Average Error: 11.6 → 2.1
Time: 2.7s
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 r567099 = x;
        double r567100 = y;
        double r567101 = z;
        double r567102 = r567100 - r567101;
        double r567103 = r567099 * r567102;
        double r567104 = t;
        double r567105 = r567104 - r567101;
        double r567106 = r567103 / r567105;
        return r567106;
}
↓
double f(double x, double y, double z, double t) {
        double r567107 = x;
        double r567108 = y;
        double r567109 = z;
        double r567110 = r567108 - r567109;
        double r567111 = t;
        double r567112 = r567111 - r567109;
        double r567113 = r567110 / r567112;
        double r567114 = r567107 * r567113;
        return r567114;
}

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

Original11.6
Target2.1
Herbie2.1
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.6

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

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

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

  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 2020100 
(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)))