Average Error: 10.9 → 1.2
Time: 7.0s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)
double f(double x, double y, double z, double t, double a) {
        double r659422 = x;
        double r659423 = y;
        double r659424 = z;
        double r659425 = t;
        double r659426 = r659424 - r659425;
        double r659427 = r659423 * r659426;
        double r659428 = a;
        double r659429 = r659428 - r659425;
        double r659430 = r659427 / r659429;
        double r659431 = r659422 + r659430;
        return r659431;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r659432 = x;
        double r659433 = y;
        double r659434 = z;
        double r659435 = a;
        double r659436 = t;
        double r659437 = r659435 - r659436;
        double r659438 = r659434 / r659437;
        double r659439 = r659436 / r659437;
        double r659440 = r659438 - r659439;
        double r659441 = r659433 * r659440;
        double r659442 = r659432 + r659441;
        return r659442;
}

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

Original10.9
Target1.0
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied *-un-lft-identity10.9

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

  4. Applied times-frac1.2

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

  5. Simplified1.2

    \[\leadsto x + \color{blue}{y} \cdot \frac{z - t}{a - t}\]
  6. Using strategy rm

  7. Applied div-sub1.2

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

  8. Final simplification1.2

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

Reproduce

herbie shell --seed 2020047 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

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

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