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

Percentage Accurate: 87.0% → 99.4%

Time: 9.4s

Alternatives: 11

Speedup: 1.0×

• 23.8% 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: 87.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 x y) (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z))) < +inf.0

   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 t around 0

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

      1. +-commutative N/A

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

      2. +-commutative N/A

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

      3. associate-*r* N/A

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

      4. distribute-rgt-out N/A

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

      5. *-commutative N/A

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

      6. lower-fma.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-fma.f64 99.9

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

   5. Applied rewrites 99.9%

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

   if +inf.0 < (+.f64 (/.f64 x y) (/.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 0.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 97.2%

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

Alternative 2: 86.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\frac{2}{z} - -2}{t}\\ t_2 := \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{+81}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{+217}:\\ \;\;\;\;\left(\frac{x}{y} - 2\right) - \frac{-2}{t}\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (- (/ 2.0 z) -2.0) t))
        (t_2 (/ (+ 2.0 (* (* z 2.0) (- 1.0 t))) (* t z))))
   (if (<= t_2 -2e+81)
     t_1
     (if (<= t_2 1e+217)
       (- (- (/ x y) 2.0) (/ -2.0 t))
       (if (<= t_2 INFINITY) t_1 (+ (/ x y) -2.0))))))

C

double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_2 <= -2e+81) {
		tmp = t_1;
	} else if (t_2 <= 1e+217) {
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = ((2.0 / z) - -2.0) / t;
	double t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	double tmp;
	if (t_2 <= -2e+81) {
		tmp = t_1;
	} else if (t_2 <= 1e+217) {
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	} else if (t_2 <= Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else {
		tmp = (x / y) + -2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = ((2.0 / z) - -2.0) / t
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z)
	tmp = 0
	if t_2 <= -2e+81:
		tmp = t_1
	elif t_2 <= 1e+217:
		tmp = ((x / y) - 2.0) - (-2.0 / t)
	elif t_2 <= math.inf:
		tmp = t_1
	else:
		tmp = (x / y) + -2.0
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(2.0 / z) - -2.0) / t)
	t_2 = Float64(Float64(2.0 + Float64(Float64(z * 2.0) * Float64(1.0 - t))) / Float64(t * z))
	tmp = 0.0
	if (t_2 <= -2e+81)
		tmp = t_1;
	elseif (t_2 <= 1e+217)
		tmp = Float64(Float64(Float64(x / y) - 2.0) - Float64(-2.0 / t));
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = Float64(Float64(x / y) + -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = ((2.0 / z) - -2.0) / t;
	t_2 = (2.0 + ((z * 2.0) * (1.0 - t))) / (t * z);
	tmp = 0.0;
	if (t_2 <= -2e+81)
		tmp = t_1;
	elseif (t_2 <= 1e+217)
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = (x / y) + -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision]}, Block[{t$95$2 = 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$2, -2e+81], t$95$1, If[LessEqual[t$95$2, 1e+217], N[(N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision] - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$2, Infinity], t$95$1, N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 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)) < -1.99999999999999984e81 or 9.9999999999999996e216 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < +inf.0

   1. Initial program 97.6%

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

   3. Taylor expanded in 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. metadata-eval N/A

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

      3. *-inverses N/A

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

      4. associate-/l* N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. div-add N/A

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

      8. +-commutative N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. div-sub N/A

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

      12. metadata-eval N/A

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

      13. associate-*r/ N/A

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

      14. associate-*l/ N/A

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

      15. metadata-eval N/A

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

      16. associate-*r/ N/A

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

      17. associate-*l* N/A

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

      18. lft-mult-inverse N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 N/A

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

      21. associate-*r/ N/A

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

      22. metadata-eval N/A

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

      23. lower-/.f64 84.1

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

   5. Applied rewrites 84.1%

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

   if -1.99999999999999984e81 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 9.9999999999999996e216

   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 inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 89.1

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

   5. Applied rewrites 89.1%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 89.1%

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

   if +inf.0 < (/.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 0.0%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 100.0%

