Average Error: 10.3 → 1.4
Time: 11.2s
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 r634226 = x;
        double r634227 = y;
        double r634228 = z;
        double r634229 = r634227 - r634228;
        double r634230 = t;
        double r634231 = r634229 * r634230;
        double r634232 = a;
        double r634233 = r634232 - r634228;
        double r634234 = r634231 / r634233;
        double r634235 = r634226 + r634234;
        return r634235;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r634236 = x;
        double r634237 = y;
        double r634238 = z;
        double r634239 = r634237 - r634238;
        double r634240 = a;
        double r634241 = r634240 - r634238;
        double r634242 = r634239 / r634241;
        double r634243 = t;
        double r634244 = r634242 * r634243;
        double r634245 = r634236 + r634244;
        return r634245;
}

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

Original10.3
Target0.5
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;t \lt -1.068297449017406694366747246993994850729 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.911094988758637497591020599238553861375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.3

    \[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
  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/1.4

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

  6. Final simplification1.4

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

Reproduce

herbie shell --seed 2019350 
(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))))