Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Average Error: 24.1 → 9.3

Time: 6.2s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} = -inf.0:\\ \;\;\;\;y + \left(z \cdot \frac{x}{t} - y \cdot \frac{z}{t}\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -6.5944503222671014 \cdot 10^{-294}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \end{array}\]

C

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

↓

double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((((double) (x + ((double) (((double) (((double) (y - x)) * ((double) (z - t)))) / ((double) (a - t)))))) <= -inf.0)) {
		VAR = ((double) (y + ((double) (((double) (z * ((double) (x / t)))) - ((double) (y * ((double) (z / t))))))));
	} else {
		double VAR_1;
		if ((((double) (x + ((double) (((double) (((double) (y - x)) * ((double) (z - t)))) / ((double) (a - t)))))) <= -6.594450322267101e-294)) {
			VAR_1 = ((double) (x + ((double) (((double) (((double) (y - x)) * ((double) (z - t)))) / ((double) (a - t))))));
		} else {
			double VAR_2;
			if ((((double) (x + ((double) (((double) (((double) (y - x)) * ((double) (z - t)))) / ((double) (a - t)))))) <= 0.0)) {
				VAR_2 = ((double) (y + ((double) (((double) (z / t)) * ((double) (x - y))))));
			} else {
				VAR_2 = ((double) (x + ((double) (((double) (y - x)) * ((double) (((double) (z - t)) * ((double) (1.0 / ((double) (a - t))))))))));
			}
			VAR_1 = VAR_2;
		}
		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	24.1
Target	9.4
Herbie	9.3

\[\begin{array}{l} \mathbf{if}\;a \lt -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \lt 3.7744031700831742 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \end{array}\]

Derivation

1. Split input into 4 regimes

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

   1. Initial program 64.0

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

   2. Simplified 18.0

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

   3. Taylor expanded around inf 40.3

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

   4. Simplified 26.7

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

   if -inf.0 < (+ x (/ (* (- y x) (- z t)) (- a t))) < -6.5944503222671014e-294

   1. Initial program 2.0

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

   if -6.5944503222671014e-294 < (+ x (/ (* (- y x) (- z t)) (- a t))) < 0.0

   1. Initial program 59.8

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

   2. Simplified 59.8

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

   4. Applied add-cube-cbrt 59.5

      \[\leadsto x + \color{blue}{\left(\sqrt[3]{\left(y - x\right) \cdot \frac{z - t}{a - t}} \cdot \sqrt[3]{\left(y - x\right) \cdot \frac{z - t}{a - t}}\right) \cdot \sqrt[3]{\left(y - x\right) \cdot \frac{z - t}{a - t}}}\]

   5. Taylor expanded around inf 19.9

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

   6. Simplified 20.1

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

   if 0.0 < (+ x (/ (* (- y x) (- z t)) (- a t)))

   1. Initial program 21.3

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

   2. Simplified 7.3

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

   4. Applied div-inv 7.4

      \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(\left(z - t\right) \cdot \frac{1}{a - t}\right)}\]
3. Recombined 4 regimes into one program.

4. Final simplification 9.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} = -inf.0:\\ \;\;\;\;y + \left(z \cdot \frac{x}{t} - y \cdot \frac{z}{t}\right)\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le -6.5944503222671014 \cdot 10^{-294}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \le 0.0:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(\left(z - t\right) \cdot \frac{1}{a - t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

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