Average Error: 10.7 → 1.3
Time: 4.2s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \frac{y - z}{a - z} \cdot t\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \frac{y - z}{a - z} \cdot t
double f(double x, double y, double z, double t, double a) {
        double r661252 = x;
        double r661253 = y;
        double r661254 = z;
        double r661255 = r661253 - r661254;
        double r661256 = t;
        double r661257 = r661255 * r661256;
        double r661258 = a;
        double r661259 = r661258 - r661254;
        double r661260 = r661257 / r661259;
        double r661261 = r661252 + r661260;
        return r661261;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r661262 = x;
        double r661263 = y;
        double r661264 = z;
        double r661265 = r661263 - r661264;
        double r661266 = a;
        double r661267 = r661266 - r661264;
        double r661268 = r661265 / r661267;
        double r661269 = t;
        double r661270 = r661268 * r661269;
        double r661271 = r661262 + r661270;
        return r661271;
}

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

Original10.7
Target0.6
Herbie1.3
\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.7

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

  3. Applied associate-/l*3.0

    \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t}}}\]
  4. Using strategy rm

  5. Applied associate-/r/1.3

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

  6. Final simplification1.3

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (if (< t -1.0682974490174067e-39) (+ x (* (/ (- y z) (- a z)) t)) (if (< t 3.9110949887586375e-141) (+ x (/ (* (- y z) t) (- a z))) (+ x (* (/ (- y z) (- a z)) t))))

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