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

Percentage Accurate: 86.7% → 99.3%

Time: 13.3s

Alternatives: 12

Speedup: 1.3×

• 23.2% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 86.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 83.5%

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

   1. +-commutative 83.5%

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

   2. remove-double-neg 83.5%

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

   3. distribute-frac-neg 83.5%

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

   4. unsub-neg 83.5%

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

   5. *-commutative 83.5%

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

   6. associate-*r* 83.5%

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

   7. distribute-rgt1-in 83.5%

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

   8. associate-/l* 83.4%

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

   9. fma-neg 83.4%

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

   10. *-commutative 83.4%

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

   11. fma-define 83.4%

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

   12. *-commutative 83.4%

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

   13. distribute-frac-neg 83.4%

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

   14. remove-double-neg 83.4%

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

3. Simplified 83.4%

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

5. Taylor expanded in t around inf 99.5%

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

   1. +-commutative 99.5%

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

   2. associate--l+ 99.5%

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

   3. associate-*r/ 99.5%

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

   4. distribute-lft-in 99.5%

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

   5. metadata-eval 99.5%

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

   6. associate-*r/ 99.5%

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

   7. metadata-eval 99.5%

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

7. Simplified 99.5%

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

8. Final simplification 99.5%

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

Alternative 2: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{z \cdot t}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -4.3 \cdot 10^{-53}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-178}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-298}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-272}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-233}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-110}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* z t))) (t_2 (- (/ x y) 2.0)))
   (if (<= t -4.3e-53)
     t_2
     (if (<= t -1e-121)
       t_1
       (if (<= t -7.2e-178)
         t_2
         (if (<= t 5.2e-298)
           t_1
           (if (<= t 1.95e-272)
             (/ 2.0 t)
             (if (<= t 3.25e-233)
               t_1
               (if (<= t 3.9e-110) (/ 2.0 t) t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -4.3e-53) {
		tmp = t_2;
	} else if (t <= -1e-121) {
		tmp = t_1;
	} else if (t <= -7.2e-178) {
		tmp = t_2;
	} else if (t <= 5.2e-298) {
		tmp = t_1;
	} else if (t <= 1.95e-272) {
		tmp = 2.0 / t;
	} else if (t <= 3.25e-233) {
		tmp = t_1;
	} else if (t <= 3.9e-110) {
		tmp = 2.0 / t;
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_1 = 2.0d0 / (z * t)
    t_2 = (x / y) - 2.0d0
    if (t <= (-4.3d-53)) then
        tmp = t_2
    else if (t <= (-1d-121)) then
        tmp = t_1
    else if (t <= (-7.2d-178)) then
        tmp = t_2
    else if (t <= 5.2d-298) then
        tmp = t_1
    else if (t <= 1.95d-272) then
        tmp = 2.0d0 / t
    else if (t <= 3.25d-233) then
        tmp = t_1
    else if (t <= 3.9d-110) then
        tmp = 2.0d0 / t
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = 2.0 / (z * t);
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -4.3e-53) {
		tmp = t_2;
	} else if (t <= -1e-121) {
		tmp = t_1;
	} else if (t <= -7.2e-178) {
		tmp = t_2;
	} else if (t <= 5.2e-298) {
		tmp = t_1;
	} else if (t <= 1.95e-272) {
		tmp = 2.0 / t;
	} else if (t <= 3.25e-233) {
		tmp = t_1;
	} else if (t <= 3.9e-110) {
		tmp = 2.0 / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = 2.0 / (z * t)
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -4.3e-53:
		tmp = t_2
	elif t <= -1e-121:
		tmp = t_1
	elif t <= -7.2e-178:
		tmp = t_2
	elif t <= 5.2e-298:
		tmp = t_1
	elif t <= 1.95e-272:
		tmp = 2.0 / t
	elif t <= 3.25e-233:
		tmp = t_1
	elif t <= 3.9e-110:
		tmp = 2.0 / t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(z * t))
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -4.3e-53)
		tmp = t_2;
	elseif (t <= -1e-121)
		tmp = t_1;
	elseif (t <= -7.2e-178)
		tmp = t_2;
	elseif (t <= 5.2e-298)
		tmp = t_1;
	elseif (t <= 1.95e-272)
		tmp = Float64(2.0 / t);
	elseif (t <= 3.25e-233)
		tmp = t_1;
	elseif (t <= 3.9e-110)
		tmp = Float64(2.0 / t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = 2.0 / (z * t);
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -4.3e-53)
		tmp = t_2;
	elseif (t <= -1e-121)
		tmp = t_1;
	elseif (t <= -7.2e-178)
		tmp = t_2;
	elseif (t <= 5.2e-298)
		tmp = t_1;
	elseif (t <= 1.95e-272)
		tmp = 2.0 / t;
	elseif (t <= 3.25e-233)
		tmp = t_1;
	elseif (t <= 3.9e-110)
		tmp = 2.0 / t;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[t, -4.3e-53], t$95$2, If[LessEqual[t, -1e-121], t$95$1, If[LessEqual[t, -7.2e-178], t$95$2, If[LessEqual[t, 5.2e-298], t$95$1, If[LessEqual[t, 1.95e-272], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 3.25e-233], t$95$1, If[LessEqual[t, 3.9e-110], N[(2.0 / t), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -4.3e-53 or -9.9999999999999998e-122 < t < -7.19999999999999987e-178 or 3.9e-110 < t

