Average Error: 0.2 → 0.5
Time: 5.4s
Precision: binary64
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
↓
\[\left(\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \left(\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}}\right) + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(a + 3\right)\right)\right) - 1\]
\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1
↓
\left(\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \left(\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}}\right) + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(a + 3\right)\right)\right) - 1
double code(double a, double b) {
	return ((double) (((double) (((double) pow(((double) (((double) (a * a)) + ((double) (b * b)))), 2.0)) + ((double) (4.0 * ((double) (((double) (((double) (a * a)) * ((double) (1.0 - a)))) + ((double) (((double) (b * b)) * ((double) (3.0 + a)))))))))) - 1.0));
}
↓
double code(double a, double b) {
	return ((double) (((double) (((double) (((double) cbrt(((double) pow(((double) (((double) (b * b)) + ((double) (a * a)))), 2.0)))) * ((double) (((double) cbrt(((double) pow(((double) (((double) (b * b)) + ((double) (a * a)))), 2.0)))) * ((double) cbrt(((double) pow(((double) (((double) (b * b)) + ((double) (a * a)))), 2.0)))))))) + ((double) (4.0 * ((double) (((double) (((double) (a * a)) * ((double) (1.0 - a)))) + ((double) (((double) (b * b)) * ((double) (a + 3.0)))))))))) - 1.0));
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.5

    \[\leadsto \left(\color{blue}{\left(\sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}} \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}}\right) \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}}} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]

  4. Simplified0.5

    \[\leadsto \left(\color{blue}{\left(\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}}\right)} \cdot \sqrt[3]{{\left(a \cdot a + b \cdot b\right)}^{2}} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]

  5. Simplified0.5

    \[\leadsto \left(\left(\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}}\right) \cdot \color{blue}{\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}}} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(3 + a\right)\right)\right) - 1\]

  6. Final simplification0.5

    \[\leadsto \left(\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \left(\sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}} \cdot \sqrt[3]{{\left(b \cdot b + a \cdot a\right)}^{2}}\right) + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 - a\right) + \left(b \cdot b\right) \cdot \left(a + 3\right)\right)\right) - 1\]

Reproduce

herbie shell --seed 2020184 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  :precision binary64
  (- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 1.0))