Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTick from plot-0.2.3.4, A

Average Error: 11.0 → 0.2

Time: 5.0s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 6.3021334972798484 \cdot 10^{302}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r755599 = x;
        double r755600 = y;
        double r755601 = z;
        double r755602 = r755600 - r755601;
        double r755603 = t;
        double r755604 = r755602 * r755603;
        double r755605 = a;
        double r755606 = r755605 - r755601;
        double r755607 = r755604 / r755606;
        double r755608 = r755599 + r755607;
        return r755608;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r755609 = y;
        double r755610 = z;
        double r755611 = r755609 - r755610;
        double r755612 = t;
        double r755613 = r755611 * r755612;
        double r755614 = a;
        double r755615 = r755614 - r755610;
        double r755616 = r755613 / r755615;
        double r755617 = -inf.0;
        bool r755618 = r755616 <= r755617;
        double r755619 = 6.3021334972798484e+302;
        bool r755620 = r755616 <= r755619;
        double r755621 = !r755620;
        bool r755622 = r755618 || r755621;
        double r755623 = x;
        double r755624 = r755612 / r755615;
        double r755625 = r755611 * r755624;
        double r755626 = r755623 + r755625;
        double r755627 = r755623 + r755616;
        double r755628 = r755622 ? r755626 : r755627;
        return r755628;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	11.0
Target	0.6
Herbie	0.2

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

Derivation

1. Split input into 2 regimes

2. if (/ (* (- y z) t) (- a z)) < -inf.0 or 6.3021334972798484e+302 < (/ (* (- y z) t) (- a z))

   1. Initial program 63.6

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

   3. Applied *-un-lft-identity 63.6

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

   4. Applied times-frac 0.2

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

   5. Simplified 0.2

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

   if -inf.0 < (/ (* (- y z) t) (- a z)) < 6.3021334972798484e+302

   1. Initial program 0.2

      \[x + \frac{\left(y - z\right) \cdot t}{a - z}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 6.3021334972798484 \cdot 10^{302}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020060 
(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))))