Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D

Average Error: 0.1 → 0.1

Time: 11.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]

↓

\[3 + x \cdot \left(9 \cdot x - 12\right)\]

C

double f(double x) {
        double r911827 = 3.0;
        double r911828 = x;
        double r911829 = r911828 * r911827;
        double r911830 = r911829 * r911828;
        double r911831 = 4.0;
        double r911832 = r911828 * r911831;
        double r911833 = r911830 - r911832;
        double r911834 = 1.0;
        double r911835 = r911833 + r911834;
        double r911836 = r911827 * r911835;
        return r911836;
}

↓

double f(double x) {
        double r911837 = 3.0;
        double r911838 = x;
        double r911839 = 9.0;
        double r911840 = r911839 * r911838;
        double r911841 = 12.0;
        double r911842 = r911840 - r911841;
        double r911843 = r911838 * r911842;
        double r911844 = r911837 + r911843;
        return r911844;
}

Error

Bits error versus x

Target

Original	0.1
Target	0.1
Herbie	0.1

\[3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right)\]

Derivation

1. Initial program 0.1

   \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]

2. Simplified 0.1

   \[\leadsto \color{blue}{3 \cdot \mathsf{fma}\left(x, x \cdot 3 - 4, 1\right)}\]

3. Taylor expanded around 0 0.1

   \[\leadsto \color{blue}{\left(9 \cdot {x}^{2} + 3\right) - 12 \cdot x}\]

4. Simplified 0.1

   \[\leadsto \color{blue}{3 + x \cdot \left(9 \cdot x - 12\right)}\]

5. Final simplification 0.1

   \[\leadsto 3 + x \cdot \left(9 \cdot x - 12\right)\]

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (+ 3 (- (* (* 9 x) x) (* 12 x)))

  (* 3 (+ (- (* (* x 3) x) (* x 4)) 1)))