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

Percentage Accurate: 86.5% → 99.4%

Time: 10.7s

Alternatives: 14

Speedup: 1.3×

• 22.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 87.4%

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

   1. +-commutative 87.4%

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

   2. remove-double-neg 87.4%

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

   3. distribute-frac-neg 87.4%

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

   4. unsub-neg 87.4%

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

   5. *-commutative 87.4%

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

   6. associate-*r* 87.4%

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

   7. distribute-rgt1-in 87.4%

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

   8. associate-*r/ 87.4%

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

   9. /-rgt-identity 87.4%

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

   10. fma-neg 87.4%

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

   11. /-rgt-identity 87.4%

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

   12. *-commutative 87.4%

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

   13. fma-def 87.4%

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

   14. *-commutative 87.4%

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

   15. distribute-frac-neg 87.4%

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

   16. remove-double-neg 87.4%

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

3. Simplified 87.4%

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

5. Taylor expanded in t around 0 98.7%

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

   1. +-commutative 98.7%

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

   2. div-inv 98.6%

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

   3. fma-def 99.4%

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

   4. *-commutative 99.4%

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

   5. *-commutative 99.4%

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

7. Applied egg-rr 99.4%

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

8. Final simplification 99.4%

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

Alternative 2: 70.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t} + -2\\ \mathbf{if}\;\frac{x}{y} \leq -6.1 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -6.2 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;\frac{x}{y} \leq -1.72 \cdot 10^{-184}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;\frac{x}{y} \leq 86000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ 2.0 (* z t)) -2.0)))
   (if (<= (/ x y) -6.1e+81)
     (/ x y)
     (if (<= (/ x y) -6.2e-121)
       t_1
       (if (<= (/ x y) -1.72e-184)
         (+ (/ 2.0 t) -2.0)
         (if (<= (/ x y) 86000000.0) t_1 (+ (/ x y) -2.0)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / (z * t)) + -2.0;
	double tmp;
	if ((x / y) <= -6.1e+81) {
		tmp = x / y;
	} else if ((x / y) <= -6.2e-121) {
		tmp = t_1;
	} else if ((x / y) <= -1.72e-184) {
		tmp = (2.0 / t) + -2.0;
	} else if ((x / y) <= 86000000.0) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -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)) + (-2.0d0)
    if ((x / y) <= (-6.1d+81)) then
        tmp = x / y
    else if ((x / y) <= (-6.2d-121)) then
        tmp = t_1
    else if ((x / y) <= (-1.72d-184)) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else if ((x / y) <= 86000000.0d0) then
        tmp = t_1
    else
        tmp = (x / y) + (-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)) + -2.0;
	double tmp;
	if ((x / y) <= -6.1e+81) {
		tmp = x / y;
	} else if ((x / y) <= -6.2e-121) {
		tmp = t_1;
	} else if ((x / y) <= -1.72e-184) {
		tmp = (2.0 / t) + -2.0;
	} else if ((x / y) <= 86000000.0) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / (z * t)) + -2.0
	tmp = 0
	if (x / y) <= -6.1e+81:
		tmp = x / y
	elif (x / y) <= -6.2e-121:
		tmp = t_1
	elif (x / y) <= -1.72e-184:
		tmp = (2.0 / t) + -2.0
	elif (x / y) <= 86000000.0:
		tmp = t_1
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / Float64(z * t)) + -2.0)
	tmp = 0.0
	if (Float64(x / y) <= -6.1e+81)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -6.2e-121)
		tmp = t_1;
	elseif (Float64(x / y) <= -1.72e-184)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	elseif (Float64(x / y) <= 86000000.0)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / (z * t)) + -2.0;
	tmp = 0.0;
	if ((x / y) <= -6.1e+81)
		tmp = x / y;
	elseif ((x / y) <= -6.2e-121)
		tmp = t_1;
	elseif ((x / y) <= -1.72e-184)
		tmp = (2.0 / t) + -2.0;
	elseif ((x / y) <= 86000000.0)
		tmp = t_1;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -6.1e+81], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -6.2e-121], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], -1.72e-184], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 86000000.0], t$95$1, N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (/.f64 x y) < -6.10000000000000038e81

   1. Initial program 69.8%

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

   3. Taylor expanded in x around inf 76.4%

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

   if -6.10000000000000038e81 < (/.f64 x y) < -6.1999999999999997e-121 or -1.72e-184 < (/.f64 x y) < 8.6e7

