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

Percentage Accurate: 86.6% → 98.9%

Time: 11.1s

Alternatives: 14

Speedup: 1.1×

• 23.0% 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: 86.6% 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: 98.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_1 \leq 2.2 \cdot 10^{+306}:\\ \;\;\;\;\frac{x}{y} + t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(\frac{\frac{2}{z}}{t} - 2, y, x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_1 2.2e+306)
     (+ (/ x y) t_1)
     (/ (fma (- (/ (/ 2.0 z) t) 2.0) y x) y))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_1 <= 2.2e+306) {
		tmp = (x / y) + t_1;
	} else {
		tmp = fma((((2.0 / z) / t) - 2.0), y, x) / y;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_1 <= 2.2e+306)
		tmp = Float64(Float64(x / y) + t_1);
	else
		tmp = Float64(fma(Float64(Float64(Float64(2.0 / z) / t) - 2.0), y, x) / y);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 + N[(N[(z * 2.0), $MachinePrecision] * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, 2.2e+306], N[(N[(x / y), $MachinePrecision] + t$95$1), $MachinePrecision], N[(N[(N[(N[(N[(2.0 / z), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision] * y + x), $MachinePrecision] / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 2.2e306

   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

   if 2.2e306 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))

   1. Initial program 41.7%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 100.0%

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

   6. Taylor expanded in z around 0

      \[\leadsto \frac{\mathsf{fma}\left(\frac{\frac{2}{z}}{t} - 2, y, x\right)}{y} \]
   7. Step-by-step derivation

   8. Applied rewrites 100.0%

      \[\leadsto \frac{\mathsf{fma}\left(\frac{\frac{2}{z}}{t} - 2, y, x\right)}{y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 98.1% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -2.0) (not (<= (/ x y) 2e-14)))
   (+ (/ x y) (/ (fma 2.0 z 2.0) (* t z)))
   (- (/ (- (/ 2.0 z) -2.0) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -2.0) || !((x / y) <= 2e-14)) {
		tmp = (x / y) + (fma(2.0, z, 2.0) / (t * z));
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -2.0) || !(Float64(x / y) <= 2e-14))
		tmp = Float64(Float64(x / y) + Float64(fma(2.0, z, 2.0) / Float64(t * z)));
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -2.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 2e-14]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 90.8%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 97.7

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

   5. Applied rewrites 97.7%

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

   if -2 < (/.f64 x y) < 2e-14

   1. Initial program 86.9%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-+r- N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.0%

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

4. Final simplification 98.3%

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

Alternative 3: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{-12}:\\ \;\;\;\;\frac{\mathsf{fma}\left(t\_1, y, x\right)}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2 \cdot 10^{-14}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (- (/ (- (/ 2.0 z) -2.0) t) 2.0)))
   (if (<= (/ x y) -1e-12)
     (/ (fma t_1 y x) y)
     (if (<= (/ x y) 2e-14) t_1 (+ (/ x y) (/ (fma 2.0 z 2.0) (* t z)))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((2.0 / z) - -2.0) / t) - 2.0;
	double tmp;
	if ((x / y) <= -1e-12) {
		tmp = fma(t_1, y, x) / y;
	} else if ((x / y) <= 2e-14) {
		tmp = t_1;
	} else {
		tmp = (x / y) + (fma(2.0, z, 2.0) / (t * z));
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0)
	tmp = 0.0
	if (Float64(x / y) <= -1e-12)
		tmp = Float64(fma(t_1, y, x) / y);
	elseif (Float64(x / y) <= 2e-14)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) + Float64(fma(2.0, z, 2.0) / Float64(t * z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e-12], N[(N[(t$95$1 * y + x), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 2e-14], t$95$1, N[(N[(x / y), $MachinePrecision] + N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -9.9999999999999998e-13

   1. Initial program 91.5%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 97.3%

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

   if -9.9999999999999998e-13 < (/.f64 x y) < 2e-14

   1. Initial program 87.2%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-+r- N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 99.8%

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

   if 2e-14 < (/.f64 x y)

