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

Percentage Accurate: 86.4% → 99.0%

Time: 9.7s

Alternatives: 11

Speedup: 1.1×

• 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: 99.0% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(N[(N[(2.0 * N[(N[(1.0 + z), $MachinePrecision] / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision] + -2.0), $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-def 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 0 98.7%

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

6. Final simplification 98.7%

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

Alternative 2: 68.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;z \leq -4 \cdot 10^{+246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+104}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-48} \lor \neg \left(z \leq 3.8 \cdot 10^{-13}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= z -4e+246)
     t_1
     (if (<= z -5.5e+104)
       (+ (/ 2.0 t) -2.0)
       (if (or (<= z -5.5e-48) (not (<= z 3.8e-13)))
         t_1
         (+ (/ 2.0 (* z t)) -2.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (z <= -4e+246) {
		tmp = t_1;
	} else if (z <= -5.5e+104) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -5.5e-48) || !(z <= 3.8e-13)) {
		tmp = t_1;
	} else {
		tmp = (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) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if (z <= (-4d+246)) then
        tmp = t_1
    else if (z <= (-5.5d+104)) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else if ((z <= (-5.5d-48)) .or. (.not. (z <= 3.8d-13))) then
        tmp = t_1
    else
        tmp = (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 t_1 = (x / y) + -2.0;
	double tmp;
	if (z <= -4e+246) {
		tmp = t_1;
	} else if (z <= -5.5e+104) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -5.5e-48) || !(z <= 3.8e-13)) {
		tmp = t_1;
	} else {
		tmp = (2.0 / (z * t)) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if z <= -4e+246:
		tmp = t_1
	elif z <= -5.5e+104:
		tmp = (2.0 / t) + -2.0
	elif (z <= -5.5e-48) or not (z <= 3.8e-13):
		tmp = t_1
	else:
		tmp = (2.0 / (z * t)) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (z <= -4e+246)
		tmp = t_1;
	elseif (z <= -5.5e+104)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	elseif ((z <= -5.5e-48) || !(z <= 3.8e-13))
		tmp = t_1;
	else
		tmp = Float64(Float64(2.0 / Float64(z * t)) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if (z <= -4e+246)
		tmp = t_1;
	elseif (z <= -5.5e+104)
		tmp = (2.0 / t) + -2.0;
	elseif ((z <= -5.5e-48) || ~((z <= 3.8e-13)))
		tmp = t_1;
	else
		tmp = (2.0 / (z * t)) + -2.0;
	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, -4e+246], t$95$1, If[LessEqual[z, -5.5e+104], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], If[Or[LessEqual[z, -5.5e-48], N[Not[LessEqual[z, 3.8e-13]], $MachinePrecision]], t$95$1, N[(N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.00000000000000027e246 or -5.50000000000000017e104 < z < -5.50000000000000047e-48 or 3.8e-13 < z

   1. Initial program 68.1%

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

   3. Taylor expanded in t around inf 81.8%

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

   if -4.00000000000000027e246 < z < -5.50000000000000017e104

   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-def 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 0 99.8%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x around 0 84.6%

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

   if -5.50000000000000047e-48 < z < 3.8e-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-def 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 0 98.2%

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

   6. Taylor expanded in z around 0 79.7%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4 \cdot 10^{+246}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+104}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-48} \lor \neg \left(z \leq 3.8 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+246}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+105}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-92} \lor \neg \left(z \leq 6.4 \cdot 10^{-21}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= z -1.15e+246)
     t_1
     (if (<= z -2.1e+105)
       (+ (/ 2.0 t) -2.0)
       (if (or (<= z -1.5e-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 <= -1.15e+246) {
		tmp = t_1;
	} else if (z <= -2.1e+105) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -1.5e-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 <= (-1.15d+246)) then
        tmp = t_1
    else if (z <= (-2.1d+105)) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else if ((z <= (-1.5d-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 <= -1.15e+246) {
		tmp = t_1;
	} else if (z <= -2.1e+105) {
		tmp = (2.0 / t) + -2.0;
	} else if ((z <= -1.5e-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 <= -1.15e+246:
		tmp = t_1
	elif z <= -2.1e+105:
		tmp = (2.0 / t) + -2.0
	elif (z <= -1.5e-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 <= -1.15e+246)
		tmp = t_1;
	elseif (z <= -2.1e+105)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	elseif ((z <= -1.5e-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 <= -1.15e+246)
		tmp = t_1;
	elseif (z <= -2.1e+105)
		tmp = (2.0 / t) + -2.0;
	elseif ((z <= -1.5e-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, -1.15e+246], t$95$1, If[LessEqual[z, -2.1e+105], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], If[Or[LessEqual[z, -1.5e-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 < -1.15000000000000007e246 or -2.1000000000000001e105 < z < -1.50000000000000007e-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 -1.15000000000000007e246 < z < -2.1000000000000001e105

