Average Error: 1.2 → 1.3
Time: 15.7s
Precision: 64
\[x + y \cdot \frac{z - t}{a - t}\]
↓
\[x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\]
x + y \cdot \frac{z - t}{a - t}
↓
x + y \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)
double f(double x, double y, double z, double t, double a) {
        double r26787063 = x;
        double r26787064 = y;
        double r26787065 = z;
        double r26787066 = t;
        double r26787067 = r26787065 - r26787066;
        double r26787068 = a;
        double r26787069 = r26787068 - r26787066;
        double r26787070 = r26787067 / r26787069;
        double r26787071 = r26787064 * r26787070;
        double r26787072 = r26787063 + r26787071;
        return r26787072;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r26787073 = x;
        double r26787074 = y;
        double r26787075 = z;
        double r26787076 = t;
        double r26787077 = r26787075 - r26787076;
        double r26787078 = 1.0;
        double r26787079 = a;
        double r26787080 = r26787079 - r26787076;
        double r26787081 = r26787078 / r26787080;
        double r26787082 = r26787077 * r26787081;
        double r26787083 = r26787074 * r26787082;
        double r26787084 = r26787073 + r26787083;
        return r26787084;
}

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

Original1.2
Target0.4
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;y \lt -8.508084860551241 \cdot 10^{-17}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;y \lt 2.894426862792089 \cdot 10^{-49}:\\ \;\;\;\;x + \left(y \cdot \left(z - t\right)\right) \cdot \frac{1}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

  1. Initial program 1.2

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

  3. Applied div-inv1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisLine from plot-0.2.3.4, B"

  :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)))))