   1. Initial program 93.3%

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

      1. +-commutative 93.3%

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

      2. remove-double-neg 93.3%

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

      3. distribute-frac-neg 93.3%

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

      4. unsub-neg 93.3%

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

      5. *-commutative 93.3%

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

      6. associate-*r* 93.3%

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

      7. distribute-rgt1-in 93.3%

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

      8. associate-*r/ 93.3%

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

      9. /-rgt-identity 93.3%

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

      10. fma-neg 93.3%

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

      11. /-rgt-identity 93.3%

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

      12. *-commutative 93.3%

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

      13. fma-def 93.3%

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

      14. *-commutative 93.3%

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

      15. distribute-frac-neg 93.3%

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

      16. remove-double-neg 93.3%

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

   3. Simplified 93.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, 1 - t, 1\right), \frac{2}{z \cdot t}, \frac{x}{y}\right)} \]
   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 0 71.1%

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

   if -6.1999999999999997e-121 < (/.f64 x y) < -1.72e-184

   1. Initial program 81.2%

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

      1. +-commutative 81.2%

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

      2. remove-double-neg 81.2%

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

      3. distribute-frac-neg 81.2%

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

      4. unsub-neg 81.2%

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

      5. *-commutative 81.2%

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

      6. associate-*r* 81.2%

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

      7. distribute-rgt1-in 81.2%

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

      8. associate-*r/ 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 85.2%

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

      1. associate-*r/ 85.2%

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

      2. metadata-eval 85.2%

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

      3. +-commutative 85.2%

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

   8. Simplified 85.2%

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

   9. Taylor expanded in x around 0 85.2%

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

       1. sub-neg 85.2%

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

       2. associate-*r/ 85.2%

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

       3. metadata-eval 85.2%

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

       4. metadata-eval 85.2%

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

   11. Simplified 85.2%

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

   if 8.6e7 < (/.f64 x y)

   1. Initial program 92.0%

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

   3. Taylor expanded in t around inf 70.8%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -6.1 \cdot 10^{+81}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -6.2 \cdot 10^{-121}:\\ \;\;\;\;\frac{2}{z \cdot t} + -2\\ \mathbf{elif}\;\frac{x}{y} \leq -1.72 \cdot 10^{-184}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;\frac{x}{y} \leq 86000000:\\ \;\;\;\;\frac{2}{z \cdot t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 81.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{t}}{z}\\ t_2 := \frac{x}{y} + t_1\\ t_3 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{+111}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-35}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-80}:\\ \;\;\;\;\frac{2}{t} + t_1\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+158}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ 2.0 t) z)) (t_2 (+ (/ x y) t_1)) (t_3 (+ (/ x y) -2.0)))
   (if (<= t -2.5e+111)
     t_3
     (if (<= t -4.5e-35)
       t_2
       (if (<= t 1.25e-80) (+ (/ 2.0 t) t_1) (if (<= t 3e+158) t_2 t_3))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) / z;
	double t_2 = (x / y) + t_1;
	double t_3 = (x / y) + -2.0;
	double tmp;
	if (t <= -2.5e+111) {
		tmp = t_3;
	} else if (t <= -4.5e-35) {
		tmp = t_2;
	} else if (t <= 1.25e-80) {
		tmp = (2.0 / t) + t_1;
	} else if (t <= 3e+158) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = (2.0d0 / t) / z
    t_2 = (x / y) + t_1
    t_3 = (x / y) + (-2.0d0)
    if (t <= (-2.5d+111)) then
        tmp = t_3
    else if (t <= (-4.5d-35)) then
        tmp = t_2
    else if (t <= 1.25d-80) then
        tmp = (2.0d0 / t) + t_1
    else if (t <= 3d+158) then
        tmp = t_2
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) / z;
	double t_2 = (x / y) + t_1;
	double t_3 = (x / y) + -2.0;
	double tmp;
	if (t <= -2.5e+111) {
		tmp = t_3;
	} else if (t <= -4.5e-35) {
		tmp = t_2;
	} else if (t <= 1.25e-80) {
		tmp = (2.0 / t) + t_1;
	} else if (t <= 3e+158) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / t) / z
	t_2 = (x / y) + t_1
	t_3 = (x / y) + -2.0
	tmp = 0
	if t <= -2.5e+111:
		tmp = t_3
	elif t <= -4.5e-35:
		tmp = t_2
	elif t <= 1.25e-80:
		tmp = (2.0 / t) + t_1
	elif t <= 3e+158:
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / t) / z)
	t_2 = Float64(Float64(x / y) + t_1)
	t_3 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -2.5e+111)
		tmp = t_3;
	elseif (t <= -4.5e-35)
		tmp = t_2;
	elseif (t <= 1.25e-80)
		tmp = Float64(Float64(2.0 / t) + t_1);
	elseif (t <= 3e+158)
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / t) / z;
	t_2 = (x / y) + t_1;
	t_3 = (x / y) + -2.0;
	tmp = 0.0;
	if (t <= -2.5e+111)
		tmp = t_3;
	elseif (t <= -4.5e-35)
		tmp = t_2;
	elseif (t <= 1.25e-80)
		tmp = (2.0 / t) + t_1;
	elseif (t <= 3e+158)
		tmp = t_2;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision]}, Block[{t$95$3 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t, -2.5e+111], t$95$3, If[LessEqual[t, -4.5e-35], t$95$2, If[LessEqual[t, 1.25e-80], N[(N[(2.0 / t), $MachinePrecision] + t$95$1), $MachinePrecision], If[LessEqual[t, 3e+158], t$95$2, t$95$3]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.4999999999999998e111 or 3e158 < t

