Average Error: 10.6 → 1.3
Time: 13.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[y \cdot \frac{z - t}{z - a} + x\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
y \cdot \frac{z - t}{z - a} + x
double f(double x, double y, double z, double t, double a) {
        double r556429 = x;
        double r556430 = y;
        double r556431 = z;
        double r556432 = t;
        double r556433 = r556431 - r556432;
        double r556434 = r556430 * r556433;
        double r556435 = a;
        double r556436 = r556431 - r556435;
        double r556437 = r556434 / r556436;
        double r556438 = r556429 + r556437;
        return r556438;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r556439 = y;
        double r556440 = z;
        double r556441 = t;
        double r556442 = r556440 - r556441;
        double r556443 = a;
        double r556444 = r556440 - r556443;
        double r556445 = r556442 / r556444;
        double r556446 = r556439 * r556445;
        double r556447 = x;
        double r556448 = r556446 + r556447;
        return r556448;
}

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
Target1.2
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. Simplified10.6

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

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

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

  5. Applied times-frac1.3

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

  6. Simplified1.3

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

  7. Final simplification1.3

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

Reproduce

herbie shell --seed 2019179 
(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))))