Average Error: 10.9 → 2.2
Time: 8.2s
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 r10542633 = x;
        double r10542634 = y;
        double r10542635 = z;
        double r10542636 = r10542634 - r10542635;
        double r10542637 = r10542633 * r10542636;
        double r10542638 = t;
        double r10542639 = r10542638 - r10542635;
        double r10542640 = r10542637 / r10542639;
        return r10542640;
}
↓
double f(double x, double y, double z, double t) {
        double r10542641 = x;
        double r10542642 = y;
        double r10542643 = z;
        double r10542644 = r10542642 - r10542643;
        double r10542645 = t;
        double r10542646 = r10542645 - r10542643;
        double r10542647 = r10542644 / r10542646;
        double r10542648 = r10542641 * r10542647;
        return r10542648;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.9
Target2.2
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied *-un-lft-identity10.9

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

  4. Applied times-frac2.2

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

  5. Simplified2.2

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

  6. Final simplification2.2

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

Reproduce

herbie shell --seed 2019156 +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)))