Average Error: 11.6 → 3.4
Time: 10.5s
Precision: 64
\[\frac{x \cdot \left(y + z\right)}{z}\]
↓
\[\frac{y + z}{z} \cdot x\]
\frac{x \cdot \left(y + z\right)}{z}
↓
\frac{y + z}{z} \cdot x
double f(double x, double y, double z) {
        double r20248533 = x;
        double r20248534 = y;
        double r20248535 = z;
        double r20248536 = r20248534 + r20248535;
        double r20248537 = r20248533 * r20248536;
        double r20248538 = r20248537 / r20248535;
        return r20248538;
}
↓
double f(double x, double y, double z) {
        double r20248539 = y;
        double r20248540 = z;
        double r20248541 = r20248539 + r20248540;
        double r20248542 = r20248541 / r20248540;
        double r20248543 = x;
        double r20248544 = r20248542 * r20248543;
        return r20248544;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Your Program's Arguments

Results

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Target

Original11.6
Target3.1
Herbie3.4
\[\frac{x}{\frac{z}{y + z}}\]

Derivation

  1. Initial program 11.6

    \[\frac{x \cdot \left(y + z\right)}{z}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity11.6

    \[\leadsto \frac{x \cdot \left(y + z\right)}{\color{blue}{1 \cdot z}}\]

  4. Applied times-frac3.4

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

  5. Simplified3.4

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

  6. Final simplification3.4

    \[\leadsto \frac{y + z}{z} \cdot x\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:choose from math-functions-0.1.5.2"

  :herbie-target
  (/ x (/ z (+ y z)))

  (/ (* x (+ y z)) z))