Average Error: 11.8 → 2.2
Time: 32.4s
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 r32958129 = x;
        double r32958130 = y;
        double r32958131 = z;
        double r32958132 = r32958130 - r32958131;
        double r32958133 = r32958129 * r32958132;
        double r32958134 = t;
        double r32958135 = r32958134 - r32958131;
        double r32958136 = r32958133 / r32958135;
        return r32958136;
}
↓
double f(double x, double y, double z, double t) {
        double r32958137 = x;
        double r32958138 = y;
        double r32958139 = z;
        double r32958140 = r32958138 - r32958139;
        double r32958141 = t;
        double r32958142 = r32958141 - r32958139;
        double r32958143 = r32958140 / r32958142;
        double r32958144 = r32958137 * r32958143;
        return r32958144;
}

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 
(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)))