Average Error: 11.1 → 2.1
Time: 16.9s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[x \cdot \frac{y - z}{t - z}\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
x \cdot \frac{y - z}{t - z}
double f(double x, double y, double z, double t) {
        double r25215953 = x;
        double r25215954 = y;
        double r25215955 = z;
        double r25215956 = r25215954 - r25215955;
        double r25215957 = r25215953 * r25215956;
        double r25215958 = t;
        double r25215959 = r25215958 - r25215955;
        double r25215960 = r25215957 / r25215959;
        return r25215960;
}
↓
double f(double x, double y, double z, double t) {
        double r25215961 = x;
        double r25215962 = y;
        double r25215963 = z;
        double r25215964 = r25215962 - r25215963;
        double r25215965 = t;
        double r25215966 = r25215965 - r25215963;
        double r25215967 = r25215964 / r25215966;
        double r25215968 = r25215961 * r25215967;
        return r25215968;
}

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

Original11.1
Target2.1
Herbie2.1
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.1

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

  3. Applied *-un-lft-identity11.1

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

  4. Applied times-frac2.1

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

  5. Simplified2.1

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

  6. Final simplification2.1

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Plot.AreaSpots:renderAreaSpots4D from Chart-1.5.3"

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

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