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

Percentage Accurate: 86.7% → 99.0%

Time: 9.5s

Alternatives: 11

Speedup: 1.1×

• 23.5% 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: 86.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.4%

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

2. Taylor expanded in t around 0 98.4%

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

   1. associate--l+ 98.4%

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

   2. *-commutative 98.4%

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

   3. associate-*r/ 98.4%

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

   4. metadata-eval 98.4%

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

   5. *-commutative 98.4%

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

4. Simplified 98.4%

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

5. Final simplification 98.4%

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

Alternative 2: 70.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + \frac{2}{t}\\ \mathbf{if}\;\frac{x}{y} \leq -3300000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq 3.2 \cdot 10^{-39}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;\frac{x}{y} \leq 68000000000:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) (/ 2.0 t))))
   (if (<= (/ x y) -3300000.0)
     t_1
     (if (<= (/ x y) 3.2e-39)
       (+ (/ 2.0 t) -2.0)
       (if (<= (/ x y) 68000000000.0) (/ 2.0 (* t z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if ((x / y) <= -3300000.0) {
		tmp = t_1;
	} else if ((x / y) <= 3.2e-39) {
		tmp = (2.0 / t) + -2.0;
	} else if ((x / y) <= 68000000000.0) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (2.0d0 / t)
    if ((x / y) <= (-3300000.0d0)) then
        tmp = t_1
    else if ((x / y) <= 3.2d-39) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else if ((x / y) <= 68000000000.0d0) then
        tmp = 2.0d0 / (t * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + (2.0 / t);
	double tmp;
	if ((x / y) <= -3300000.0) {
		tmp = t_1;
	} else if ((x / y) <= 3.2e-39) {
		tmp = (2.0 / t) + -2.0;
	} else if ((x / y) <= 68000000000.0) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + (2.0 / t)
	tmp = 0
	if (x / y) <= -3300000.0:
		tmp = t_1
	elif (x / y) <= 3.2e-39:
		tmp = (2.0 / t) + -2.0
	elif (x / y) <= 68000000000.0:
		tmp = 2.0 / (t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + Float64(2.0 / t))
	tmp = 0.0
	if (Float64(x / y) <= -3300000.0)
		tmp = t_1;
	elseif (Float64(x / y) <= 3.2e-39)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	elseif (Float64(x / y) <= 68000000000.0)
		tmp = Float64(2.0 / Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + (2.0 / t);
	tmp = 0.0;
	if ((x / y) <= -3300000.0)
		tmp = t_1;
	elseif ((x / y) <= 3.2e-39)
		tmp = (2.0 / t) + -2.0;
	elseif ((x / y) <= 68000000000.0)
		tmp = 2.0 / (t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -3300000.0], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 3.2e-39], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 68000000000.0], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -3.3e6 or 6.8e10 < (/.f64 x y)

   1. Initial program 80.3%

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

   2. Taylor expanded in t around 0 96.8%

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

      1. associate--l+ 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*r/ 96.8%

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

      4. metadata-eval 96.8%

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

      5. *-commutative 96.8%

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

   4. Simplified 96.8%

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

   5. Taylor expanded in z around inf 85.7%

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

      1. +-commutative 85.7%

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

      2. associate-*r/ 85.7%

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

      3. metadata-eval 85.7%

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

      4. associate--l+ 85.7%

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

      5. sub-neg 85.7%

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

      6. metadata-eval 85.7%

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

      7. +-commutative 85.7%

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

   7. Simplified 85.7%

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

   8. Taylor expanded in t around 0 84.8%

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

   if -3.3e6 < (/.f64 x y) < 3.1999999999999998e-39

   1. Initial program 90.5%

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

   2. Taylor expanded in t around 0 99.9%

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

      1. associate--l+ 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

   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 x around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate-/l/ 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. metadata-eval 99.9%

