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

Percentage Accurate: 86.5% → 99.2%

Time: 15.6s

Alternatives: 14

Speedup: 1.3×

• 23.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.5% 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: 99.2% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.8%

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

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 x around 0 99.9%

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

   1. +-commutative 99.9%

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

   2. distribute-lft-out 99.9%

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

   3. fma-def 99.9%

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

   4. +-commutative 99.9%

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

   5. fma-def 99.9%

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

   6. distribute-lft-out 99.9%

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

   7. associate--l+ 99.9%

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

   8. sub-neg 99.9%

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

   9. metadata-eval 99.9%

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

   10. +-commutative 99.9%

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

7. Simplified 99.9%

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

8. Final simplification 99.9%

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

Alternative 2: 97.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+20} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{\frac{2}{z}}{t}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+20) (not (<= (/ x y) 2e-17)))
   (+ (/ x y) (/ (+ 2.0 (* 2.0 z)) (* z t)))
   (+ -2.0 (+ (/ 2.0 t) (/ (/ 2.0 z) t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+20) || !((x / y) <= 2e-17)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = -2.0 + ((2.0 / t) + ((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) <= (-5d+20)) .or. (.not. ((x / y) <= 2d-17))) then
        tmp = (x / y) + ((2.0d0 + (2.0d0 * z)) / (z * t))
    else
        tmp = (-2.0d0) + ((2.0d0 / t) + ((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) <= -5e+20) || !((x / y) <= 2e-17)) {
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	} else {
		tmp = -2.0 + ((2.0 / t) + ((2.0 / z) / t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+20) or not ((x / y) <= 2e-17):
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t))
	else:
		tmp = -2.0 + ((2.0 / t) + ((2.0 / z) / t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+20) || !(Float64(x / y) <= 2e-17))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 + Float64(2.0 * z)) / Float64(z * t)));
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) + Float64(Float64(2.0 / z) / t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e+20) || ~(((x / y) <= 2e-17)))
		tmp = (x / y) + ((2.0 + (2.0 * z)) / (z * t));
	else
		tmp = -2.0 + ((2.0 / t) + ((2.0 / z) / t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+20], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-17]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 + N[(2.0 * z), $MachinePrecision]), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5e20 or 2.00000000000000014e-17 < (/.f64 x y)

   1. Initial program 92.2%

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

   2. Taylor expanded in t around 0 99.6%

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

   if -5e20 < (/.f64 x y) < 2.00000000000000014e-17

   1. Initial program 89.7%

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

   2. Taylor expanded in t around 0 99.9%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   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 x around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. distribute-lft-out 99.9%

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

      3. fma-def 99.9%

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

      4. +-commutative 99.9%

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

      5. fma-def 99.9%

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

      6. distribute-lft-out 99.9%

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

      7. associate--l+ 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

      10. +-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{\left(2 \cdot \frac{1}{t} + 2 \cdot \frac{1}{t \cdot z}\right) - 2} \]
   9. 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. associate-*r/ 99.9%

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

      3. metadata-eval 99.9%

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

      4. associate-*r/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. metadata-eval 99.9%

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

   10. Simplified 99.9%

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

   11. Taylor expanded in z around 0 99.9%

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

       1. distribute-lft-out 99.9%

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

       2. +-commutative 99.9%

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

       3. distribute-lft-out 99.9%

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

       4. associate-*r/ 99.9%

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

       5. metadata-eval 99.9%

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

       6. associate-*r/ 99.9%

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

       7. metadata-eval 99.9%

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

       8. associate-/l/ 99.9%

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

   13. Simplified 99.9%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+20} \lor \neg \left(\frac{x}{y} \leq 2 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2 + 2 \cdot z}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{\frac{2}{z}}{t}\right)\\ \end{array} \]

