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

Percentage Accurate: 86.9% → 99.1%

Time: 13.5s

Alternatives: 10

Speedup: 1.3×

• 22.3% 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: 86.9% 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, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.8%

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

2. 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. Simplified 99.9%

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

5. Taylor expanded in t around 0 99.9%

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

   1. associate--l+ 99.9%

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

   2. associate-*r/ 99.9%

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

   3. metadata-eval 99.9%

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

   4. +-commutative 99.9%

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

   5. sub-neg 99.9%

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

   6. metadata-eval 99.9%

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

   7. associate-+r+ 99.9%

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

   8. +-commutative 99.9%

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

   9. +-commutative 99.9%

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

   10. +-commutative 99.9%

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

   11. associate-+l+ 99.9%

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

   12. metadata-eval 99.9%

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

   13. associate-*l/ 99.9%

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

   14. metadata-eval 99.9%

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

   15. associate-*l/ 99.9%

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

   16. associate-/r/ 99.9%

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

   17. associate-/l* 99.9%

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

   18. metadata-eval 99.9%

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

   19. associate-*r/ 99.9%

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

   20. associate-/r/ 99.9%

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

   21. distribute-lft-in 99.9%

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

7. Simplified 100.0%

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

8. Final simplification 100.0%

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

Alternative 2: 81.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := \frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{if}\;z \leq -3.35 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-51}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)) (t_2 (+ (/ x y) (+ -2.0 (/ 2.0 t)))))
   (if (<= z -3.35e-46)
     t_2
     (if (<= z -5.6e-66)
       t_1
       (if (<= z -8e-102) (+ (/ x y) -2.0) (if (<= z 3.6e-51) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -3.35e-46) {
		tmp = t_2;
	} else if (z <= -5.6e-66) {
		tmp = t_1;
	} else if (z <= -8e-102) {
		tmp = (x / y) + -2.0;
	} else if (z <= 3.6e-51) {
		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 + (2.0d0 / z)) / t
    t_2 = (x / y) + ((-2.0d0) + (2.0d0 / t))
    if (z <= (-3.35d-46)) then
        tmp = t_2
    else if (z <= (-5.6d-66)) then
        tmp = t_1
    else if (z <= (-8d-102)) then
        tmp = (x / y) + (-2.0d0)
    else if (z <= 3.6d-51) 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 + (2.0 / z)) / t;
	double t_2 = (x / y) + (-2.0 + (2.0 / t));
	double tmp;
	if (z <= -3.35e-46) {
		tmp = t_2;
	} else if (z <= -5.6e-66) {
		tmp = t_1;
	} else if (z <= -8e-102) {
		tmp = (x / y) + -2.0;
	} else if (z <= 3.6e-51) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = (x / y) + (-2.0 + (2.0 / t))
	tmp = 0
	if z <= -3.35e-46:
		tmp = t_2
	elif z <= -5.6e-66:
		tmp = t_1
	elif z <= -8e-102:
		tmp = (x / y) + -2.0
	elif z <= 3.6e-51:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	t_2 = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)))
	tmp = 0.0
	if (z <= -3.35e-46)
		tmp = t_2;
	elseif (z <= -5.6e-66)
		tmp = t_1;
	elseif (z <= -8e-102)
		tmp = Float64(Float64(x / y) + -2.0);
	elseif (z <= 3.6e-51)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	t_2 = (x / y) + (-2.0 + (2.0 / t));
	tmp = 0.0;
	if (z <= -3.35e-46)
		tmp = t_2;
	elseif (z <= -5.6e-66)
		tmp = t_1;
	elseif (z <= -8e-102)
		tmp = (x / y) + -2.0;
	elseif (z <= 3.6e-51)
		tmp = t_1;
	else
		tmp = t_2;
	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[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.35e-46], t$95$2, If[LessEqual[z, -5.6e-66], t$95$1, If[LessEqual[z, -8e-102], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], If[LessEqual[z, 3.6e-51], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.35e-46 or 3.6e-51 < z