   1. Initial program 89.2%

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

   3. Taylor expanded in t around 0

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

      1. +-commutative N/A

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

      2. lower-fma.f64 99.3

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

   5. Applied rewrites 99.3%

      \[\leadsto \frac{x}{y} + \frac{\color{blue}{\mathsf{fma}\left(2, z, 2\right)}}{t \cdot z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 4: 89.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+43} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -5e+43) (not (<= (/ x y) 5e+81)))
   (+ (/ x y) (- -2.0 (/ -2.0 t)))
   (- (/ (- (/ 2.0 z) -2.0) t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -5e+43) || !((x / y) <= 5e+81)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (((2.0 / z) - -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) <= (-5d+43)) .or. (.not. ((x / y) <= 5d+81))) then
        tmp = (x / y) + ((-2.0d0) - ((-2.0d0) / t))
    else
        tmp = (((2.0d0 / z) - (-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) <= -5e+43) || !((x / y) <= 5e+81)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -5e+43) or not ((x / y) <= 5e+81):
		tmp = (x / y) + (-2.0 - (-2.0 / t))
	else:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -5e+43) || !(Float64(x / y) <= 5e+81))
		tmp = Float64(Float64(x / y) + Float64(-2.0 - Float64(-2.0 / t)));
	else
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -5e+43) || ~(((x / y) <= 5e+81)))
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	else
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -5e+43], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5e+81]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -5.0000000000000004e43 or 4.9999999999999998e81 < (/.f64 x y)

   1. Initial program 90.8%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. mul-1-neg N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. lower-/.f64 82.3

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

   5. Applied rewrites 82.3%

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

   if -5.0000000000000004e43 < (/.f64 x y) < 4.9999999999999998e81

   1. Initial program 87.6%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-+r- N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 95.3%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -5 \cdot 10^{+43} \lor \neg \left(\frac{x}{y} \leq 5 \cdot 10^{+81}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 52.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 9 \cdot 10^{-122}:\\ \;\;\;\;-2\\ \mathbf{elif}\;\frac{x}{y} \leq 9.2 \cdot 10^{+48}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2.0)
   (/ x y)
   (if (<= (/ x y) 9e-122) -2.0 (if (<= (/ x y) 9.2e+48) (/ 2.0 t) (/ x y)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= 9e-122) {
		tmp = -2.0;
	} else if ((x / y) <= 9.2e+48) {
		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) <= (-2.0d0)) then
        tmp = x / y
    else if ((x / y) <= 9d-122) then
        tmp = -2.0d0
    else if ((x / y) <= 9.2d+48) 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) <= -2.0) {
		tmp = x / y;
	} else if ((x / y) <= 9e-122) {
		tmp = -2.0;
	} else if ((x / y) <= 9.2e+48) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2.0:
		tmp = x / y
	elif (x / y) <= 9e-122:
		tmp = -2.0
	elif (x / y) <= 9.2e+48:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2.0)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 9e-122)
		tmp = -2.0;
	elseif (Float64(x / y) <= 9.2e+48)
		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) <= -2.0)
		tmp = x / y;
	elseif ((x / y) <= 9e-122)
		tmp = -2.0;
	elseif ((x / y) <= 9.2e+48)
		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], -2.0], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 9e-122], -2.0, If[LessEqual[N[(x / y), $MachinePrecision], 9.2e+48], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2 or 9.2000000000000001e48 < (/.f64 x y)

   1. Initial program 90.9%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-+r- N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 36.2%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   7. Step-by-step derivation

      1. lower-/.f64 64.8

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

   8. Applied rewrites 64.8%

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

   if -2 < (/.f64 x y) < 8.99999999999999959e-122

   1. Initial program 84.4%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-+r- N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 98.7%

