Average Error: 10.6 → 1.3
Time: 18.7s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + y \cdot \frac{z - t}{z - a}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + y \cdot \frac{z - t}{z - a}
double f(double x, double y, double z, double t, double a) {
        double r22572856 = x;
        double r22572857 = y;
        double r22572858 = z;
        double r22572859 = t;
        double r22572860 = r22572858 - r22572859;
        double r22572861 = r22572857 * r22572860;
        double r22572862 = a;
        double r22572863 = r22572858 - r22572862;
        double r22572864 = r22572861 / r22572863;
        double r22572865 = r22572856 + r22572864;
        return r22572865;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r22572866 = x;
        double r22572867 = y;
        double r22572868 = z;
        double r22572869 = t;
        double r22572870 = r22572868 - r22572869;
        double r22572871 = a;
        double r22572872 = r22572868 - r22572871;
        double r22572873 = r22572870 / r22572872;
        double r22572874 = r22572867 * r22572873;
        double r22572875 = r22572866 + r22572874;
        return r22572875;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.6
Target1.3
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.6

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

  3. Applied *-un-lft-identity10.6

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

  4. Applied times-frac1.3

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

  5. Simplified1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"

  :herbie-target
  (+ x (/ y (/ (- z a) (- z t))))

  (+ x (/ (* y (- z t)) (- z a))))