Average Error: 0.2 → 0.2
Time: 3.0s
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 r798642 = 3.0;
        double r798643 = 2.0;
        double r798644 = x;
        double r798645 = r798644 * r798642;
        double r798646 = r798643 - r798645;
        double r798647 = r798642 * r798646;
        double r798648 = r798647 * r798644;
        return r798648;
}
↓
double f(double x) {
        double r798649 = 6.0;
        double r798650 = 9.0;
        double r798651 = x;
        double r798652 = r798650 * r798651;
        double r798653 = r798649 - r798652;
        double r798654 = r798653 * r798651;
        return r798654;
}

Error

Bits error versus x

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Results

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Target

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

Derivation

  1. Initial program 0.2

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

  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 2019353 +o rules:numerics
(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))