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

Average Error: 10.2 → 0.4

Time: 7.8s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 6.28653381395309557 \cdot 10^{268}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r513781 = x;
        double r513782 = y;
        double r513783 = z;
        double r513784 = r513782 - r513783;
        double r513785 = t;
        double r513786 = r513784 * r513785;
        double r513787 = a;
        double r513788 = r513787 - r513783;
        double r513789 = r513786 / r513788;
        double r513790 = r513781 + r513789;
        return r513790;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r513791 = y;
        double r513792 = z;
        double r513793 = r513791 - r513792;
        double r513794 = t;
        double r513795 = r513793 * r513794;
        double r513796 = a;
        double r513797 = r513796 - r513792;
        double r513798 = r513795 / r513797;
        double r513799 = -inf.0;
        bool r513800 = r513798 <= r513799;
        double r513801 = 6.2865338139530956e+268;
        bool r513802 = r513798 <= r513801;
        double r513803 = !r513802;
        bool r513804 = r513800 || r513803;
        double r513805 = x;
        double r513806 = r513794 / r513797;
        double r513807 = r513793 * r513806;
        double r513808 = r513805 + r513807;
        double r513809 = r513805 + r513798;
        double r513810 = r513804 ? r513808 : r513809;
        return r513810;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.2
Target	0.6
Herbie	0.4

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

Derivation

1. Split input into 2 regimes

2. if (/ (* (- y z) t) (- a z)) < -inf.0 or 6.2865338139530956e+268 < (/ (* (- y z) t) (- a z))

   1. Initial program 60.8

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

   3. Applied *-un-lft-identity 60.8

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

   4. Applied times-frac 1.2

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

   5. Simplified 1.2

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

   if -inf.0 < (/ (* (- y z) t) (- a z)) < 6.2865338139530956e+268

   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 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 6.28653381395309557 \cdot 10^{268}\right):\\ \;\;\;\;x + \left(y - z\right) \cdot \frac{t}{a - z}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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))))