   1. Initial program 70.2%

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

   3. Taylor expanded in t around inf 89.4%

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

   if -2.4999999999999998e111 < t < -4.5000000000000001e-35 or 1.25e-80 < t < 3e158

   1. Initial program 90.8%

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

   3. Taylor expanded in z around 0 84.0%

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

      1. associate-/r* 84.1%

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

   5. Simplified 84.1%

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

   if -4.5000000000000001e-35 < t < 1.25e-80

   1. Initial program 96.9%

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

   3. Taylor expanded in t around 0 87.0%

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

      1. associate-*r/ 87.0%

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

      2. metadata-eval 87.0%

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

   5. Simplified 87.0%

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

   6. Taylor expanded in z around 0 87.0%

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

      1. associate-*r/ 87.0%

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

      2. metadata-eval 87.0%

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

      3. associate-*r/ 87.0%

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

      4. metadata-eval 87.0%

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

      5. associate-/r* 87.0%

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

   8. Simplified 87.0%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.5 \cdot 10^{+111}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-35}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-80}:\\ \;\;\;\;\frac{2}{t} + \frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+158}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 93.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+25} \lor \neg \left(\frac{x}{y} \leq 500000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+25) (not (<= (/ x y) 500000000000.0)))
   (+ (/ x y) (/ (/ 2.0 t) z))
   (+ (/ (+ 2.0 (/ 2.0 z)) t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+25) || !((x / y) <= 500000000000.0)) {
		tmp = (x / y) + ((2.0 / t) / z);
	} 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) <= (-5d+25)) .or. (.not. ((x / y) <= 500000000000.0d0))) then
        tmp = (x / y) + ((2.0d0 / t) / z)
    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) <= -5e+25) || !((x / y) <= 500000000000.0)) {
		tmp = (x / y) + ((2.0 / t) / z);
	} else {
		tmp = ((2.0 + (2.0 / z)) / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+25) or not ((x / y) <= 500000000000.0):
		tmp = (x / y) + ((2.0 / t) / z)
	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) <= -5e+25) || !(Float64(x / y) <= 500000000000.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	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) <= -5e+25) || ~(((x / y) <= 500000000000.0)))
		tmp = (x / y) + ((2.0 / t) / z);
	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], -5e+25], N[Not[LessEqual[N[(x / y), $MachinePrecision], 500000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $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 (/.f64 x y) < -5.00000000000000024e25 or 5e11 < (/.f64 x y)

   1. Initial program 82.8%

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

   3. Taylor expanded in z around 0 88.8%

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

      1. associate-/r* 88.7%

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

   5. Simplified 88.7%

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

   if -5.00000000000000024e25 < (/.f64 x y) < 5e11

   1. Initial program 91.9%

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

      1. +-commutative 91.9%

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

      2. remove-double-neg 91.9%

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

      3. distribute-frac-neg 91.9%

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

      4. unsub-neg 91.9%

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

      5. *-commutative 91.9%

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

      6. associate-*r* 91.9%

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

      7. distribute-rgt1-in 91.9%

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

      8. associate-*r/ 91.9%

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

      9. /-rgt-identity 91.9%

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

      10. fma-neg 91.9%

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

      11. /-rgt-identity 91.9%

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

      12. *-commutative 91.9%

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

      13. fma-def 91.9%

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

      14. *-commutative 91.9%

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

      15. distribute-frac-neg 91.9%

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

      16. remove-double-neg 91.9%

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

   3. Simplified 91.9%

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

   5. Taylor expanded in t around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. div-inv 99.8%

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

      3. fma-def 99.8%

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

      4. *-commutative 99.8%

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

      5. *-commutative 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in x around 0 97.9%

