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 r667024 = x;
        double r667025 = y;
        double r667026 = z;
        double r667027 = r667025 - r667026;
        double r667028 = t;
        double r667029 = r667027 * r667028;
        double r667030 = a;
        double r667031 = r667030 - r667026;
        double r667032 = r667029 / r667031;
        double r667033 = r667024 + r667032;
        return r667033;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r667034 = y;
        double r667035 = z;
        double r667036 = r667034 - r667035;
        double r667037 = t;
        double r667038 = r667036 * r667037;
        double r667039 = a;
        double r667040 = r667039 - r667035;
        double r667041 = r667038 / r667040;
        double r667042 = -inf.0;
        bool r667043 = r667041 <= r667042;
        double r667044 = 6.3021334972798484e+302;
        bool r667045 = r667041 <= r667044;
        double r667046 = !r667045;
        bool r667047 = r667043 || r667046;
        double r667048 = x;
        double r667049 = r667037 / r667040;
        double r667050 = r667036 * r667049;
        double r667051 = r667048 + r667050;
        double r667052 = r667048 + r667041;
        double r667053 = r667047 ? r667051 : r667052;
        return r667053;
}

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))))