Alternative 3: 49.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -205000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -6.3 \cdot 10^{-81}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 9.6 \cdot 10^{-246}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 7.5 \cdot 10^{+90}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -205000000000.0)
   (/ x y)
   (if (<= (/ x y) -6.3e-81)
     (/ 2.0 t)
     (if (<= (/ x y) 9.6e-246)
       -2.0
       (if (<= (/ x y) 7.5e+90) (/ 2.0 t) (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -205000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= -6.3e-81) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 9.6e-246) {
		tmp = -2.0;
	} else if ((x / y) <= 7.5e+90) {
		tmp = 2.0 / t;
	} 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) <= (-205000000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= (-6.3d-81)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 9.6d-246) then
        tmp = -2.0d0
    else if ((x / y) <= 7.5d+90) then
        tmp = 2.0d0 / t
    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) <= -205000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= -6.3e-81) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 9.6e-246) {
		tmp = -2.0;
	} else if ((x / y) <= 7.5e+90) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -205000000000.0:
		tmp = x / y
	elif (x / y) <= -6.3e-81:
		tmp = 2.0 / t
	elif (x / y) <= 9.6e-246:
		tmp = -2.0
	elif (x / y) <= 7.5e+90:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -205000000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -6.3e-81)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 9.6e-246)
		tmp = -2.0;
	elseif (Float64(x / y) <= 7.5e+90)
		tmp = Float64(2.0 / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -205000000000.0)
		tmp = x / y;
	elseif ((x / y) <= -6.3e-81)
		tmp = 2.0 / t;
	elseif ((x / y) <= 9.6e-246)
		tmp = -2.0;
	elseif ((x / y) <= 7.5e+90)
		tmp = 2.0 / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -205000000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -6.3e-81], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 9.6e-246], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 7.5e+90], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2.05e11 or 7.50000000000000014e90 < (/.f64 x y)

   1. Initial program 90.8%

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

   2. Taylor expanded in x around inf 69.1%

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

   if -2.05e11 < (/.f64 x y) < -6.30000000000000023e-81 or 9.5999999999999992e-246 < (/.f64 x y) < 7.50000000000000014e90

   1. Initial program 97.2%

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

   2. Taylor expanded in z around inf 56.5%

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

      1. associate-*r/ 56.5%

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

      2. associate-/l* 56.5%

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

   4. Simplified 56.5%

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

   5. Taylor expanded in t around 0 41.9%

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

   6. Taylor expanded in x around 0 39.3%

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

   if -6.30000000000000023e-81 < (/.f64 x y) < 9.5999999999999992e-246

   1. Initial program 84.3%

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

   2. Taylor expanded in z around inf 59.4%

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

      1. associate-*r/ 59.4%

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

      2. associate-/l* 59.4%

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

   4. Simplified 59.4%

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

   5. Taylor expanded in x around 0 59.4%

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

      1. div-sub 59.4%

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

      2. sub-neg 59.4%

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

      3. *-inverses 59.4%

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

      4. metadata-eval 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in t around inf 40.8%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -205000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -6.3 \cdot 10^{-81}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 9.6 \cdot 10^{-246}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 7.5 \cdot 10^{+90}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 4: 91.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ \mathbf{if}\;\frac{x}{y} \leq -100000000 \lor \neg \left(\frac{x}{y} \leq 3.9 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{x}{y} + t_1\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(\frac{2}{t} + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* z t))))
   (if (or (<= (/ x y) -100000000.0) (not (<= (/ x y) 3.9e+91)))
     (+ (/ x y) t_1)
     (+ -2.0 (+ (/ 2.0 t) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double tmp;
	if (((x / y) <= -100000000.0) || !((x / y) <= 3.9e+91)) {
		tmp = (x / y) + t_1;
	} else {
		tmp = -2.0 + ((2.0 / t) + 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 = 2.0d0 / (z * t)
    if (((x / y) <= (-100000000.0d0)) .or. (.not. ((x / y) <= 3.9d+91))) then
        tmp = (x / y) + t_1
    else
        tmp = (-2.0d0) + ((2.0d0 / t) + t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double tmp;
	if (((x / y) <= -100000000.0) || !((x / y) <= 3.9e+91)) {
		tmp = (x / y) + t_1;
	} else {
		tmp = -2.0 + ((2.0 / t) + t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (z * t)
	tmp = 0
	if ((x / y) <= -100000000.0) or not ((x / y) <= 3.9e+91):
		tmp = (x / y) + t_1
	else:
		tmp = -2.0 + ((2.0 / t) + t_1)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(z * t))
	tmp = 0.0
	if ((Float64(x / y) <= -100000000.0) || !(Float64(x / y) <= 3.9e+91))
		tmp = Float64(Float64(x / y) + t_1);
	else
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) + t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (z * t);
	tmp = 0.0;
	if (((x / y) <= -100000000.0) || ~(((x / y) <= 3.9e+91)))
		tmp = (x / y) + t_1;
	else
		tmp = -2.0 + ((2.0 / t) + t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[N[(x / y), $MachinePrecision], -100000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3.9e+91]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1e8 or 3.89999999999999968e91 < (/.f64 x y)

