Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Average Error: 10.2 → 3.1

Time: 9.1s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r468214 = x;
        double r468215 = y;
        double r468216 = z;
        double r468217 = r468215 - r468216;
        double r468218 = t;
        double r468219 = r468217 * r468218;
        double r468220 = a;
        double r468221 = r468220 - r468216;
        double r468222 = r468219 / r468221;
        double r468223 = r468214 + r468222;
        return r468223;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r468224 = x;
        double r468225 = y;
        double r468226 = z;
        double r468227 = r468225 - r468226;
        double r468228 = a;
        double r468229 = r468228 - r468226;
        double r468230 = t;
        double r468231 = r468229 / r468230;
        double r468232 = r468227 / r468231;
        double r468233 = r468224 + r468232;
        return r468233;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.2
Target	0.5
Herbie	3.1

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

Derivation

1. Split input into 2 regimes

2. if z < -6.812794228353364e+53 or 9.139927293791955e-103 < z

   1. Initial program 15.3

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

   3. Applied associate-/l* 3.7

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

   5. Applied associate-/r/ 0.3

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

   if -6.812794228353364e+53 < z < 9.139927293791955e-103

   1. Initial program 3.4

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

   3. Applied associate-/l* 2.5

      \[\leadsto x + \color{blue}{\frac{y - z}{\frac{a - z}{t}}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 3.1

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

Reproduce

herbie shell --seed 2019294 
(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))))