Average Error: 12.1 → 2.0
Time: 5.8s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\frac{x}{1 \cdot \frac{t - z}{y - z}}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\frac{x}{1 \cdot \frac{t - z}{y - z}}
double f(double x, double y, double z, double t) {
        double r2259 = x;
        double r2260 = y;
        double r2261 = z;
        double r2262 = r2260 - r2261;
        double r2263 = r2259 * r2262;
        double r2264 = t;
        double r2265 = r2264 - r2261;
        double r2266 = r2263 / r2265;
        return r2266;
}
↓
double f(double x, double y, double z, double t) {
        double r2267 = x;
        double r2268 = 1.0;
        double r2269 = t;
        double r2270 = z;
        double r2271 = r2269 - r2270;
        double r2272 = y;
        double r2273 = r2272 - r2270;
        double r2274 = r2271 / r2273;
        double r2275 = r2268 * r2274;
        double r2276 = r2267 / r2275;
        return r2276;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Results

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Target

Original12.1
Target2.0
Herbie2.0
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 12.1

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

  3. Applied associate-/l*2.0

    \[\leadsto \color{blue}{\frac{x}{\frac{t - z}{y - z}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity2.0

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

  6. Applied *-un-lft-identity2.0

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

  7. Applied times-frac2.0

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

  8. Simplified2.0

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

  9. Final simplification2.0

    \[\leadsto \frac{x}{1 \cdot \frac{t - z}{y - z}}\]

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"
  :precision binary64

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

  (/ (* x (- y z)) (- t z)))