Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B

Average Error: 10.7 → 0.2

Time: 6.4s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty:\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \le 6.8624750184523979 \cdot 10^{306}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \end{array}\]

C

double code(double x, double y, double z, double t, double a) {
	return (x + ((y * (z - t)) / (a - t)));
}

↓

double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((((y * (z - t)) / (a - t)) <= -inf.0)) {
		VAR = (((z - t) / ((a - t) / y)) + x);
	} else {
		double VAR_1;
		if ((((y * (z - t)) / (a - t)) <= 6.862475018452398e+306)) {
			VAR_1 = (x + ((y * (z - t)) / (a - t)));
		} else {
			VAR_1 = fma((y / (a - t)), (z - t), x);
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	10.7
Target	1.3
Herbie	0.2

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

Derivation

1. Split input into 3 regimes

2. if (/ (* y (- z t)) (- a t)) < -inf.0

   1. Initial program 64.0

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

   2. Simplified 0.2

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

   4. Applied clear-num 0.3

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right)\]
   5. Using strategy rm

   6. Applied fma-udef 0.3

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

   7. Simplified 0.2

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

   if -inf.0 < (/ (* y (- z t)) (- a t)) < 6.862475018452398e+306

   1. Initial program 0.2

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

   if 6.862475018452398e+306 < (/ (* y (- z t)) (- a t))

   1. Initial program 63.8

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

   2. Simplified 0.2

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)}\]
3. Recombined 3 regimes into one program.

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a - t} = -\infty:\\ \;\;\;\;\frac{z - t}{\frac{a - t}{y}} + x\\ \mathbf{elif}\;\frac{y \cdot \left(z - t\right)}{a - t} \le 6.8624750184523979 \cdot 10^{306}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020091 +o rules:numerics
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

  (+ x (/ (* y (- z t)) (- a t))))