   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-def 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 0 99.8%

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

   6. Taylor expanded in z around inf 100.0%

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

      1. associate-*r/ 100.0%

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

      2. metadata-eval 100.0%

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

      3. +-commutative 100.0%

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

   8. Simplified 100.0%

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

   9. Taylor expanded in x around 0 84.6%

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

   if -1.50000000000000007e-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. Add Preprocessing

   3. Taylor expanded in z around 0 88.7%

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

      1. associate-/r* 88.6%

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

   5. Simplified 88.6%

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

      1. clear-num 88.5%

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

      2. frac-add 70.9%

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

      3. *-un-lft-identity 70.9%

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

   7. Applied egg-rr 70.9%

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

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+246}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+105}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-92} \lor \neg \left(z \leq 6.4 \cdot 10^{-21}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 80.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ \mathbf{if}\;\frac{x}{y} \leq -2 \lor \neg \left(\frac{x}{y} \leq 0.00012\right):\\ \;\;\;\;\frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_1 + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* z t))))
   (if (or (<= (/ x y) -2.0) (not (<= (/ x y) 0.00012)))
     (+ (/ x y) t_1)
     (+ t_1 -2.0))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double tmp;
	if (((x / y) <= -2.0) || !((x / y) <= 0.00012)) {
		tmp = (x / y) + t_1;
	} else {
		tmp = t_1 + -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = 2.0d0 / (z * t)
    if (((x / y) <= (-2.0d0)) .or. (.not. ((x / y) <= 0.00012d0))) then
        tmp = (x / y) + t_1
    else
        tmp = t_1 + (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double tmp;
	if (((x / y) <= -2.0) || !((x / y) <= 0.00012)) {
		tmp = (x / y) + t_1;
	} else {
		tmp = t_1 + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (z * t)
	tmp = 0
	if ((x / y) <= -2.0) or not ((x / y) <= 0.00012):
		tmp = (x / y) + t_1
	else:
		tmp = t_1 + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(z * t))
	tmp = 0.0
	if ((Float64(x / y) <= -2.0) || !(Float64(x / y) <= 0.00012))
		tmp = Float64(Float64(x / y) + t_1);
	else
		tmp = Float64(t_1 + -2.0);
	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) <= -2.0) || ~(((x / y) <= 0.00012)))
		tmp = (x / y) + t_1;
	else
		tmp = t_1 + -2.0;
	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], -2.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.00012]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(t$95$1 + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2 or 1.20000000000000003e-4 < (/.f64 x y)

   1. Initial program 83.2%

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

   3. Taylor expanded in z around 0 85.8%

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

   if -2 < (/.f64 x y) < 1.20000000000000003e-4

   1. Initial program 81.5%

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

      1. +-commutative 81.5%

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

      2. remove-double-neg 81.5%

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

      3. distribute-frac-neg 81.5%

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

      4. unsub-neg 81.5%

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

      5. *-commutative 81.5%

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

      6. associate-*r* 81.5%

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

      7. distribute-rgt1-in 81.5%

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

      8. associate-*r/ 81.4%

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

      9. /-rgt-identity 81.4%

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

      10. fma-neg 81.4%

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

      11. /-rgt-identity 81.4%

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

      12. *-commutative 81.4%

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

      13. fma-def 81.4%

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

      14. *-commutative 81.4%

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

      15. distribute-frac-neg 81.4%

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

      16. remove-double-neg 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in t around 0 99.9%

