Average Error: 11.8 → 2.2
Time: 35.6s
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 r27788213 = x;
        double r27788214 = y;
        double r27788215 = z;
        double r27788216 = r27788214 - r27788215;
        double r27788217 = r27788213 * r27788216;
        double r27788218 = t;
        double r27788219 = r27788218 - r27788215;
        double r27788220 = r27788217 / r27788219;
        return r27788220;
}
↓
double f(double x, double y, double z, double t) {
        double r27788221 = x;
        double r27788222 = y;
        double r27788223 = z;
        double r27788224 = r27788222 - r27788223;
        double r27788225 = t;
        double r27788226 = r27788225 - r27788223;
        double r27788227 = r27788224 / r27788226;
        double r27788228 = r27788221 * r27788227;
        return r27788228;
}

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

Original11.8
Target2.1
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

Derivation

  1. Initial program 11.8

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

  3. Applied *-un-lft-identity11.8

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

  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 2019168 +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)))