Average Error: 16.6 → 0.3
Time: 4.4s
Precision: binary64
\[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b \]
↓
\[-\left(a \cdot b\right) \cdot \left(a \cdot b\right) \]
-\left(\left(a \cdot a\right) \cdot b\right) \cdot b
↓
-\left(a \cdot b\right) \cdot \left(a \cdot b\right)

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

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 16.6

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

  2. Applied add-sqr-sqrt_binary6416.7

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

  3. Simplified28.2

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

  4. Simplified0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2022076 
(FPCore (a b)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))