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

Average Error: 2.1 → 1.4

Time: 2.4s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} = -inf.0:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if ((((double) (x + ((double) (((double) (y - x)) * ((double) (z / t)))))) <= -inf.0)) {
		VAR = ((double) (x + ((double) (1.0 / ((double) (t / ((double) (((double) (y - x)) * z))))))));
	} else {
		VAR = ((double) (x + ((double) (((double) (y - x)) / ((double) (t / z))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.1
Target	2.2
Herbie	1.4

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 64.0

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

   3. Applied associate-*r/ 0.2

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

   5. Applied clear-num 0.4

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

   if -inf.0 < (+ x (* (- y x) (/ z t)))

   1. Initial program 1.4

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

   3. Applied associate-*r/ 6.3

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

   5. Applied associate-/l* 1.4

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

4. Final simplification 1.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \left(y - x\right) \cdot \frac{z}{t} = -inf.0:\\ \;\;\;\;x + \frac{1}{\frac{t}{\left(y - x\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020128 
(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)) -1013646692435.8867) (+ 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))))