   1. Initial program 90.8%

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

   2. Taylor expanded in z around 0 92.1%

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

   if -1e8 < (/.f64 x y) < 3.89999999999999968e91

   1. Initial program 90.8%

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

   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 x around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. distribute-lft-out 99.9%

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

      3. fma-def 99.9%

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

      4. +-commutative 99.9%

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

      5. fma-def 99.9%

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

      6. distribute-lft-out 99.9%

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

      7. associate--l+ 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

      10. +-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 98.4%

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

      1. sub-neg 98.4%

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

      2. associate-*r/ 98.4%

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

      3. metadata-eval 98.4%

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

      4. associate-*r/ 98.4%

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

      5. metadata-eval 98.4%

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

      6. metadata-eval 98.4%

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

   10. Simplified 98.4%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -100000000 \lor \neg \left(\frac{x}{y} \leq 3.9 \cdot 10^{+91}\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{2}{z \cdot t}\right)\\ \end{array} \]

Alternative 5: 91.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y} + 2 \cdot \frac{\frac{1}{t}}{z}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+89}:\\ \;\;\;\;-2 + \left(\frac{2}{t} + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* z t))))
   (if (<= (/ x y) -5e+20)
     (+ (/ x y) (* 2.0 (/ (/ 1.0 t) z)))
     (if (<= (/ x y) 5e+89) (+ -2.0 (+ (/ 2.0 t) t_1)) (+ (/ x y) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double tmp;
	if ((x / y) <= -5e+20) {
		tmp = (x / y) + (2.0 * ((1.0 / t) / z));
	} else if ((x / y) <= 5e+89) {
		tmp = -2.0 + ((2.0 / t) + t_1);
	} else {
		tmp = (x / y) + 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 = 2.0d0 / (z * t)
    if ((x / y) <= (-5d+20)) then
        tmp = (x / y) + (2.0d0 * ((1.0d0 / t) / z))
    else if ((x / y) <= 5d+89) then
        tmp = (-2.0d0) + ((2.0d0 / t) + t_1)
    else
        tmp = (x / y) + t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double tmp;
	if ((x / y) <= -5e+20) {
		tmp = (x / y) + (2.0 * ((1.0 / t) / z));
	} else if ((x / y) <= 5e+89) {
		tmp = -2.0 + ((2.0 / t) + t_1);
	} else {
		tmp = (x / y) + t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (z * t)
	tmp = 0
	if (x / y) <= -5e+20:
		tmp = (x / y) + (2.0 * ((1.0 / t) / z))
	elif (x / y) <= 5e+89:
		tmp = -2.0 + ((2.0 / t) + t_1)
	else:
		tmp = (x / y) + t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(z * t))
	tmp = 0.0
	if (Float64(x / y) <= -5e+20)
		tmp = Float64(Float64(x / y) + Float64(2.0 * Float64(Float64(1.0 / t) / z)));
	elseif (Float64(x / y) <= 5e+89)
		tmp = Float64(-2.0 + Float64(Float64(2.0 / t) + t_1));
	else
		tmp = Float64(Float64(x / y) + t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (z * t);
	tmp = 0.0;
	if ((x / y) <= -5e+20)
		tmp = (x / y) + (2.0 * ((1.0 / t) / z));
	elseif ((x / y) <= 5e+89)
		tmp = -2.0 + ((2.0 / t) + t_1);
	else
		tmp = (x / y) + t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -5e+20], N[(N[(x / y), $MachinePrecision] + N[(2.0 * N[(N[(1.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5e+89], N[(-2.0 + N[(N[(2.0 / t), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5e20

   1. Initial program 93.3%

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

   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. 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 z around 0 90.3%

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

      1. *-commutative 90.3%

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

      2. associate-/r* 90.3%

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

   7. Simplified 90.3%

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

      1. associate-/l/ 90.3%

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

      2. associate-/r* 90.3%

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

      3. div-inv 90.3%

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

      4. *-un-lft-identity 90.3%

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

      5. times-frac 90.3%

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

      6. metadata-eval 90.3%

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

   9. Applied egg-rr 90.3%

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

   if -5e20 < (/.f64 x y) < 4.99999999999999983e89

   1. Initial program 90.8%

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

   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 x around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. distribute-lft-out 99.9%