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

      9. +-commutative 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-*l/ 99.9%

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

      12. associate-*r/ 99.8%

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

      13. metadata-eval 99.8%

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

      14. associate-*r/ 99.8%

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

      15. distribute-rgt-in 99.8%

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

      16. +-commutative 99.8%

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

      17. associate-*l/ 99.9%

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

      18. associate-*r/ 99.9%

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

      19. *-lft-identity 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 65.3%

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

      1. associate-*r/ 65.3%

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

      2. metadata-eval 65.3%

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

      3. sub-neg 65.3%

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

      4. metadata-eval 65.3%

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

   10. Simplified 65.3%

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

   if 3.1999999999999998e-39 < (/.f64 x y) < 6.8e10

   1. Initial program 89.7%

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

   2. Taylor expanded in t around 0 99.7%

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

      1. associate--l+ 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r/ 99.7%

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

      4. metadata-eval 99.7%

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

      5. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in z around 0 71.2%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3300000:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.2 \cdot 10^{-39}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;\frac{x}{y} \leq 68000000000:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \end{array} \]

Alternative 3: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.2 \cdot 10^{+20} \lor \neg \left(\frac{x}{y} \leq 2800000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5.2e+20) (not (<= (/ x y) 2800000000000.0)))
   (+ (/ x y) (/ 2.0 t))
   (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5.2e+20) || !((x / y) <= 2800000000000.0)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-5.2d+20)) .or. (.not. ((x / y) <= 2800000000000.0d0))) then
        tmp = (x / y) + (2.0d0 / t)
    else
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5.2e+20) || !((x / y) <= 2800000000000.0)) {
		tmp = (x / y) + (2.0 / t);
	} else {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5.2e+20) or not ((x / y) <= 2800000000000.0):
		tmp = (x / y) + (2.0 / t)
	else:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5.2e+20) || !(Float64(x / y) <= 2800000000000.0))
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5.2e+20) || ~(((x / y) <= 2800000000000.0)))
		tmp = (x / y) + (2.0 / t);
	else
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5.2e+20], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2800000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.2e20 or 2.8e12 < (/.f64 x y)

   1. Initial program 79.7%

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

   2. Taylor expanded in t around 0 96.6%

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

      1. associate--l+ 96.6%

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

      2. *-commutative 96.6%

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

      3. associate-*r/ 96.6%

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

      4. metadata-eval 96.6%

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

      5. *-commutative 96.6%

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

   4. Simplified 96.6%

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

   5. Taylor expanded in z around inf 88.6%

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

      1. +-commutative 88.6%

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

      2. associate-*r/ 88.6%

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

      3. metadata-eval 88.6%

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

      4. associate--l+ 88.6%

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

      5. sub-neg 88.6%

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

      6. metadata-eval 88.6%

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

      7. +-commutative 88.6%

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

   7. Simplified 88.6%

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

   8. Taylor expanded in t around 0 88.5%

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

   if -5.2e20 < (/.f64 x y) < 2.8e12

   1. Initial program 90.3%

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

   2. Taylor expanded in t around 0 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. *-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

