Average Error: 10.8 → 2.8
Time: 4.4s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \frac{1}{\frac{\frac{a - z}{t}}{y - z}}\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \frac{1}{\frac{\frac{a - z}{t}}{y - z}}
double f(double x, double y, double z, double t, double a) {
        double r719208 = x;
        double r719209 = y;
        double r719210 = z;
        double r719211 = r719209 - r719210;
        double r719212 = t;
        double r719213 = r719211 * r719212;
        double r719214 = a;
        double r719215 = r719214 - r719210;
        double r719216 = r719213 / r719215;
        double r719217 = r719208 + r719216;
        return r719217;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r719218 = x;
        double r719219 = 1.0;
        double r719220 = a;
        double r719221 = z;
        double r719222 = r719220 - r719221;
        double r719223 = t;
        double r719224 = r719222 / r719223;
        double r719225 = y;
        double r719226 = r719225 - r719221;
        double r719227 = r719224 / r719226;
        double r719228 = r719219 / r719227;
        double r719229 = r719218 + r719228;
        return r719229;
}

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
Target0.6
Herbie2.8
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.8

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

  3. Applied associate-/l*2.7

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

  5. Applied clear-num2.8

    \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - z}{t}}{y - z}}}\]

  6. Final simplification2.8

    \[\leadsto x + \frac{1}{\frac{\frac{a - z}{t}}{y - z}}\]

Reproduce

herbie shell --seed 2020047 
(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))))