Average Error: 10.8 → 1.2
Time: 2.9s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a - t}\]
↓
\[x + \frac{y}{\frac{a - t}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{a - t}
↓
x + \frac{y}{\frac{a - t}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r631016 = x;
        double r631017 = y;
        double r631018 = z;
        double r631019 = t;
        double r631020 = r631018 - r631019;
        double r631021 = r631017 * r631020;
        double r631022 = a;
        double r631023 = r631022 - r631019;
        double r631024 = r631021 / r631023;
        double r631025 = r631016 + r631024;
        return r631025;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r631026 = x;
        double r631027 = y;
        double r631028 = a;
        double r631029 = t;
        double r631030 = r631028 - r631029;
        double r631031 = z;
        double r631032 = r631031 - r631029;
        double r631033 = r631030 / r631032;
        double r631034 = r631027 / r631033;
        double r631035 = r631026 + r631034;
        return r631035;
}

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

Original10.8
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{a - t}{z - t}}\]

Derivation

  1. Initial program 10.8

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

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