Average Error: 11.7 → 0.2
Time: 4.2s
Precision: binary64
\[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
↓
\[-{\left(a \cdot b\right)}^{2} \]
-\left(\left(a \cdot a\right) \cdot b\right) \cdot b
↓
-{\left(a \cdot b\right)}^{2}

(FPCore (a b) :precision binary64 (- (* (* (* a a) b) b)))
↓
(FPCore (a b) :precision binary64 (- (pow (* a b) 2.0)))
double code(double a, double b) {
	return -(((a * a) * b) * b);
}
↓
double code(double a, double b) {
	return -pow((a * b), 2.0);
}

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 11.7

    \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]

  2. Applied add-sqr-sqrt_binary6411.7

    \[\leadsto -\color{blue}{\sqrt{\left(\left(a \cdot a\right) \cdot b\right) \cdot b} \cdot \sqrt{\left(\left(a \cdot a\right) \cdot b\right) \cdot b}} \]

  3. Simplified28.8

    \[\leadsto -\color{blue}{\left(a \cdot b\right)} \cdot \sqrt{\left(\left(a \cdot a\right) \cdot b\right) \cdot b} \]

  4. Simplified0.2

    \[\leadsto -\left(a \cdot b\right) \cdot \color{blue}{\left(a \cdot b\right)} \]

  5. Taylor expanded in a around 0 15.7

    \[\leadsto -\color{blue}{{a}^{2} \cdot {b}^{2}} \]

  6. Simplified0.2

    \[\leadsto -\color{blue}{{\left(a \cdot b\right)}^{2}} \]

  7. Final simplification0.2

    \[\leadsto -{\left(a \cdot b\right)}^{2} \]

Reproduce

herbie shell --seed 2022067 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))