Average Error: 11.6 → 2.2
Time: 39.3s
Precision: 64
\[\frac{x \cdot \left(y - z\right)}{t - z}\]
↓
\[\frac{y - z}{t - z} \cdot x\]
\frac{x \cdot \left(y - z\right)}{t - z}
↓
\frac{y - z}{t - z} \cdot x
double f(double x, double y, double z, double t) {
        double r25720211 = x;
        double r25720212 = y;
        double r25720213 = z;
        double r25720214 = r25720212 - r25720213;
        double r25720215 = r25720211 * r25720214;
        double r25720216 = t;
        double r25720217 = r25720216 - r25720213;
        double r25720218 = r25720215 / r25720217;
        return r25720218;
}
↓
double f(double x, double y, double z, double t) {
        double r25720219 = y;
        double r25720220 = z;
        double r25720221 = r25720219 - r25720220;
        double r25720222 = t;
        double r25720223 = r25720222 - r25720220;
        double r25720224 = r25720221 / r25720223;
        double r25720225 = x;
        double r25720226 = r25720224 * r25720225;
        return r25720226;
}

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

Original11.6
Target2.2
Herbie2.2
\[\frac{x}{\frac{t - z}{y - z}}\]

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-frac2.2

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

  5. Simplified2.2

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

  6. Final simplification2.2

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

Reproduce

herbie shell --seed 2019200 +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)))