   1. Initial program 76.4%

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

   3. Taylor expanded in t around inf 81.9%

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

   if -4.3e-53 < t < -9.9999999999999998e-122 or -7.19999999999999987e-178 < t < 5.1999999999999998e-298 or 1.9499999999999999e-272 < t < 3.24999999999999995e-233

   1. Initial program 97.9%

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

      1. +-commutative 97.9%

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

      2. remove-double-neg 97.9%

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

      3. distribute-frac-neg 97.9%

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

      4. unsub-neg 97.9%

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

      5. *-commutative 97.9%

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

      6. associate-*r* 97.9%

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

      7. distribute-rgt1-in 97.9%

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

      8. associate-/l* 97.9%

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

      9. fma-neg 97.8%

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

      10. *-commutative 97.8%

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

      11. fma-define 97.8%

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

      12. *-commutative 97.8%

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

      13. distribute-frac-neg 97.8%

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

      14. remove-double-neg 97.8%

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

   3. Simplified 97.8%

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

   5. Taylor expanded in t around inf 97.9%

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

      1. +-commutative 97.9%

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

      2. associate--l+ 97.9%

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

      3. associate-*r/ 97.9%

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

      4. distribute-lft-in 97.9%

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

      5. metadata-eval 97.9%

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

      6. associate-*r/ 97.9%

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

      7. metadata-eval 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in z around 0 65.0%

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

   if 5.1999999999999998e-298 < t < 1.9499999999999999e-272 or 3.24999999999999995e-233 < t < 3.9e-110