   1. Initial program 73.9%

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

   2. 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. Simplified 100.0%

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

   5. Taylor expanded in z around inf 95.7%

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

      1. sub-neg 95.7%

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

      2. associate-*r/ 95.7%

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

      3. metadata-eval 95.7%

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

      4. metadata-eval 95.7%

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

      5. +-commutative 95.7%

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

   7. Simplified 95.7%

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

   if -3.35e-46 < z < -5.6000000000000001e-66 or -7.99999999999999946e-102 < z < 3.6e-51

   1. Initial program 99.8%

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

   2. Taylor expanded in t around 0 69.2%

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

      1. associate-*r/ 69.2%

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

      2. metadata-eval 69.2%

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

   4. Simplified 69.2%

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

   if -5.6000000000000001e-66 < z < -7.99999999999999946e-102

   1. Initial program 100.0%

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

   2. Taylor expanded in t around inf 94.2%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.35 \cdot 10^{-46}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-66}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-51}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \end{array} \]

Alternative 3: 79.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \frac{2}{z}}{t}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -1.35 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;t \leq 1080000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (/ 2.0 z)) t)) (t_2 (+ (/ x y) -2.0)))
   (if (<= t -1.35e-9)
     t_2
     (if (<= t 3.4e-113)
       t_1
       (if (<= t 4.2e-52)
         (+ (/ x y) (/ 2.0 t))
         (if (<= t 1080000000.0) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + (2.0 / z)) / t;
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t <= -1.35e-9) {
		tmp = t_2;
	} else if (t <= 3.4e-113) {
		tmp = t_1;
	} else if (t <= 4.2e-52) {
		tmp = (x / y) + (2.0 / t);
	} else if (t <= 1080000000.0) {
		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 + (2.0d0 / z)) / t
    t_2 = (x / y) + (-2.0d0)
    if (t <= (-1.35d-9)) then
        tmp = t_2
    else if (t <= 3.4d-113) then
        tmp = t_1
    else if (t <= 4.2d-52) then
        tmp = (x / y) + (2.0d0 / t)
    else if (t <= 1080000000.0d0) 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 + (2.0 / z)) / t;
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t <= -1.35e-9) {
		tmp = t_2;
	} else if (t <= 3.4e-113) {
		tmp = t_1;
	} else if (t <= 4.2e-52) {
		tmp = (x / y) + (2.0 / t);
	} else if (t <= 1080000000.0) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 + (2.0 / z)) / t
	t_2 = (x / y) + -2.0
	tmp = 0
	if t <= -1.35e-9:
		tmp = t_2
	elif t <= 3.4e-113:
		tmp = t_1
	elif t <= 4.2e-52:
		tmp = (x / y) + (2.0 / t)
	elif t <= 1080000000.0:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(2.0 / z)) / t)
	t_2 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -1.35e-9)
		tmp = t_2;
	elseif (t <= 3.4e-113)
		tmp = t_1;
	elseif (t <= 4.2e-52)
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	elseif (t <= 1080000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 + (2.0 / z)) / t;
	t_2 = (x / y) + -2.0;
	tmp = 0.0;
	if (t <= -1.35e-9)
		tmp = t_2;
	elseif (t <= 3.4e-113)
		tmp = t_1;
	elseif (t <= 4.2e-52)
		tmp = (x / y) + (2.0 / t);
	elseif (t <= 1080000000.0)
		tmp = t_1;
	else
		tmp = t_2;
	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[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t, -1.35e-9], t$95$2, If[LessEqual[t, 3.4e-113], t$95$1, If[LessEqual[t, 4.2e-52], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1080000000.0], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.3500000000000001e-9 or 1.08e9 < t

   1. Initial program 71.4%

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

   2. Taylor expanded in t around inf 82.6%

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

   if -1.3500000000000001e-9 < t < 3.4000000000000002e-113 or 4.1999999999999997e-52 < t < 1.08e9

   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 79.9%

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

      1. associate-*r/ 79.9%

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

      2. metadata-eval 79.9%

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

   4. Simplified 79.9%

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

   if 3.4000000000000002e-113 < t < 4.1999999999999997e-52

   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 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. Simplified 99.9%

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

   5. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. +-commutative 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

