Average Error: 16.3 → 0.3
Time: 2.9s
Precision: binary64
Cost: 26176
\[-\left(\left(a \cdot a\right) \cdot b\right) \cdot b\]
↓
\[-\sqrt{\left|a \cdot b\right|} \cdot {\left(\left|a \cdot b\right|\right)}^{1.5}\]
-\left(\left(a \cdot a\right) \cdot b\right) \cdot b
↓
-\sqrt{\left|a \cdot b\right|} \cdot {\left(\left|a \cdot b\right|\right)}^{1.5}
(FPCore (a b angle) :precision binary64 (- (* (* (* a a) b) b)))
↓
(FPCore (a b angle)
 :precision binary64
 (- (* (sqrt (fabs (* a b))) (pow (fabs (* a b)) 1.5))))
double code(double a, double b, double angle) {
	return -(((a * a) * b) * b);
}
↓
double code(double a, double b, double angle) {
	return -(sqrt(fabs(a * b)) * pow(fabs(a * b), 1.5));
}

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
Error0.3
Cost512
\[-\left(a \cdot b\right) \cdot \left(a \cdot b\right)\]
Alternative 2
Error16.3
Cost512
\[-b \cdot \left(b \cdot \left(a \cdot a\right)\right)\]
Alternative 3
Error37.8
Cost64
\[0\]
Alternative 4
Error62.6
Cost64
\[1\]

Error

Derivation

  1. Initial program 16.3

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

  3. Applied add-sqr-sqrt_binary6416.4

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

  4. Simplified16.3

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

  5. Simplified0.3

    \[\leadsto -\left|a \cdot b\right| \cdot \color{blue}{\left|a \cdot b\right|}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt_binary640.4

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

  8. Applied associate-*l*_binary640.4

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

  9. Simplified0.3

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

  10. Simplified0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2021044 
(FPCore (a b angle)
  :name "ab-angle->ABCF D"
  :precision binary64
  (- (* (* (* a a) b) b)))