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 96.8%

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

      1. associate-*r/ 96.8%

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

      2. metadata-eval 96.8%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in z around inf 69.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -4.3 \cdot 10^{-53}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-121}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq -7.2 \cdot 10^{-178}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-298}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{-272}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{-233}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-110}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{t}}{z}\\ t_2 := \frac{x}{y} - 2\\ \mathbf{if}\;t \leq -1.58 \cdot 10^{-55}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-117}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-179}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-297}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-272}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-110}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (/ 2.0 t) z)) (t_2 (- (/ x y) 2.0)))
   (if (<= t -1.58e-55)
     t_2
     (if (<= t -4.2e-117)
       t_1
       (if (<= t -2e-179)
         t_2
         (if (<= t 5e-297)
           (/ 2.0 (* z t))
           (if (<= t 1.1e-272)
             (/ 2.0 t)
             (if (<= t 1.5e-232)
               t_1
               (if (<= t 1.02e-110) (/ 2.0 t) t_2)))))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 / t) / z;
	double t_2 = (x / y) - 2.0;
	double tmp;
	if (t <= -1.58e-55) {
		tmp = t_2;
	} else if (t <= -4.2e-117) {
		tmp = t_1;
	} else if (t <= -2e-179) {
		tmp = t_2;
	} else if (t <= 5e-297) {
		tmp = 2.0 / (z * t);
	} else if (t <= 1.1e-272) {
		tmp = 2.0 / t;
	} else if (t <= 1.5e-232) {
		tmp = t_1;
	} else if (t <= 1.02e-110) {
		tmp = 2.0 / t;
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_1 = (2.0d0 / t) / z
    t_2 = (x / y) - 2.0d0
    if (t <= (-1.58d-55)) then
        tmp = t_2
    else if (t <= (-4.2d-117)) then
        tmp = t_1
    else if (t <= (-2d-179)) then
        tmp = t_2
    else if (t <= 5d-297) then
        tmp = 2.0d0 / (z * t)
    else if (t <= 1.1d-272) then
        tmp = 2.0d0 / t
    else if (t <= 1.5d-232) then
        tmp = t_1
    else if (t <= 1.02d-110) then
        tmp = 2.0d0 / t
    else
        tmp = t_2
    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) - 2.0;
	double tmp;
	if (t <= -1.58e-55) {
		tmp = t_2;
	} else if (t <= -4.2e-117) {
		tmp = t_1;
	} else if (t <= -2e-179) {
		tmp = t_2;
	} else if (t <= 5e-297) {
		tmp = 2.0 / (z * t);
	} else if (t <= 1.1e-272) {
		tmp = 2.0 / t;
	} else if (t <= 1.5e-232) {
		tmp = t_1;
	} else if (t <= 1.02e-110) {
		tmp = 2.0 / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (2.0 / t) / z
	t_2 = (x / y) - 2.0
	tmp = 0
	if t <= -1.58e-55:
		tmp = t_2
	elif t <= -4.2e-117:
		tmp = t_1
	elif t <= -2e-179:
		tmp = t_2
	elif t <= 5e-297:
		tmp = 2.0 / (z * t)
	elif t <= 1.1e-272:
		tmp = 2.0 / t
	elif t <= 1.5e-232:
		tmp = t_1
	elif t <= 1.02e-110:
		tmp = 2.0 / t
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 / t) / z)
	t_2 = Float64(Float64(x / y) - 2.0)
	tmp = 0.0
	if (t <= -1.58e-55)
		tmp = t_2;
	elseif (t <= -4.2e-117)
		tmp = t_1;
	elseif (t <= -2e-179)
		tmp = t_2;
	elseif (t <= 5e-297)
		tmp = Float64(2.0 / Float64(z * t));
	elseif (t <= 1.1e-272)
		tmp = Float64(2.0 / t);
	elseif (t <= 1.5e-232)
		tmp = t_1;
	elseif (t <= 1.02e-110)
		tmp = Float64(2.0 / t);
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (2.0 / t) / z;
	t_2 = (x / y) - 2.0;
	tmp = 0.0;
	if (t <= -1.58e-55)
		tmp = t_2;
	elseif (t <= -4.2e-117)
		tmp = t_1;
	elseif (t <= -2e-179)
		tmp = t_2;
	elseif (t <= 5e-297)
		tmp = 2.0 / (z * t);
	elseif (t <= 1.1e-272)
		tmp = 2.0 / t;
	elseif (t <= 1.5e-232)
		tmp = t_1;
	elseif (t <= 1.02e-110)
		tmp = 2.0 / t;
	else
		tmp = t_2;
	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] - 2.0), $MachinePrecision]}, If[LessEqual[t, -1.58e-55], t$95$2, If[LessEqual[t, -4.2e-117], t$95$1, If[LessEqual[t, -2e-179], t$95$2, If[LessEqual[t, 5e-297], N[(2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.1e-272], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 1.5e-232], t$95$1, If[LessEqual[t, 1.02e-110], N[(2.0 / t), $MachinePrecision], t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.58000000000000007e-55 or -4.1999999999999998e-117 < t < -2e-179 or 1.02000000000000006e-110 < t

   1. Initial program 76.4%

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

   3. Taylor expanded in t around inf 81.9%

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

   if -1.58000000000000007e-55 < t < -4.1999999999999998e-117 or 1.09999999999999994e-272 < t < 1.49999999999999995e-232

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. frac-2neg 99.7%

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

      3. frac-add 91.1%

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

      4. +-commutative 91.1%

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

      5. fma-define 91.1%

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

      6. *-commutative 91.1%

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

      7. *-commutative 91.1%

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

      8. *-commutative 91.1%

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

   4. Applied egg-rr 91.1%

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

   5. Taylor expanded in t around 0 90.0%

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

   6. Taylor expanded in z around 0 68.6%

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

      1. associate-/r* 68.7%

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

   8. Simplified 68.7%

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

   if -2e-179 < t < 5e-297

   1. Initial program 96.4%

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

      1. +-commutative 96.4%

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

      2. remove-double-neg 96.4%

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

      3. distribute-frac-neg 96.4%

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

      4. unsub-neg 96.4%

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

      5. *-commutative 96.4%

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

      6. associate-*r* 96.4%

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

      7. distribute-rgt1-in 96.4%

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

      8. associate-/l* 96.4%

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

      9. fma-neg 96.4%

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

      10. *-commutative 96.4%

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

      11. fma-define 96.4%

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

      12. *-commutative 96.4%

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

      13. distribute-frac-neg 96.4%

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

      14. remove-double-neg 96.4%

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

   3. Simplified 96.4%

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

   5. Taylor expanded in t around inf 96.4%

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

      1. +-commutative 96.4%

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

      2. associate--l+ 96.4%

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

      3. associate-*r/ 96.4%

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

      4. distribute-lft-in 96.4%

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

      5. metadata-eval 96.4%

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

      6. associate-*r/ 96.4%

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

      7. metadata-eval 96.4%

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

   7. Simplified 96.4%

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

   8. Taylor expanded in z around 0 62.1%

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

   if 5e-297 < t < 1.09999999999999994e-272 or 1.49999999999999995e-232 < t < 1.02000000000000006e-110

