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

Average Error: 0.2 → 0.1

Time: 13.2s

Precision: 64

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 r537915 = 3.0;
        double r537916 = x;
        double r537917 = r537916 * r537915;
        double r537918 = r537917 * r537916;
        double r537919 = 4.0;
        double r537920 = r537916 * r537919;
        double r537921 = r537918 - r537920;
        double r537922 = 1.0;
        double r537923 = r537921 + r537922;
        double r537924 = r537915 * r537923;
        return r537924;
}

↓

double f(double x) {
        double r537925 = 3.0;
        double r537926 = x;
        double r537927 = 9.0;
        double r537928 = r537927 * r537926;
        double r537929 = 12.0;
        double r537930 = r537928 - r537929;
        double r537931 = r537926 * r537930;
        double r537932 = r537925 + r537931;
        return r537932;
}

Error

Bits error versus x

Target

Original	0.2
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 0.2

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

2. Taylor expanded around 0 0.1

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

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 2019198 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"

  :herbie-target
  (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x)))

  (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))