Average Error: 16.1 → 0.3
Time: 2.6s
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 angle) :precision binary64 (- (* (* (* a a) b) b)))
↓
(FPCore (a b angle) :precision binary64 (- (pow (* a b) 2.0)))
double code(double a, double b, double angle) {
	return -(((a * a) * b) * b);
}
↓
double code(double a, double b, double angle) {
	return -pow((a * b), 2.0);
}

Error

Bits error versus a

Bits error versus b

Bits error versus angle

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.1

    \[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt_binary6416.2

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

  4. Simplified16.1

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

  5. Simplified0.3

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

  6. Taylor expanded around 0 0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020355 
(FPCore (a b angle)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))