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

Percentage Accurate: 86.6% → 99.4%

Time: 10.5s

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: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(z * 2.0 + N[(z * N[(-2.0 * t), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(x / y), $MachinePrecision]), $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 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lift-*.f64 N/A

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

      4. lift--.f64 N/A

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

      5. sub-neg N/A

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

      6. distribute-lft-in N/A

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

      7. *-rgt-identity N/A

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

      8. associate-+l+ N/A

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

      9. lift-*.f64 N/A

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

      10. lower-fma.f64 N/A

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

      11. lift-*.f64 N/A

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

      12. associate-*l* N/A

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

      13. lower-fma.f64 N/A

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

      14. neg-mul-1 N/A

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

      15. associate-*r* N/A

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

      16. metadata-eval N/A

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

      17. metadata-eval N/A

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

      18. lower-*.f64 N/A

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

      19. metadata-eval 99.8

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

   4. Applied rewrites 99.8%

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

   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 97.6%

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

4. Final simplification 99.5%

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

Alternative 2: 84.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z}\\ t_2 := -2 + \frac{x}{y}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+28}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (+ (* (- 1.0 t) (* z 2.0)) 2.0) (* t z)))
        (t_2 (+ -2.0 (/ x y))))
   (if (<= t_1 -5e+14)
     (/ (fma 2.0 z 2.0) (* t z))
     (if (<= t_1 5e+28)
       t_2
       (if (<= t_1 INFINITY) (/ (- (/ 2.0 z) -2.0) t) t_2)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_2 = -2.0 + (x / y);
	double tmp;
	if (t_1 <= -5e+14) {
		tmp = fma(2.0, z, 2.0) / (t * z);
	} else if (t_1 <= 5e+28) {
		tmp = t_2;
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = ((2.0 / z) - -2.0) / t;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(Float64(Float64(1.0 - t) * Float64(z * 2.0)) + 2.0) / Float64(t * z))
	t_2 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t_1 <= -5e+14)
		tmp = Float64(fma(2.0, z, 2.0) / Float64(t * z));
	elseif (t_1 <= 5e+28)
		tmp = t_2;
	elseif (t_1 <= Inf)
		tmp = Float64(Float64(Float64(2.0 / z) - -2.0) / t);
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e+14], N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+28], t$95$2, If[LessEqual[t$95$1, Infinity], N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision], t$95$2]]]]]

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)) < -5e14

   1. Initial program 99.8%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   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 76.2

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

   5. Applied rewrites 76.2%

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

   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 77.3%

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

   if -5e14 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.99999999999999957e28 or +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 59.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 96.4%

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

   if 4.99999999999999957e28 < (/.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 97.2%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   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 75.8

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

   5. Applied rewrites 75.8%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 5 \cdot 10^{+28}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ t_2 := \frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z}\\ t_3 := -2 + \frac{x}{y}\\ \mathbf{if}\;t\_2 \leq -5 \cdot 10^{+14}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{+28}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_2 \leq \infty:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (/ (fma 2.0 z 2.0) (* t z)))
        (t_2 (/ (+ (* (- 1.0 t) (* z 2.0)) 2.0) (* t z)))
        (t_3 (+ -2.0 (/ x y))))
   (if (<= t_2 -5e+14)
     t_1
     (if (<= t_2 5e+28) t_3 (if (<= t_2 INFINITY) t_1 t_3)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = fma(2.0, z, 2.0) / (t * z);
	double t_2 = (((1.0 - t) * (z * 2.0)) + 2.0) / (t * z);
	double t_3 = -2.0 + (x / y);
	double tmp;
	if (t_2 <= -5e+14) {
		tmp = t_1;
	} else if (t_2 <= 5e+28) {
		tmp = t_3;
	} else if (t_2 <= ((double) INFINITY)) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(fma(2.0, z, 2.0) / Float64(t * z))
	t_2 = Float64(Float64(Float64(Float64(1.0 - t) * Float64(z * 2.0)) + 2.0) / Float64(t * z))
	t_3 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t_2 <= -5e+14)
		tmp = t_1;
	elseif (t_2 <= 5e+28)
		tmp = t_3;
	elseif (t_2 <= Inf)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -5e+14], t$95$1, If[LessEqual[t$95$2, 5e+28], t$95$3, If[LessEqual[t$95$2, Infinity], t$95$1, t$95$3]]]]]]