   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 x around 0 96.5%

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

      1. sub-neg 96.5%

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

      2. +-commutative 96.5%

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

      3. associate-*r/ 96.5%

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

      4. metadata-eval 96.5%

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

      5. associate-/l/ 96.6%

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

      6. associate-*r/ 96.6%

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

      7. metadata-eval 96.6%

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

      8. metadata-eval 96.6%

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

      9. +-commutative 96.6%

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

      10. metadata-eval 96.6%

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

      11. associate-*l/ 96.6%

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

      12. associate-*r/ 96.5%

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

      13. metadata-eval 96.5%

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

      14. associate-*r/ 96.5%

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

      15. distribute-rgt-in 96.5%

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

      16. +-commutative 96.5%

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

      17. associate-*l/ 96.6%

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

      18. associate-*r/ 96.6%

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

      19. *-lft-identity 96.6%

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

   7. Simplified 96.6%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.2 \cdot 10^{+20} \lor \neg \left(\frac{x}{y} \leq 2800000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 4: 89.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -9.9 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 3200000000000:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -9.9e+20)
   (+ (/ x y) (/ 2.0 t))
   (if (<= (/ x y) 3200000000000.0)
     (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))
     (+ (/ x y) (+ (/ 2.0 t) -2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -9.9e+20) {
		tmp = (x / y) + (2.0 / t);
	} else if ((x / y) <= 3200000000000.0) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-9.9d+20)) then
        tmp = (x / y) + (2.0d0 / t)
    else if ((x / y) <= 3200000000000.0d0) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    else
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -9.9e+20) {
		tmp = (x / y) + (2.0 / t);
	} else if ((x / y) <= 3200000000000.0) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -9.9e+20:
		tmp = (x / y) + (2.0 / t)
	elif (x / y) <= 3200000000000.0:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	else:
		tmp = (x / y) + ((2.0 / t) + -2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -9.9e+20)
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	elseif (Float64(x / y) <= 3200000000000.0)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -9.9e+20)
		tmp = (x / y) + (2.0 / t);
	elseif ((x / y) <= 3200000000000.0)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	else
		tmp = (x / y) + ((2.0 / t) + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -9.9e+20], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3200000000000.0], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.9e20

   1. Initial program 77.8%

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

   2. Taylor expanded in t around 0 94.9%

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

      1. associate--l+ 94.9%

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

      2. *-commutative 94.9%

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

      3. associate-*r/ 94.9%

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

      4. metadata-eval 94.9%

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

      5. *-commutative 94.9%

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

   4. Simplified 94.9%

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

   5. Taylor expanded in z around inf 89.5%

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

      1. +-commutative 89.5%

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

      2. associate-*r/ 89.5%

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

      3. metadata-eval 89.5%

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

      4. associate--l+ 89.5%

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

      5. sub-neg 89.5%

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

      6. metadata-eval 89.5%

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

      7. +-commutative 89.5%

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

   7. Simplified 89.5%

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

   8. Taylor expanded in t around 0 89.5%

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

   if -9.9e20 < (/.f64 x y) < 3.2e12

   1. Initial program 90.3%

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

   2. Taylor expanded in t around 0 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. *-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

   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 x around 0 96.5%

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

      1. sub-neg 96.5%

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

      2. +-commutative 96.5%

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

      3. associate-*r/ 96.5%

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

      4. metadata-eval 96.5%

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

      5. associate-/l/ 96.6%

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

      6. associate-*r/ 96.6%

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

      7. metadata-eval 96.6%

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

      8. metadata-eval 96.6%

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

      9. +-commutative 96.6%

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

      10. metadata-eval 96.6%

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

      11. associate-*l/ 96.6%

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

      12. associate-*r/ 96.5%

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

      13. metadata-eval 96.5%

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

      14. associate-*r/ 96.5%

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

      15. distribute-rgt-in 96.5%

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

      16. +-commutative 96.5%

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

      17. associate-*l/ 96.6%

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

      18. associate-*r/ 96.6%

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

      19. *-lft-identity 96.6%

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

   7. Simplified 96.6%

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

   if 3.2e12 < (/.f64 x y)

   1. Initial program 81.5%

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

   2. Taylor expanded in t around 0 98.3%

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

      1. associate--l+ 98.3%

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

      2. *-commutative 98.3%

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

      3. associate-*r/ 98.3%

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

      4. metadata-eval 98.3%

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

      5. *-commutative 98.3%

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

   4. Simplified 98.3%

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

   5. Taylor expanded in z around inf 87.7%

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

      1. +-commutative 87.7%

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

      2. associate-*r/ 87.7%

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

      3. metadata-eval 87.7%

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

      4. associate--l+ 87.7%

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

      5. sub-neg 87.7%

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

      6. metadata-eval 87.7%

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

      7. +-commutative 87.7%

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

   7. Simplified 87.7%

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

4. Final simplification 92.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -9.9 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 3200000000000:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \end{array} \]

