Average Error: 0.2 → 0.1
Time: 2.2s
Precision: binary64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]
↓
\[x \cdot \left(3 \cdot x\right) - 2 \cdot {x}^{3} \]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
x \cdot \left(3 \cdot x\right) - 2 \cdot {x}^{3}

(FPCore (x) :precision binary64 (* (* x x) (- 3.0 (* x 2.0))))
↓
(FPCore (x) :precision binary64 (- (* x (* 3.0 x)) (* 2.0 (pow x 3.0))))
double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}
↓
double code(double x) {
	return (x * (3.0 * x)) - (2.0 * pow(x, 3.0));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.2

    \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right) \]

  2. Simplified0.2

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

  3. Taylor expanded in x around 0 0.1

    \[\leadsto \color{blue}{3 \cdot {x}^{2} - 2 \cdot {x}^{3}} \]

  4. Applied unpow2_binary640.1

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

  5. Applied associate-*r*_binary640.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2021313 
(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))))