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)) < -5e14 or 4.99999999999999957e28 < (/.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 98.5%

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

   3. Taylor expanded in t around 0

      \[\leadsto \color{blue}{\frac{2 + 2 \cdot \frac{1}{z}}{t}} \]
   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 76.0

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

   5. Applied rewrites 76.0%

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

   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 76.5%

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

   if -5e14 < (/.f64 (+.f64 #s(literal 2 binary64) (*.f64 (*.f64 z #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) t))) (*.f64 t z)) < 4.99999999999999957e28 or +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 59.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 96.4%

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

4. Final simplification 84.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq -5 \cdot 10^{+14}:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq 5 \cdot 10^{+28}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;\frac{\left(1 - t\right) \cdot \left(z \cdot 2\right) + 2}{t \cdot z} \leq \infty:\\ \;\;\;\;\frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(N[(N[(N[(N[(1.0 - t), $MachinePrecision] * N[(z * 2.0), $MachinePrecision]), $MachinePrecision] + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], Infinity], N[(N[(N[(N[(-2.0 * t + 2.0), $MachinePrecision] * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(-2.0 + N[(x / y), $MachinePrecision]), $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 99.8%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 99.8

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

   4. Applied rewrites 99.8%

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

   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 97.6%

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

4. Final simplification 99.5%

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

Alternative 5: 97.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{\mathsf{fma}\left(2, z, 2\right)}{t \cdot z} + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1 \cdot 10^{+38}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 1:\\ \;\;\;\;\frac{\mathsf{fma}\left(t, -2, \frac{2}{z}\right) - -2}{t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (/ (fma 2.0 z 2.0) (* t z)) (/ x y))))
   (if (<= (/ x y) -1e+38)
     t_1
     (if (<= (/ x y) 1.0) (/ (- (fma t -2.0 (/ 2.0 z)) -2.0) t) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (fma(2.0, z, 2.0) / (t * z)) + (x / y);
	double tmp;
	if ((x / y) <= -1e+38) {
		tmp = t_1;
	} else if ((x / y) <= 1.0) {
		tmp = (fma(t, -2.0, (2.0 / z)) - -2.0) / t;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(fma(2.0, z, 2.0) / Float64(t * z)) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -1e+38)
		tmp = t_1;
	elseif (Float64(x / y) <= 1.0)
		tmp = Float64(Float64(fma(t, -2.0, Float64(2.0 / z)) - -2.0) / t);
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(N[(2.0 * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1e+38], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 1.0], N[(N[(N[(t * -2.0 + N[(2.0 / z), $MachinePrecision]), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -9.99999999999999977e37 or 1 < (/.f64 x y)

   1. Initial program 83.5%

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

   3. Taylor expanded in t around 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 -9.99999999999999977e37 < (/.f64 x y) < 1

   1. Initial program 83.4%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-lft-identity N/A

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

      7. associate-*l/ N/A

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

      8. lower--.f64 N/A

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

      9. associate-*l/ N/A

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

      10. *-lft-identity N/A

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

      11. lower-/.f64 N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. associate-*r/ N/A