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0 96.8%

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

      1. associate-*r/ 96.8%

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

      2. metadata-eval 96.8%

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

   5. Simplified 96.8%

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

   6. Taylor expanded in z around inf 69.5%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.58 \cdot 10^{-55}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-117}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-179}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-297}:\\ \;\;\;\;\frac{2}{z \cdot t}\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-272}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-232}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-110}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.15 \cdot 10^{-27}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.65 \cdot 10^{-20}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.6 \cdot 10^{+26}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -5.8e+30)
   (/ x y)
   (if (<= (/ x y) -2.15e-27)
     (/ 2.0 t)
     (if (<= (/ x y) 2.65e-20)
       -2.0
       (if (<= (/ x y) 1.6e+26) (/ 2.0 t) (/ x y))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5.8e+30) {
		tmp = x / y;
	} else if ((x / y) <= -2.15e-27) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.65e-20) {
		tmp = -2.0;
	} else if ((x / y) <= 1.6e+26) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-5.8d+30)) then
        tmp = x / y
    else if ((x / y) <= (-2.15d-27)) then
        tmp = 2.0d0 / t
    else if ((x / y) <= 2.65d-20) then
        tmp = -2.0d0
    else if ((x / y) <= 1.6d+26) then
        tmp = 2.0d0 / t
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -5.8e+30) {
		tmp = x / y;
	} else if ((x / y) <= -2.15e-27) {
		tmp = 2.0 / t;
	} else if ((x / y) <= 2.65e-20) {
		tmp = -2.0;
	} else if ((x / y) <= 1.6e+26) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -5.8e+30:
		tmp = x / y
	elif (x / y) <= -2.15e-27:
		tmp = 2.0 / t
	elif (x / y) <= 2.65e-20:
		tmp = -2.0
	elif (x / y) <= 1.6e+26:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -5.8e+30)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= -2.15e-27)
		tmp = Float64(2.0 / t);
	elseif (Float64(x / y) <= 2.65e-20)
		tmp = -2.0;
	elseif (Float64(x / y) <= 1.6e+26)
		tmp = Float64(2.0 / t);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -5.8e+30)
		tmp = x / y;
	elseif ((x / y) <= -2.15e-27)
		tmp = 2.0 / t;
	elseif ((x / y) <= 2.65e-20)
		tmp = -2.0;
	elseif ((x / y) <= 1.6e+26)
		tmp = 2.0 / t;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -5.8e+30], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], -2.15e-27], N[(2.0 / t), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2.65e-20], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 1.6e+26], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -5.7999999999999996e30 or 1.60000000000000014e26 < (/.f64 x y)

   1. Initial program 78.4%

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

   3. Taylor expanded in x around inf 79.8%

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

   if -5.7999999999999996e30 < (/.f64 x y) < -2.15000000000000001e-27 or 2.6500000000000001e-20 < (/.f64 x y) < 1.60000000000000014e26