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

      1. *-commutative 97.9%

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

      2. associate-/l/ 97.9%

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

      3. associate-*l/ 97.9%

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

      4. *-lft-identity 97.9%

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

      5. associate-*l/ 97.8%

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

      6. distribute-rgt-in 97.8%

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

      7. *-lft-identity 97.8%

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

      8. rgt-mult-inverse 97.9%

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

      9. distribute-rgt1-in 97.9%

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

      10. *-commutative 97.9%

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

      11. associate-*r/ 97.9%

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

      12. metadata-eval 97.9%

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

   10. Simplified 97.9%

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

4. Final simplification 93.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+25} \lor \neg \left(\frac{x}{y} \leq 500000000000\right):\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.7 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.42 \cdot 10^{-295}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 3400000:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5.7e+23)
   (/ x y)
   (if (<= (/ x y) 1.42e-295)
     (/ 2.0 t)
     (if (<= (/ x y) 3400000.0) -2.0 (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5.7e+23) {
		tmp = x / y;
	} else if ((x / y) <= 1.42e-295) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 3400000.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5.7d+23)) then
        tmp = x / y
    else if ((x / y) <= 1.42d-295) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 3400000.0d0) then
        tmp = -2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5.7e+23) {
		tmp = x / y;
	} else if ((x / y) <= 1.42e-295) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 3400000.0) {
		tmp = -2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5.7e+23:
		tmp = x / y
	elif (x / y) <= 1.42e-295:
		tmp = 2.0 / t
	elif (x / y) <= 3400000.0:
		tmp = -2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5.7e+23)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1.42e-295)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 3400000.0)
		tmp = -2.0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5.7e+23)
		tmp = x / y;
	elseif ((x / y) <= 1.42e-295)
		tmp = 2.0 / t;
	elseif ((x / y) <= 3400000.0)
		tmp = -2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5.7e+23], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.42e-295], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 3400000.0], -2.0, N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.7e23 or 3.4e6 < (/.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 68.7%

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

   if -5.7e23 < (/.f64 x y) < 1.42000000000000005e-295

   1. Initial program 92.3%

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

   3. Taylor expanded in t around 0 72.5%

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

      1. associate-*r/ 72.5%

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

      2. metadata-eval 72.5%

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

   5. Simplified 72.5%

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

   6. Taylor expanded in z around inf 31.5%

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

   if 1.42000000000000005e-295 < (/.f64 x y) < 3.4e6

   1. Initial program 90.2%

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

      1. +-commutative 90.2%

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

      2. remove-double-neg 90.2%

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

      3. distribute-frac-neg 90.2%

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

      4. unsub-neg 90.2%

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

      5. *-commutative 90.2%

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

      6. associate-*r* 90.2%

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

      7. distribute-rgt1-in 90.2%

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

      8. associate-*r/ 90.1%

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

      9. /-rgt-identity 90.1%

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

      10. fma-neg 90.1%

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

      11. /-rgt-identity 90.1%

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

      12. *-commutative 90.1%

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

      13. fma-def 90.1%

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

      14. *-commutative 90.1%

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

      15. distribute-frac-neg 90.1%

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

      16. remove-double-neg 90.1%

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

   3. Simplified 90.1%

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

   5. Taylor expanded in x around 0 88.3%

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

   6. Taylor expanded in t around inf 33.2%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.7 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.42 \cdot 10^{-295}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 3400000:\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.1% 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 87.4%

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

   1. +-commutative 87.4%

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

   2. remove-double-neg 87.4%

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

   3. distribute-frac-neg 87.4%

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

   4. unsub-neg 87.4%

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

   5. *-commutative 87.4%

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

   6. associate-*r* 87.4%

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

   7. distribute-rgt1-in 87.4%

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

   8. associate-*r/ 87.4%

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

   9. /-rgt-identity 87.4%

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

   10. fma-neg 87.4%

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

   11. /-rgt-identity 87.4%

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

   12. *-commutative 87.4%

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

   13. fma-def 87.4%

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

   14. *-commutative 87.4%

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

   15. distribute-frac-neg 87.4%

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

   16. remove-double-neg 87.4%

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

3. Simplified 87.4%

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

5. Taylor expanded in t around 0 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 7: 65.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.7 \cdot 10^{+23} \lor \neg \left(\frac{x}{y} \leq 126000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5.7e+23) (not (<= (/ x y) 126000000000.0)))
   (/ x y)
   (+ (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5.7e+23) || !((x / y) <= 126000000000.0)) {
		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) <= (-5.7d+23)) .or. (.not. ((x / y) <= 126000000000.0d0))) 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) <= -5.7e+23) || !((x / y) <= 126000000000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5.7e+23) or not ((x / y) <= 126000000000.0):
		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) <= -5.7e+23) || !(Float64(x / y) <= 126000000000.0))
		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) <= -5.7e+23) || ~(((x / y) <= 126000000000.0)))
		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], -5.7e+23], N[Not[LessEqual[N[(x / y), $MachinePrecision], 126000000000.0]], $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) < -5.7e23 or 1.26e11 < (/.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 68.7%