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

   6. Taylor expanded in t around inf

      \[\leadsto -2 \]
   7. Step-by-step derivation

   8. Applied rewrites 38.1%

      \[\leadsto -2 \]

   if 8.99999999999999959e-122 < (/.f64 x y) < 9.2000000000000001e48

   1. Initial program 92.9%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 77.3

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

   5. Applied rewrites 77.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 39.1%

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

Alternative 6: 64.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+96} \lor \neg \left(\frac{x}{y} \leq 7.5 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -1e+96) (not (<= (/ x y) 7.5e+41)))
   (/ x y)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -1e+96) || !((x / y) <= 7.5e+41)) {
		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) <= (-1d+96)) .or. (.not. ((x / y) <= 7.5d+41))) 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) <= -1e+96) || !((x / y) <= 7.5e+41)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -1e+96) or not ((x / y) <= 7.5e+41):
		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) <= -1e+96) || !(Float64(x / y) <= 7.5e+41))
		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) <= -1e+96) || ~(((x / y) <= 7.5e+41)))
		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], -1e+96], N[Not[LessEqual[N[(x / y), $MachinePrecision], 7.5e+41]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.00000000000000005e96 or 7.50000000000000072e41 < (/.f64 x y)

   1. Initial program 91.9%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-+r- N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 33.5%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   7. Step-by-step derivation

      1. lower-/.f64 68.1

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

   8. Applied rewrites 68.1%

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

   if -1.00000000000000005e96 < (/.f64 x y) < 7.50000000000000072e41

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-+r- N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 95.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 55.4%

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

4. Final simplification 61.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+96} \lor \neg \left(\frac{x}{y} \leq 7.5 \cdot 10^{+41}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 64.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 7.5 \cdot 10^{+41}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1e+96)
   (/ x y)
   (if (<= (/ x y) 7.5e+41) (- (/ 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) <= -1e+96) {
		tmp = x / y;
	} else if ((x / y) <= 7.5e+41) {
		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) <= (-1d+96)) then
        tmp = x / y
    else if ((x / y) <= 7.5d+41) 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) <= -1e+96) {
		tmp = x / y;
	} else if ((x / y) <= 7.5e+41) {
		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) <= -1e+96:
		tmp = x / y
	elif (x / y) <= 7.5e+41:
		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) <= -1e+96)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 7.5e+41)
		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) <= -1e+96)
		tmp = x / y;
	elseif ((x / y) <= 7.5e+41)
		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], -1e+96], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 7.5e+41], 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) < -1.00000000000000005e96

   1. Initial program 94.5%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-+r- N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 31.9%

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

   6. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\frac{x}{y}} \]
   7. Step-by-step derivation

      1. lower-/.f64 71.2

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

   8. Applied rewrites 71.2%

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

   if -1.00000000000000005e96 < (/.f64 x y) < 7.50000000000000072e41

   1. Initial program 86.6%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-+r- N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 95.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 55.4%

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

   if 7.50000000000000072e41 < (/.f64 x y)

   1. Initial program 89.4%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 65.2%

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

Alternative 8: 90.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-83} \lor \neg \left(z \leq 3.8 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= z -2.5e-83) (not (<= z 3.8e-8)))
   (+ (/ x y) (- -2.0 (/ -2.0 t)))
   (+ (/ x y) (/ 2.0 (* t z)))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((z <= -2.5e-83) || !(z <= 3.8e-8)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} 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 <= (-2.5d-83)) .or. (.not. (z <= 3.8d-8))) then
        tmp = (x / y) + ((-2.0d0) - ((-2.0d0) / t))
    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 <= -2.5e-83) || !(z <= 3.8e-8)) {
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (z <= -2.5e-83) or not (z <= 3.8e-8):
		tmp = (x / y) + (-2.0 - (-2.0 / t))
	else:
		tmp = (x / y) + (2.0 / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((z <= -2.5e-83) || !(z <= 3.8e-8))
		tmp = Float64(Float64(x / y) + Float64(-2.0 - Float64(-2.0 / t)));
	else
		tmp = Float64(Float64(x / y) + Float64(2.0 / Float64(t * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((z <= -2.5e-83) || ~((z <= 3.8e-8)))
		tmp = (x / y) + (-2.0 - (-2.0 / t));
	else
		tmp = (x / y) + (2.0 / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[z, -2.5e-83], N[Not[LessEqual[z, 3.8e-8]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.5e-83 or 3.80000000000000028e-8 < z

