Average Error: 11.1 → 2.2
Time: 19.3s
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 r26577428 = x;
        double r26577429 = y;
        double r26577430 = z;
        double r26577431 = r26577429 - r26577430;
        double r26577432 = r26577428 * r26577431;
        double r26577433 = t;
        double r26577434 = r26577433 - r26577430;
        double r26577435 = r26577432 / r26577434;
        return r26577435;
}
↓
double f(double x, double y, double z, double t) {
        double r26577436 = x;
        double r26577437 = y;
        double r26577438 = z;
        double r26577439 = r26577437 - r26577438;
        double r26577440 = t;
        double r26577441 = r26577440 - r26577438;
        double r26577442 = r26577439 / r26577441;
        double r26577443 = r26577436 * r26577442;
        return r26577443;
}

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

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

Derivation

  1. Initial program 11.1

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

  3. Applied *-un-lft-identity11.1

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

  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 2019162 +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)))