Average Error: 7.7 → 0.1
Time: 7.3s
Precision: 64
\[\frac{x \cdot y}{y + 1}\]
↓
\[\frac{x}{\frac{y + 1}{y}}\]
\frac{x \cdot y}{y + 1}
↓
\frac{x}{\frac{y + 1}{y}}
double f(double x, double y) {
        double r894230 = x;
        double r894231 = y;
        double r894232 = r894230 * r894231;
        double r894233 = 1.0;
        double r894234 = r894231 + r894233;
        double r894235 = r894232 / r894234;
        return r894235;
}
↓
double f(double x, double y) {
        double r894236 = x;
        double r894237 = y;
        double r894238 = 1.0;
        double r894239 = r894237 + r894238;
        double r894240 = r894239 / r894237;
        double r894241 = r894236 / r894240;
        return r894241;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.7
Target0.0
Herbie0.1
\[\begin{array}{l} \mathbf{if}\;y \lt -3693.848278829724677052581682801246643066:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y \lt 6799310503.41891002655029296875:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

Derivation

  1. Initial program 7.7

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

  3. Applied associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :herbie-target
  (if (< y -3693.84827882972468) (- (/ x (* y y)) (- (/ x y) x)) (if (< y 6799310503.41891003) (/ (* x y) (+ y 1)) (- (/ x (* y y)) (- (/ x y) x))))

  (/ (* x y) (+ y 1)))