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

   6. Taylor expanded in z around 0 83.5%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \lor \neg \left(\frac{x}{y} \leq 0.00012\right):\\ \;\;\;\;\frac{x}{y} + \frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{z \cdot t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.22 \cdot 10^{+35} \lor \neg \left(\frac{x}{y} \leq 215000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1.22e+35) (not (<= (/ x y) 215000.0)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1.22e+35) || !((x / y) <= 215000.0)) {
		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) <= (-1.22d+35)) .or. (.not. ((x / y) <= 215000.0d0))) 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) <= -1.22e+35) || !((x / y) <= 215000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1.22e+35) or not ((x / y) <= 215000.0):
		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) <= -1.22e+35) || !(Float64(x / y) <= 215000.0))
		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) <= -1.22e+35) || ~(((x / y) <= 215000.0)))
		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], -1.22e+35], N[Not[LessEqual[N[(x / y), $MachinePrecision], 215000.0]], $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) < -1.21999999999999999e35 or 215000 < (/.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 -1.21999999999999999e35 < (/.f64 x y) < 215000

   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-def 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 0 99.9%

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

   6. Taylor expanded in z around inf 62.9%

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

      1. associate-*r/ 62.9%

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

      2. metadata-eval 62.9%

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

      3. +-commutative 62.9%

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

   8. Simplified 62.9%

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

   9. Taylor expanded in x around 0 59.8%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.22 \cdot 10^{+35} \lor \neg \left(\frac{x}{y} \leq 215000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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-def 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 0 99.8%

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

   6. Taylor expanded in z around inf 63.1%

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

      1. associate-*r/ 63.1%

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

      2. metadata-eval 63.1%

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

      3. +-commutative 63.1%

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

   8. Simplified 63.1%

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

   9. Taylor expanded in x around 0 63.1%

      \[\leadsto \color{blue}{\frac{2}{t}} - 2 \]
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 7: 91.4% accurate, 0.9× speedup

Math

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

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(Float64(x / y) + 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[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision] + -2.0), $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. Step-by-step derivation

      1. +-commutative 70.0%

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

      2. remove-double-neg 70.0%

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

      3. distribute-frac-neg 70.0%

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

      4. unsub-neg 70.0%

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

      5. *-commutative 70.0%

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

      6. associate-*r* 70.0%

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

      7. distribute-rgt1-in 70.0%

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

      8. associate-*r/ 69.9%

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

      9. /-rgt-identity 69.9%

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

      10. fma-neg 69.9%

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

      11. /-rgt-identity 69.9%

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

      12. *-commutative 69.9%

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

      13. fma-def 69.9%

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

      14. *-commutative 69.9%

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

      15. distribute-frac-neg 69.9%

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

      16. remove-double-neg 69.9%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in t around 0 99.2%

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

   6. Taylor expanded in z around inf 98.3%

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

      1. associate-*r/ 98.3%

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

      2. metadata-eval 98.3%

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

      3. +-commutative 98.3%

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

   8. Simplified 98.3%

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

   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%

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

Alternative 8: 53.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \lor \neg \left(\frac{x}{y} \leq 0.00012\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.0) (not (<= (/ x y) 0.00012))) (/ x y) -2.0))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.0) || !((x / y) <= 0.00012)) {
		tmp = x / y;
	} 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 (((x / y) <= (-2.0d0)) .or. (.not. ((x / y) <= 0.00012d0))) then
        tmp = x / y
    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 (((x / y) <= -2.0) || !((x / y) <= 0.00012)) {
		tmp = x / y;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -2.0) or not ((x / y) <= 0.00012):
		tmp = x / y
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2.0) || !(Float64(x / y) <= 0.00012))
		tmp = Float64(x / y);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -2.0) || ~(((x / y) <= 0.00012)))
		tmp = x / y;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 0.00012]], $MachinePrecision]], N[(x / y), $MachinePrecision], -2.0]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -2 or 1.20000000000000003e-4 < (/.f64 x y)