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

   if -5.7e23 < (/.f64 x y) < 1.26e11

   1. Initial program 91.8%

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

      1. +-commutative 91.8%

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

      2. remove-double-neg 91.8%

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

      3. distribute-frac-neg 91.8%

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

      4. unsub-neg 91.8%

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

      5. *-commutative 91.8%

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

      6. associate-*r* 91.8%

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

      7. distribute-rgt1-in 91.8%

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

      8. associate-*r/ 91.8%

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

      9. /-rgt-identity 91.8%

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

      10. fma-neg 91.8%

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

      11. /-rgt-identity 91.8%

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

      12. *-commutative 91.8%

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

      13. fma-def 91.8%

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

      14. *-commutative 91.8%

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

      15. distribute-frac-neg 91.8%

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

      16. remove-double-neg 91.8%

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

   3. Simplified 91.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, 1 - t, 1\right), \frac{2}{z \cdot t}, \frac{x}{y}\right)} \]
   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 56.4%

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

      1. associate-*r/ 56.4%

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

      2. metadata-eval 56.4%

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

      3. +-commutative 56.4%

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

   8. Simplified 56.4%

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

   9. Taylor expanded in x around 0 55.2%

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

       1. sub-neg 55.2%

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

       2. associate-*r/ 55.2%

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

       3. metadata-eval 55.2%

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

       4. metadata-eval 55.2%

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

   11. Simplified 55.2%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.7 \cdot 10^{+23} \lor \neg \left(\frac{x}{y} \leq 126000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 80.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-33} \lor \neg \left(t \leq 1.8 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -9.5e-33) (not (<= t 1.8e+43)))
   (+ (/ x y) -2.0)
   (+ (/ 2.0 t) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.5e-33) || !(t <= 1.8e+43)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) + ((2.0 / t) / z);
	}
	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 <= (-9.5d-33)) .or. (.not. (t <= 1.8d+43))) then
        tmp = (x / y) + (-2.0d0)
    else
        tmp = (2.0d0 / t) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -9.5e-33) || !(t <= 1.8e+43)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -9.5e-33) or not (t <= 1.8e+43):
		tmp = (x / y) + -2.0
	else:
		tmp = (2.0 / t) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -9.5e-33) || !(t <= 1.8e+43))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(Float64(2.0 / t) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -9.5e-33) || ~((t <= 1.8e+43)))
		tmp = (x / y) + -2.0;
	else
		tmp = (2.0 / t) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -9.5e-33], N[Not[LessEqual[t, 1.8e+43]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -9.50000000000000019e-33 or 1.80000000000000005e43 < t

   1. Initial program 76.5%

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

   3. Taylor expanded in t around inf 81.3%

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

   if -9.50000000000000019e-33 < t < 1.80000000000000005e43

   1. Initial program 97.5%

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

   3. Taylor expanded in t around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. metadata-eval 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in z around 0 82.1%