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

      3. fma-def 99.9%

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

      4. +-commutative 99.9%

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

      5. fma-def 99.9%

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

      6. distribute-lft-out 99.9%

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

      7. associate--l+ 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

      10. +-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 98.4%

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

      1. sub-neg 98.4%

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

      2. associate-*r/ 98.4%

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

      3. metadata-eval 98.4%

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

      4. associate-*r/ 98.4%

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

      5. metadata-eval 98.4%

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

      6. metadata-eval 98.4%

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

   10. Simplified 98.4%

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

   if 4.99999999999999983e89 < (/.f64 x y)

   1. Initial program 86.8%

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

   2. Taylor expanded in z around 0 95.0%

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

4. Final simplification 96.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y} + 2 \cdot \frac{\frac{1}{t}}{z}\\ \mathbf{elif}\;\frac{x}{y} \leq 5 \cdot 10^{+89}:\\ \;\;\;\;-2 + \left(\frac{2}{t} + \frac{2}{z \cdot t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]

Alternative 6: 80.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;t \leq -1.05 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+19}:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= t -1.05e+154)
     t_1
     (if (<= t -6.5e-52)
       (+ (/ x y) (/ 2.0 (* z t)))
       (if (<= t 4.6e+19) (* (+ 2.0 (/ 2.0 z)) (/ 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (t <= -1.05e+154) {
		tmp = t_1;
	} else if (t <= -6.5e-52) {
		tmp = (x / y) + (2.0 / (z * t));
	} else if (t <= 4.6e+19) {
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) + (x / y)
    if (t <= (-1.05d+154)) then
        tmp = t_1
    else if (t <= (-6.5d-52)) then
        tmp = (x / y) + (2.0d0 / (z * t))
    else if (t <= 4.6d+19) then
        tmp = (2.0d0 + (2.0d0 / z)) * (1.0d0 / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (t <= -1.05e+154) {
		tmp = t_1;
	} else if (t <= -6.5e-52) {
		tmp = (x / y) + (2.0 / (z * t));
	} else if (t <= 4.6e+19) {
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	tmp = 0
	if t <= -1.05e+154:
		tmp = t_1
	elif t <= -6.5e-52:
		tmp = (x / y) + (2.0 / (z * t))
	elif t <= 4.6e+19:
		tmp = (2.0 + (2.0 / z)) * (1.0 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t <= -1.05e+154)
		tmp = t_1;
	elseif (t <= -6.5e-52)
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	elseif (t <= 4.6e+19)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) * Float64(1.0 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	tmp = 0.0;
	if (t <= -1.05e+154)
		tmp = t_1;
	elseif (t <= -6.5e-52)
		tmp = (x / y) + (2.0 / (z * t));
	elseif (t <= 4.6e+19)
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.05e+154], t$95$1, If[LessEqual[t, -6.5e-52], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 4.6e+19], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.04999999999999997e154 or 4.6e19 < t

   1. Initial program 71.7%

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

   2. Taylor expanded in t around inf 88.9%

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

   if -1.04999999999999997e154 < t < -6.5e-52

   1. Initial program 97.4%

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

   2. Taylor expanded in z around 0 79.8%

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

   if -6.5e-52 < t < 4.6e19

   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 86.4%

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

      1. associate-*r/ 86.4%

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

      2. metadata-eval 86.4%

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

   4. Simplified 86.4%

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

      1. div-inv 86.4%

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

   6. Applied egg-rr 86.4%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.05 \cdot 10^{+154}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{-52}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq 4.6 \cdot 10^{+19}:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]

