Average Error: 0.3 → 0.2
Time: 2.8s
Precision: 64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[\left(6 - 9 \cdot x\right) \cdot x\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
\left(6 - 9 \cdot x\right) \cdot x
double f(double x) {
        double r773398 = 3.0;
        double r773399 = 2.0;
        double r773400 = x;
        double r773401 = r773400 * r773398;
        double r773402 = r773399 - r773401;
        double r773403 = r773398 * r773402;
        double r773404 = r773403 * r773400;
        return r773404;
}
↓
double f(double x) {
        double r773405 = 6.0;
        double r773406 = 9.0;
        double r773407 = x;
        double r773408 = r773406 * r773407;
        double r773409 = r773405 - r773408;
        double r773410 = r773409 * r773407;
        return r773410;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

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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. Taylor expanded around 0 0.2

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

  3. Final simplification0.2

    \[\leadsto \left(6 - 9 \cdot x\right) \cdot x\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"
  :precision binary64

  :herbie-target
  (- (* 6 x) (* 9 (* x x)))

  (* (* 3 (- 2 (* x 3))) x))