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

Alternative 3: 90.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -2 \cdot 10^{-16}:\\ \;\;\;\;\left(\frac{x}{y} - 2\right) - \frac{-2}{t}\\ \mathbf{elif}\;\frac{x}{y} \leq 5000000:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + \frac{2}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -2e-16)
   (- (- (/ x y) 2.0) (/ -2.0 t))
   (if (<= (/ x y) 5000000.0)
     (- -2.0 (/ (- (/ -2.0 z) 2.0) t))
     (+ (/ x y) (/ 2.0 (* t z))))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -2e-16) {
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	} else if ((x / y) <= 5000000.0) {
		tmp = -2.0 - (((-2.0 / z) - 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 ((x / y) <= (-2d-16)) then
        tmp = ((x / y) - 2.0d0) - ((-2.0d0) / t)
    else if ((x / y) <= 5000000.0d0) then
        tmp = (-2.0d0) - ((((-2.0d0) / z) - 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 ((x / y) <= -2e-16) {
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	} else if ((x / y) <= 5000000.0) {
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	} else {
		tmp = (x / y) + (2.0 / (t * z));
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -2e-16:
		tmp = ((x / y) - 2.0) - (-2.0 / t)
	elif (x / y) <= 5000000.0:
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t)
	else:
		tmp = (x / y) + (2.0 / (t * z))
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -2e-16)
		tmp = Float64(Float64(Float64(x / y) - 2.0) - Float64(-2.0 / t));
	elseif (Float64(x / y) <= 5000000.0)
		tmp = Float64(-2.0 - Float64(Float64(Float64(-2.0 / z) - 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 ((x / y) <= -2e-16)
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	elseif ((x / y) <= 5000000.0)
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	else
		tmp = (x / y) + (2.0 / (t * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -2e-16], N[(N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision] - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 5000000.0], N[(-2.0 - N[(N[(N[(-2.0 / z), $MachinePrecision] - 2.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], N[(N[(x / y), $MachinePrecision] + N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 x y) < -2e-16

   1. Initial program 84.0%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 87.7

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

   5. Applied rewrites 87.7%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 87.7%

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

   if -2e-16 < (/.f64 x y) < 5e6

   1. Initial program 87.4%

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

   3. Taylor expanded in x around 0

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/l* N/A

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

      5. div-add-rev N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. count-2-rev N/A

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

   8. Applied rewrites 98.1%

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

   if 5e6 < (/.f64 x y)

   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 z around 0

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

   5. Applied rewrites 92.5%

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

Alternative 4: 89.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.4 \cdot 10^{-16} \lor \neg \left(\frac{x}{y} \leq 1.12 \cdot 10^{-5}\right):\\ \;\;\;\;\left(\frac{x}{y} - 2\right) - \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -3.4e-16) (not (<= (/ x y) 1.12e-5)))
   (- (- (/ x y) 2.0) (/ -2.0 t))
   (- -2.0 (/ (- (/ -2.0 z) 2.0) t))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -3.4e-16) || !((x / y) <= 1.12e-5)) {
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	} else {
		tmp = -2.0 - (((-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 (((x / y) <= (-3.4d-16)) .or. (.not. ((x / y) <= 1.12d-5))) then
        tmp = ((x / y) - 2.0d0) - ((-2.0d0) / t)
    else
        tmp = (-2.0d0) - ((((-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 (((x / y) <= -3.4e-16) || !((x / y) <= 1.12e-5)) {
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	} else {
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -3.4e-16) or not ((x / y) <= 1.12e-5):
		tmp = ((x / y) - 2.0) - (-2.0 / t)
	else:
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t)
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -3.4e-16) || !(Float64(x / y) <= 1.12e-5))
		tmp = Float64(Float64(Float64(x / y) - 2.0) - Float64(-2.0 / t));
	else
		tmp = Float64(-2.0 - 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 (((x / y) <= -3.4e-16) || ~(((x / y) <= 1.12e-5)))
		tmp = ((x / y) - 2.0) - (-2.0 / t);
	else
		tmp = -2.0 - (((-2.0 / z) - 2.0) / t);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -3.4e-16], N[Not[LessEqual[N[(x / y), $MachinePrecision], 1.12e-5]], $MachinePrecision]], N[(N[(N[(x / y), $MachinePrecision] - 2.0), $MachinePrecision] - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision], N[(-2.0 - N[(N[(N[(-2.0 / z), $MachinePrecision] - 2.0), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -3.4e-16 or 1.11999999999999995e-5 < (/.f64 x y)

