Average Error: 1.3 → 1.3
Time: 7.7s
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 r592508 = x;
        double r592509 = y;
        double r592510 = z;
        double r592511 = t;
        double r592512 = r592510 - r592511;
        double r592513 = a;
        double r592514 = r592513 - r592511;
        double r592515 = r592512 / r592514;
        double r592516 = r592509 * r592515;
        double r592517 = r592508 + r592516;
        return r592517;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r592518 = x;
        double r592519 = y;
        double r592520 = z;
        double r592521 = t;
        double r592522 = r592520 - r592521;
        double r592523 = a;
        double r592524 = r592523 - r592521;
        double r592525 = r592522 / r592524;
        double r592526 = r592519 * r592525;
        double r592527 = r592518 + r592526;
        return r592527;
}

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

Derivation

  1. Initial program 1.3

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

  2. Final simplification1.3

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

Reproduce

herbie shell --seed 2020018 +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)))))