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

Percentage Accurate: 86.4% → 99.1%

Time: 9.9s

Alternatives: 10

Speedup: 1.3×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 82.3%

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

   1. +-commutative 82.3%

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

   2. remove-double-neg 82.3%

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

   3. distribute-frac-neg 82.3%

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

   4. unsub-neg 82.3%

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

   5. *-commutative 82.3%

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

   6. associate-*r* 82.3%

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

   7. distribute-rgt1-in 82.3%

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

   8. associate-*r/ 82.3%

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

   9. /-rgt-identity 82.3%

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

   10. fma-neg 82.3%

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

   11. /-rgt-identity 82.3%

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

   12. *-commutative 82.3%

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

   13. fma-define 82.3%

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

   14. *-commutative 82.3%

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

   15. distribute-frac-neg 82.3%

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

   16. remove-double-neg 82.3%

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

3. Simplified 82.3%

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

5. Taylor expanded in t around inf 98.8%

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

   1. +-commutative 98.8%

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

   2. associate--l+ 98.8%

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

   3. associate-*r/ 98.4%

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

   4. distribute-lft-in 98.4%

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

   5. metadata-eval 98.4%

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

   6. associate-*r/ 98.4%

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

   7. metadata-eval 98.4%

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

7. Simplified 98.4%

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

8. Final simplification 98.4%

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

Alternative 2: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} - 2\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+105}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-92} \lor \neg \left(z \leq 6.4 \cdot 10^{-21}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ x y) 2.0)))
   (if (<= z -2.1e+246)
     t_1
     (if (<= z -1.05e+105)
       (+ (/ 2.0 t) -2.0)
       (if (or (<= z -2.5e-92) (not (<= z 6.4e-21))) t_1 (/ 2.0 (* z t)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -2.1e+246) {
		tmp = t_1;
	} else if (z <= -1.05e+105) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -2.5e-92) || !(z <= 6.4e-21)) {
		tmp = t_1;
	} else {
		tmp = 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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) - 2.0d0
    if (z <= (-2.1d+246)) then
        tmp = t_1
    else if (z <= (-1.05d+105)) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else if ((z <= (-2.5d-92)) .or. (.not. (z <= 6.4d-21))) then
        tmp = t_1
    else
        tmp = 2.0d0 / (z * t)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) - 2.0;
	double tmp;
	if (z <= -2.1e+246) {
		tmp = t_1;
	} else if (z <= -1.05e+105) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -2.5e-92) || !(z <= 6.4e-21)) {
		tmp = t_1;
	} else {
		tmp = 2.0 / (z * t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) - 2.0
	tmp = 0
	if z <= -2.1e+246:
		tmp = t_1
	elif z <= -1.05e+105:
		tmp = (2.0 / t) + -2.0
	elif (z <= -2.5e-92) or not (z <= 6.4e-21):
		tmp = t_1
	else:
		tmp = 2.0 / (z * t)
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (z <= -2.1e+246)
		tmp = t_1;
	elseif (z <= -1.05e+105)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	elseif ((z <= -2.5e-92) || !(z <= 6.4e-21))
		tmp = t_1;
	else
		tmp = Float64(2.0 / Float64(z * t));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) - 2.0;
	tmp = 0.0;
	if (z <= -2.1e+246)
		tmp = t_1;
	elseif (z <= -1.05e+105)
		tmp = (2.0 / t) + -2.0;
	elseif ((z <= -2.5e-92) || ~((z <= 6.4e-21)))
		tmp = t_1;
	else
		tmp = 2.0 / (z * t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[z, -2.1e+246], t$95$1, If[LessEqual[z, -1.05e+105], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], If[Or[LessEqual[z, -2.5e-92], N[Not[LessEqual[z, 6.4e-21]], $MachinePrecision]], t$95$1, N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.1e246 or -1.05000000000000005e105 < z < -2.50000000000000006e-92 or 6.4000000000000003e-21 < z