      7. associate-+r+ 99.9%

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

      8. +-commutative 99.9%

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

      9. +-commutative 99.9%

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

      10. +-commutative 99.9%

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

      11. associate-+l+ 99.9%

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

      12. metadata-eval 99.9%

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

      13. associate-*l/ 99.9%

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

      14. metadata-eval 99.9%

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

      15. associate-*l/ 99.9%

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

      16. associate-/r/ 99.9%

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

      17. associate-/l* 99.9%

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

      18. metadata-eval 99.9%

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

      19. associate-*r/ 99.9%

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

      20. associate-/r/ 99.9%

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

      21. distribute-lft-in 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 75.8%

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

      1. sub-neg 75.8%

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

      2. associate-*r/ 75.8%

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

      3. metadata-eval 75.8%

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

      4. metadata-eval 75.8%

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

   10. Simplified 75.8%

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

   11. Taylor expanded in t around 0 75.8%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{-113}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;t \leq 1080000000:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]

Alternative 4: 52.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -45000000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.027:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -45000000000000.0)
   (/ x y)
   (if (<= (/ x y) -2.5e-28) (/ 2.0 t) (if (<= (/ x y) 0.027) -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -45000000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= -2.5e-28) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 0.027) {
		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) <= (-45000000000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= (-2.5d-28)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 0.027d0) 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) <= -45000000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= -2.5e-28) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 0.027) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -45000000000000.0:
		tmp = x / y
	elif (x / y) <= -2.5e-28:
		tmp = 2.0 / t
	elif (x / y) <= 0.027:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -45000000000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -2.5e-28)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 0.027)
		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) <= -45000000000000.0)
		tmp = x / y;
	elseif ((x / y) <= -2.5e-28)
		tmp = 2.0 / t;
	elseif ((x / y) <= 0.027)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -45000000000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2.5e-28], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 0.027], -2.0, N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -4.5e13 or 0.0269999999999999997 < (/.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 x around inf 73.2%

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

   if -4.5e13 < (/.f64 x y) < -2.5000000000000001e-28

   1. Initial program 88.4%

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

   2. Taylor expanded in t around 0 78.3%

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

      1. associate-*r/ 78.3%

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

      2. metadata-eval 78.3%

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

   4. Simplified 78.3%

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

      1. div-inv 78.1%

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

   6. Applied egg-rr 78.1%

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

   7. Taylor expanded in z around inf 57.1%

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

   if -2.5000000000000001e-28 < (/.f64 x y) < 0.0269999999999999997

   1. Initial program 82.8%

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

   2. Taylor expanded in z around inf 64.3%

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

      1. div-sub 64.4%

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

      2. sub-neg 64.4%

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

      3. *-inverses 64.4%

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

      4. metadata-eval 64.4%

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

   4. Simplified 64.4%

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

   5. Taylor expanded in x around 0 64.1%

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

   6. Taylor expanded in t around inf 43.0%

      \[\leadsto 2 \cdot \color{blue}{-1} \]
3. Recombined 3 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -45000000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.5 \cdot 10^{-28}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 0.027:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 5: 64.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -15500000000000 \lor \neg \left(\frac{x}{y} \leq 9.6 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{1}{t} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -15500000000000.0) (not (<= (/ x y) 9.6e-18)))
   (+ (/ x y) -2.0)
   (* 2.0 (+ (/ 1.0 t) -1.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -15500000000000.0) || !((x / y) <= 9.6e-18)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = 2.0 * ((1.0 / t) + -1.0);
	}
	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) <= (-15500000000000.0d0)) .or. (.not. ((x / y) <= 9.6d-18))) then
        tmp = (x / y) + (-2.0d0)
    else
        tmp = 2.0d0 * ((1.0d0 / t) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -15500000000000.0) || !((x / y) <= 9.6e-18)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = 2.0 * ((1.0 / t) + -1.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -15500000000000.0) or not ((x / y) <= 9.6e-18):
		tmp = (x / y) + -2.0
	else:
		tmp = 2.0 * ((1.0 / t) + -1.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -15500000000000.0) || !(Float64(x / y) <= 9.6e-18))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(2.0 * Float64(Float64(1.0 / t) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -15500000000000.0) || ~(((x / y) <= 9.6e-18)))
		tmp = (x / y) + -2.0;
	else
		tmp = 2.0 * ((1.0 / t) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -15500000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 9.6e-18]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(2.0 * N[(N[(1.0 / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.55e13 or 9.59999999999999976e-18 < (/.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 t around inf 74.0%