   1. Initial program 99.7%

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

   3. Taylor expanded in t around 0 87.3%

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

      1. associate-*r/ 87.3%

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

      2. metadata-eval 87.3%

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

   5. Simplified 87.3%

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

   6. Taylor expanded in z around inf 51.8%

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

   if -2.15000000000000001e-27 < (/.f64 x y) < 2.6500000000000001e-20

   1. Initial program 85.2%

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

   3. Taylor expanded in t around inf 48.3%

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

   4. Taylor expanded in x around 0 48.3%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5.8 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq -2.15 \cdot 10^{-27}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.65 \cdot 10^{-20}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 1.6 \cdot 10^{+26}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 - \frac{-2}{z \cdot t}\\ t_2 := \frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{-9}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-225}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-133}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-29}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- -2.0 (/ -2.0 (* z t)))) (t_2 (+ (/ x y) (+ (/ 2.0 t) -2.0))))
   (if (<= z -1.9e-9)
     t_2
     (if (<= z 2.1e-225)
       t_1
       (if (<= z 6.2e-133) (- (/ x y) 2.0) (if (<= z 9e-29) t_1 t_2))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 - (-2.0 / (z * t));
	double t_2 = (x / y) + ((2.0 / t) + -2.0);
	double tmp;
	if (z <= -1.9e-9) {
		tmp = t_2;
	} else if (z <= 2.1e-225) {
		tmp = t_1;
	} else if (z <= 6.2e-133) {
		tmp = (x / y) - 2.0;
	} else if (z <= 9e-29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	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) :: tmp
    t_1 = (-2.0d0) - ((-2.0d0) / (z * t))
    t_2 = (x / y) + ((2.0d0 / t) + (-2.0d0))
    if (z <= (-1.9d-9)) then
        tmp = t_2
    else if (z <= 2.1d-225) then
        tmp = t_1
    else if (z <= 6.2d-133) then
        tmp = (x / y) - 2.0d0
    else if (z <= 9d-29) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 - (-2.0 / (z * t));
	double t_2 = (x / y) + ((2.0 / t) + -2.0);
	double tmp;
	if (z <= -1.9e-9) {
		tmp = t_2;
	} else if (z <= 2.1e-225) {
		tmp = t_1;
	} else if (z <= 6.2e-133) {
		tmp = (x / y) - 2.0;
	} else if (z <= 9e-29) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 - (-2.0 / (z * t))
	t_2 = (x / y) + ((2.0 / t) + -2.0)
	tmp = 0
	if z <= -1.9e-9:
		tmp = t_2
	elif z <= 2.1e-225:
		tmp = t_1
	elif z <= 6.2e-133:
		tmp = (x / y) - 2.0
	elif z <= 9e-29:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 - Float64(-2.0 / Float64(z * t)))
	t_2 = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0))
	tmp = 0.0
	if (z <= -1.9e-9)
		tmp = t_2;
	elseif (z <= 2.1e-225)
		tmp = t_1;
	elseif (z <= 6.2e-133)
		tmp = Float64(Float64(x / y) - 2.0);
	elseif (z <= 9e-29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 - (-2.0 / (z * t));
	t_2 = (x / y) + ((2.0 / t) + -2.0);
	tmp = 0.0;
	if (z <= -1.9e-9)
		tmp = t_2;
	elseif (z <= 2.1e-225)
		tmp = t_1;
	elseif (z <= 6.2e-133)
		tmp = (x / y) - 2.0;
	elseif (z <= 9e-29)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 - N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e-9], t$95$2, If[LessEqual[z, 2.1e-225], t$95$1, If[LessEqual[z, 6.2e-133], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], If[LessEqual[z, 9e-29], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.90000000000000006e-9 or 8.9999999999999996e-29 < z

   1. Initial program 72.4%

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

   3. Taylor expanded in z around inf 98.2%

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

      1. div-sub 98.2%

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

      2. sub-neg 98.2%

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

      3. *-inverses 98.2%

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

      4. metadata-eval 98.2%

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

      5. distribute-lft-in 98.2%

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

      6. associate-*r/ 98.2%

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

      7. metadata-eval 98.2%

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

      8. metadata-eval 98.2%

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

   5. Simplified 98.2%

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

   if -1.90000000000000006e-9 < z < 2.1e-225 or 6.20000000000000032e-133 < z < 8.9999999999999996e-29