   1. Initial program 71.2%

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

   3. Taylor expanded in t around inf 80.5%

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

   if -2.1e246 < z < -1.05000000000000005e105

   1. Initial program 71.3%

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

      1. +-commutative 71.3%

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

      2. remove-double-neg 71.3%

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

      3. distribute-frac-neg 71.3%

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

      4. unsub-neg 71.3%

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

      5. *-commutative 71.3%

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

      6. associate-*r* 71.3%

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

      7. distribute-rgt1-in 71.3%

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

      8. associate-*r/ 71.3%

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

      9. /-rgt-identity 71.3%

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

      10. fma-neg 71.3%

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

      11. /-rgt-identity 71.3%

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

      12. *-commutative 71.3%

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

      13. fma-define 71.3%

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

      14. *-commutative 71.3%

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

      15. distribute-frac-neg 71.3%

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

      16. remove-double-neg 71.3%

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

   3. Simplified 71.3%

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

   5. Taylor expanded in t around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. associate-*r/ 100.0%

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

      4. distribute-lft-in 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 84.6%

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

      1. sub-neg 84.6%

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

      2. associate-*r/ 84.6%

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

      3. metadata-eval 84.6%

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

      4. *-commutative 84.6%

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

      5. associate-/r* 84.6%

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

      6. metadata-eval 84.6%

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

      7. associate-*r/ 84.6%

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

      8. *-rgt-identity 84.6%

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

      9. associate-*r/ 84.6%

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

      10. *-commutative 84.6%

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

      11. associate-*l* 84.6%

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

      12. associate-*r/ 84.6%

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

      13. metadata-eval 84.6%

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

      14. distribute-lft-in 84.6%

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

      15. associate-*l/ 84.6%

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

      16. *-lft-identity 84.6%

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

      17. metadata-eval 84.6%

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

      18. +-commutative 84.6%

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

   10. Simplified 84.6%

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

   11. Taylor expanded in z around inf 84.6%

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

   if -2.50000000000000006e-92 < z < 6.4000000000000003e-21

   1. Initial program 98.0%

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

      1. +-commutative 98.0%

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

      2. remove-double-neg 98.0%

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

      3. distribute-frac-neg 98.0%

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

      4. unsub-neg 98.0%

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

      5. *-commutative 98.0%

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

      6. associate-*r* 98.0%

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

      7. distribute-rgt1-in 98.0%

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

      8. associate-*r/ 98.0%

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

      9. /-rgt-identity 98.0%

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

      10. fma-neg 98.0%

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

      11. /-rgt-identity 98.0%

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

      12. *-commutative 98.0%

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

      13. fma-define 98.0%

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

      14. *-commutative 98.0%

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

      15. distribute-frac-neg 98.0%

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

      16. remove-double-neg 98.0%

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

   3. Simplified 98.0%

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

   5. Taylor expanded in t around inf 98.0%

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

      1. +-commutative 98.0%

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

      2. associate--l+ 98.0%

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

      3. associate-*r/ 97.1%

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

      4. distribute-lft-in 97.1%

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

      5. metadata-eval 97.1%

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

      6. associate-*r/ 97.1%

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

      7. metadata-eval 97.1%

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

   7. Simplified 97.1%

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

   8. Taylor expanded in z around 0 70.6%

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

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+246}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+105}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-92} \lor \neg \left(z \leq 6.4 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 82.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.2 \cdot 10^{+234} \lor \neg \left(\frac{x}{y} \leq 6.5 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -6.2e+234) (not (<= (/ x y) 6.5e+31)))
   (/ x y)
   (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6.2e+234) || !((x / y) <= 6.5e+31)) {
		tmp = x / y;
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-6.2d+234)) .or. (.not. ((x / y) <= 6.5d+31))) then
        tmp = x / y
    else
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -6.2e+234) || !((x / y) <= 6.5e+31)) {
		tmp = x / y;
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -6.2e+234) or not ((x / y) <= 6.5e+31):
		tmp = x / y
	else:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -6.2e+234) || !(Float64(x / y) <= 6.5e+31))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -6.2e+234) || ~(((x / y) <= 6.5e+31)))
		tmp = x / y;
	else
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -6.2e+234], N[Not[LessEqual[N[(x / y), $MachinePrecision], 6.5e+31]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.19999999999999979e234 or 6.5000000000000004e31 < (/.f64 x y)

