Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, B

Average Error: 8.2 → 0.1

Time: 13.4s

Precision: 64

Math

\[\frac{x \cdot y}{y + 1}\]

↓

\[\frac{x}{\frac{1}{y} + 1}\]

C

double f(double x, double y) {
        double r31901015 = x;
        double r31901016 = y;
        double r31901017 = r31901015 * r31901016;
        double r31901018 = 1.0;
        double r31901019 = r31901016 + r31901018;
        double r31901020 = r31901017 / r31901019;
        return r31901020;
}

↓

double f(double x, double y) {
        double r31901021 = x;
        double r31901022 = 1.0;
        double r31901023 = y;
        double r31901024 = r31901022 / r31901023;
        double r31901025 = 1.0;
        double r31901026 = r31901024 + r31901025;
        double r31901027 = r31901021 / r31901026;
        return r31901027;
}

Error

Bits error versus x

Bits error versus y

Target

Original	8.2
Target	0.0
Herbie	0.1

\[\begin{array}{l} \mathbf{if}\;y \lt -3693.848278829724677052581682801246643066:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y \lt 6799310503.41891002655029296875:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

Derivation

1. Initial program 8.2

   \[\frac{x \cdot y}{y + 1}\]
2. Using strategy rm

3. Applied associate-/l* 0.1

   \[\leadsto \color{blue}{\frac{x}{\frac{y + 1}{y}}}\]

4. Taylor expanded around 0 0.1

   \[\leadsto \frac{x}{\color{blue}{1 + 1 \cdot \frac{1}{y}}}\]

5. Simplified 0.1

   \[\leadsto \frac{x}{\color{blue}{\frac{1}{y} + 1}}\]

6. Final simplification 0.1

   \[\leadsto \frac{x}{\frac{1}{y} + 1}\]

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, B"

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ x (* y y)) (- (/ x y) x)) (if (< y 6799310503.41891) (/ (* x y) (+ y 1.0)) (- (/ x (* y y)) (- (/ x y) x))))

  (/ (* x y) (+ y 1.0)))