Alternative 7: 80.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+18}:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= t -4.7e+153)
     t_1
     (if (<= t -1.2e-51)
       (+ (/ x y) (/ (/ 2.0 z) t))
       (if (<= t 6.8e+18) (* (+ 2.0 (/ 2.0 z)) (/ 1.0 t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (t <= -4.7e+153) {
		tmp = t_1;
	} else if (t <= -1.2e-51) {
		tmp = (x / y) + ((2.0 / z) / t);
	} else if (t <= 6.8e+18) {
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) + (x / y)
    if (t <= (-4.7d+153)) then
        tmp = t_1
    else if (t <= (-1.2d-51)) then
        tmp = (x / y) + ((2.0d0 / z) / t)
    else if (t <= 6.8d+18) then
        tmp = (2.0d0 + (2.0d0 / z)) * (1.0d0 / t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (t <= -4.7e+153) {
		tmp = t_1;
	} else if (t <= -1.2e-51) {
		tmp = (x / y) + ((2.0 / z) / t);
	} else if (t <= 6.8e+18) {
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	tmp = 0
	if t <= -4.7e+153:
		tmp = t_1
	elif t <= -1.2e-51:
		tmp = (x / y) + ((2.0 / z) / t)
	elif t <= 6.8e+18:
		tmp = (2.0 + (2.0 / z)) * (1.0 / t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t <= -4.7e+153)
		tmp = t_1;
	elseif (t <= -1.2e-51)
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / z) / t));
	elseif (t <= 6.8e+18)
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) * Float64(1.0 / t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	tmp = 0.0;
	if (t <= -4.7e+153)
		tmp = t_1;
	elseif (t <= -1.2e-51)
		tmp = (x / y) + ((2.0 / z) / t);
	elseif (t <= 6.8e+18)
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -4.7e+153], t$95$1, If[LessEqual[t, -1.2e-51], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 6.8e+18], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.69999999999999968e153 or 6.8e18 < t

   1. Initial program 71.7%

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

   2. Taylor expanded in t around inf 88.9%

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

   if -4.69999999999999968e153 < t < -1.2e-51

   1. Initial program 97.4%

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

   2. Taylor expanded in t around 0 99.7%

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

      1. associate--l+ 99.7%

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

      2. associate-*r/ 99.7%

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

      3. metadata-eval 99.7%

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

   4. 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 79.8%

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

      1. *-commutative 79.8%

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

      2. associate-/r* 79.9%

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

   7. Simplified 79.9%

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

   if -1.2e-51 < t < 6.8e18

   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 86.4%

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

      1. associate-*r/ 86.4%

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

      2. metadata-eval 86.4%

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

   4. Simplified 86.4%

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

      1. div-inv 86.4%

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

   6. Applied egg-rr 86.4%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.7 \cdot 10^{+153}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{-51}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{z}}{t}\\ \mathbf{elif}\;t \leq 6.8 \cdot 10^{+18}:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]

Alternative 8: 80.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-7} \lor \neg \left(t \leq 7.2 \cdot 10^{+18}\right):\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.6e-7) (not (<= t 7.2e+18)))
   (+ -2.0 (/ x y))
   (* (+ 2.0 (/ 2.0 z)) (/ 1.0 t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e-7) || !(t <= 7.2e+18)) {
		tmp = -2.0 + (x / y);
	} else {
		tmp = (2.0 + (2.0 / z)) * (1.0 / 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 <= (-6.6d-7)) .or. (.not. (t <= 7.2d+18))) then
        tmp = (-2.0d0) + (x / y)
    else
        tmp = (2.0d0 + (2.0d0 / z)) * (1.0d0 / t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e-7) || !(t <= 7.2e+18)) {
		tmp = -2.0 + (x / y);
	} else {
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.6e-7) or not (t <= 7.2e+18):
		tmp = -2.0 + (x / y)
	else:
		tmp = (2.0 + (2.0 / z)) * (1.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.6e-7) || !(t <= 7.2e+18))
		tmp = Float64(-2.0 + Float64(x / y));
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) * Float64(1.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.6e-7) || ~((t <= 7.2e+18)))
		tmp = -2.0 + (x / y);
	else
		tmp = (2.0 + (2.0 / z)) * (1.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.6e-7], N[Not[LessEqual[t, 7.2e+18]], $MachinePrecision]], N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] * N[(1.0 / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.6000000000000003e-7 or 7.2e18 < t

   1. Initial program 79.5%

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

   2. Taylor expanded in t around inf 82.1%

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

   if -6.6000000000000003e-7 < t < 7.2e18

   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 85.8%

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

      1. associate-*r/ 85.8%

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

      2. metadata-eval 85.8%

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

   4. Simplified 85.8%

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

      1. div-inv 85.8%

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

   6. Applied egg-rr 85.8%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-7} \lor \neg \left(t \leq 7.2 \cdot 10^{+18}\right):\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(2 + \frac{2}{z}\right) \cdot \frac{1}{t}\\ \end{array} \]