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

      1. associate-*r/ 82.1%

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

      2. metadata-eval 82.1%

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

      3. associate-*r/ 82.1%

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

      4. metadata-eval 82.1%

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

      5. associate-/r* 82.0%

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

   8. Simplified 82.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -9.5 \cdot 10^{-33} \lor \neg \left(t \leq 1.8 \cdot 10^{+43}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 91.7% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-48} \lor \neg \left(z \leq 4.2 \cdot 10^{-21}\right):\\ \;\;\;\;\left(\frac{x}{y} + \frac{2}{t}\right) + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.12e-48) (not (<= z 4.2e-21)))
   (+ (+ (/ x y) (/ 2.0 t)) -2.0)
   (+ (/ x y) (/ (/ 2.0 t) z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.12e-48) || !(z <= 4.2e-21)) {
		tmp = ((x / y) + (2.0 / t)) + -2.0;
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-1.12d-48)) .or. (.not. (z <= 4.2d-21))) then
        tmp = ((x / y) + (2.0d0 / t)) + (-2.0d0)
    else
        tmp = (x / y) + ((2.0d0 / t) / z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -1.12e-48) || !(z <= 4.2e-21)) {
		tmp = ((x / y) + (2.0 / t)) + -2.0;
	} else {
		tmp = (x / y) + ((2.0 / t) / z);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -1.12e-48) or not (z <= 4.2e-21):
		tmp = ((x / y) + (2.0 / t)) + -2.0
	else:
		tmp = (x / y) + ((2.0 / t) / z)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -1.12e-48) || !(z <= 4.2e-21))
		tmp = Float64(Float64(Float64(x / y) + Float64(2.0 / t)) + -2.0);
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) / z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -1.12e-48) || ~((z <= 4.2e-21)))
		tmp = ((x / y) + (2.0 / t)) + -2.0;
	else
		tmp = (x / y) + ((2.0 / t) / z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -1.12e-48], N[Not[LessEqual[z, 4.2e-21]], $MachinePrecision]], N[(N[(N[(x / y), $MachinePrecision] + N[(2.0 / t), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -1.11999999999999999e-48 or 4.20000000000000025e-21 < z

   1. Initial program 77.6%

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

      1. +-commutative 77.6%

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

      2. remove-double-neg 77.6%

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

      3. distribute-frac-neg 77.6%

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

      4. unsub-neg 77.6%

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

      5. *-commutative 77.6%

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

      6. associate-*r* 77.6%

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

      7. distribute-rgt1-in 77.6%

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

      8. associate-*r/ 77.5%

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

      9. /-rgt-identity 77.5%

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

      10. fma-neg 77.5%

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

      11. /-rgt-identity 77.5%

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

      12. *-commutative 77.5%

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

      13. fma-def 77.5%

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

      14. *-commutative 77.5%

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

      15. distribute-frac-neg 77.5%

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

      16. remove-double-neg 77.5%

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

   3. Simplified 77.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, 1 - t, 1\right), \frac{2}{z \cdot t}, \frac{x}{y}\right)} \]
   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 95.6%

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

      1. associate-*r/ 95.6%

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

      2. metadata-eval 95.6%

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

      3. +-commutative 95.6%

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

   8. Simplified 95.6%

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

   if -1.11999999999999999e-48 < z < 4.20000000000000025e-21

   1. Initial program 97.5%

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

   3. Taylor expanded in z around 0 88.8%

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

      1. associate-/r* 88.7%

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

   5. Simplified 88.7%

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

4. Final simplification 92.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-48} \lor \neg \left(z \leq 4.2 \cdot 10^{-21}\right):\\ \;\;\;\;\left(\frac{x}{y} + \frac{2}{t}\right) + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 65.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.1 \cdot 10^{-5}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -7.8e+23)
   (/ x y)
   (if (<= (/ x y) 2.1e-5) (+ (/ 2.0 t) -2.0) (+ (/ x y) -2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -7.8e+23) {
		tmp = x / y;
	} else if ((x / y) <= 2.1e-5) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = (x / y) + -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) <= (-7.8d+23)) then
        tmp = x / y
    else if ((x / y) <= 2.1d-5) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else
        tmp = (x / y) + (-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) <= -7.8e+23) {
		tmp = x / y;
	} else if ((x / y) <= 2.1e-5) {
		tmp = (2.0 / t) + -2.0;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -7.8e+23:
		tmp = x / y
	elif (x / y) <= 2.1e-5:
		tmp = (2.0 / t) + -2.0
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -7.8e+23)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 2.1e-5)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -7.8e+23)
		tmp = x / y;
	elseif ((x / y) <= 2.1e-5)
		tmp = (2.0 / t) + -2.0;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -7.8e+23], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.1e-5], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -7.8000000000000001e23

   1. Initial program 75.0%

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

   3. Taylor expanded in x around inf 67.2%

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

   if -7.8000000000000001e23 < (/.f64 x y) < 2.09999999999999988e-5

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. remove-double-neg 91.6%

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

      3. distribute-frac-neg 91.6%

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

      4. unsub-neg 91.6%

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

      5. *-commutative 91.6%

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

      6. associate-*r* 91.6%

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

      7. distribute-rgt1-in 91.6%

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

      8. associate-*r/ 91.6%

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

      9. /-rgt-identity 91.6%

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

      10. fma-neg 91.6%

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

      11. /-rgt-identity 91.6%

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

      12. *-commutative 91.6%

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

      13. fma-def 91.6%

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

      14. *-commutative 91.6%

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

      15. distribute-frac-neg 91.6%

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

      16. remove-double-neg 91.6%

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

   3. Simplified 91.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, 1 - t, 1\right), \frac{2}{z \cdot t}, \frac{x}{y}\right)} \]
   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 56.4%

