Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A

Average Error: 6.2 → 1.6

Time: 8.9s

Precision: binary64

Math

\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]

↓

\[\begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c \le -4.81786069780753334 \cdot 10^{50} \lor \neg \left(\left(a + b \cdot c\right) \cdot c \le 1.15502025043079641 \cdot 10^{221}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot \left(\sqrt[3]{i} \cdot \sqrt[3]{i}\right)\right) \cdot \sqrt[3]{i}\right)\\ \end{array}\]

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((double) (2.0 * ((double) (((double) (((double) (x * y)) + ((double) (z * t)))) - ((double) (((double) (((double) (a + ((double) (b * c)))) * c)) * i))))));
}

↓

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double VAR;
	if (((((double) (((double) (a + ((double) (b * c)))) * c)) <= -4.817860697807533e+50) || !(((double) (((double) (a + ((double) (b * c)))) * c)) <= 1.1550202504307964e+221))) {
		VAR = ((double) (2.0 * ((double) (((double) (((double) (x * y)) + ((double) (z * t)))) - ((double) (((double) (a + ((double) (b * c)))) * ((double) (c * i))))))));
	} else {
		VAR = ((double) (2.0 * ((double) (((double) (((double) (x * y)) + ((double) (z * t)))) - ((double) (((double) (((double) (((double) (a + ((double) (b * c)))) * c)) * ((double) (((double) cbrt(i)) * ((double) cbrt(i)))))) * ((double) cbrt(i))))))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Target

Original	6.2
Target	1.9
Herbie	1.6

\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

1. Split input into 2 regimes

2. if (* (+ a (* b c)) c) < -4.81786069780753334e50 or 1.15502025043079641e221 < (* (+ a (* b c)) c)

   1. Initial program 21.2

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
   2. Using strategy rm

   3. Applied associate-*l* 4.2

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]

   if -4.81786069780753334e50 < (* (+ a (* b c)) c) < 1.15502025043079641e221

   1. Initial program 0.3

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
   2. Using strategy rm

   3. Applied add-cube-cbrt 0.6

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot \color{blue}{\left(\left(\sqrt[3]{i} \cdot \sqrt[3]{i}\right) \cdot \sqrt[3]{i}\right)}\right)\]

   4. Applied associate-*r* 0.6

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

4. Final simplification 1.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c \le -4.81786069780753334 \cdot 10^{50} \lor \neg \left(\left(a + b \cdot c\right) \cdot c \le 1.15502025043079641 \cdot 10^{221}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot \left(\sqrt[3]{i} \cdot \sqrt[3]{i}\right)\right) \cdot \sqrt[3]{i}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020155 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"
  :precision binary64

  :herbie-target
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))