   1. Initial program 98.9%

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

      1. +-commutative 98.9%

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

      2. remove-double-neg 98.9%

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

      3. distribute-frac-neg 98.9%

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

      4. unsub-neg 98.9%

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

      5. *-commutative 98.9%

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

      6. associate-*r* 98.9%

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

      7. distribute-rgt1-in 98.9%

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

      8. associate-/l* 98.8%

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

      9. fma-neg 98.8%

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

      10. *-commutative 98.8%

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

      11. fma-define 98.8%

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

      12. *-commutative 98.8%

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

      13. distribute-frac-neg 98.8%

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

      14. remove-double-neg 98.8%

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

   3. Simplified 98.8%

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

   5. Taylor expanded in t around inf 98.9%

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

      1. +-commutative 98.9%

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

      2. associate--l+ 98.9%

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

      3. associate-*r/ 98.9%

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

      4. distribute-lft-in 98.9%

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

      5. metadata-eval 98.9%

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

      6. associate-*r/ 98.9%

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

      7. metadata-eval 98.9%

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

   7. Simplified 98.9%

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

   8. Taylor expanded in z around 0 98.5%

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

   9. Taylor expanded in x around 0 78.0%

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

       1. sub-neg 78.0%

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

       2. associate-*r/ 78.0%

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

       3. metadata-eval 78.0%

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

       4. *-commutative 78.0%

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

       5. metadata-eval 78.0%

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

       6. +-commutative 78.0%

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

       7. metadata-eval 78.0%

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

       8. distribute-neg-frac 78.0%

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

       9. unsub-neg 78.0%

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

       10. *-commutative 78.0%

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

   11. Simplified 78.0%

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

   if 2.1e-225 < z < 6.20000000000000032e-133

   1. Initial program 100.0%

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

   3. Taylor expanded in t around inf 87.9%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-225}:\\ \;\;\;\;-2 - \frac{-2}{z \cdot t}\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-133}:\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{elif}\;z \leq 9 \cdot 10^{-29}:\\ \;\;\;\;-2 - \frac{-2}{z \cdot t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+38} \lor \neg \left(\frac{x}{y} \leq 6.5 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{-2}{z \cdot t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+38) (not (<= (/ x y) 6.5e+25)))
   (/ x y)
   (- -2.0 (/ -2.0 (* z t)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+38) || !((x / y) <= 6.5e+25)) {
		tmp = x / y;
	} else {
		tmp = -2.0 - (-2.0 / (z * t));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-1d+38)) .or. (.not. ((x / y) <= 6.5d+25))) then
        tmp = x / y
    else
        tmp = (-2.0d0) - ((-2.0d0) / (z * t))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+38) || !((x / y) <= 6.5e+25)) {
		tmp = x / y;
	} else {
		tmp = -2.0 - (-2.0 / (z * t));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+38) or not ((x / y) <= 6.5e+25):
		tmp = x / y
	else:
		tmp = -2.0 - (-2.0 / (z * t))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -1e+38) || !(Float64(x / y) <= 6.5e+25))
		tmp = Float64(x / y);
	else
		tmp = Float64(-2.0 - Float64(-2.0 / Float64(z * t)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -1e+38) || ~(((x / y) <= 6.5e+25)))
		tmp = x / y;
	else
		tmp = -2.0 - (-2.0 / (z * t));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -1e+38], N[Not[LessEqual[N[(x / y), $MachinePrecision], 6.5e+25]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(-2.0 - N[(-2.0 / N[(z * t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999977e37 or 6.50000000000000005e25 < (/.f64 x y)

   1. Initial program 78.2%

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

   3. Taylor expanded in x around inf 80.5%

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

   if -9.99999999999999977e37 < (/.f64 x y) < 6.50000000000000005e25

   1. Initial program 87.5%

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

      1. +-commutative 87.5%

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

      2. remove-double-neg 87.5%

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

      3. distribute-frac-neg 87.5%

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

      4. unsub-neg 87.5%

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

      5. *-commutative 87.5%

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

      6. associate-*r* 87.5%

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

      7. distribute-rgt1-in 87.5%

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

      8. associate-/l* 87.4%

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

      9. fma-neg 87.4%

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

      10. *-commutative 87.4%

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

      11. fma-define 87.4%

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

      12. *-commutative 87.4%

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

      13. distribute-frac-neg 87.4%

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

      14. 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 inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. associate-*r/ 99.9%

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

      4. distribute-lft-in 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*r/ 99.9%

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

      7. metadata-eval 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around 0 75.3%

