1;
	elseif (t <= -1.05e-193)
		tmp = t_2;
	elseif (t <= 6.2e+18)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	t_2 = -2.0 + ((2.0 / t) + (x / y));
	tmp = 0.0;
	if (t <= -5.5e-77)
		tmp = t_2;
	elseif (t <= -7.2e-115)
		tmp = t_1;
	elseif (t <= -1.05e-193)
		tmp = t_2;
	elseif (t <= 6.2e+18)
		tmp = t_1;
	else
		tmp = (x / y) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -5.5e-77], t$95$2, If[LessEqual[t, -7.2e-115], t$95$1, If[LessEqual[t, -1.05e-193], t$95$2, If[LessEqual[t, 6.2e+18], t$95$1, N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -5.49999999999999998e-77 or -7.20000000000000018e-115 < t < -1.05e-193

   1. Initial program 86.8%

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

   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%

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

      3. metadata-eval 100.0%

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

      4. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in z around inf 86.6%

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

      1. +-commutative 86.6%

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

      2. associate-*r/ 86.6%

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

      3. metadata-eval 86.6%

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

   7. Simplified 86.6%

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

   if -5.49999999999999998e-77 < t < -7.20000000000000018e-115 or -1.05e-193 < t < 6.2e18

   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 87.5%

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

      1. associate-*r/ 87.5%

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

      2. metadata-eval 87.5%

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

   4. Simplified 87.5%

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

   if 6.2e18 < t

   1. Initial program 64.2%

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

   2. Taylor expanded in t around inf 97.6%

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

4. Final simplification 88.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-77}:\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-115}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-193}:\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 7: 78.6% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-193}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= t -1.0)
     t_1
     (if (<= t -1.8e-193)
       (+ (/ 2.0 t) (/ x y))
       (if (<= t 6.2e+18) (/ (+ 2.0 (/ 2.0 z)) t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.0) {
		tmp = t_1;
	} else if (t <= -1.8e-193) {
		tmp = (2.0 / t) + (x / y);
	} else if (t <= 6.2e+18) {
		tmp = (2.0 + (2.0 / z)) / t;
	} 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 <= (-1.0d0)) then
        tmp = t_1
    else if (t <= (-1.8d-193)) then
        tmp = (2.0d0 / t) + (x / y)
    else if (t <= 6.2d+18) then
        tmp = (2.0d0 + (2.0d0 / z)) / t
    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 <= -1.0) {
		tmp = t_1;
	} else if (t <= -1.8e-193) {
		tmp = (2.0 / t) + (x / y);
	} else if (t <= 6.2e+18) {
		tmp = (2.0 + (2.0 / z)) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if t <= -1.0:
		tmp = t_1
	elif t <= -1.8e-193:
		tmp = (2.0 / t) + (x / y)
	elif t <= 6.2e+18:
		tmp = (2.0 + (2.0 / z)) / t
	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 <= -1.0)
		tmp = t_1;
	elseif (t <= -1.8e-193)
		tmp = Float64(Float64(2.0 / t) + Float64(x / y));
	elseif (t <= 6.2e+18)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	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 <= -1.0)
		tmp = t_1;
	elseif (t <= -1.8e-193)
		tmp = (2.0 / t) + (x / y);
	elseif (t <= 6.2e+18)
		tmp = (2.0 + (2.0 / z)) / t;
	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, -1.0], t$95$1, If[LessEqual[t, -1.8e-193], N[(N[(2.0 / t), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.2e+18], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1 or 6.2e18 < t

   1. Initial program 72.7%

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

   2. Taylor expanded in t around inf 91.6%

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

   if -1 < t < -1.7999999999999999e-193

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 73.2%

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

      1. associate-*r/ 73.2%

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

      2. associate-/l* 73.2%

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

   4. Simplified 73.2%

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

   5. Taylor expanded in t around 0 72.3%

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

   if -1.7999999999999999e-193 < t < 6.2e18

   1. Initial program 96.0%

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

   2. Taylor expanded in t around 0 87.4%

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

      1. associate-*r/ 87.4%

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

      2. metadata-eval 87.4%

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

   4. Simplified 87.4%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-193}:\\ \;\;\;\;\frac{2}{t} + \frac{x}{y}\\ \mathbf{elif}\;t \leq 6.2 \cdot 10^{+18}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 8: 91.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.00032 \lor \neg \left(z \leq 7 \cdot 10^{-9}\right):\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -0.00032) (not (<= z 7e-9)))
   (+ -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 <= -0.00032) || !(z <= 7e-9)) {
		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 <= (-0.00032d0)) .or. (.not. (z <= 7d-9))) 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 <= -0.00032) || !(z <= 7e-9)) {
		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 <= -0.00032) or not (z <= 7e-9):
		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 <= -0.00032) || !(z <= 7e-9))
		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 <= -0.00032) || ~((z <= 7e-9)))
		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, -0.00032], N[Not[LessEqual[z, 7e-9]], $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 < -3.20000000000000026e-4 or 6.9999999999999998e-9 < z

   1. Initial program 77.9%

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

   2. Taylor expanded in t around 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%

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

      3. metadata-eval 100.0%

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

      4. metadata-eval 100.0%

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

   4. Simplified 100.0%

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

   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. +-commutative 100.0%

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

      2. associate-*r/ 100.0%

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

      3. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   if -3.20000000000000026e-4 < z < 6.9999999999999998e-9