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

      17. metadata-eval N/A

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

      18. lower-/.f64 99.9

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

   5. Applied rewrites 99.9%

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

   7. Applied rewrites 99.9%

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

   8. Taylor expanded in x around 0

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

   10. Applied rewrites 98.9%

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

4. Final simplification 98.3%

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

Alternative 6: 88.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-2 - \frac{-2}{t}\right) + \frac{x}{y}\\ \mathbf{if}\;\frac{x}{y} \leq -1.72 \cdot 10^{+50}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;\frac{x}{y} \leq 2.9 \cdot 10^{+105}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- -2.0 (/ -2.0 t)) (/ x y))))
   (if (<= (/ x y) -1.72e+50)
     t_1
     (if (<= (/ x y) 2.9e+105) (- (/ (- (/ 2.0 z) -2.0) t) 2.0) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-2.0 - (-2.0 / t)) + (x / y);
	double tmp;
	if ((x / y) <= -1.72e+50) {
		tmp = t_1;
	} else if ((x / y) <= 2.9e+105) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-2.0d0) - ((-2.0d0) / t)) + (x / y)
    if ((x / y) <= (-1.72d+50)) then
        tmp = t_1
    else if ((x / y) <= 2.9d+105) then
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (-2.0 - (-2.0 / t)) + (x / y);
	double tmp;
	if ((x / y) <= -1.72e+50) {
		tmp = t_1;
	} else if ((x / y) <= 2.9e+105) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-2.0 - (-2.0 / t)) + (x / y)
	tmp = 0
	if (x / y) <= -1.72e+50:
		tmp = t_1
	elif (x / y) <= 2.9e+105:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-2.0 - Float64(-2.0 / t)) + Float64(x / y))
	tmp = 0.0
	if (Float64(x / y) <= -1.72e+50)
		tmp = t_1;
	elseif (Float64(x / y) <= 2.9e+105)
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (-2.0 - (-2.0 / t)) + (x / y);
	tmp = 0.0;
	if ((x / y) <= -1.72e+50)
		tmp = t_1;
	elseif ((x / y) <= 2.9e+105)
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x / y), $MachinePrecision], -1.72e+50], t$95$1, If[LessEqual[N[(x / y), $MachinePrecision], 2.9e+105], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.72e50 or 2.9000000000000001e105 < (/.f64 x y)

   1. Initial program 82.6%

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

   3. Taylor expanded in 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. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. lower-/.f64 91.3

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

   5. Applied rewrites 91.3%

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

   if -1.72e50 < (/.f64 x y) < 2.9000000000000001e105

   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 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

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

      12. metadata-eval N/A

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

      13. associate--l+ N/A

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

      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 93.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.72 \cdot 10^{+50}:\\ \;\;\;\;\left(-2 - \frac{-2}{t}\right) + \frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 2.9 \cdot 10^{+105}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\left(-2 - \frac{-2}{t}\right) + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.15 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 1.2 \cdot 10^{+113}:\\ \;\;\;\;\frac{\frac{2}{z} - -2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.15e+51)
   (/ x y)
   (if (<= (/ x y) 1.2e+113) (- (/ (- (/ 2.0 z) -2.0) t) 2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.15e+51) {
		tmp = x / y;
	} else if ((x / y) <= 1.2e+113) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.15d+51)) then
        tmp = x / y
    else if ((x / y) <= 1.2d+113) then
        tmp = (((2.0d0 / z) - (-2.0d0)) / t) - 2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.15e+51) {
		tmp = x / y;
	} else if ((x / y) <= 1.2e+113) {
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.15e+51:
		tmp = x / y
	elif (x / y) <= 1.2e+113:
		tmp = (((2.0 / z) - -2.0) / t) - 2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.15e+51)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 1.2e+113)
		tmp = Float64(Float64(Float64(Float64(2.0 / z) - -2.0) / t) - 2.0);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.15e+51)
		tmp = x / y;
	elseif ((x / y) <= 1.2e+113)
		tmp = (((2.0 / z) - -2.0) / t) - 2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.15e+51], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 1.2e+113], N[(N[(N[(N[(2.0 / z), $MachinePrecision] - -2.0), $MachinePrecision] / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.15000000000000003e51 or 1.19999999999999992e113 < (/.f64 x y)

