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

Average Error: 0.3 → 0.2

Time: 3.8s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r1437 = 3.0;
        double r1438 = 2.0;
        double r1439 = x;
        double r1440 = r1439 * r1437;
        double r1441 = r1438 - r1440;
        double r1442 = r1437 * r1441;
        double r1443 = r1442 * r1439;
        return r1443;
}

↓

double f(double x) {
        double r1444 = x;
        double r1445 = 6.0;
        double r1446 = 9.0;
        double r1447 = r1444 * r1446;
        double r1448 = r1445 - r1447;
        double r1449 = r1444 * r1448;
        return r1449;
}

Error

Bits error versus x

Target

Original	0.3
Target	0.2
Herbie	0.2

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

Derivation

1. Initial program 0.3

   \[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
2. Using strategy rm

3. Applied associate-*l* 0.3

   \[\leadsto \color{blue}{3 \cdot \left(\left(2 - x \cdot 3\right) \cdot x\right)}\]
4. Using strategy rm

5. Applied add-cube-cbrt 0.3

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

6. Applied associate-*l* 0.5

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

7. Taylor expanded around 0 0.2

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

8. Simplified 0.2

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

9. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020025 
(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))