Alternative 9: 64.4% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1450000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.2 \cdot 10^{+89}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1450000000000.0)
   (/ x y)
   (if (<= (/ x y) 4.2e+89) (+ -2.0 (/ 2.0 t)) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1450000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 4.2e+89) {
		tmp = -2.0 + (2.0 / t);
	} 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) <= (-1450000000000.0d0)) then
        tmp = x / y
    else if ((x / y) <= 4.2d+89) then
        tmp = (-2.0d0) + (2.0d0 / t)
    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) <= -1450000000000.0) {
		tmp = x / y;
	} else if ((x / y) <= 4.2e+89) {
		tmp = -2.0 + (2.0 / t);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1450000000000.0:
		tmp = x / y
	elif (x / y) <= 4.2e+89:
		tmp = -2.0 + (2.0 / t)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1450000000000.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 4.2e+89)
		tmp = Float64(-2.0 + Float64(2.0 / t));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1450000000000.0)
		tmp = x / y;
	elseif ((x / y) <= 4.2e+89)
		tmp = -2.0 + (2.0 / t);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1450000000000.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4.2e+89], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.45e12 or 4.19999999999999972e89 < (/.f64 x y)

   1. Initial program 90.8%

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

   2. Taylor expanded in x around inf 69.1%

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

   if -1.45e12 < (/.f64 x y) < 4.19999999999999972e89

   1. Initial program 90.8%

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

   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 x around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. distribute-lft-out 99.9%

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

      3. fma-def 99.9%

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

      4. +-commutative 99.9%

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

      5. fma-def 99.9%

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

      6. distribute-lft-out 99.9%

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

      7. associate--l+ 99.9%

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

      8. sub-neg 99.9%

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

      9. metadata-eval 99.9%

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

      10. +-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 98.4%

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

      1. sub-neg 98.4%

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

      2. associate-*r/ 98.4%

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

      3. metadata-eval 98.4%

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

      4. associate-*r/ 98.4%

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

      5. metadata-eval 98.4%

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

      6. metadata-eval 98.4%

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

   10. Simplified 98.4%

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

   11. Taylor expanded in z around inf 56.5%

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

4. Final simplification 61.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1450000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.2 \cdot 10^{+89}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 10: 62.7% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{2}{t}\\ \mathbf{if}\;z \leq -1.1 \cdot 10^{+125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-121}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-28}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ 2.0 t))))
   (if (<= z -1.1e+125)
     t_1
     (if (<= z -1.1e-121)
       (+ -2.0 (/ x y))
       (if (<= z 3.7e-28) (/ 2.0 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -1.1e+125) {
		tmp = t_1;
	} else if (z <= -1.1e-121) {
		tmp = -2.0 + (x / y);
	} else if (z <= 3.7e-28) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) + (2.0d0 / t)
    if (z <= (-1.1d+125)) then
        tmp = t_1
    else if (z <= (-1.1d-121)) then
        tmp = (-2.0d0) + (x / y)
    else if (z <= 3.7d-28) then
        tmp = 2.0d0 / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (2.0 / t);
	double tmp;
	if (z <= -1.1e+125) {
		tmp = t_1;
	} else if (z <= -1.1e-121) {
		tmp = -2.0 + (x / y);
	} else if (z <= 3.7e-28) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (2.0 / t)
	tmp = 0
	if z <= -1.1e+125:
		tmp = t_1
	elif z <= -1.1e-121:
		tmp = -2.0 + (x / y)
	elif z <= 3.7e-28:
		tmp = 2.0 / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(2.0 / t))
	tmp = 0.0
	if (z <= -1.1e+125)
		tmp = t_1;
	elseif (z <= -1.1e-121)
		tmp = Float64(-2.0 + Float64(x / y));
	elseif (z <= 3.7e-28)
		tmp = Float64(2.0 / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (2.0 / t);
	tmp = 0.0;
	if (z <= -1.1e+125)
		tmp = t_1;
	elseif (z <= -1.1e-121)
		tmp = -2.0 + (x / y);
	elseif (z <= 3.7e-28)
		tmp = 2.0 / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.1e+125], t$95$1, If[LessEqual[z, -1.1e-121], N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.7e-28], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.09999999999999995e125 or 3.7000000000000002e-28 < z

   1. Initial program 78.6%

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

   2. Taylor expanded in t around 0 100.0%

      \[\leadsto \frac{x}{y} + \color{blue}{\left(\left(2 \cdot \frac{1}{t \cdot z} + \frac{2}{t}\right) - 2\right)} \]
   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 x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-out 100.0%

