Average Error: 11.6 → 2.1
Time: 6.2s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[x \cdot \left(\frac{y}{t - z} - \frac{z}{t - z}\right)\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
x \cdot \left(\frac{y}{t - z} - \frac{z}{t - z}\right)
double f(double x, double y, double z, double t) {
        double r671320 = x;
        double r671321 = y;
        double r671322 = z;
        double r671323 = r671321 - r671322;
        double r671324 = r671320 * r671323;
        double r671325 = t;
        double r671326 = r671325 - r671322;
        double r671327 = r671324 / r671326;
        return r671327;
}
↓
double f(double x, double y, double z, double t) {
        double r671328 = x;
        double r671329 = y;
        double r671330 = t;
        double r671331 = z;
        double r671332 = r671330 - r671331;
        double r671333 = r671329 / r671332;
        double r671334 = r671331 / r671332;
        double r671335 = r671333 - r671334;
        double r671336 = r671328 * r671335;
        return r671336;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  7. Applied div-sub2.1

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

  8. Final simplification2.1

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

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(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)))