   1. Initial program 82.9%

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

   3. Taylor expanded in x around inf 77.9%

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

   if -6.19999999999999979e234 < (/.f64 x y) < 6.5000000000000004e31

   1. Initial program 82.0%

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

      1. +-commutative 82.0%

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

      2. remove-double-neg 82.0%

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

      3. distribute-frac-neg 82.0%

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

      4. unsub-neg 82.0%

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

      5. *-commutative 82.0%

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

      6. associate-*r* 82.0%

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

      7. distribute-rgt1-in 82.0%

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

      8. associate-*r/ 81.9%

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

      9. /-rgt-identity 81.9%

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

      10. fma-neg 81.9%

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

      11. /-rgt-identity 81.9%

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

      12. *-commutative 81.9%

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

      13. fma-define 81.9%

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

      14. *-commutative 81.9%

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

      15. distribute-frac-neg 81.9%

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

      16. remove-double-neg 81.9%

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

   3. Simplified 81.9%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-*r/ 99.3%

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

      4. distribute-lft-in 99.3%

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

      5. metadata-eval 99.3%

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

      6. associate-*r/ 99.3%

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

      7. metadata-eval 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in x around 0 90.2%

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

      1. sub-neg 90.2%

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

      2. associate-*r/ 90.2%

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

      3. metadata-eval 90.2%

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

      4. *-commutative 90.2%

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

      5. associate-/r* 90.2%

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

      6. metadata-eval 90.2%

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

      7. associate-*r/ 90.2%

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

      8. *-rgt-identity 90.2%

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

      9. associate-*r/ 90.1%

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

      10. *-commutative 90.1%

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

      11. associate-*l* 89.6%

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

      12. associate-*r/ 89.6%

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

      13. metadata-eval 89.6%

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

      14. distribute-lft-in 89.6%

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

      15. associate-*l/ 89.6%

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

      16. *-lft-identity 89.6%

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

      17. metadata-eval 89.6%

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

      18. +-commutative 89.6%

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

   10. Simplified 89.6%

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

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.2 \cdot 10^{+234} \lor \neg \left(\frac{x}{y} \leq 6.5 \cdot 10^{+31}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.3 \cdot 10^{+33} \lor \neg \left(\frac{x}{y} \leq 72000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4.3e+33) (not (<= (/ x y) 72000.0)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4.3e+33) || !((x / y) <= 72000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-4.3d+33)) .or. (.not. ((x / y) <= 72000.0d0))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4.3e+33) || !((x / y) <= 72000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4.3e+33) or not ((x / y) <= 72000.0):
		tmp = x / y
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4.3e+33) || !(Float64(x / y) <= 72000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -4.3e+33) || ~(((x / y) <= 72000.0)))
		tmp = x / y;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4.3e+33], N[Not[LessEqual[N[(x / y), $MachinePrecision], 72000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.30000000000000028e33 or 72000 < (/.f64 x y)