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

      3. fma-def 100.0%

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

      4. +-commutative 100.0%

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

      5. fma-def 100.0%

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

      6. distribute-lft-out 100.0%

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

      7. associate--l+ 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 74.3%

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

      1. sub-neg 74.3%

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

      2. associate-*r/ 74.3%

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

      3. metadata-eval 74.3%

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

      4. associate-*r/ 74.3%

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

      5. metadata-eval 74.3%

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

      6. metadata-eval 74.3%

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

   10. Simplified 74.3%

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

   11. Taylor expanded in z around inf 70.1%

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

   if -1.09999999999999995e125 < z < -1.10000000000000011e-121

   1. Initial program 95.0%

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

   2. Taylor expanded in t around inf 68.4%

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

   if -1.10000000000000011e-121 < z < 3.7000000000000002e-28

   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 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. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

   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 x around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. distribute-lft-out 99.8%

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

      3. fma-def 99.8%

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

      4. +-commutative 99.8%

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

      5. fma-def 99.8%

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

      6. distribute-lft-out 99.8%

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

      7. associate--l+ 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

      10. +-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 72.7%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+125}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-121}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-28}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 11: 65.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-123}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-28}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= z -2.7e+25)
   (+ (/ x y) (/ 2.0 t))
   (if (<= z -2.25e-123)
     (+ -2.0 (/ x y))
     (if (<= z 4e-28) (/ 2.0 (* z t)) (+ -2.0 (/ 2.0 t))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (z <= -2.7e+25) {
		tmp = (x / y) + (2.0 / t);
	} else if (z <= -2.25e-123) {
		tmp = -2.0 + (x / y);
	} else if (z <= 4e-28) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = -2.0 + (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 (z <= (-2.7d+25)) then
        tmp = (x / y) + (2.0d0 / t)
    else if (z <= (-2.25d-123)) then
        tmp = (-2.0d0) + (x / y)
    else if (z <= 4d-28) then
        tmp = 2.0d0 / (z * t)
    else
        tmp = (-2.0d0) + (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 (z <= -2.7e+25) {
		tmp = (x / y) + (2.0 / t);
	} else if (z <= -2.25e-123) {
		tmp = -2.0 + (x / y);
	} else if (z <= 4e-28) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = -2.0 + (2.0 / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if z <= -2.7e+25:
		tmp = (x / y) + (2.0 / t)
	elif z <= -2.25e-123:
		tmp = -2.0 + (x / y)
	elif z <= 4e-28:
		tmp = 2.0 / (z * t)
	else:
		tmp = -2.0 + (2.0 / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (z <= -2.7e+25)
		tmp = Float64(Float64(x / y) + Float64(2.0 / t));
	elseif (z <= -2.25e-123)
		tmp = Float64(-2.0 + Float64(x / y));
	elseif (z <= 4e-28)
		tmp = Float64(2.0 / Float64(z * t));
	else
		tmp = Float64(-2.0 + Float64(2.0 / t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (z <= -2.7e+25)
		tmp = (x / y) + (2.0 / t);
	elseif (z <= -2.25e-123)
		tmp = -2.0 + (x / y);
	elseif (z <= 4e-28)
		tmp = 2.0 / (z * t);
	else
		tmp = -2.0 + (2.0 / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[z, -2.7e+25], N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.25e-123], N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4e-28], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(2.0 / t), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7e25

   1. Initial program 80.8%

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

   2. Taylor expanded in z around inf 99.9%

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

      1. associate-*r/ 99.9%

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

      2. associate-/l* 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in t around 0 82.3%

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

   if -2.7e25 < z < -2.24999999999999997e-123

   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 inf 72.6%

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

   if -2.24999999999999997e-123 < z < 3.99999999999999988e-28

   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 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. associate-*r/ 99.8%

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

      3. metadata-eval 99.8%

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

   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 x around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. distribute-lft-out 99.8%

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

      3. fma-def 99.8%

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

      4. +-commutative 99.8%

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

      5. fma-def 99.8%

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

      6. distribute-lft-out 99.8%

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

      7. associate--l+ 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

      10. +-commutative 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in z around 0 72.7%

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

   if 3.99999999999999988e-28 < z

   1. Initial program 79.8%

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

   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 x around 0 100.0%

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

      1. +-commutative 100.0%

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

      2. distribute-lft-out 100.0%

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

      3. fma-def 100.0%

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

      4. +-commutative 100.0%

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

      5. fma-def 100.0%

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

      6. distribute-lft-out 100.0%

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

      7. associate--l+ 100.0%

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

      8. sub-neg 100.0%

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

      9. metadata-eval 100.0%

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

      10. +-commutative 100.0%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 75.2%