Alternative 5: 91.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7000000:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 1000000000000:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -7000000.0)
   (+ (/ x y) (/ 2.0 (* t z)))
   (if (<= (/ x y) 1000000000000.0)
     (+ -2.0 (/ (+ 2.0 (/ 2.0 z)) t))
     (+ (/ x y) (+ (/ 2.0 t) -2.0)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -7000000.0) {
		tmp = (x / y) + (2.0 / (t * z));
	} else if ((x / y) <= 1000000000000.0) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-7000000.0d0)) then
        tmp = (x / y) + (2.0d0 / (t * z))
    else if ((x / y) <= 1000000000000.0d0) then
        tmp = (-2.0d0) + ((2.0d0 + (2.0d0 / z)) / t)
    else
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -7000000.0) {
		tmp = (x / y) + (2.0 / (t * z));
	} else if ((x / y) <= 1000000000000.0) {
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	} else {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -7000000.0:
		tmp = (x / y) + (2.0 / (t * z))
	elif (x / y) <= 1000000000000.0:
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t)
	else:
		tmp = (x / y) + ((2.0 / t) + -2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -7000000.0)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	elseif (Float64(x / y) <= 1000000000000.0)
		tmp = Float64(-2.0 + Float64(Float64(2.0 + Float64(2.0 / z)) / t));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -7000000.0)
		tmp = (x / y) + (2.0 / (t * z));
	elseif ((x / y) <= 1000000000000.0)
		tmp = -2.0 + ((2.0 + (2.0 / z)) / t);
	else
		tmp = (x / y) + ((2.0 / t) + -2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -7000000.0], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1000000000000.0], N[(-2.0 + N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -7e6

   1. Initial program 79.3%

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

   2. Taylor expanded in z around 0 87.8%

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

   if -7e6 < (/.f64 x y) < 1e12

   1. Initial program 90.4%

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

   2. Taylor expanded in t around 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. *-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

   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 x around 0 99.1%

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

      1. sub-neg 99.1%

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

      2. +-commutative 99.1%

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

      3. associate-*r/ 99.1%

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

      4. metadata-eval 99.1%

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

      5. associate-/l/ 99.1%

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

      6. associate-*r/ 99.1%

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

      7. metadata-eval 99.1%

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

      8. metadata-eval 99.1%

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

      9. +-commutative 99.1%

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

      10. metadata-eval 99.1%

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

      11. associate-*l/ 99.1%

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

      12. associate-*r/ 99.0%

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

      13. metadata-eval 99.0%

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

      14. associate-*r/ 99.0%

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

      15. distribute-rgt-in 99.0%

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

      16. +-commutative 99.0%

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

      17. associate-*l/ 99.1%

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

      18. associate-*r/ 99.1%

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

      19. *-lft-identity 99.1%

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

   7. Simplified 99.1%

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

   if 1e12 < (/.f64 x y)

   1. Initial program 81.5%

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

   2. Taylor expanded in t around 0 98.3%

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

      1. associate--l+ 98.3%

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

      2. *-commutative 98.3%

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

      3. associate-*r/ 98.3%

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

      4. metadata-eval 98.3%

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

      5. *-commutative 98.3%

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

   4. Simplified 98.3%

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

   5. Taylor expanded in z around inf 87.7%

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

      1. +-commutative 87.7%

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

      2. associate-*r/ 87.7%

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

      3. metadata-eval 87.7%

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

      4. associate--l+ 87.7%

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

      5. sub-neg 87.7%

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

      6. metadata-eval 87.7%

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

      7. +-commutative 87.7%

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

   7. Simplified 87.7%

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

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7000000:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \mathbf{elif}\;\frac{x}{y} \leq 1000000000000:\\ \;\;\;\;-2 + \frac{2 + \frac{2}{z}}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \end{array} \]