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

   if -1.55e13 < (/.f64 x y) < 9.59999999999999976e-18

   1. Initial program 84.2%

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

   2. Taylor expanded in z around inf 65.8%

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

      1. div-sub 65.8%

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

      2. sub-neg 65.8%

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

      3. *-inverses 65.8%

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

      4. metadata-eval 65.8%

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

   4. Simplified 65.8%

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

   5. Taylor expanded in x around 0 64.5%

      \[\leadsto \color{blue}{2 \cdot \left(\frac{1}{t} - 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -15500000000000 \lor \neg \left(\frac{x}{y} \leq 9.6 \cdot 10^{-18}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\frac{1}{t} + -1\right)\\ \end{array} \]

Alternative 6: 91.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-35} \lor \neg \left(z \leq 4.1 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.65e-35) (not (<= z 4.1e-10)))
   (+ (/ x y) (+ -2.0 (/ 2.0 t)))
   (+ (/ x y) (/ 2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.65e-35) || !(z <= 4.1e-10)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (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 <= (-1.65d-35)) .or. (.not. (z <= 4.1d-10))) then
        tmp = (x / y) + ((-2.0d0) + (2.0d0 / t))
    else
        tmp = (x / y) + (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 <= -1.65e-35) || !(z <= 4.1e-10)) {
		tmp = (x / y) + (-2.0 + (2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.65e-35) or not (z <= 4.1e-10):
		tmp = (x / y) + (-2.0 + (2.0 / t))
	else:
		tmp = (x / y) + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.65e-35) || !(z <= 4.1e-10))
		tmp = Float64(Float64(x / y) + Float64(-2.0 + Float64(2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.65e-35) || ~((z <= 4.1e-10)))
		tmp = (x / y) + (-2.0 + (2.0 / t));
	else
		tmp = (x / y) + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.65e-35], N[Not[LessEqual[z, 4.1e-10]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.65e-35 or 4.0999999999999998e-10 < z

   1. Initial program 71.8%

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

   2. Taylor expanded in t around 0 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   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. Simplified 100.0%

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

   5. Taylor expanded in z around inf 98.0%

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

      1. sub-neg 98.0%

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

      2. associate-*r/ 98.0%

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

      3. metadata-eval 98.0%

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

      4. metadata-eval 98.0%

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

      5. +-commutative 98.0%

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

   7. Simplified 98.0%

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

   if -1.65e-35 < z < 4.0999999999999998e-10

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 91.7%

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

4. Final simplification 95.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.65 \cdot 10^{-35} \lor \neg \left(z \leq 4.1 \cdot 10^{-10}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 + \frac{2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]

Alternative 7: 69.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+24} \lor \neg \left(t \leq 0.095\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8e+24) (not (<= t 0.095)))
   (+ (/ x y) -2.0)
   (+ (/ x y) (/ 2.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8e+24) || !(t <= 0.095)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (x / y) + (2.0 / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-8d+24)) .or. (.not. (t <= 0.095d0))) then
        tmp = (x / y) + (-2.0d0)
    else
        tmp = (x / y) + (2.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -8e+24) || !(t <= 0.095)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (x / y) + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -8e+24) or not (t <= 0.095):
		tmp = (x / y) + -2.0
	else:
		tmp = (x / y) + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -8e+24) || !(t <= 0.095))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -8e+24) || ~((t <= 0.095)))
		tmp = (x / y) + -2.0;
	else
		tmp = (x / y) + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -8e+24], N[Not[LessEqual[t, 0.095]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -7.9999999999999999e24 or 0.095000000000000001 < t

   1. Initial program 71.0%

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

   2. Taylor expanded in t around inf 81.2%

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

   if -7.9999999999999999e24 < t < 0.095000000000000001

   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 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   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. Simplified 99.9%

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

   5. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. +-commutative 99.9%

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

      5. sub-neg 99.9%

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

      6. metadata-eval 99.9%

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

      7. associate-+r+ 99.9%

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

      8. +-commutative 99.9%

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

      9. +-commutative 99.9%

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

      10. +-commutative 99.9%

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

      11. associate-+l+ 99.9%

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

      12. metadata-eval 99.9%

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

      13. associate-*l/ 99.9%

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

      14. metadata-eval 99.9%

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

      15. associate-*l/ 99.9%

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

      16. associate-/r/ 99.9%

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

      17. associate-/l* 99.9%

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

      18. metadata-eval 99.9%

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

      19. associate-*r/ 99.9%

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

      20. associate-/r/ 99.9%

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

      21. distribute-lft-in 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 62.4%