   1. Initial program 82.4%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 82.4

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

   4. Applied rewrites 82.4%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 82.3

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

   7. Applied rewrites 82.3%

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

   if -1.15000000000000003e51 < (/.f64 x y) < 1.19999999999999992e113

   1. Initial program 84.1%

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

   3. Taylor expanded in 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

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

      12. metadata-eval N/A

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

      13. associate--l+ N/A

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

      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%

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

Alternative 8: 98.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-2 - \frac{-2}{t}\right) + \frac{x}{y}\\ \mathbf{if}\;z \leq -1:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2 \cdot t, z, 2\right)}{t \cdot z} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- -2.0 (/ -2.0 t)) (/ x y))))
   (if (<= z -1.0)
     t_1
     (if (<= z 5.5e-12) (+ (/ (fma (* -2.0 t) z 2.0) (* t z)) (/ x y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-2.0 - (-2.0 / t)) + (x / y);
	double tmp;
	if (z <= -1.0) {
		tmp = t_1;
	} else if (z <= 5.5e-12) {
		tmp = (fma((-2.0 * t), z, 2.0) / (t * z)) + (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-2.0 - Float64(-2.0 / t)) + Float64(x / y))
	tmp = 0.0
	if (z <= -1.0)
		tmp = t_1;
	elseif (z <= 5.5e-12)
		tmp = Float64(Float64(fma(Float64(-2.0 * t), z, 2.0) / Float64(t * z)) + Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.0], t$95$1, If[LessEqual[z, 5.5e-12], N[(N[(N[(N[(-2.0 * t), $MachinePrecision] * z + 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -1 or 5.5000000000000004e-12 < z

   1. Initial program 71.5%

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

   3. Taylor expanded in z around 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. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. lower-/.f64 99.7

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

   5. Applied rewrites 99.7%

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

   if -1 < z < 5.5000000000000004e-12

   1. Initial program 98.1%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 98.1

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

   4. Applied rewrites 98.1%

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

   5. Taylor expanded in t around inf

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

      1. lower-*.f64 97.8

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

   7. Applied rewrites 97.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;\left(-2 - \frac{-2}{t}\right) + \frac{x}{y}\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-12}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-2 \cdot t, z, 2\right)}{t \cdot z} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 - \frac{-2}{t}\right) + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 64.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.65 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{2}{t} - 2\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.65e+35)
   (/ x y)
   (if (<= (/ x y) 4.5e+59) (- (/ 2.0 t) 2.0) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.65e+35) {
		tmp = x / y;
	} else if ((x / y) <= 4.5e+59) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: tmp
    if ((x / y) <= (-1.65d+35)) then
        tmp = x / y
    else if ((x / y) <= 4.5d+59) then
        tmp = (2.0d0 / t) - 2.0d0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.65e+35) {
		tmp = x / y;
	} else if ((x / y) <= 4.5e+59) {
		tmp = (2.0 / t) - 2.0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.65e+35:
		tmp = x / y
	elif (x / y) <= 4.5e+59:
		tmp = (2.0 / t) - 2.0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.65e+35)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 4.5e+59)
		tmp = Float64(Float64(2.0 / t) - 2.0);
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	tmp = 0.0;
	if ((x / y) <= -1.65e+35)
		tmp = x / y;
	elseif ((x / y) <= 4.5e+59)
		tmp = (2.0 / t) - 2.0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := If[LessEqual[N[(x / y), $MachinePrecision], -1.65e+35], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4.5e+59], N[(N[(2.0 / t), $MachinePrecision] - 2.0), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.6500000000000001e35 or 4.49999999999999959e59 < (/.f64 x y)

   1. Initial program 83.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 83.7

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

   4. Applied rewrites 83.7%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 79.0

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

   7. Applied rewrites 79.0%

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

   if -1.6500000000000001e35 < (/.f64 x y) < 4.49999999999999959e59

   1. Initial program 83.3%

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

   3. Taylor expanded in 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

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

      12. metadata-eval N/A

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

      13. associate--l+ N/A

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

      14. lower--.f64 N/A

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

   5. Applied rewrites 97.0%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 62.0%

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

Alternative 10: 46.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{x}{y} \leq -1.65 \cdot 10^{+35}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;\frac{x}{y} \leq 4.5 \cdot 10^{+59}:\\ \;\;\;\;\frac{2}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (if (<= (/ x y) -1.65e+35)
   (/ x y)
   (if (<= (/ x y) 4.5e+59) (/ 2.0 t) (/ x y))))