Alternative 6: 52.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -26500000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -3.3 \cdot 10^{-121}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.3 \cdot 10^{-33}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -26500000.0)
   (/ x y)
   (if (<= (/ x y) -3.3e-121)
     (/ 2.0 t)
     (if (<= (/ x y) 3.3e-33) -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -26500000.0) {
		tmp = x / y;
	} else if ((x / y) <= -3.3e-121) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 3.3e-33) {
		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) <= (-26500000.0d0)) then
        tmp = x / y
    else if ((x / y) <= (-3.3d-121)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 3.3d-33) 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) <= -26500000.0) {
		tmp = x / y;
	} else if ((x / y) <= -3.3e-121) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 3.3e-33) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -26500000.0:
		tmp = x / y
	elif (x / y) <= -3.3e-121:
		tmp = 2.0 / t
	elif (x / y) <= 3.3e-33:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -26500000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -3.3e-121)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 3.3e-33)
		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) <= -26500000.0)
		tmp = x / y;
	elseif ((x / y) <= -3.3e-121)
		tmp = 2.0 / t;
	elseif ((x / y) <= 3.3e-33)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -26500000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -3.3e-121], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3.3e-33], -2.0, N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.65e7 or 3.3000000000000003e-33 < (/.f64 x y)

   1. Initial program 80.7%

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

   2. Taylor expanded in x around inf 71.8%

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

   if -2.65e7 < (/.f64 x y) < -3.3000000000000001e-121

   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 99.8%

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

      1. associate--l+ 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r/ 99.8%

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

      4. metadata-eval 99.8%

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

      5. *-commutative 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around inf 56.9%

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

      1. +-commutative 56.9%

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

      2. associate-*r/ 56.9%

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

      3. metadata-eval 56.9%

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

      4. associate--l+ 56.9%

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

      5. sub-neg 56.9%

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

      6. metadata-eval 56.9%

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

      7. +-commutative 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in t around 0 39.8%

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

   9. Taylor expanded in x around 0 39.3%

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

   if -3.3000000000000001e-121 < (/.f64 x y) < 3.3000000000000003e-33

   1. Initial program 89.1%

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

   2. Taylor expanded in t around 0 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. *-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

   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 x around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate-/l/ 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. metadata-eval 99.9%

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

      9. +-commutative 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-*l/ 99.9%

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

      12. associate-*r/ 99.9%

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

      13. metadata-eval 99.9%

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

      14. associate-*r/ 99.9%

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

      15. distribute-rgt-in 99.9%

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

      16. +-commutative 99.9%

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

      17. associate-*l/ 99.9%

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

      18. associate-*r/ 99.9%

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

      19. *-lft-identity 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in t around inf 45.0%

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

4. Final simplification 58.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -26500000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -3.3 \cdot 10^{-121}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 3.3 \cdot 10^{-33}:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 7: 65.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4300000 \lor \neg \left(\frac{x}{y} \leq 1.22 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4300000.0) (not (<= (/ x y) 1.22e-14)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4300000.0) || !((x / y) <= 1.22e-14)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-4300000.0d0)) .or. (.not. ((x / y) <= 1.22d-14))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4300000.0) || !((x / y) <= 1.22e-14)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4300000.0) or not ((x / y) <= 1.22e-14):
		tmp = x / y
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4300000.0) || !(Float64(x / y) <= 1.22e-14))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -4300000.0) || ~(((x / y) <= 1.22e-14)))
		tmp = x / y;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4300000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.22e-14]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.3e6 or 1.21999999999999994e-14 < (/.f64 x y)

   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 x around inf 73.9%

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

   if -4.3e6 < (/.f64 x y) < 1.21999999999999994e-14

   1. Initial program 90.9%

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

   2. Taylor expanded in t around 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. *-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

   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 x around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate-/l/ 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. metadata-eval 99.9%