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

      1. sub-neg 62.4%

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

      2. associate-*r/ 62.4%

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

      3. metadata-eval 62.4%

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

      4. metadata-eval 62.4%

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

   10. Simplified 62.4%

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

   11. Taylor expanded in t around 0 61.3%

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

4. Final simplification 72.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{+24} \lor \neg \left(t \leq 0.095\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \]

Alternative 8: 59.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{-123} \lor \neg \left(t \leq 3.4 \cdot 10^{-132}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.85e-123) (not (<= t 3.4e-132))) (+ (/ x y) -2.0) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.85e-123) || !(t <= 3.4e-132)) {
		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 <= (-2.85d-123)) .or. (.not. (t <= 3.4d-132))) 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 <= -2.85e-123) || !(t <= 3.4e-132)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.85e-123) or not (t <= 3.4e-132):
		tmp = (x / y) + -2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.85e-123) || !(t <= 3.4e-132))
		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 <= -2.85e-123) || ~((t <= 3.4e-132)))
		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, -2.85e-123], N[Not[LessEqual[t, 3.4e-132]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.85000000000000014e-123 or 3.39999999999999983e-132 < t

   1. Initial program 79.1%

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

   2. Taylor expanded in t around inf 70.3%

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

   if -2.85000000000000014e-123 < t < 3.39999999999999983e-132

   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 88.7%

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

      1. associate-*r/ 88.7%

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

      2. metadata-eval 88.7%

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

   4. Simplified 88.7%

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

      1. div-inv 88.7%

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

   6. Applied egg-rr 88.7%

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

   7. Taylor expanded in z around inf 45.5%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.85 \cdot 10^{-123} \lor \neg \left(t \leq 3.4 \cdot 10^{-132}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]

Alternative 9: 37.3% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-8}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 0.095:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -8.2e-8) -2.0 (if (<= t 0.095) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -8.2e-8) {
		tmp = -2.0;
	} else if (t <= 0.095) {
		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 <= (-8.2d-8)) then
        tmp = -2.0d0
    else if (t <= 0.095d0) 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 <= -8.2e-8) {
		tmp = -2.0;
	} else if (t <= 0.095) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -8.2e-8:
		tmp = -2.0
	elif t <= 0.095:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -8.2e-8)
		tmp = -2.0;
	elseif (t <= 0.095)
		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 <= -8.2e-8)
		tmp = -2.0;
	elseif (t <= 0.095)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -8.2e-8], -2.0, If[LessEqual[t, 0.095], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -8.20000000000000063e-8 or 0.095000000000000001 < t

   1. Initial program 72.4%

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

   2. Taylor expanded in z around inf 80.6%

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

      1. div-sub 80.6%

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

      2. sub-neg 80.6%

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

      3. *-inverses 80.6%

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

      4. metadata-eval 80.6%

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

   4. Simplified 80.6%

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

   5. Taylor expanded in x around 0 37.1%

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

   6. Taylor expanded in t around inf 36.6%

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

   if -8.20000000000000063e-8 < t < 0.095000000000000001

   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 74.4%

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

      1. associate-*r/ 74.4%

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

      2. metadata-eval 74.4%

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

   4. Simplified 74.4%

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

      1. div-inv 74.4%

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

   6. Applied egg-rr 74.4%

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

   7. Taylor expanded in z around inf 36.3%

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

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{-8}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 0.095:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 10: 20.1% 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 83.8%

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

2. Taylor expanded in z around inf 73.1%

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

   1. div-sub 73.1%

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

   2. sub-neg 73.1%

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

   3. *-inverses 73.1%

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

   4. metadata-eval 73.1%

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

4. Simplified 73.1%

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

5. Taylor expanded in x around 0 37.3%

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

6. Taylor expanded in t around inf 22.4%

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

7. Final simplification 22.4%

   \[\leadsto -2 \]

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 2023275 
(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))))