   1. Initial program 84.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 86.2

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

   5. Applied rewrites 86.2%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 86.2%

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

   if -3.4e-16 < (/.f64 x y) < 1.11999999999999995e-5

   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

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

      1. associate-+r+ N/A

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

      2. +-commutative N/A

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

      3. associate-*r/ N/A

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

      4. *-commutative N/A

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

      5. associate-/l* N/A

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

      6. metadata-eval N/A

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

      7. associate-*r/ N/A

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

      8. associate-/r* N/A

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

      9. associate-*r/ N/A

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

      10. metadata-eval N/A

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

      11. associate-*r* N/A

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

      12. associate-*l/ N/A

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

      13. distribute-rgt-out N/A

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

      14. lower-fma.f64 N/A

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

   5. Applied rewrites 99.7%

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

   6. Taylor expanded in x around 0

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

      1. associate-*r/ N/A

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

      2. *-commutative N/A

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

      3. associate-/r* N/A

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

      4. associate-/l* N/A

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

      5. div-add-rev N/A

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

      6. distribute-lft-out N/A

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

      7. +-commutative N/A

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

      8. associate--l+ N/A

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

      9. +-commutative N/A

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

      10. count-2-rev N/A

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

   8. Applied rewrites 99.9%

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

4. Final simplification 92.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -3.4 \cdot 10^{-16} \lor \neg \left(\frac{x}{y} \leq 1.12 \cdot 10^{-5}\right):\\ \;\;\;\;\left(\frac{x}{y} - 2\right) - \frac{-2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 - \frac{\frac{-2}{z} - 2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -45000000000 \lor \neg \left(\frac{x}{y} \leq 5400000\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -45000000000.0) (not (<= (/ x y) 5400000.0)))
   (+ (/ x y) -2.0)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -45000000000.0) || !((x / y) <= 5400000.0)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-45000000000.0d0)) .or. (.not. ((x / y) <= 5400000.0d0))) then
        tmp = (x / y) + (-2.0d0)
    else
        tmp = (2.0d0 / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -45000000000.0) || !((x / y) <= 5400000.0)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -45000000000.0) or not ((x / y) <= 5400000.0):
		tmp = (x / y) + -2.0
	else:
		tmp = (2.0 / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -45000000000.0) || !(Float64(x / y) <= 5400000.0))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(Float64(2.0 / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -45000000000.0) || ~(((x / y) <= 5400000.0)))
		tmp = (x / y) + -2.0;
	else
		tmp = (2.0 / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -45000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 5400000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -4.5e10 or 5.4e6 < (/.f64 x y)

   1. Initial program 84.7%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 75.3%

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

   if -4.5e10 < (/.f64 x y) < 5.4e6

   1. Initial program 86.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 70.6

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

   5. Applied rewrites 70.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 68.9%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -45000000000 \lor \neg \left(\frac{x}{y} \leq 5400000\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 65.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -65000000000 \lor \neg \left(\frac{x}{y} \leq 11500000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -65000000000.0) (not (<= (/ x y) 11500000000000.0)))
   (/ x y)
   (- (/ 2.0 t) 2.0)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -65000000000.0) || !((x / y) <= 11500000000000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-65000000000.0d0)) .or. (.not. ((x / y) <= 11500000000000.0d0))) then
        tmp = x / y
    else
        tmp = (2.0d0 / t) - 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -65000000000.0) || !((x / y) <= 11500000000000.0)) {
		tmp = x / y;
	} else {
		tmp = (2.0 / t) - 2.0;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -65000000000.0) or not ((x / y) <= 11500000000000.0):
		tmp = x / y
	else:
		tmp = (2.0 / t) - 2.0
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -65000000000.0) || !(Float64(x / y) <= 11500000000000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(Float64(2.0 / t) - 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -65000000000.0) || ~(((x / y) <= 11500000000000.0)))
		tmp = x / y;
	else
		tmp = (2.0 / t) - 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -65000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 11500000000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.5e10 or 1.15e13 < (/.f64 x y)