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

      1. associate-*r/ 56.4%

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

      2. metadata-eval 56.4%

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

      3. +-commutative 56.4%

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

   8. Simplified 56.4%

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

   9. Taylor expanded in x around 0 55.7%

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

       1. sub-neg 55.7%

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

       2. associate-*r/ 55.7%

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

       3. metadata-eval 55.7%

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

       4. metadata-eval 55.7%

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

   11. Simplified 55.7%

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

   if 2.09999999999999988e-5 < (/.f64 x y)

   1. Initial program 92.2%

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

   3. Taylor expanded in t around inf 70.2%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -7.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.1 \cdot 10^{-5}:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{x}{y} + -2\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -0.185:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-111}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ x y) -2.0)))
   (if (<= z -4.2e+84)
     t_1
     (if (<= z -0.185)
       (+ (/ 2.0 t) -2.0)
       (if (<= z 4.2e-111) (/ 2.0 (* z t)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (z <= -4.2e+84) {
		tmp = t_1;
	} else if (z <= -0.185) {
		tmp = (2.0 / t) + -2.0;
	} else if (z <= 4.2e-111) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (x / y) + (-2.0d0)
    if (z <= (-4.2d+84)) then
        tmp = t_1
    else if (z <= (-0.185d0)) then
        tmp = (2.0d0 / t) + (-2.0d0)
    else if (z <= 4.2d-111) then
        tmp = 2.0d0 / (z * t)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (x / y) + -2.0;
	double tmp;
	if (z <= -4.2e+84) {
		tmp = t_1;
	} else if (z <= -0.185) {
		tmp = (2.0 / t) + -2.0;
	} else if (z <= 4.2e-111) {
		tmp = 2.0 / (z * t);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (x / y) + -2.0
	tmp = 0
	if z <= -4.2e+84:
		tmp = t_1
	elif z <= -0.185:
		tmp = (2.0 / t) + -2.0
	elif z <= 4.2e-111:
		tmp = 2.0 / (z * t)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (z <= -4.2e+84)
		tmp = t_1;
	elseif (z <= -0.185)
		tmp = Float64(Float64(2.0 / t) + -2.0);
	elseif (z <= 4.2e-111)
		tmp = Float64(2.0 / Float64(z * t));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (x / y) + -2.0;
	tmp = 0.0;
	if (z <= -4.2e+84)
		tmp = t_1;
	elseif (z <= -0.185)
		tmp = (2.0 / t) + -2.0;
	elseif (z <= 4.2e-111)
		tmp = 2.0 / (z * t);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[z, -4.2e+84], t$95$1, If[LessEqual[z, -0.185], N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision], If[LessEqual[z, 4.2e-111], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.20000000000000037e84 or 4.1999999999999997e-111 < z

   1. Initial program 77.2%

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

   3. Taylor expanded in t around inf 66.4%

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

   if -4.20000000000000037e84 < z < -0.185

   1. Initial program 91.6%

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

      1. +-commutative 91.6%

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

      2. remove-double-neg 91.6%

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

      3. distribute-frac-neg 91.6%

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

      4. unsub-neg 91.6%

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

      5. *-commutative 91.6%

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

      6. associate-*r* 91.6%

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

      7. distribute-rgt1-in 91.6%

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

      8. associate-*r/ 91.5%

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

      9. /-rgt-identity 91.5%

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

      10. fma-neg 91.5%

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

      11. /-rgt-identity 91.5%

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

      12. *-commutative 91.5%

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

      13. fma-def 91.5%

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

      14. *-commutative 91.5%

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

      15. distribute-frac-neg 91.5%

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

      16. remove-double-neg 91.5%

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

   3. Simplified 91.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(z, 1 - t, 1\right), \frac{2}{z \cdot t}, \frac{x}{y}\right)} \]
   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 94.6%

