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

Average Error: 24.3 → 9.6

Time: 12.0s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \le -4.5719742657633988 \cdot 10^{124}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \le 5.6077084680207815 \cdot 10^{178}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \left(\sqrt[3]{z - t} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right)\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z \cdot \frac{x}{t} - y \cdot \frac{z}{t}\right)\\ \end{array}\]

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 ((t <= -4.571974265763399e+124)) {
		VAR = ((double) (y + ((double) (((double) (z / t)) * ((double) (x - y))))));
	} else {
		double VAR_1;
		if ((t <= 5.6077084680207815e+178)) {
			VAR_1 = ((double) (x + ((double) (((double) (((double) (y - x)) * ((double) (((double) cbrt(((double) (z - t)))) * ((double) (((double) cbrt(((double) (z - t)))) / ((double) (((double) cbrt(((double) (a - t)))) * ((double) cbrt(((double) (a - t)))))))))))) * ((double) (((double) cbrt(((double) (z - t)))) / ((double) cbrt(((double) (a - t))))))))));
		} else {
			VAR_1 = ((double) (y + ((double) (((double) (z * ((double) (x / t)))) - ((double) (y * ((double) (z / t))))))));
		}
		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	24.3
Target	9.5
Herbie	9.6

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

Derivation

1. Split input into 3 regimes

2. if t < -4.5719742657633988e124

   1. Initial program 47.1

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

   2. Simplified 22.5

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

   3. Taylor expanded around inf 26.9

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

   4. Simplified 16.6

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

   if -4.5719742657633988e124 < t < 5.6077084680207815e178

   1. Initial program 14.4

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

   2. Simplified 7.3

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

   4. Applied add-cube-cbrt 7.9

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

   5. Applied add-cube-cbrt 7.9

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

   6. Applied times-frac 7.9

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

   7. Applied associate-*r* 7.0

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

   8. Simplified 7.0

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

   if 5.6077084680207815e178 < t

   1. Initial program 48.3

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

   2. Simplified 24.4

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

   4. Applied add-cube-cbrt 25.2

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

   5. Applied add-cube-cbrt 24.7

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

   6. Applied times-frac 24.7

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

   7. Applied associate-*r* 24.7

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

   8. Simplified 24.8

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

   9. Taylor expanded around inf 25.2

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

   10. Simplified 15.1

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

4. Final simplification 9.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -4.5719742657633988 \cdot 10^{124}:\\ \;\;\;\;y + \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;t \le 5.6077084680207815 \cdot 10^{178}:\\ \;\;\;\;x + \left(\left(y - x\right) \cdot \left(\sqrt[3]{z - t} \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t} \cdot \sqrt[3]{a - t}}\right)\right) \cdot \frac{\sqrt[3]{z - t}}{\sqrt[3]{a - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \left(z \cdot \frac{x}{t} - y \cdot \frac{z}{t}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020181 
(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))))