   1. Initial program 84.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 96.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 74.9%

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

   if -6.5e10 < (/.f64 x y) < 1.15e13

   1. Initial program 86.8%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-fma.f64 N/A

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

      3. lower-/.f64 N/A

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

      4. lower--.f64 N/A

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

      5. lower-/.f64 70.6

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

   5. Applied rewrites 70.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 68.9%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -65000000000 \lor \neg \left(\frac{x}{y} \leq 11500000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t} - 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 48.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -65000000000 \lor \neg \left(\frac{x}{y} \leq 11500000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= (/ x y) -65000000000.0) (not (<= (/ x y) 11500000000000.0)))
   (/ x y)
   (/ 2.0 t)))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -65000000000.0) || !((x / y) <= 11500000000000.0)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if (((x / y) <= (-65000000000.0d0)) .or. (.not. ((x / y) <= 11500000000000.0d0))) then
        tmp = x / y
    else
        tmp = 2.0d0 / t
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if (((x / y) <= -65000000000.0) || !((x / y) <= 11500000000000.0)) {
		tmp = x / y;
	} else {
		tmp = 2.0 / t;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if ((x / y) <= -65000000000.0) or not ((x / y) <= 11500000000000.0):
		tmp = x / y
	else:
		tmp = 2.0 / t
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((Float64(x / y) <= -65000000000.0) || !(Float64(x / y) <= 11500000000000.0))
		tmp = Float64(x / y);
	else
		tmp = Float64(2.0 / t);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if (((x / y) <= -65000000000.0) || ~(((x / y) <= 11500000000000.0)))
		tmp = x / y;
	else
		tmp = 2.0 / t;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[N[(x / y), $MachinePrecision], -65000000000.0], N[Not[LessEqual[N[(x / y), $MachinePrecision], 11500000000000.0]], $MachinePrecision]], N[(x / y), $MachinePrecision], N[(2.0 / t), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -6.5e10 or 1.15e13 < (/.f64 x y)

   1. Initial program 84.7%

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

   3. Taylor expanded in x around inf

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

   5. Applied rewrites 96.7%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 74.9%

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

   if -6.5e10 < (/.f64 x y) < 1.15e13

   1. Initial program 86.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. metadata-eval N/A

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

      3. *-inverses N/A

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

      4. associate-/l* N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. div-add N/A

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

      8. +-commutative N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. div-sub N/A

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

      12. metadata-eval N/A

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

      13. associate-*r/ N/A

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

      14. associate-*l/ N/A

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

      15. metadata-eval N/A

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

      16. associate-*r/ N/A

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

      17. associate-*l* N/A

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

      18. lft-mult-inverse N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 N/A

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

      21. associate-*r/ N/A

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

      22. metadata-eval N/A

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

      23. lower-/.f64 59.3

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

   5. Applied rewrites 59.3%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 30.7%

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

4. Final simplification 52.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -65000000000 \lor \neg \left(\frac{x}{y} \leq 11500000000000\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

