Average Error: 0.1 → 0
Time: 6.1s
Precision: binary64
Cost: 192
\[\left(x \cdot x\right) \cdot x\]
↓
\[{x}^{3}\]
\left(x \cdot x\right) \cdot x
↓
{x}^{3}
(FPCore (x) :precision binary64 (* (* x x) x))
↓
(FPCore (x) :precision binary64 (pow x 3.0))
double code(double x) {
	return (x * x) * x;
}
↓
double code(double x) {
	return pow(x, 3.0);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs
Alternative 1
Accuracy0.1
Cost320
\[x \cdot \left(x \cdot x\right)\]
Alternative 2
Accuracy0.7
Cost768
\[\sqrt[3]{x} \cdot \left(\left(x \cdot x\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right)\right)\]
Alternative 3
Accuracy32.0
Cost384
\[{x}^{2.5} \cdot \sqrt{x}\]

Derivation

  1. Initial program 0.1

    \[\left(x \cdot x\right) \cdot x\]
  2. Using strategy rm

  3. Applied pow1_binary64_59360.1

    \[\leadsto \left(x \cdot x\right) \cdot \color{blue}{{x}^{1}}\]

  4. Applied pow1_binary64_59360.1

    \[\leadsto \left(x \cdot \color{blue}{{x}^{1}}\right) \cdot {x}^{1}\]

  5. Applied pow1_binary64_59360.1

    \[\leadsto \left(\color{blue}{{x}^{1}} \cdot {x}^{1}\right) \cdot {x}^{1}\]

  6. Applied pow-prod-down_binary64_59460.1

    \[\leadsto \color{blue}{{\left(x \cdot x\right)}^{1}} \cdot {x}^{1}\]

  7. Applied pow-prod-down_binary64_59460.1

    \[\leadsto \color{blue}{{\left(\left(x \cdot x\right) \cdot x\right)}^{1}}\]

  8. Simplified0

    \[\leadsto {\color{blue}{\left({x}^{3}\right)}}^{1}\]

  9. Final simplification0

    \[\leadsto {x}^{3}\]

Reproduce

herbie shell --seed 2020322 
(FPCore (x)
  :name "Diagrams.Segment:$catParam from diagrams-lib-1.3.0.3, C"
  :precision binary64
  (* (* x x) x))