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

   9. Taylor expanded in x around 0 74.0%

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

       1. sub-neg 74.0%

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

       2. associate-*r/ 74.0%

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

       3. metadata-eval 74.0%

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

       4. *-commutative 74.0%

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

       5. metadata-eval 74.0%

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

       6. +-commutative 74.0%

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

       7. metadata-eval 74.0%

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

       8. distribute-neg-frac 74.0%

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

       9. unsub-neg 74.0%

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

       10. *-commutative 74.0%

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

   11. Simplified 74.0%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+38} \lor \neg \left(\frac{x}{y} \leq 6.5 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{-2}{z \cdot t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -90000000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{\frac{2}{z}}{t} - 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -90000000000000.0) (not (<= z 1.0)))
   (+ (/ x y) (+ (/ 2.0 t) -2.0))
   (+ (/ x y) (- (/ (/ 2.0 z) t) 2.0))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -90000000000000.0) || !(z <= 1.0)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (((2.0 / z) / t) - 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((z <= (-90000000000000.0d0)) .or. (.not. (z <= 1.0d0))) then
        tmp = (x / y) + ((2.0d0 / t) + (-2.0d0))
    else
        tmp = (x / y) + (((2.0d0 / z) / t) - 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -90000000000000.0) || !(z <= 1.0)) {
		tmp = (x / y) + ((2.0 / t) + -2.0);
	} else {
		tmp = (x / y) + (((2.0 / z) / t) - 2.0);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -90000000000000.0) or not (z <= 1.0):
		tmp = (x / y) + ((2.0 / t) + -2.0)
	else:
		tmp = (x / y) + (((2.0 / z) / t) - 2.0)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -90000000000000.0) || !(z <= 1.0))
		tmp = Float64(Float64(x / y) + Float64(Float64(2.0 / t) + -2.0));
	else
		tmp = Float64(Float64(x / y) + Float64(Float64(Float64(2.0 / z) / t) - 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -90000000000000.0) || ~((z <= 1.0)))
		tmp = (x / y) + ((2.0 / t) + -2.0);
	else
		tmp = (x / y) + (((2.0 / z) / t) - 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -90000000000000.0], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -9e13 or 1 < z

   1. Initial program 70.0%

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

   3. Taylor expanded in z around inf 100.0%

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

      1. div-sub 100.0%

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

      2. sub-neg 100.0%

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

      3. *-inverses 100.0%

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

      4. metadata-eval 100.0%

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

      5. distribute-lft-in 100.0%

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

      6. associate-*r/ 100.0%

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

      7. metadata-eval 100.0%

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

      8. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

   if -9e13 < z < 1

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      2. remove-double-neg 99.0%

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

      3. distribute-frac-neg 99.0%

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

      4. unsub-neg 99.0%

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

      5. *-commutative 99.0%

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

      6. associate-*r* 99.0%

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

      7. distribute-rgt1-in 99.0%

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

      8. associate-/l* 99.0%

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

      9. fma-neg 99.0%

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

      10. *-commutative 99.0%

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

      11. fma-define 99.0%

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

      12. *-commutative 99.0%

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

      13. distribute-frac-neg 99.0%

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

      14. remove-double-neg 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in t around inf 99.0%

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

      1. +-commutative 99.0%

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

      2. associate--l+ 99.0%

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

      3. associate-*r/ 99.0%

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

      4. distribute-lft-in 99.0%

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

      5. metadata-eval 99.0%

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

      6. associate-*r/ 99.0%

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

      7. metadata-eval 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in z around 0 97.7%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -90000000000000 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \left(\frac{\frac{2}{z}}{t} - 2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 90.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-10} \lor \neg \left(z \leq 3.3 \cdot 10^{-115}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -1.26e-10) (not (<= z 3.3e-115)))
   (+ (/ 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 <= -1.26e-10) || !(z <= 3.3e-115)) {
		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 <= (-1.26d-10)) .or. (.not. (z <= 3.3d-115))) 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 <= -1.26e-10) || !(z <= 3.3e-115)) {
		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 <= -1.26e-10) or not (z <= 3.3e-115):
		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 <= -1.26e-10) || !(z <= 3.3e-115))
		tmp = Float64(Float64(x / y) + Float64(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 <= -1.26e-10) || ~((z <= 3.3e-115)))
		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, -1.26e-10], N[Not[LessEqual[z, 3.3e-115]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 / t), $MachinePrecision] + -2.0), $MachinePrecision]), $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 < -1.26000000000000004e-10 or 3.2999999999999999e-115 < z

   1. Initial program 74.9%

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

   3. Taylor expanded in z around inf 94.6%

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

      1. div-sub 94.6%

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

      2. sub-neg 94.6%

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

      3. *-inverses 94.6%

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

      4. metadata-eval 94.6%

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

      5. distribute-lft-in 94.6%

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

      6. associate-*r/ 94.6%

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

      7. metadata-eval 94.6%

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

      8. metadata-eval 94.6%

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

   5. Simplified 94.6%

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

   if -1.26000000000000004e-10 < z < 3.2999999999999999e-115

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 88.0%

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

      1. associate-/r* 88.0%

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

   5. Simplified 88.0%

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

4. Final simplification 92.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.26 \cdot 10^{-10} \lor \neg \left(z \leq 3.3 \cdot 10^{-115}\right):\\ \;\;\;\;\frac{x}{y} + \left(\frac{2}{t} + -2\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\frac{2}{t}}{z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 80.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-45} \lor \neg \left(t \leq 1150000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -8e-45) (not (<= t 1150000000.0)))
   (- (/ 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 <= -8e-45) || !(t <= 1150000000.0)) {
		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 <= (-8d-45)) .or. (.not. (t <= 1150000000.0d0))) 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 <= -8e-45) || !(t <= 1150000000.0)) {
		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 <= -8e-45) or not (t <= 1150000000.0):
		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 <= -8e-45) || !(t <= 1150000000.0))
		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 <= -8e-45) || ~((t <= 1150000000.0)))
		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, -8e-45], N[Not[LessEqual[t, 1150000000.0]], $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 < -7.99999999999999987e-45 or 1.15e9 < t

