Average Error: 10.5 → 1.3
Time: 17.3s
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 r497541 = x;
        double r497542 = y;
        double r497543 = z;
        double r497544 = t;
        double r497545 = r497543 - r497544;
        double r497546 = r497542 * r497545;
        double r497547 = a;
        double r497548 = r497543 - r497547;
        double r497549 = r497546 / r497548;
        double r497550 = r497541 + r497549;
        return r497550;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r497551 = y;
        double r497552 = z;
        double r497553 = t;
        double r497554 = r497552 - r497553;
        double r497555 = a;
        double r497556 = r497552 - r497555;
        double r497557 = r497554 / r497556;
        double r497558 = r497551 * r497557;
        double r497559 = x;
        double r497560 = r497558 + r497559;
        return r497560;
}

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

Original10.5
Target1.2
Herbie1.3
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.5

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

  2. Simplified10.5

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

  4. Applied *-un-lft-identity10.5

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

  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 2019194 
(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))))