   1. Initial program 83.7%

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

   3. Taylor expanded in x around inf 69.0%

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

   if -4.30000000000000028e33 < (/.f64 x y) < 72000

   1. Initial program 81.1%

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

      1. +-commutative 81.1%

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

      2. remove-double-neg 81.1%

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

      3. distribute-frac-neg 81.1%

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

      4. unsub-neg 81.1%

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

      5. *-commutative 81.1%

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

      6. associate-*r* 81.1%

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

      7. distribute-rgt1-in 81.1%

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

      8. associate-*r/ 81.1%

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

      9. /-rgt-identity 81.1%

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

      10. fma-neg 81.1%

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

      11. /-rgt-identity 81.1%

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

      12. *-commutative 81.1%

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

      13. fma-define 81.1%

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

      14. *-commutative 81.1%

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

      15. distribute-frac-neg 81.1%

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

      16. remove-double-neg 81.1%

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

   3. Simplified 81.1%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-*r/ 99.2%

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

      4. distribute-lft-in 99.2%

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

      5. metadata-eval 99.2%

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

      6. associate-*r/ 99.2%

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

      7. metadata-eval 99.2%

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

   7. Simplified 99.2%

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

   8. Taylor expanded in x around 0 96.8%

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

      1. sub-neg 96.8%

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

      2. associate-*r/ 96.8%

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

      3. metadata-eval 96.8%

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

      4. *-commutative 96.8%

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

      5. associate-/r* 96.7%

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

      6. metadata-eval 96.7%

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

      7. associate-*r/ 96.7%

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

      8. *-rgt-identity 96.7%

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

      9. associate-*r/ 96.7%

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

      10. *-commutative 96.7%

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

      11. associate-*l* 96.0%

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

      12. associate-*r/ 96.0%

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

      13. metadata-eval 96.0%

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

      14. distribute-lft-in 96.0%

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

      15. associate-*l/ 96.0%

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

      16. *-lft-identity 96.0%

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

      17. metadata-eval 96.0%

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

      18. +-commutative 96.0%

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

   10. Simplified 96.0%

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

   11. Taylor expanded in z around inf 59.8%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.3 \cdot 10^{+33} \lor \neg \left(\frac{x}{y} \leq 72000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 66.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.2 \cdot 10^{-14} \lor \neg \left(\frac{x}{y} \leq 3.7 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4.2e-14) (not (<= (/ x y) 3.7e-17)))
   (- (/ x y) 2.0)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4.2e-14) || !((x / y) <= 3.7e-17)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-4.2d-14)) .or. (.not. ((x / y) <= 3.7d-17))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4.2e-14) || !((x / y) <= 3.7e-17)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4.2e-14) or not ((x / y) <= 3.7e-17):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4.2e-14) || !(Float64(x / y) <= 3.7e-17))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -4.2e-14) || ~(((x / y) <= 3.7e-17)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4.2e-14], N[Not[LessEqual[N[(x / y), $MachinePrecision], 3.7e-17]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.1999999999999998e-14 or 3.6999999999999997e-17 < (/.f64 x y)

