Average Error: 1.4 → 1.4
Time: 7.0s
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 r537649 = x;
        double r537650 = y;
        double r537651 = z;
        double r537652 = t;
        double r537653 = r537651 - r537652;
        double r537654 = a;
        double r537655 = r537654 - r537652;
        double r537656 = r537653 / r537655;
        double r537657 = r537650 * r537656;
        double r537658 = r537649 + r537657;
        return r537658;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r537659 = x;
        double r537660 = y;
        double r537661 = z;
        double r537662 = t;
        double r537663 = r537661 - r537662;
        double r537664 = a;
        double r537665 = r537664 - r537662;
        double r537666 = r537663 / r537665;
        double r537667 = r537660 * r537666;
        double r537668 = r537659 + r537667;
        return r537668;
}

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 2020021 
(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)))))