Average Error: 11.2 → 1.4
Time: 18.4s
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 r391474 = x;
        double r391475 = y;
        double r391476 = z;
        double r391477 = r391475 - r391476;
        double r391478 = t;
        double r391479 = r391477 * r391478;
        double r391480 = a;
        double r391481 = r391480 - r391476;
        double r391482 = r391479 / r391481;
        double r391483 = r391474 + r391482;
        return r391483;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r391484 = x;
        double r391485 = y;
        double r391486 = z;
        double r391487 = r391485 - r391486;
        double r391488 = a;
        double r391489 = r391488 - r391486;
        double r391490 = r391487 / r391489;
        double r391491 = t;
        double r391492 = r391490 * r391491;
        double r391493 = r391484 + r391492;
        return r391493;
}

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

Original11.2
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 11.2

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

  2. Simplified3.0

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

  4. Applied pow13.0

    \[\leadsto \left(y - z\right) \cdot \color{blue}{{\left(\frac{t}{a - z}\right)}^{1}} + x\]

  5. Applied pow13.0

    \[\leadsto \color{blue}{{\left(y - z\right)}^{1}} \cdot {\left(\frac{t}{a - z}\right)}^{1} + x\]

  6. Applied pow-prod-down3.0

    \[\leadsto \color{blue}{{\left(\left(y - z\right) \cdot \frac{t}{a - z}\right)}^{1}} + x\]

  7. Simplified3.0

    \[\leadsto {\color{blue}{\left(\frac{y - z}{\frac{a - z}{t}}\right)}}^{1} + x\]
  8. Using strategy rm

  9. Applied associate-/r/1.4

    \[\leadsto {\color{blue}{\left(\frac{y - z}{a - z} \cdot t\right)}}^{1} + x\]

  10. Final simplification1.4

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A"

  :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))))