Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4

Average Error: 1.9 → 1.3

Time: 3.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{z}{t} \le 5.18686974469537707 \cdot 10^{246}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if (((z / t) <= 5.186869744695377e+246)) {
		VAR = (x + ((y - x) * (z / t)));
	} else {
		VAR = (x + (((y - x) * z) / t));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	1.9
Target	2.1
Herbie	1.3

\[\begin{array}{l} \mathbf{if}\;\left(y - x\right) \cdot \frac{z}{t} \lt -1013646692435.887:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{elif}\;\left(y - x\right) \cdot \frac{z}{t} \lt -0.0:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (/ z t) < 5.186869744695377e+246

   1. Initial program 1.3

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

   if 5.186869744695377e+246 < (/ z t)

   1. Initial program 31.7

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

   3. Applied associate-*r/ 1.1

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

4. Final simplification 1.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{z}{t} \le 5.18686974469537707 \cdot 10^{246}:\\ \;\;\;\;x + \left(y - x\right) \cdot \frac{z}{t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020106 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:tickPosition from plot-0.2.3.4"
  :precision binary64

  :herbie-target
  (if (< (* (- y x) (/ z t)) -1013646692435.887) (+ x (/ (- y x) (/ t z))) (if (< (* (- y x) (/ z t)) -0.0) (+ x (/ (* (- y x) z) t)) (+ x (/ (- y x) (/ t z)))))

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