   1. Initial program 79.0%

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

   3. Taylor expanded in z around inf

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. +-commutative N/A

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

      6. distribute-lft-in N/A

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

      7. metadata-eval N/A

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

      8. remove-double-neg N/A

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

      9. mul-1-neg N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. lower-/.f64 95.8

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

   5. Applied rewrites 95.8%

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

   if -2.5e-83 < z < 3.80000000000000028e-8

   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

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

   5. Applied rewrites 91.5%

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

4. Final simplification 93.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-83} \lor \neg \left(z \leq 3.8 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} + \left(-2 - \frac{-2}{t}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -2.2 \cdot 10^{-159}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{-170}:\\ \;\;\;\;\frac{z \cdot 2}{t \cdot z}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (+ (/ x y) -2.0)))
   (if (<= t -1.15e-20)
     t_2
     (if (<= t -2.2e-159)
       t_1
       (if (<= t 1.9e-170)
         (/ (* z 2.0) (* t z))
         (if (<= t 3.1e-31) t_1 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 <= -1.15e-20) {
		tmp = t_2;
	} else if (t <= -2.2e-159) {
		tmp = t_1;
	} else if (t <= 1.9e-170) {
		tmp = (z * 2.0) / (t * z);
	} else if (t <= 3.1e-31) {
		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 / (t * z)
    t_2 = (x / y) + (-2.0d0)
    if (t <= (-1.15d-20)) then
        tmp = t_2
    else if (t <= (-2.2d-159)) then
        tmp = t_1
    else if (t <= 1.9d-170) then
        tmp = (z * 2.0d0) / (t * z)
    else if (t <= 3.1d-31) 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 / (t * z);
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t <= -1.15e-20) {
		tmp = t_2;
	} else if (t <= -2.2e-159) {
		tmp = t_1;
	} else if (t <= 1.9e-170) {
		tmp = (z * 2.0) / (t * z);
	} else if (t <= 3.1e-31) {
		tmp = t_1;
	} 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 <= -1.15e-20:
		tmp = t_2
	elif t <= -2.2e-159:
		tmp = t_1
	elif t <= 1.9e-170:
		tmp = (z * 2.0) / (t * z)
	elif t <= 3.1e-31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -1.15e-20)
		tmp = t_2;
	elseif (t <= -2.2e-159)
		tmp = t_1;
	elseif (t <= 1.9e-170)
		tmp = Float64(Float64(z * 2.0) / Float64(t * z));
	elseif (t <= 3.1e-31)
		tmp = t_1;
	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 <= -1.15e-20)
		tmp = t_2;
	elseif (t <= -2.2e-159)
		tmp = t_1;
	elseif (t <= 1.9e-170)
		tmp = (z * 2.0) / (t * z);
	elseif (t <= 3.1e-31)
		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[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t, -1.15e-20], t$95$2, If[LessEqual[t, -2.2e-159], t$95$1, If[LessEqual[t, 1.9e-170], N[(N[(z * 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.1e-31], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15e-20 or 3.1e-31 < t

   1. Initial program 77.8%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 86.4%

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

   if -1.15e-20 < t < -2.2e-159 or 1.8999999999999999e-170 < t < 3.1e-31

   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 z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 70.7

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

   5. Applied rewrites 70.7%

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

   if -2.2e-159 < t < 1.8999999999999999e-170

   1. Initial program 98.4%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 84.4

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

   5. Applied rewrites 84.4%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 84.3%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 62.8%

       \[\leadsto \frac{z \cdot 2}{t \cdot z} \]
3. Recombined 3 regimes into one program.
4. Add Preprocessing

