Average Error: 10.5 → 1.4
Time: 4.2s
Precision: 64
\[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
↓
\[x + \left(\frac{y}{a - z} - \frac{z}{a - z}\right) \cdot t\]
x + \frac{\left(y - z\right) \cdot t}{a - z}
↓
x + \left(\frac{y}{a - z} - \frac{z}{a - z}\right) \cdot t
double f(double x, double y, double z, double t, double a) {
        double r467415 = x;
        double r467416 = y;
        double r467417 = z;
        double r467418 = r467416 - r467417;
        double r467419 = t;
        double r467420 = r467418 * r467419;
        double r467421 = a;
        double r467422 = r467421 - r467417;
        double r467423 = r467420 / r467422;
        double r467424 = r467415 + r467423;
        return r467424;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r467425 = x;
        double r467426 = y;
        double r467427 = a;
        double r467428 = z;
        double r467429 = r467427 - r467428;
        double r467430 = r467426 / r467429;
        double r467431 = r467428 / r467429;
        double r467432 = r467430 - r467431;
        double r467433 = t;
        double r467434 = r467432 * r467433;
        double r467435 = r467425 + r467434;
        return r467435;
}

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

Original10.5
Target0.7
Herbie1.4
\[\begin{array}{l} \mathbf{if}\;t \lt -1.0682974490174067 \cdot 10^{-39}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \mathbf{elif}\;t \lt 3.9110949887586375 \cdot 10^{-141}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - z}{a - z} \cdot t\\ \end{array}\]

Derivation

  1. Initial program 10.5

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

  7. Applied div-sub1.4

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

  8. Final simplification1.4

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

Reproduce

herbie shell --seed 2020035 
(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))))