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

      9. +-commutative 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-*l/ 99.9%

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

      12. associate-*r/ 99.8%

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

      13. metadata-eval 99.8%

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

      14. associate-*r/ 99.8%

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

      15. distribute-rgt-in 99.8%

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

      16. +-commutative 99.8%

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

      17. associate-*l/ 99.9%

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

      18. associate-*r/ 99.9%

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

      19. *-lft-identity 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 63.9%

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

      1. associate-*r/ 63.9%

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

      2. metadata-eval 63.9%

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

      3. sub-neg 63.9%

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

      4. metadata-eval 63.9%

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

   10. Simplified 63.9%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4300000 \lor \neg \left(\frac{x}{y} \leq 1.22 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]

Alternative 8: 66.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7400000 \lor \neg \left(\frac{x}{y} \leq 1.22 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -7400000.0) (not (<= (/ x y) 1.22e-14)))
   (- (/ x y) 2.0)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -7400000.0) || !((x / y) <= 1.22e-14)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-7400000.0d0)) .or. (.not. ((x / y) <= 1.22d-14))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -7400000.0) || !((x / y) <= 1.22e-14)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -7400000.0) or not ((x / y) <= 1.22e-14):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -7400000.0) || !(Float64(x / y) <= 1.22e-14))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -7400000.0) || ~(((x / y) <= 1.22e-14)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -7400000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.22e-14]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -7.4e6 or 1.21999999999999994e-14 < (/.f64 x y)

   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 75.2%

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

   if -7.4e6 < (/.f64 x y) < 1.21999999999999994e-14

   1. Initial program 90.9%

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

   2. Taylor expanded in t around 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. *-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

   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 x around 0 99.9%

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

      1. sub-neg 99.9%

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

      2. +-commutative 99.9%

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. associate-/l/ 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

      8. metadata-eval 99.9%

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

      9. +-commutative 99.9%

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

      10. metadata-eval 99.9%

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

      11. associate-*l/ 99.9%

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

      12. associate-*r/ 99.8%

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

      13. metadata-eval 99.8%

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

      14. associate-*r/ 99.8%

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

      15. distribute-rgt-in 99.8%

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

      16. +-commutative 99.8%

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

      17. associate-*l/ 99.9%

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

      18. associate-*r/ 99.9%

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

      19. *-lft-identity 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 63.9%

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

      1. associate-*r/ 63.9%

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

      2. metadata-eval 63.9%

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

      3. sub-neg 63.9%

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

      4. metadata-eval 63.9%

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

   10. Simplified 63.9%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7400000 \lor \neg \left(\frac{x}{y} \leq 1.22 \cdot 10^{-14}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]

Alternative 9: 80.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-11} \lor \neg \left(t \leq 1.42 \cdot 10^{+24}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -3.2e-11) (not (<= t 1.42e+24)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e-11) || !(t <= 1.42e+24)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-3.2d-11)) .or. (.not. (t <= 1.42d+24))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -3.2e-11) || !(t <= 1.42e+24)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -3.2e-11) or not (t <= 1.42e+24):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -3.2e-11) || !(t <= 1.42e+24))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -3.2e-11) || ~((t <= 1.42e+24)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -3.2e-11], N[Not[LessEqual[t, 1.42e+24]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.19999999999999994e-11 or 1.42e24 < t

   1. Initial program 74.9%

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

   2. Taylor expanded in t around inf 84.3%

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

   if -3.19999999999999994e-11 < t < 1.42e24

   1. Initial program 96.5%

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

   2. Taylor expanded in t around 0 72.7%

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

      1. associate-*r/ 72.7%

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

      2. metadata-eval 72.7%

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

   4. Simplified 72.7%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{-11} \lor \neg \left(t \leq 1.42 \cdot 10^{+24}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 10: 36.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -375:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -375.0) -2.0 (if (<= t 1.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -375.0) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		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 <= (-375.0d0)) then
        tmp = -2.0d0
    else if (t <= 1.0d0) 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 <= -375.0) {
		tmp = -2.0;
	} else if (t <= 1.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -375.0:
		tmp = -2.0
	elif t <= 1.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -375.0)
		tmp = -2.0;
	elseif (t <= 1.0)
		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 <= -375.0)
		tmp = -2.0;
	elseif (t <= 1.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -375.0], -2.0, If[LessEqual[t, 1.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -375 or 1 < t

