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

Average Error: 0.1 → 0.1

Time: 2.6s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r793359 = 3.0;
        double r793360 = x;
        double r793361 = r793360 * r793359;
        double r793362 = r793361 * r793360;
        double r793363 = 4.0;
        double r793364 = r793360 * r793363;
        double r793365 = r793362 - r793364;
        double r793366 = 1.0;
        double r793367 = r793365 + r793366;
        double r793368 = r793359 * r793367;
        return r793368;
}

↓

double f(double x) {
        double r793369 = x;
        double r793370 = 9.0;
        double r793371 = r793369 * r793370;
        double r793372 = 12.0;
        double r793373 = r793371 - r793372;
        double r793374 = r793369 * r793373;
        double r793375 = 3.0;
        double r793376 = r793374 + r793375;
        return r793376;
}

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. 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

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

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020021 
(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)))