Average Error: 0.3 → 0.2
Time: 1.7s
Precision: binary64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[6 \cdot x - 9 \cdot {x}^{2}\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
6 \cdot x - 9 \cdot {x}^{2}
(FPCore (x) :precision binary64 (* (* 3.0 (- 2.0 (* x 3.0))) x))
↓
(FPCore (x) :precision binary64 (- (* 6.0 x) (* 9.0 (pow x 2.0))))
double code(double x) {
	return (3.0 * (2.0 - (x * 3.0))) * x;
}
↓
double code(double x) {
	return (6.0 * x) - (9.0 * pow(x, 2.0));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.2
\[6 \cdot x - 9 \cdot \left(x \cdot x\right)\]

Derivation

  1. Initial program 0.3

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

  2. Simplified0.2

    \[\leadsto \color{blue}{x \cdot \left(6 + x \cdot -9\right)}\]

  3. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{6 \cdot x - 9 \cdot {x}^{2}}\]

  4. Final simplification0.2

    \[\leadsto 6 \cdot x - 9 \cdot {x}^{2}\]

Reproduce

herbie shell --seed 2021168 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"
  :precision binary64

  :herbie-target
  (- (* 6.0 x) (* 9.0 (* x x)))

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