Average Error: 12.1 → 2.0
Time: 2.7s
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 r675806 = x;
        double r675807 = y;
        double r675808 = z;
        double r675809 = r675807 - r675808;
        double r675810 = r675806 * r675809;
        double r675811 = t;
        double r675812 = r675811 - r675808;
        double r675813 = r675810 / r675812;
        return r675813;
}
↓
double f(double x, double y, double z, double t) {
        double r675814 = x;
        double r675815 = 1.0;
        double r675816 = t;
        double r675817 = z;
        double r675818 = r675816 - r675817;
        double r675819 = y;
        double r675820 = r675819 - r675817;
        double r675821 = r675818 / r675820;
        double r675822 = r675815 * r675821;
        double r675823 = r675814 / r675822;
        return r675823;
}

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 
(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)))