   1. Initial program 82.5%

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

   3. Taylor expanded in t around inf 66.9%

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

   if -4.1999999999999998e-14 < (/.f64 x y) < 3.6999999999999997e-17

   1. Initial program 82.1%

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

      1. +-commutative 82.1%

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

      2. remove-double-neg 82.1%

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

      3. distribute-frac-neg 82.1%

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

      4. unsub-neg 82.1%

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

      5. *-commutative 82.1%

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

      6. associate-*r* 82.1%

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

      7. distribute-rgt1-in 82.1%

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

      8. associate-*r/ 82.0%

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

      9. /-rgt-identity 82.0%

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

      10. fma-neg 82.0%

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

      11. /-rgt-identity 82.0%

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

      12. *-commutative 82.0%

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

      13. fma-define 82.0%

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

      14. *-commutative 82.0%

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

      15. distribute-frac-neg 82.0%

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

      16. remove-double-neg 82.0%

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

   3. Simplified 82.0%

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

   5. Taylor expanded in t around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-*r/ 99.1%

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

      4. distribute-lft-in 99.1%

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

      5. metadata-eval 99.1%

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

      6. associate-*r/ 99.1%

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

      7. metadata-eval 99.1%

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

   7. Simplified 99.1%

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

   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%

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

      3. metadata-eval 99.9%

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

      4. *-commutative 99.9%

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

      5. associate-/r* 99.9%

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

      6. metadata-eval 99.9%

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

      7. associate-*r/ 99.9%

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

      8. *-rgt-identity 99.9%

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

      9. associate-*r/ 99.8%

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

      10. *-commutative 99.8%

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

      11. associate-*l* 99.1%

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

      12. associate-*r/ 99.1%

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

      13. metadata-eval 99.1%

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

      14. distribute-lft-in 99.1%

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

      15. associate-*l/ 99.1%

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

      16. *-lft-identity 99.1%

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

      17. metadata-eval 99.1%

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

      18. +-commutative 99.1%

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

   10. Simplified 99.1%

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

   11. Taylor expanded in z around inf 63.1%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4.2 \cdot 10^{-14} \lor \neg \left(\frac{x}{y} \leq 3.7 \cdot 10^{-17}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-48} \lor \neg \left(z \leq 3.9 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -4.4e-48) (not (<= z 3.9e-13)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.4e-48) || !(z <= 3.9e-13)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-4.4d-48)) .or. (.not. (z <= 3.9d-13))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = ((2.0d0 + (2.0d0 / z)) / t) + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -4.4e-48) || !(z <= 3.9e-13)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -4.4e-48) or not (z <= 3.9e-13):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -4.4e-48) || !(z <= 3.9e-13))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(Float64(2.0 + Float64(2.0 / z)) / t) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -4.4e-48) || ~((z <= 3.9e-13)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -4.4e-48], N[Not[LessEqual[z, 3.9e-13]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision] + -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.40000000000000025e-48 or 3.90000000000000004e-13 < z

   1. Initial program 68.8%

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

   3. Taylor expanded in z around inf 98.9%

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

      1. div-sub 98.9%

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

      2. sub-neg 98.9%

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

      3. *-inverses 98.9%

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

      4. metadata-eval 98.9%

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

      5. distribute-lft-in 98.9%

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

      6. metadata-eval 98.9%

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

      7. associate-*r/ 98.9%

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

      8. metadata-eval 98.9%

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

   5. Simplified 98.9%

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

   if -4.40000000000000025e-48 < z < 3.90000000000000004e-13

   1. Initial program 98.2%

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

      1. +-commutative 98.2%

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

      2. remove-double-neg 98.2%

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

      3. distribute-frac-neg 98.2%

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

      4. unsub-neg 98.2%

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

      5. *-commutative 98.2%

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

      6. associate-*r* 98.2%

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

      7. distribute-rgt1-in 98.2%

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

      8. associate-*r/ 98.2%

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

      9. /-rgt-identity 98.2%

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

      10. fma-neg 98.2%

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

      11. /-rgt-identity 98.2%

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

      12. *-commutative 98.2%

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

      13. fma-define 98.2%

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

      14. *-commutative 98.2%

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

      15. distribute-frac-neg 98.2%

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

      16. remove-double-neg 98.2%

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

   3. Simplified 98.2%

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

   5. Taylor expanded in t around inf 98.2%

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

      1. +-commutative 98.2%

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

      2. associate--l+ 98.2%

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

      3. associate-*r/ 97.3%

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

      4. distribute-lft-in 97.3%

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

      5. metadata-eval 97.3%

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

      6. associate-*r/ 97.3%

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

      7. metadata-eval 97.3%

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

   7. Simplified 97.3%

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

   8. Taylor expanded in x around 0 79.8%

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

      1. sub-neg 79.8%

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

      2. associate-*r/ 79.8%

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

      3. metadata-eval 79.8%

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

      4. *-commutative 79.8%

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

      5. associate-/r* 79.8%

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

      6. metadata-eval 79.8%

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

      7. associate-*r/ 79.8%

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

      8. *-rgt-identity 79.8%

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

      9. associate-*r/ 79.7%

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

      10. *-commutative 79.7%

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

      11. associate-*l* 78.9%

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

      12. associate-*r/ 78.9%

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

      13. metadata-eval 78.9%

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

      14. distribute-lft-in 78.9%

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

      15. associate-*l/ 79.0%

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

      16. *-lft-identity 79.0%

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

      17. metadata-eval 79.0%

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

      18. +-commutative 79.0%

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

   10. Simplified 79.0%

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

4. Final simplification 89.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.4 \cdot 10^{-48} \lor \neg \left(z \leq 3.9 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 91.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-55} \lor \neg \left(z \leq 9.5 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -5e-55) (not (<= z 9.5e-21)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ x y) (/ 2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5e-55) || !(z <= 9.5e-21)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-5d-55)) .or. (.not. (z <= 9.5d-21))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (x / y) + (2.0d0 / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -5e-55) || !(z <= 9.5e-21)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -5e-55) or not (z <= 9.5e-21):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (x / y) + (2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -5e-55) || !(z <= 9.5e-21))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -5e-55) || ~((z <= 9.5e-21)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = (x / y) + (2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -5e-55], N[Not[LessEqual[z, 9.5e-21]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.0000000000000002e-55 or 9.4999999999999994e-21 < z