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

      1. sub-neg 75.2%

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

      2. associate-*r/ 75.2%

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

      3. metadata-eval 75.2%

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

      4. associate-*r/ 75.2%

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

      5. metadata-eval 75.2%

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

      6. metadata-eval 75.2%

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

   10. Simplified 75.2%

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

   11. Taylor expanded in z around inf 68.2%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+25}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t}\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-123}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-28}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{2}{t}\\ \end{array} \]

Alternative 12: 80.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0029 \lor \neg \left(t \leq 6.5 \cdot 10^{+18}\right):\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -0.0029) (not (<= t 6.5e+18)))
   (+ -2.0 (/ x y))
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -0.0029) || !(t <= 6.5e+18)) {
		tmp = -2.0 + (x / y);
	} 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 <= (-0.0029d0)) .or. (.not. (t <= 6.5d+18))) then
        tmp = (-2.0d0) + (x / y)
    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 <= -0.0029) || !(t <= 6.5e+18)) {
		tmp = -2.0 + (x / y);
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -0.0029) or not (t <= 6.5e+18):
		tmp = -2.0 + (x / y)
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -0.0029) || !(t <= 6.5e+18))
		tmp = Float64(-2.0 + Float64(x / y));
	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 <= -0.0029) || ~((t <= 6.5e+18)))
		tmp = -2.0 + (x / y);
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -0.0029], N[Not[LessEqual[t, 6.5e+18]], $MachinePrecision]], N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0029 or 6.5e18 < t

   1. Initial program 79.5%

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

   2. Taylor expanded in t around inf 82.1%

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

   if -0.0029 < t < 6.5e18

   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 85.8%

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

      1. associate-*r/ 85.8%

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

      2. metadata-eval 85.8%

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

   4. Simplified 85.8%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0029 \lor \neg \left(t \leq 6.5 \cdot 10^{+18}\right):\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]

Alternative 13: 36.9% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.46:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+20}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -0.46) -2.0 (if (<= t 3.4e+20) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -0.46) {
		tmp = -2.0;
	} else if (t <= 3.4e+20) {
		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 <= (-0.46d0)) then
        tmp = -2.0d0
    else if (t <= 3.4d+20) 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 <= -0.46) {
		tmp = -2.0;
	} else if (t <= 3.4e+20) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -0.46:
		tmp = -2.0
	elif t <= 3.4e+20:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -0.46)
		tmp = -2.0;
	elseif (t <= 3.4e+20)
		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 <= -0.46)
		tmp = -2.0;
	elseif (t <= 3.4e+20)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -0.46], -2.0, If[LessEqual[t, 3.4e+20], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -0.46000000000000002 or 3.4e20 < t

   1. Initial program 79.4%

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

   2. Taylor expanded in z around inf 81.9%

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

      1. associate-*r/ 81.9%

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

      2. associate-/l* 81.9%

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

   4. Simplified 81.9%

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

   5. Taylor expanded in x around 0 39.5%

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

      1. div-sub 39.5%

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

      2. sub-neg 39.5%

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

      3. *-inverses 39.5%

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

      4. metadata-eval 39.5%

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

   7. Simplified 39.5%

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

   8. Taylor expanded in t around inf 39.5%

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

   if -0.46000000000000002 < t < 3.4e20

   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 inf 52.0%

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

      1. associate-*r/ 52.0%

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

      2. associate-/l* 52.0%

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

   4. Simplified 52.0%

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

   5. Taylor expanded in t around 0 51.4%

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

   6. Taylor expanded in x around 0 36.9%

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

4. Final simplification 38.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.46:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 3.4 \cdot 10^{+20}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]

Alternative 14: 20.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 90.8%

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

2. Taylor expanded in z around inf 65.1%

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

   1. associate-*r/ 65.1%

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

   2. associate-/l* 65.1%

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

4. Simplified 65.1%

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

5. Taylor expanded in x around 0 38.4%

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

   1. div-sub 38.4%

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

   2. sub-neg 38.4%

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

   3. *-inverses 38.4%

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

   4. metadata-eval 38.4%

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

7. Simplified 38.4%

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

8. Taylor expanded in t around inf 18.7%

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

9. Final simplification 18.7%

   \[\leadsto -2 \]

Developer target: 99.2% 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 2023279 
(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))))