Average Error: 0.2 → 0.1
Time: 2.7s
Precision: binary64
Cost: 7040
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[3 \cdot \left(x \cdot x\right) + {x}^{3} \cdot -2\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
3 \cdot \left(x \cdot x\right) + {x}^{3} \cdot -2
(FPCore (x) :precision binary64 (* (* x x) (- 3.0 (* x 2.0))))
↓
(FPCore (x) :precision binary64 (+ (* 3.0 (* x x)) (* (pow x 3.0) -2.0)))
double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}
↓
double code(double x) {
	return (3.0 * (x * x)) + (pow(x, 3.0) * -2.0);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.1
\[x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)\]

Alternatives

Alternative 1
Error0.2
Cost832
\[3 \cdot \left(x \cdot x\right) + \left(x \cdot x\right) \cdot \left(x \cdot -2\right)\]
Alternative 2
Error0.2
Cost576
\[\left(x \cdot x\right) \cdot \left(3 + x \cdot -2\right)\]
Alternative 3
Error2.3
Cost776
\[\begin{array}{l} \mathbf{if}\;x \leq -1.5141405204876162 \lor \neg \left(x \leq 1.4962902966217095\right):\\ \;\;\;\;x \cdot \left(x \cdot \left(x \cdot -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(x \cdot x\right)\\ \end{array}\]
Alternative 4
Error16.8
Cost320
\[3 \cdot \left(x \cdot x\right)\]
Alternative 5
Error16.8
Cost320
\[x \cdot \left(3 \cdot x\right)\]
Alternative 6
Error38.8
Cost64
\[0\]
Alternative 7
Error61.4
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.2

    \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
  2. Using strategy rm

  3. Applied sub-neg_binary64_222360.2

    \[\leadsto \left(x \cdot x\right) \cdot \color{blue}{\left(3 + \left(-x \cdot 2\right)\right)}\]

  4. Applied distribute-rgt-in_binary64_221930.2

    \[\leadsto \color{blue}{3 \cdot \left(x \cdot x\right) + \left(-x \cdot 2\right) \cdot \left(x \cdot x\right)}\]

  5. Simplified0.2

    \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot 3} + \left(-x \cdot 2\right) \cdot \left(x \cdot x\right)\]

  6. Simplified0.1

    \[\leadsto \left(x \cdot x\right) \cdot 3 + \color{blue}{{x}^{3} \cdot -2}\]

  7. Simplified0.1

    \[\leadsto \color{blue}{3 \cdot \left(x \cdot x\right) + {x}^{3} \cdot -2}\]

  8. Final simplification0.1

    \[\leadsto 3 \cdot \left(x \cdot x\right) + {x}^{3} \cdot -2\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"
  :precision binary64

  :herbie-target
  (* x (* x (- 3.0 (* x 2.0))))

  (* (* x x) (- 3.0 (* x 2.0))))