   1. Initial program 71.1%

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

   3. Taylor expanded in t around inf 90.1%

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

   if -7.99999999999999987e-45 < t < 1.15e9

   1. Initial program 98.9%

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

   3. Taylor expanded in t around 0 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 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8 \cdot 10^{-45} \lor \neg \left(t \leq 1150000000\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2 + \frac{2}{z}}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-179} \lor \neg \left(t \leq 2 \cdot 10^{-111}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.9e-179) (not (<= t 2e-111))) (- (/ x y) 2.0) (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.9e-179) || !(t <= 2e-111)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((t <= (-2.9d-179)) .or. (.not. (t <= 2d-111))) then
        tmp = (x / y) - 2.0d0
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.9e-179) || !(t <= 2e-111)) {
		tmp = (x / y) - 2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -2.9e-179) or not (t <= 2e-111):
		tmp = (x / y) - 2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.9e-179) || !(t <= 2e-111))
		tmp = Float64(Float64(x / y) - 2.0);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -2.9e-179) || ~((t <= 2e-111)))
		tmp = (x / y) - 2.0;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.9e-179], N[Not[LessEqual[t, 2e-111]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.8999999999999999e-179 or 2.00000000000000018e-111 < t

   1. Initial program 78.3%

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

   3. Taylor expanded in t around inf 76.3%

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

   if -2.8999999999999999e-179 < t < 2.00000000000000018e-111

   1. Initial program 98.3%

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

   3. Taylor expanded in t around 0 94.0%

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

      1. associate-*r/ 94.0%

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

      2. metadata-eval 94.0%

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

   5. Simplified 94.0%

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

   6. Taylor expanded in z around inf 47.8%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-179} \lor \neg \left(t \leq 2 \cdot 10^{-111}\right):\\ \;\;\;\;\frac{x}{y} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.55 \cdot 10^{+25}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 4400000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= t -3.55e+25) -2.0 (if (<= t 4400000.0) (/ 2.0 t) -2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.55e+25) {
		tmp = -2.0;
	} else if (t <= 4400000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (t <= (-3.55d+25)) then
        tmp = -2.0d0
    else if (t <= 4400000.0d0) then
        tmp = 2.0d0 / t
    else
        tmp = -2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (t <= -3.55e+25) {
		tmp = -2.0;
	} else if (t <= 4400000.0) {
		tmp = 2.0 / t;
	} else {
		tmp = -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if t <= -3.55e+25:
		tmp = -2.0
	elif t <= 4400000.0:
		tmp = 2.0 / t
	else:
		tmp = -2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (t <= -3.55e+25)
		tmp = -2.0;
	elseif (t <= 4400000.0)
		tmp = Float64(2.0 / t);
	else
		tmp = -2.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (t <= -3.55e+25)
		tmp = -2.0;
	elseif (t <= 4400000.0)
		tmp = 2.0 / t;
	else
		tmp = -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[t, -3.55e+25], -2.0, If[LessEqual[t, 4400000.0], N[(2.0 / t), $MachinePrecision], -2.0]]

Derivation

1. Split input into 2 regimes

2. if t < -3.5500000000000001e25 or 4.4e6 < t

   1. Initial program 68.4%

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

   3. Taylor expanded in t around inf 92.4%

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

   4. Taylor expanded in x around 0 46.5%

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

   if -3.5500000000000001e25 < t < 4.4e6

   1. Initial program 99.0%

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

   3. Taylor expanded in t around 0 77.7%

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

      1. associate-*r/ 77.7%

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

      2. metadata-eval 77.7%

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

   5. Simplified 77.7%

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

   6. Taylor expanded in z around inf 35.0%

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

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.55 \cdot 10^{+25}:\\ \;\;\;\;-2\\ \mathbf{elif}\;t \leq 4400000:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 20.1% 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 83.5%

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

3. Taylor expanded in t around inf 59.0%

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

4. Taylor expanded in x around 0 24.8%

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

5. Final simplification 24.8%

   \[\leadsto -2 \]
6. Add Preprocessing

Developer target: 99.3% 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 2024043 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (- (/ (+ (/ 2.0 z) 2.0) t) (- 2.0 (/ x y)))

  (+ (/ x y) (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))