Alternative 10: 62.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{2}{t \cdot z}\\ t_2 := \frac{x}{y} + -2\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{-20}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -1.25 \cdot 10^{-176}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-170}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{-31}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ 2.0 (* t z))) (t_2 (+ (/ x y) -2.0)))
   (if (<= t -1.15e-20)
     t_2
     (if (<= t -1.25e-176)
       t_1
       (if (<= t 1.55e-170) (/ 2.0 t) (if (<= t 3.1e-31) t_1 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 <= -1.15e-20) {
		tmp = t_2;
	} else if (t <= -1.25e-176) {
		tmp = t_1;
	} else if (t <= 1.55e-170) {
		tmp = 2.0 / t;
	} else if (t <= 3.1e-31) {
		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 / (t * z)
    t_2 = (x / y) + (-2.0d0)
    if (t <= (-1.15d-20)) then
        tmp = t_2
    else if (t <= (-1.25d-176)) then
        tmp = t_1
    else if (t <= 1.55d-170) then
        tmp = 2.0d0 / t
    else if (t <= 3.1d-31) 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 / (t * z);
	double t_2 = (x / y) + -2.0;
	double tmp;
	if (t <= -1.15e-20) {
		tmp = t_2;
	} else if (t <= -1.25e-176) {
		tmp = t_1;
	} else if (t <= 1.55e-170) {
		tmp = 2.0 / t;
	} else if (t <= 3.1e-31) {
		tmp = t_1;
	} 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 <= -1.15e-20:
		tmp = t_2
	elif t <= -1.25e-176:
		tmp = t_1
	elif t <= 1.55e-170:
		tmp = 2.0 / t
	elif t <= 3.1e-31:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(2.0 / Float64(t * z))
	t_2 = Float64(Float64(x / y) + -2.0)
	tmp = 0.0
	if (t <= -1.15e-20)
		tmp = t_2;
	elseif (t <= -1.25e-176)
		tmp = t_1;
	elseif (t <= 1.55e-170)
		tmp = Float64(2.0 / t);
	elseif (t <= 3.1e-31)
		tmp = t_1;
	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 <= -1.15e-20)
		tmp = t_2;
	elseif (t <= -1.25e-176)
		tmp = t_1;
	elseif (t <= 1.55e-170)
		tmp = 2.0 / t;
	elseif (t <= 3.1e-31)
		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[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]}, If[LessEqual[t, -1.15e-20], t$95$2, If[LessEqual[t, -1.25e-176], t$95$1, If[LessEqual[t, 1.55e-170], N[(2.0 / t), $MachinePrecision], If[LessEqual[t, 3.1e-31], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.15e-20 or 3.1e-31 < t

   1. Initial program 77.8%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 86.4%

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

   if -1.15e-20 < t < -1.25e-176 or 1.54999999999999993e-170 < t < 3.1e-31

   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 z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 69.7

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

   5. Applied rewrites 69.7%

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

   if -1.25e-176 < t < 1.54999999999999993e-170

   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

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 83.4

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

   5. Applied rewrites 83.4%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 51.9%

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

Alternative 11: 79.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-20} \lor \neg \left(t \leq 3.6 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.35e-20) (not (<= t 3.6e-31)))
   (+ (/ x y) -2.0)
   (/ (- (/ 2.0 z) -2.0) t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.35e-20) || !(t <= 3.6e-31)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = ((2.0 / z) - -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 <= (-1.35d-20)) .or. (.not. (t <= 3.6d-31))) then
        tmp = (x / y) + (-2.0d0)
    else
        tmp = ((2.0d0 / z) - (-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 <= -1.35e-20) || !(t <= 3.6e-31)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = ((2.0 / z) - -2.0) / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.35e-20) or not (t <= 3.6e-31):
		tmp = (x / y) + -2.0
	else:
		tmp = ((2.0 / z) - -2.0) / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.35e-20) || !(t <= 3.6e-31))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((t <= -1.35e-20) || ~((t <= 3.6e-31)))
		tmp = (x / y) + -2.0;
	else
		tmp = ((2.0 / z) - -2.0) / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.35e-20], N[Not[LessEqual[t, 3.6e-31]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35e-20 or 3.60000000000000004e-31 < t

