Average Error: 12.1 → 2.0
Time: 6.0s
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 r3275 = x;
        double r3276 = y;
        double r3277 = z;
        double r3278 = r3276 - r3277;
        double r3279 = r3275 * r3278;
        double r3280 = t;
        double r3281 = r3280 - r3277;
        double r3282 = r3279 / r3281;
        return r3282;
}
↓
double f(double x, double y, double z, double t) {
        double r3283 = x;
        double r3284 = 1.0;
        double r3285 = t;
        double r3286 = z;
        double r3287 = r3285 - r3286;
        double r3288 = y;
        double r3289 = r3288 - r3286;
        double r3290 = r3287 / r3289;
        double r3291 = r3284 * r3290;
        double r3292 = r3283 / r3291;
        return r3292;
}

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)))