   1. Initial program 75.6%

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

   2. Taylor expanded in t around 0 99.9%

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

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

      3. associate-*r/ 99.9%

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

      4. metadata-eval 99.9%

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

      5. *-commutative 99.9%

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

   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 x around 0 53.6%

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

      1. sub-neg 53.6%

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

      2. +-commutative 53.6%

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

      3. associate-*r/ 53.6%

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

      4. metadata-eval 53.6%

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

      5. associate-/l/ 53.6%

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

      6. associate-*r/ 53.6%

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

      7. metadata-eval 53.6%

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

      8. metadata-eval 53.6%

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

      9. +-commutative 53.6%

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

      10. metadata-eval 53.6%

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

      11. associate-*l/ 53.6%

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

      12. associate-*r/ 53.6%

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

      13. metadata-eval 53.6%

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

      14. associate-*r/ 53.6%

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

      15. distribute-rgt-in 53.6%

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

      16. +-commutative 53.6%

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

      17. associate-*l/ 53.6%

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

      18. associate-*r/ 53.6%

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

      19. *-lft-identity 53.6%

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

   7. Simplified 53.6%

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

   8. Taylor expanded in t around inf 35.4%

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

   if -375 < t < 1

   1. Initial program 96.4%

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

   2. Taylor expanded in t around 0 96.6%

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

      1. associate--l+ 96.6%

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

      2. *-commutative 96.6%

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

      3. associate-*r/ 96.6%

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

      4. metadata-eval 96.6%

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

      5. *-commutative 96.6%

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

   4. Simplified 96.6%

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

   5. Taylor expanded in z around inf 64.4%

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

      1. +-commutative 64.4%

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

      2. associate-*r/ 64.4%

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

      3. metadata-eval 64.4%

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

      4. associate--l+ 64.4%

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

      5. sub-neg 64.4%

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

      6. metadata-eval 64.4%

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

      7. +-commutative 64.4%

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

   7. Simplified 64.4%

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

   8. Taylor expanded in t around 0 62.9%

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

   9. Taylor expanded in x around 0 35.1%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -375:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 1:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 11: 19.8% 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 85.4%

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

2. Taylor expanded in t around 0 98.4%

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

   1. associate--l+ 98.4%

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

   2. *-commutative 98.4%

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

   3. associate-*r/ 98.4%

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

   4. metadata-eval 98.4%

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

   5. *-commutative 98.4%

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

4. Simplified 98.4%

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

5. Taylor expanded in x around 0 62.7%

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

   1. sub-neg 62.7%

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

   2. +-commutative 62.7%

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

   3. associate-*r/ 62.7%

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

   4. metadata-eval 62.7%

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

   5. associate-/l/ 62.8%

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

   6. associate-*r/ 62.8%

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

   7. metadata-eval 62.8%

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

   8. metadata-eval 62.8%

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

   9. +-commutative 62.8%

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

   10. metadata-eval 62.8%

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

   11. associate-*l/ 62.8%

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

   12. associate-*r/ 62.7%

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

   13. metadata-eval 62.7%

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

   14. associate-*r/ 62.7%

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

   15. distribute-rgt-in 62.7%

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

   16. +-commutative 62.7%

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

   17. associate-*l/ 62.8%

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

   18. associate-*r/ 62.8%

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

   19. *-lft-identity 62.8%

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

7. Simplified 62.8%

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

8. Taylor expanded in t around inf 20.1%

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

9. Final simplification 20.1%

   \[\leadsto -2 \]

Developer target: 99.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023301 
(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))))