   1. Initial program 77.8%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 86.4%

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

   if -1.35e-20 < t < 3.60000000000000004e-31

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 85.8

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

   5. Applied rewrites 85.8%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-20} \lor \neg \left(t \leq 3.6 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 79.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-20} \lor \neg \left(t \leq 3.6 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.35e-20) (not (<= t 3.6e-31)))
   (+ (/ x y) -2.0)
   (/ (fma z 2.0 2.0) (* t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.35e-20) || !(t <= 3.6e-31)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = fma(z, 2.0, 2.0) / (t * z);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.35e-20) || !(t <= 3.6e-31))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(fma(z, 2.0, 2.0) / Float64(t * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.35e-20], N[Not[LessEqual[t, 3.6e-31]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(z * 2.0 + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.35e-20 or 3.60000000000000004e-31 < t

   1. Initial program 77.8%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 86.4%

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

   if -1.35e-20 < t < 3.60000000000000004e-31

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 85.8

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

   5. Applied rewrites 85.8%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 85.7%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.35 \cdot 10^{-20} \lor \neg \left(t \leq 3.6 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(z, 2, 2\right)}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1 \lor \neg \left(t \leq 98\right):\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -1.0) (not (<= t 98.0))) -2.0 (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -1.0) || !(t <= 98.0)) {
		tmp = -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 <= (-1.0d0)) .or. (.not. (t <= 98.0d0))) then
        tmp = -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 <= -1.0) || !(t <= 98.0)) {
		tmp = -2.0;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (t <= -1.0) or not (t <= 98.0):
		tmp = -2.0
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -1.0) || !(t <= 98.0))
		tmp = -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 <= -1.0) || ~((t <= 98.0)))
		tmp = -2.0;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -1.0], N[Not[LessEqual[t, 98.0]], $MachinePrecision]], -2.0, N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1 or 98 < t

   1. Initial program 75.4%

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

   3. Taylor expanded in x around 0

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

      1. div-sub N/A

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

      2. sub-neg N/A

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

      3. *-inverses N/A

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

      4. metadata-eval N/A

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

      5. distribute-lft-in N/A

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

      6. metadata-eval N/A

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

      7. associate-+r+ N/A

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

      8. +-commutative N/A

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

      9. metadata-eval N/A

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

      10. sub-neg N/A

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

      11. associate-+r- N/A

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

      12. associate-*r/ N/A

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

      13. metadata-eval N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 51.6%

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

   6. Taylor expanded in t around inf

      \[\leadsto -2 \]
   7. Step-by-step derivation

   8. Applied rewrites 39.5%

      \[\leadsto -2 \]

   if -1 < t < 98

   1. Initial program 99.1%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

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

      4. sub-neg N/A

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

      5. lower--.f64 N/A

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

      6. associate-*r/ N/A

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

      7. metadata-eval N/A

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

      8. lower-/.f64 80.3

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

   5. Applied rewrites 80.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 33.3%

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

4. Final simplification 35.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1 \lor \neg \left(t \leq 98\right):\\ \;\;\;\;-2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 19.8% accurate, 47.0× 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 88.9%

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

3. Taylor expanded in x around 0

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

   1. div-sub N/A

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

   2. sub-neg N/A

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

   3. *-inverses N/A

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

   4. metadata-eval N/A

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

   5. distribute-lft-in N/A

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

   6. metadata-eval N/A

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

   7. associate-+r+ N/A

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

   8. +-commutative N/A

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

   9. metadata-eval N/A

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

   10. sub-neg N/A

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

   11. associate-+r- N/A

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

   12. associate-*r/ N/A

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

   13. metadata-eval N/A

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

   14. lower--.f64 N/A

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

5. Applied rewrites 68.3%

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

6. Taylor expanded in t around inf

   \[\leadsto -2 \]
7. Step-by-step derivation

8. Applied rewrites 18.3%

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

Developer Target 1: 99.1% accurate, 1.1× 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 2024313 
(FPCore (x y z t)
  :name "Data.HashTable.ST.Basic:computeOverhead from hashtables-1.2.0.2"
  :precision binary64

  :alt
  (! :herbie-platform default (- (/ (+ (/ 2 z) 2) t) (- 2 (/ x y))))

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