   1. Initial program 96.8%

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

   2. Taylor expanded in z around 0 87.5%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.00032 \lor \neg \left(z \leq 7 \cdot 10^{-9}\right):\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \end{array} \]

Alternative 9: 64.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e+59)
   (/ x y)
   (if (<= (/ x y) 1.6e+15) (+ (/ 2.0 t) -2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1e+59) {
		tmp = x / y;
	} else if ((x / y) <= 1.6e+15) {
		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) <= (-1d+59)) then
        tmp = x / y
    else if ((x / y) <= 1.6d+15) 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) <= -1e+59) {
		tmp = x / y;
	} else if ((x / y) <= 1.6e+15) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1e+59:
		tmp = x / y
	elif (x / y) <= 1.6e+15:
		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) <= -1e+59)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1.6e+15)
		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) <= -1e+59)
		tmp = x / y;
	elseif ((x / y) <= 1.6e+15)
		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], -1e+59], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.6e+15], 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) < -9.99999999999999972e58 or 1.6e15 < (/.f64 x y)

   1. Initial program 86.9%

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

   2. Taylor expanded in x around inf 73.5%

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

   if -9.99999999999999972e58 < (/.f64 x y) < 1.6e15

   1. Initial program 87.7%

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

   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%

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

      3. metadata-eval 99.9%

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

      4. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 62.2%

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

      1. +-commutative 62.2%

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

      2. associate-*r/ 62.2%

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

      3. metadata-eval 62.2%

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

   7. Simplified 62.2%

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

   8. Taylor expanded in x around 0 58.7%

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

      1. associate-*r/ 58.7%

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

      2. metadata-eval 58.7%

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

      3. sub-neg 58.7%

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

      4. metadata-eval 58.7%

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

   10. Simplified 58.7%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.6 \cdot 10^{+15}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 10: 64.2% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.6 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2500:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -6.6e+59)
   (/ x y)
   (if (<= (/ x y) 2500.0) (+ (/ 2.0 t) -2.0) (- (/ x y) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -6.6e+59) {
		tmp = x / y;
	} else if ((x / y) <= 2500.0) {
		tmp = (2.0 / t) + -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) <= (-6.6d+59)) then
        tmp = x / y
    else if ((x / y) <= 2500.0d0) then
        tmp = (2.0d0 / t) + (-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) <= -6.6e+59) {
		tmp = x / y;
	} else if ((x / y) <= 2500.0) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = (x / y) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -6.6e+59:
		tmp = x / y
	elif (x / y) <= 2500.0:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = (x / y) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -6.6e+59)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2500.0)
		tmp = Float64(Float64(2.0 / t) + -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) <= -6.6e+59)
		tmp = x / y;
	elseif ((x / y) <= 2500.0)
		tmp = (2.0 / t) + -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], -6.6e+59], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2500.0], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -6.5999999999999999e59

   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 x around inf 79.3%

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

   if -6.5999999999999999e59 < (/.f64 x y) < 2500

   1. Initial program 87.5%

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

   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%

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

      3. metadata-eval 99.9%

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

      4. metadata-eval 99.9%

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

   4. Simplified 99.9%

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

   5. Taylor expanded in z around inf 61.6%

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

      1. +-commutative 61.6%

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

      2. associate-*r/ 61.6%

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

      3. metadata-eval 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in x around 0 58.8%

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

      1. associate-*r/ 58.8%

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

      2. metadata-eval 58.8%

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

      3. sub-neg 58.8%

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

      4. metadata-eval 58.8%

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

   10. Simplified 58.8%

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

   if 2500 < (/.f64 x y)

   1. Initial program 84.5%

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

   2. Taylor expanded in t around inf 67.5%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.6 \cdot 10^{+59}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2500:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]

Alternative 11: 36.1% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1050:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.0) -2.0 (if (<= t 1050.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.0) {
		tmp = -2.0;
	} else if (t <= 1050.0) {
		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 <= (-1.0d0)) then
        tmp = -2.0d0
    else if (t <= 1050.0d0) 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 <= -1.0) {
		tmp = -2.0;
	} else if (t <= 1050.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.0:
		tmp = -2.0
	elif t <= 1050.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.0)
		tmp = -2.0;
	elseif (t <= 1050.0)
		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 <= -1.0)
		tmp = -2.0;
	elseif (t <= 1050.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.0], -2.0, If[LessEqual[t, 1050.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 1050 < t

   1. Initial program 73.2%

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

   2. Taylor expanded in t around inf 89.9%

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

   3. Taylor expanded in x around 0 35.3%

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

   if -1 < t < 1050

   1. Initial program 97.1%

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

   2. Taylor expanded in t around 0 77.0%

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

      1. associate-*r/ 77.0%

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

      2. metadata-eval 77.0%

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

   4. Simplified 77.0%

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

   5. Taylor expanded in z around inf 33.2%

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

4. Final simplification 34.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1050:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 12: 19.9% 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 87.3%

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

2. Taylor expanded in t around inf 51.8%

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

3. Taylor expanded in x around 0 15.9%

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

4. Final simplification 15.9%

   \[\leadsto -2 \]

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 2023297 
(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))))