Average Error: 10.9 → 1.2
Time: 9.8s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{z - a}\]
↓
\[x + \frac{y}{\frac{z - a}{z - t}}\]
x + \frac{y \cdot \left(z - t\right)}{z - a}
↓
x + \frac{y}{\frac{z - a}{z - t}}
double f(double x, double y, double z, double t, double a) {
        double r641967 = x;
        double r641968 = y;
        double r641969 = z;
        double r641970 = t;
        double r641971 = r641969 - r641970;
        double r641972 = r641968 * r641971;
        double r641973 = a;
        double r641974 = r641969 - r641973;
        double r641975 = r641972 / r641974;
        double r641976 = r641967 + r641975;
        return r641976;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r641977 = x;
        double r641978 = y;
        double r641979 = z;
        double r641980 = a;
        double r641981 = r641979 - r641980;
        double r641982 = t;
        double r641983 = r641979 - r641982;
        double r641984 = r641981 / r641983;
        double r641985 = r641978 / r641984;
        double r641986 = r641977 + r641985;
        return r641986;
}

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

Original10.9
Target1.2
Herbie1.2
\[x + \frac{y}{\frac{z - a}{z - t}}\]

Derivation

  1. Initial program 10.9

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

  3. Applied associate-/l*1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, A"
  :precision binary64

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

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