Average Error: 10.6 → 1.3
Time: 18.0s
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 r20584312 = x;
        double r20584313 = y;
        double r20584314 = z;
        double r20584315 = t;
        double r20584316 = r20584314 - r20584315;
        double r20584317 = r20584313 * r20584316;
        double r20584318 = a;
        double r20584319 = r20584314 - r20584318;
        double r20584320 = r20584317 / r20584319;
        double r20584321 = r20584312 + r20584320;
        return r20584321;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r20584322 = x;
        double r20584323 = y;
        double r20584324 = z;
        double r20584325 = t;
        double r20584326 = r20584324 - r20584325;
        double r20584327 = a;
        double r20584328 = r20584324 - r20584327;
        double r20584329 = r20584326 / r20584328;
        double r20584330 = r20584323 * r20584329;
        double r20584331 = r20584322 + r20584330;
        return r20584331;
}

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))))