   1. Initial program 83.2%

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

   3. Taylor expanded in x around inf 65.7%

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

   if -2 < (/.f64 x y) < 1.20000000000000003e-4

   1. Initial program 81.5%

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

      1. +-commutative 81.5%

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

      2. remove-double-neg 81.5%

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

      3. distribute-frac-neg 81.5%

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

      4. unsub-neg 81.5%

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

      5. *-commutative 81.5%

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

      6. associate-*r* 81.5%

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

      7. distribute-rgt1-in 81.5%

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

      8. associate-*r/ 81.4%

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

      9. /-rgt-identity 81.4%

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

      10. fma-neg 81.4%

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

      11. /-rgt-identity 81.4%

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

      12. *-commutative 81.4%

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

      13. fma-def 81.4%

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

      14. *-commutative 81.4%

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

      15. distribute-frac-neg 81.4%

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

      16. remove-double-neg 81.4%

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

   3. Simplified 81.4%

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

   5. Taylor expanded in x around 0 80.4%

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

   6. Taylor expanded in t around inf 46.8%

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

4. Final simplification 56.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \lor \neg \left(\frac{x}{y} \leq 0.00012\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 78.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-97} \lor \neg \left(t \leq 4.4\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -6.6e-97) (not (<= t 4.4)))
   (+ (/ 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 <= 4.4)) {
		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 <= 4.4d0))) 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 <= 4.4)) {
		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 <= 4.4):
		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 <= 4.4))
		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 <= 4.4)))
		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, 4.4]], $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 4.4000000000000004 < 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 < 4.4000000000000004

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.6 \cdot 10^{-97} \lor \neg \left(t \leq 4.4\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 35.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-62}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 88000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.4e-62) -2.0 (if (<= t 88000.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.4e-62) {
		tmp = -2.0;
	} else if (t <= 88000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-1.4d-62)) then
        tmp = -2.0d0
    else if (t <= 88000.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.4e-62) {
		tmp = -2.0;
	} else if (t <= 88000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.4e-62:
		tmp = -2.0
	elif t <= 88000.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.4e-62)
		tmp = -2.0;
	elseif (t <= 88000.0)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -1.4e-62)
		tmp = -2.0;
	elseif (t <= 88000.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.4e-62], -2.0, If[LessEqual[t, 88000.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1.40000000000000001e-62 or 88000 < t

   1. Initial program 70.4%

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

      1. +-commutative 70.4%

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

      2. remove-double-neg 70.4%

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

      3. distribute-frac-neg 70.4%

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

      4. unsub-neg 70.4%

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

      5. *-commutative 70.4%

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

      6. associate-*r* 70.4%

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

      7. distribute-rgt1-in 70.4%

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

      8. associate-*r/ 70.3%

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

      9. /-rgt-identity 70.3%

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

      10. fma-neg 70.3%

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

      11. /-rgt-identity 70.3%

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

      12. *-commutative 70.3%

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

      13. fma-def 70.3%

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

      14. *-commutative 70.3%

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

      15. distribute-frac-neg 70.3%

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

      16. remove-double-neg 70.3%

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

   3. Simplified 70.3%

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

   5. Taylor expanded in x around 0 42.2%

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

   6. Taylor expanded in t around inf 43.5%

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

   if -1.40000000000000001e-62 < t < 88000

   1. Initial program 97.2%

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

   3. Taylor expanded in t around 0 79.2%

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

      1. associate-*r/ 79.2%

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

      2. metadata-eval 79.2%

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

   5. Simplified 79.2%

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

   6. Taylor expanded in z around inf 29.9%

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

4. Final simplification 37.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.4 \cdot 10^{-62}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 88000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 20.5% 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 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-def 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 x around 0 58.9%

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

6. Taylor expanded in t around inf 25.1%

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

7. Final simplification 25.1%

   \[\leadsto -2 \]
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))))