Average Error: 10.9 → 1.2
Time: 8.5s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[y \cdot \frac{z - t}{a - t} + x\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
y \cdot \frac{z - t}{a - t} + x
double f(double x, double y, double z, double t, double a) {
        double r617394 = x;
        double r617395 = y;
        double r617396 = z;
        double r617397 = t;
        double r617398 = r617396 - r617397;
        double r617399 = r617395 * r617398;
        double r617400 = a;
        double r617401 = r617400 - r617397;
        double r617402 = r617399 / r617401;
        double r617403 = r617394 + r617402;
        return r617403;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r617404 = y;
        double r617405 = z;
        double r617406 = t;
        double r617407 = r617405 - r617406;
        double r617408 = a;
        double r617409 = r617408 - r617406;
        double r617410 = r617407 / r617409;
        double r617411 = r617404 * r617410;
        double r617412 = x;
        double r617413 = r617411 + r617412;
        return r617413;
}

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. Simplified3.0

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

  4. Applied fma-udef3.0

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

  6. Applied div-inv3.0

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

  7. Applied associate-*l*1.2

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

  8. Simplified1.2

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

  9. Final simplification1.2

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(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))))