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

      1. associate-*r/ 94.6%

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

      2. metadata-eval 94.6%

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

      3. +-commutative 94.6%

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

   8. Simplified 94.6%

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

   9. Taylor expanded in x around 0 70.3%

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

       1. sub-neg 70.3%

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

       2. associate-*r/ 70.3%

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

       3. metadata-eval 70.3%

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

       4. metadata-eval 70.3%

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

   11. Simplified 70.3%

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

   if -0.185 < z < 4.1999999999999997e-111

   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 z around 0 88.4%

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

      1. associate-/r* 88.3%

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

   5. Simplified 88.3%

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

      1. +-commutative 88.3%

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

      2. frac-add 79.9%

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

   7. Applied egg-rr 79.9%

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

   8. Taylor expanded in t around 0 66.8%

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

4. Final simplification 67.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{elif}\;z \leq -0.185:\\ \;\;\;\;\frac{2}{t} + -2\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-111}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 80.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-33} \lor \neg \left(t \leq 1.4 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.25e-33) (not (<= t 1.4e+41)))
   (+ (/ 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 <= -2.25e-33) || !(t <= 1.4e+41)) {
		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 <= (-2.25d-33)) .or. (.not. (t <= 1.4d+41))) 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 <= -2.25e-33) || !(t <= 1.4e+41)) {
		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 <= -2.25e-33) or not (t <= 1.4e+41):
		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 <= -2.25e-33) || !(t <= 1.4e+41))
		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 <= -2.25e-33) || ~((t <= 1.4e+41)))
		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, -2.25e-33], N[Not[LessEqual[t, 1.4e+41]], $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 < -2.24999999999999995e-33 or 1.4e41 < t

   1. Initial program 76.5%

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

   3. Taylor expanded in t around inf 81.3%

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

   if -2.24999999999999995e-33 < t < 1.4e41

   1. Initial program 97.5%

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

   3. Taylor expanded in t around 0 82.0%

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

      1. associate-*r/ 82.0%

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

      2. metadata-eval 82.0%

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

   5. Simplified 82.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.25 \cdot 10^{-33} \lor \neg \left(t \leq 1.4 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.8% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-32}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 0.245:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -1.12e-32) -2.0 (if (<= t 0.245) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -1.12e-32) {
		tmp = -2.0;
	} else if (t <= 0.245) {
		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 <= (-1.12d-32)) then
        tmp = -2.0d0
    else if (t <= 0.245d0) 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 <= -1.12e-32) {
		tmp = -2.0;
	} else if (t <= 0.245) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -1.12e-32:
		tmp = -2.0
	elif t <= 0.245:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -1.12e-32)
		tmp = -2.0;
	elseif (t <= 0.245)
		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 <= -1.12e-32)
		tmp = -2.0;
	elseif (t <= 0.245)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -1.12e-32], -2.0, If[LessEqual[t, 0.245], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -1.12e-32 or 0.245 < t

   1. Initial program 78.7%

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

      1. +-commutative 78.7%

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

      2. remove-double-neg 78.7%

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

      3. distribute-frac-neg 78.7%

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

      4. unsub-neg 78.7%

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

      5. *-commutative 78.7%

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

      6. associate-*r* 78.7%

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

      7. distribute-rgt1-in 78.7%

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

      8. associate-*r/ 78.7%

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

      9. /-rgt-identity 78.7%

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

      10. fma-neg 78.7%

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

      11. /-rgt-identity 78.7%

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

      12. *-commutative 78.7%

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

      13. fma-def 78.7%

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

      14. *-commutative 78.7%

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

      15. distribute-frac-neg 78.7%

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

      16. remove-double-neg 78.7%

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

   3. Simplified 78.7%

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

   5. Taylor expanded in x around 0 41.6%

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

   6. Taylor expanded in t around inf 26.1%

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

   if -1.12e-32 < t < 0.245

   1. Initial program 97.3%

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

   3. Taylor expanded in t around 0 84.3%

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

      1. associate-*r/ 84.3%

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

      2. metadata-eval 84.3%

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

   5. Simplified 84.3%

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

   6. Taylor expanded in z around inf 38.2%

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

4. Final simplification 31.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-32}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 0.245:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 20.2% accurate, 17.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.4%

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

   1. +-commutative 87.4%

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

   2. remove-double-neg 87.4%

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

   3. distribute-frac-neg 87.4%

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

   4. unsub-neg 87.4%

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

   5. *-commutative 87.4%

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

   6. associate-*r* 87.4%

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

   7. distribute-rgt1-in 87.4%

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

   8. associate-*r/ 87.4%

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

   9. /-rgt-identity 87.4%

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

   10. fma-neg 87.4%

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

   11. /-rgt-identity 87.4%

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

   12. *-commutative 87.4%

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

   13. fma-def 87.4%

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

   14. *-commutative 87.4%

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

   15. distribute-frac-neg 87.4%

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

   16. remove-double-neg 87.4%

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

3. Simplified 87.4%

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

5. Taylor expanded in x around 0 61.4%

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

6. Taylor expanded in t around inf 15.0%

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

7. Final simplification 15.0%

   \[\leadsto -2 \]
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 2024010 
(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))))