C

double code(double x, double y, double z, double t) {
	double tmp;
	if ((x / y) <= -1.65e+35) {
		tmp = x / y;
	} else if ((x / y) <= 4.5e+59) {
		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) <= (-1.65d+35)) then
        tmp = x / y
    else if ((x / y) <= 4.5d+59) 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) <= -1.65e+35) {
		tmp = x / y;
	} else if ((x / y) <= 4.5e+59) {
		tmp = 2.0 / t;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	tmp = 0
	if (x / y) <= -1.65e+35:
		tmp = x / y
	elif (x / y) <= 4.5e+59:
		tmp = 2.0 / t
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y, z, t)
	tmp = 0.0
	if (Float64(x / y) <= -1.65e+35)
		tmp = Float64(x / y);
	elseif (Float64(x / y) <= 4.5e+59)
		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) <= -1.65e+35)
		tmp = x / y;
	elseif ((x / y) <= 4.5e+59)
		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], -1.65e+35], N[(x / y), $MachinePrecision], If[LessEqual[N[(x / y), $MachinePrecision], 4.5e+59], N[(2.0 / t), $MachinePrecision], N[(x / y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 x y) < -1.6500000000000001e35 or 4.49999999999999959e59 < (/.f64 x y)

   1. Initial program 83.7%

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

      1. lift-+.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 83.7

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

   4. Applied rewrites 83.7%

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

   5. Taylor expanded in x around inf

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

      1. lower-/.f64 79.0

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

   7. Applied rewrites 79.0%

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

   if -1.6500000000000001e35 < (/.f64 x y) < 4.49999999999999959e59

   1. Initial program 83.3%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 65.6

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

   5. Applied rewrites 65.6%

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

   6. Taylor expanded in z around inf

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

   8. Applied rewrites 30.6%

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

Alternative 11: 91.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \left(-2 - \frac{-2}{t}\right) + \frac{x}{y}\\ \mathbf{if}\;z \leq -0.108:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ (- -2.0 (/ -2.0 t)) (/ x y))))
   (if (<= z -0.108) t_1 (if (<= z 4.4e-34) (+ (/ 2.0 (* t z)) (/ x y)) t_1))))

C

double code(double x, double y, double z, double t) {
	double t_1 = (-2.0 - (-2.0 / t)) + (x / y);
	double tmp;
	if (z <= -0.108) {
		tmp = t_1;
	} else if (z <= 4.4e-34) {
		tmp = (2.0 / (t * z)) + (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = ((-2.0d0) - ((-2.0d0) / t)) + (x / y)
    if (z <= (-0.108d0)) then
        tmp = t_1
    else if (z <= 4.4d-34) then
        tmp = (2.0d0 / (t * z)) + (x / y)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = (-2.0 - (-2.0 / t)) + (x / y);
	double tmp;
	if (z <= -0.108) {
		tmp = t_1;
	} else if (z <= 4.4e-34) {
		tmp = (2.0 / (t * z)) + (x / y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = (-2.0 - (-2.0 / t)) + (x / y)
	tmp = 0
	if z <= -0.108:
		tmp = t_1
	elif z <= 4.4e-34:
		tmp = (2.0 / (t * z)) + (x / y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(Float64(-2.0 - Float64(-2.0 / t)) + Float64(x / y))
	tmp = 0.0
	if (z <= -0.108)
		tmp = t_1;
	elseif (z <= 4.4e-34)
		tmp = Float64(Float64(2.0 / Float64(t * z)) + Float64(x / y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = (-2.0 - (-2.0 / t)) + (x / y);
	tmp = 0.0;
	if (z <= -0.108)
		tmp = t_1;
	elseif (z <= 4.4e-34)
		tmp = (2.0 / (t * z)) + (x / y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(N[(-2.0 - N[(-2.0 / t), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.108], t$95$1, If[LessEqual[z, 4.4e-34], N[(N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Derivation

1. Split input into 2 regimes

2. if z < -0.107999999999999999 or 4.3999999999999998e-34 < z

   1. Initial program 72.3%

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

   3. Taylor expanded in 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. associate-*r/ N/A

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

      9. metadata-eval N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-frac N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 N/A

