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

Average Error: 10.8 → 0.3

Time: 10.9s

Precision: 64

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

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 4.80072190399451909 \cdot 10^{294}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r507045 = x;
        double r507046 = y;
        double r507047 = z;
        double r507048 = r507046 - r507047;
        double r507049 = t;
        double r507050 = r507048 * r507049;
        double r507051 = a;
        double r507052 = r507051 - r507047;
        double r507053 = r507050 / r507052;
        double r507054 = r507045 + r507053;
        return r507054;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r507055 = y;
        double r507056 = z;
        double r507057 = r507055 - r507056;
        double r507058 = t;
        double r507059 = r507057 * r507058;
        double r507060 = a;
        double r507061 = r507060 - r507056;
        double r507062 = r507059 / r507061;
        double r507063 = -inf.0;
        bool r507064 = r507062 <= r507063;
        double r507065 = 4.800721903994519e+294;
        bool r507066 = r507062 <= r507065;
        double r507067 = !r507066;
        bool r507068 = r507064 || r507067;
        double r507069 = r507057 / r507061;
        double r507070 = x;
        double r507071 = fma(r507069, r507058, r507070);
        double r507072 = r507070 + r507062;
        double r507073 = r507068 ? r507071 : r507072;
        return r507073;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.8
Target	0.6
Herbie	0.3

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

Derivation

1. Split input into 2 regimes

2. if (/ (* (- y z) t) (- a z)) < -inf.0 or 4.800721903994519e+294 < (/ (* (- y z) t) (- a z))

   1. Initial program 62.7

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

   2. Simplified 0.2

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - z}{a - z}, t, x\right)}\]

   if -inf.0 < (/ (* (- y z) t) (- a z)) < 4.800721903994519e+294

   1. Initial program 0.3

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

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(y - z\right) \cdot t}{a - z} = -\infty \lor \neg \left(\frac{\left(y - z\right) \cdot t}{a - z} \le 4.80072190399451909 \cdot 10^{294}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y - z}{a - z}, t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - z\right) \cdot t}{a - z}\\ \end{array}\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(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))))