Average Error: 15.9 → 0.3
Time: 18.7s
Precision: binary64
Cost: 512
\[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b\]
↓
\[-\left(a \cdot b\right) \cdot \left(a \cdot b\right)\]
-\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 angle) :precision binary64 (- (* (* (* a a) b) b)))
↓
(FPCore (a b angle) :precision binary64 (- (* (* a b) (* a b))))
double code(double a, double b, double angle) {
	return -(((a * a) * b) * b);
}
↓
double code(double a, double b, double angle) {
	return -((a * b) * (a * b));
}

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

Alternatives

Alternative 1
Error15.9
Cost512
\[-b \cdot \left(b \cdot \left(a \cdot a\right)\right)\]
Alternative 2
Error37.4
Cost64
\[0\]
Alternative 3
Error62.6
Cost64
\[1\]

Error

Time

Derivation

  1. Initial program 15.9

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

  3. Applied add-sqr-sqrt_binary6440.2

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

  4. Applied associate-*r*_binary6440.2

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

  5. Simplified37.6

    \[\leadsto -\color{blue}{\left(a \cdot \left(a \cdot {b}^{1.5}\right)\right)} \cdot \sqrt{b}\]
  6. Using strategy rm

  7. Applied pow1_binary6437.6

    \[\leadsto -\left(a \cdot \left(a \cdot {b}^{1.5}\right)\right) \cdot \color{blue}{{\left(\sqrt{b}\right)}^{1}}\]

  8. Applied pow1_binary6437.6

    \[\leadsto -\left(a \cdot \color{blue}{{\left(a \cdot {b}^{1.5}\right)}^{1}}\right) \cdot {\left(\sqrt{b}\right)}^{1}\]

  9. Applied pow1_binary6437.6

    \[\leadsto -\left(\color{blue}{{a}^{1}} \cdot {\left(a \cdot {b}^{1.5}\right)}^{1}\right) \cdot {\left(\sqrt{b}\right)}^{1}\]

  10. Applied pow-prod-down_binary6437.6

    \[\leadsto -\color{blue}{{\left(a \cdot \left(a \cdot {b}^{1.5}\right)\right)}^{1}} \cdot {\left(\sqrt{b}\right)}^{1}\]

  11. Applied pow-prod-down_binary6437.6

    \[\leadsto -\color{blue}{{\left(\left(a \cdot \left(a \cdot {b}^{1.5}\right)\right) \cdot \sqrt{b}\right)}^{1}}\]

  12. Simplified0.3

    \[\leadsto -{\color{blue}{\left(\left(a \cdot b\right) \cdot \left(a \cdot b\right)\right)}}^{1}\]

  13. Simplified0.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2021040 
(FPCore (a b angle)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))