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

      14. lower-/.f64 99.1

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

   5. Applied rewrites 99.1%

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

   if -0.107999999999999999 < z < 4.3999999999999998e-34

   1. Initial program 98.1%

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

   3. Taylor expanded in z around 0

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

   5. Applied rewrites 87.8%

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

4. Final simplification 94.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.108:\\ \;\;\;\;\left(-2 - \frac{-2}{t}\right) + \frac{x}{y}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-34}:\\ \;\;\;\;\frac{2}{t \cdot z} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(-2 - \frac{-2}{t}\right) + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-67}:\\ \;\;\;\;\frac{z \cdot 2}{t \cdot z}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+23}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= t -2.9e-121)
     t_1
     (if (<= t 4e-67)
       (/ (* z 2.0) (* t z))
       (if (<= t 1.02e+23) (/ (/ 2.0 t) z) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (t <= -2.9e-121) {
		tmp = t_1;
	} else if (t <= 4e-67) {
		tmp = (z * 2.0) / (t * z);
	} else if (t <= 1.02e+23) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) + (x / y)
    if (t <= (-2.9d-121)) then
        tmp = t_1
    else if (t <= 4d-67) then
        tmp = (z * 2.0d0) / (t * z)
    else if (t <= 1.02d+23) then
        tmp = (2.0d0 / t) / z
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (t <= -2.9e-121) {
		tmp = t_1;
	} else if (t <= 4e-67) {
		tmp = (z * 2.0) / (t * z);
	} else if (t <= 1.02e+23) {
		tmp = (2.0 / t) / z;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	tmp = 0
	if t <= -2.9e-121:
		tmp = t_1
	elif t <= 4e-67:
		tmp = (z * 2.0) / (t * z)
	elif t <= 1.02e+23:
		tmp = (2.0 / t) / z
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t <= -2.9e-121)
		tmp = t_1;
	elseif (t <= 4e-67)
		tmp = Float64(Float64(z * 2.0) / Float64(t * z));
	elseif (t <= 1.02e+23)
		tmp = Float64(Float64(2.0 / t) / z);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	tmp = 0.0;
	if (t <= -2.9e-121)
		tmp = t_1;
	elseif (t <= 4e-67)
		tmp = (z * 2.0) / (t * z);
	elseif (t <= 1.02e+23)
		tmp = (2.0 / t) / z;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e-121], t$95$1, If[LessEqual[t, 4e-67], N[(N[(z * 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+23], N[(N[(2.0 / t), $MachinePrecision] / z), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9e-121 or 1.02e23 < t

   1. Initial program 71.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 80.0%

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

   if -2.9e-121 < t < 3.99999999999999977e-67

   1. Initial program 97.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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. +-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 83.9

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

   5. Applied rewrites 83.9%

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

   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 83.7%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 60.3%

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

   if 3.99999999999999977e-67 < t < 1.02e23

   1. Initial program 99.5%

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

   3. Taylor expanded in t around 0

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

      1. lower-/.f64 N/A

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

      2. associate-+r+ N/A

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

      3. +-commutative N/A

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

      4. *-commutative N/A

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

      5. lower-fma.f64 N/A

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

      6. *-lft-identity N/A

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

      7. associate-*l/ N/A

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

      8. lower--.f64 N/A

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

      9. associate-*l/ N/A

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

      10. *-lft-identity N/A

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

      11. lower-/.f64 N/A

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

      12. +-commutative N/A

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

      13. metadata-eval N/A

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

      14. sub-neg N/A

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

      15. lower--.f64 N/A

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

      16. associate-*r/ N/A

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

      17. metadata-eval N/A

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

      18. lower-/.f64 99.5

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

   5. Applied rewrites 99.5%

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

   6. Taylor expanded in z around 0

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

   8. Applied rewrites 58.1%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-121}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-67}:\\ \;\;\;\;\frac{z \cdot 2}{t \cdot z}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+23}:\\ \;\;\;\;\frac{\frac{2}{t}}{z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 65.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := -2 + \frac{x}{y}\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{-121}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-67}:\\ \;\;\;\;\frac{z \cdot 2}{t \cdot z}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+23}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t)
 :precision binary64
 (let* ((t_1 (+ -2.0 (/ x y))))
   (if (<= t -2.9e-121)
     t_1
     (if (<= t 4e-67)
       (/ (* z 2.0) (* t z))
       (if (<= t 1.02e+23) (/ 2.0 (* t z)) t_1)))))

