Average Error: 10.8 → 2.8
Time: 10.1s
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 r724399 = x;
        double r724400 = y;
        double r724401 = z;
        double r724402 = r724400 - r724401;
        double r724403 = t;
        double r724404 = r724402 * r724403;
        double r724405 = a;
        double r724406 = r724405 - r724401;
        double r724407 = r724404 / r724406;
        double r724408 = r724399 + r724407;
        return r724408;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r724409 = x;
        double r724410 = 1.0;
        double r724411 = a;
        double r724412 = z;
        double r724413 = r724411 - r724412;
        double r724414 = t;
        double r724415 = r724413 / r724414;
        double r724416 = y;
        double r724417 = r724416 - r724412;
        double r724418 = r724415 / r724417;
        double r724419 = r724410 / r724418;
        double r724420 = r724409 + r724419;
        return r724420;
}

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))))