   1. Initial program 70.0%

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

   3. Taylor expanded in z around inf 98.3%

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

      1. div-sub 98.3%

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

      2. sub-neg 98.3%

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

      3. *-inverses 98.3%

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

      4. metadata-eval 98.3%

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

      5. distribute-lft-in 98.3%

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

      6. metadata-eval 98.3%

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

      7. associate-*r/ 98.3%

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

      8. metadata-eval 98.3%

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

   5. Simplified 98.3%

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

   if -5.0000000000000002e-55 < z < 9.4999999999999994e-21

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0 88.4%

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

4. Final simplification 94.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-55} \lor \neg \left(z \leq 9.5 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 47.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+35} \lor \neg \left(\frac{x}{y} \leq 22000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -4e+35) (not (<= (/ x y) 22000.0))) (/ x y) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e+35) || !((x / y) <= 22000.0)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-4d+35)) .or. (.not. ((x / y) <= 22000.0d0))) then
        tmp = x / y
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -4e+35) || !((x / y) <= 22000.0)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -4e+35) or not ((x / y) <= 22000.0):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -4e+35) || !(Float64(x / y) <= 22000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -4e+35) || ~(((x / y) <= 22000.0)))
		tmp = x / y;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -4e+35], N[Not[LessEqual[N[(x / y), $MachinePrecision], 22000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.9999999999999999e35 or 22000 < (/.f64 x y)

   1. Initial program 83.7%

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

   3. Taylor expanded in x around inf 69.0%

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

   if -3.9999999999999999e35 < (/.f64 x y) < 22000

   1. Initial program 81.1%

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

   3. Taylor expanded in t around 0 53.8%

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

      1. associate-*r/ 53.8%

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

      2. metadata-eval 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in z around inf 17.6%

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

4. Final simplification 41.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -4 \cdot 10^{+35} \lor \neg \left(\frac{x}{y} \leq 22000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-97} \lor \neg \left(t \leq 7.8\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.6e-97) (not (<= t 7.8)))
   (- (/ x y) 2.0)
   (/ (+ 2.0 (/ 2.0 z)) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e-97) || !(t <= 7.8)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-6.6d-97)) .or. (.not. (t <= 7.8d0))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = (2.0d0 + (2.0d0 / z)) / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -6.6e-97) || !(t <= 7.8)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = (2.0 + (2.0 / z)) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -6.6e-97) or not (t <= 7.8):
		tmp = (x / y) - 2.0
	else:
		tmp = (2.0 + (2.0 / z)) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -6.6e-97) || !(t <= 7.8))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(Float64(2.0 + Float64(2.0 / z)) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -6.6e-97) || ~((t <= 7.8)))
		tmp = (x / y) - 2.0;
	else
		tmp = (2.0 + (2.0 / z)) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -6.6e-97], N[Not[LessEqual[t, 7.8]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(N[(2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -6.6000000000000002e-97 or 7.79999999999999982 < t

   1. Initial program 72.0%

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

   3. Taylor expanded in t around inf 84.5%

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

   if -6.6000000000000002e-97 < t < 7.79999999999999982

   1. Initial program 97.0%

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

   3. Taylor expanded in t around 0 83.9%

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

      1. associate-*r/ 83.9%

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

      2. metadata-eval 83.9%

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

   5. Simplified 83.9%

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

4. Final simplification 84.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-97} \lor \neg \left(t \leq 7.8\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 19.0% accurate, 5.7× speedup

Math

\[\begin{array}{l} \\ \frac{2}{t} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(2.0 / t), $MachinePrecision]

Derivation

1. Initial program 82.3%

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

3. Taylor expanded in t around 0 44.9%

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

   1. associate-*r/ 44.9%

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

   2. metadata-eval 44.9%

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

5. Simplified 44.9%

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

6. Taylor expanded in z around inf 14.9%

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

7. Final simplification 14.9%

   \[\leadsto \frac{2}{t} \]
8. Add Preprocessing

Developer target: 99.1% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024036 
(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))))