C

double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (t <= -2.9e-121) {
		tmp = t_1;
	} else if (t <= 4e-67) {
		tmp = (z * 2.0) / (t * z);
	} else if (t <= 1.02e+23) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8) :: t_1
    real(8) :: tmp
    t_1 = (-2.0d0) + (x / y)
    if (t <= (-2.9d-121)) then
        tmp = t_1
    else if (t <= 4d-67) then
        tmp = (z * 2.0d0) / (t * z)
    else if (t <= 1.02d+23) then
        tmp = 2.0d0 / (t * z)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t) {
	double t_1 = -2.0 + (x / y);
	double tmp;
	if (t <= -2.9e-121) {
		tmp = t_1;
	} else if (t <= 4e-67) {
		tmp = (z * 2.0) / (t * z);
	} else if (t <= 1.02e+23) {
		tmp = 2.0 / (t * z);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t):
	t_1 = -2.0 + (x / y)
	tmp = 0
	if t <= -2.9e-121:
		tmp = t_1
	elif t <= 4e-67:
		tmp = (z * 2.0) / (t * z)
	elif t <= 1.02e+23:
		tmp = 2.0 / (t * z)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t)
	t_1 = Float64(-2.0 + Float64(x / y))
	tmp = 0.0
	if (t <= -2.9e-121)
		tmp = t_1;
	elseif (t <= 4e-67)
		tmp = Float64(Float64(z * 2.0) / Float64(t * z));
	elseif (t <= 1.02e+23)
		tmp = Float64(2.0 / Float64(t * z));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t)
	t_1 = -2.0 + (x / y);
	tmp = 0.0;
	if (t <= -2.9e-121)
		tmp = t_1;
	elseif (t <= 4e-67)
		tmp = (z * 2.0) / (t * z);
	elseif (t <= 1.02e+23)
		tmp = 2.0 / (t * z);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_] := Block[{t$95$1 = N[(-2.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -2.9e-121], t$95$1, If[LessEqual[t, 4e-67], N[(N[(z * 2.0), $MachinePrecision] / N[(t * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.02e+23], N[(2.0 / N[(t * z), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if t < -2.9e-121 or 1.02e23 < t

   1. Initial program 71.6%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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 80.0%

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

   if -2.9e-121 < t < 3.99999999999999977e-67

   1. Initial program 97.8%

      \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
   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. +-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 83.9

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

   5. Applied rewrites 83.9%

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

   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 83.7%

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

   9. Taylor expanded in z around inf

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

   11. Applied rewrites 60.3%

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

   if 3.99999999999999977e-67 < t < 1.02e23

   1. Initial program 99.5%

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

   3. Taylor expanded in z around 0

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

      1. lower-/.f64 N/A

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

      2. lower-*.f64 58.1

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

   5. Applied rewrites 58.1%

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

4. Final simplification 71.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -2.9 \cdot 10^{-121}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-67}:\\ \;\;\;\;\frac{z \cdot 2}{t \cdot z}\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{+23}:\\ \;\;\;\;\frac{2}{t \cdot z}\\ \mathbf{else}:\\ \;\;\;\;-2 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 19.5% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \frac{2}{t} \end{array} \]

FPCore

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

C

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

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 / t
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_, t_] := N[(2.0 / t), $MachinePrecision]

Derivation

1. Initial program 83.5%

   \[\frac{x}{y} + \frac{2 + \left(z \cdot 2\right) \cdot \left(1 - t\right)}{t \cdot z} \]
2. 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 48.3

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

5. Applied rewrites 48.3%

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

6. Taylor expanded in z around inf

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

8. Applied rewrites 22.4%

   \[\leadsto \frac{2}{\color{blue}{t}} \]
9. Add Preprocessing

Developer Target 1: 99.2% 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 2024332 
(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))))