Average Error: 1.4 → 1.4
Time: 4.8s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[x + y \cdot \frac{z - t}{a - t}\]
x + y \cdot \frac{z - t}{a - t}
↓
x + y \cdot \frac{z - t}{a - t}
double f(double x, double y, double z, double t, double a) {
        double r583548 = x;
        double r583549 = y;
        double r583550 = z;
        double r583551 = t;
        double r583552 = r583550 - r583551;
        double r583553 = a;
        double r583554 = r583553 - r583551;
        double r583555 = r583552 / r583554;
        double r583556 = r583549 * r583555;
        double r583557 = r583548 + r583556;
        return r583557;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r583558 = x;
        double r583559 = y;
        double r583560 = z;
        double r583561 = t;
        double r583562 = r583560 - r583561;
        double r583563 = a;
        double r583564 = r583563 - r583561;
        double r583565 = r583562 / r583564;
        double r583566 = r583559 * r583565;
        double r583567 = r583558 + r583566;
        return r583567;
}

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

Original1.4
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 1.4

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

  2. Final simplification1.4

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

Reproduce

herbie shell --seed 2020083 +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)))))