3. Taylor expanded in x around 0

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

   1. associate-+r+ N/A

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

   2. +-commutative N/A

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

   3. associate-*r/ N/A

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

   4. *-commutative N/A

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

   5. associate-/l* N/A

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

   6. metadata-eval N/A

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

   7. associate-*r/ N/A

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

   8. associate-/r* N/A

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

   9. associate-*r/ N/A

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

   10. metadata-eval N/A

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

   11. associate-*r* N/A

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

   12. associate-*l/ N/A

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

   13. distribute-rgt-out N/A

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

   14. lower-fma.f64 N/A

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

5. Applied rewrites 99.5%

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

Alternative 9: 79.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{-67} \lor \neg \left(t \leq 4500\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.45e-67) (not (<= t 4500.0)))
   (+ (/ 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 <= -2.45e-67) || !(t <= 4500.0)) {
		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 <= (-2.45d-67)) .or. (.not. (t <= 4500.0d0))) 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 <= -2.45e-67) || !(t <= 4500.0)) {
		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 <= -2.45e-67) or not (t <= 4500.0):
		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 <= -2.45e-67) || !(t <= 4500.0))
		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 <= -2.45e-67) || ~((t <= 4500.0)))
		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, -2.45e-67], N[Not[LessEqual[t, 4500.0]], $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 < -2.44999999999999997e-67 or 4500 < t

   1. Initial program 76.6%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 84.7%

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

   if -2.44999999999999997e-67 < t < 4500

   1. Initial program 98.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. metadata-eval N/A

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

      3. *-inverses N/A

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

      4. associate-/l* N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. div-add N/A

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

      8. +-commutative N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. div-sub N/A

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

      12. metadata-eval N/A

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

      13. associate-*r/ N/A

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

      14. associate-*l/ N/A

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

      15. metadata-eval N/A

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

      16. associate-*r/ N/A

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

      17. associate-*l* N/A

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

      18. lft-mult-inverse N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 N/A

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

      21. associate-*r/ N/A

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

      22. metadata-eval N/A

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

      23. lower-/.f64 82.1

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

   5. Applied rewrites 82.1%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{-67} \lor \neg \left(t \leq 4500\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 79.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{-67} \lor \neg \left(t \leq 4500\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (or (<= t -2.45e-67) (not (<= t 4500.0)))
   (+ (/ x y) -2.0)
   (/ (fma 2.0 z 2.0) (* t z))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((t <= -2.45e-67) || !(t <= 4500.0)) {
		tmp = (x / y) + -2.0;
	} else {
		tmp = fma(2.0, z, 2.0) / (t * z);
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	tmp = 0.0
	if ((t <= -2.45e-67) || !(t <= 4500.0))
		tmp = Float64(Float64(x / y) + -2.0);
	else
		tmp = Float64(fma(2.0, z, 2.0) / Float64(t * z));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := If[Or[LessEqual[t, -2.45e-67], N[Not[LessEqual[t, 4500.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + -2.0), $MachinePrecision], N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -2.44999999999999997e-67 or 4500 < t

   1. Initial program 76.6%

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

   3. Taylor expanded in t around inf

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

   5. Applied rewrites 84.7%

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

   if -2.44999999999999997e-67 < t < 4500

   1. Initial program 98.8%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. metadata-eval N/A

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

      3. *-inverses N/A

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

      4. associate-/l* N/A

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

      5. associate-*r/ N/A

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

      6. metadata-eval N/A

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

      7. div-add N/A

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

      8. +-commutative N/A

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

      9. fp-cancel-sign-sub-inv N/A

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

      10. metadata-eval N/A

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

      11. div-sub N/A

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

      12. metadata-eval N/A

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

      13. associate-*r/ N/A

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

      14. associate-*l/ N/A

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

      15. metadata-eval N/A

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

      16. associate-*r/ N/A

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

      17. associate-*l* N/A

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

      18. lft-mult-inverse N/A

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

      19. metadata-eval N/A

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

      20. lower--.f64 N/A

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

      21. associate-*r/ N/A

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

      22. metadata-eval N/A

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

      23. lower-/.f64 82.1

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

   5. Applied rewrites 82.1%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 81.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.45 \cdot 10^{-67} \lor \neg \left(t \leq 4500\right):\\ \;\;\;\;\frac{x}{y} + -2\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 35.8% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \frac{x}{y} \end{array} \]

FPCore

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

C

double code(double x, double y, double z, double t) {
	return 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 = x / y
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 85.8%

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

3. Taylor expanded in x around inf

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

5. Applied rewrites 87.6%

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

6. Taylor expanded in x around inf

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

8. Applied rewrites 38.2%

   \[\leadsto \frac{x}{\color{blue}{y}} \]
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 2024320 
(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))))