Average Error: 1.3 → 1.4
Time: 17.4s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[x + \left(\frac{\frac{z}{a - t}}{\frac{1}{y}} + y \cdot \left(-\frac{t}{a - t}\right)\right)\]
x + y \cdot \frac{z - t}{a - t}
↓
x + \left(\frac{\frac{z}{a - t}}{\frac{1}{y}} + y \cdot \left(-\frac{t}{a - t}\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r643382 = x;
        double r643383 = y;
        double r643384 = z;
        double r643385 = t;
        double r643386 = r643384 - r643385;
        double r643387 = a;
        double r643388 = r643387 - r643385;
        double r643389 = r643386 / r643388;
        double r643390 = r643383 * r643389;
        double r643391 = r643382 + r643390;
        return r643391;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r643392 = x;
        double r643393 = z;
        double r643394 = a;
        double r643395 = t;
        double r643396 = r643394 - r643395;
        double r643397 = r643393 / r643396;
        double r643398 = 1.0;
        double r643399 = y;
        double r643400 = r643398 / r643399;
        double r643401 = r643397 / r643400;
        double r643402 = r643395 / r643396;
        double r643403 = -r643402;
        double r643404 = r643399 * r643403;
        double r643405 = r643401 + r643404;
        double r643406 = r643392 + r643405;
        return r643406;
}

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

Original1.3
Target0.4
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;y \lt -8.50808486055124107 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.3

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

  3. Applied div-sub1.3

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

  5. Applied sub-neg1.3

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

  6. Applied distribute-lft-in1.3

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

  7. Simplified1.7

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

  9. Applied div-inv1.8

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

  10. Applied associate-/r*1.4

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

  11. Final simplification1.4

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (if (< y -8.508084860551241e-17) (+ x (* y (/ (- z t) (- a t)))) (if (< y 2.894426862792089e-49) (+ x (* (* y (- z t)) (/ 1 (- a t)))) (+ x (* y (/ (- z t) (- a t))))))

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