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

Average Error: 5.9 → 1.3

Time: 7.3s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i = -\infty:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le 4.4752237138994016 \cdot 10^{290}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \sqrt{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \sqrt{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\\ \end{array}\]

C

double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (2.0 * (((x * y) + (z * t)) - (((a + (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 (((((a + (b * c)) * c) * i) <= -inf.0)) {
		VAR = (2.0 * (((x * y) + (z * t)) - ((a + (b * c)) * (c * i))));
	} else {
		double VAR_1;
		if (((((a + (b * c)) * c) * i) <= 4.4752237138994016e+290)) {
			VAR_1 = (2.0 * (((x * y) + (z * t)) - (((a + (b * c)) * c) * i)));
		} else {
			VAR_1 = (2.0 * (((x * y) + (z * t)) - (sqrt(((a + (b * c)) * (c * i))) * sqrt(((a + (b * c)) * (c * i))))));
		}
		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

Bits error versus b

Bits error versus c

Bits error versus i

Target

Original	5.9
Target	1.7
Herbie	1.3

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

Derivation

1. Split input into 3 regimes

2. if (* (* (+ a (* b c)) c) i) < -inf.0

   1. Initial program 64.0

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

   3. Applied associate-*l* 12.2

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

   if -inf.0 < (* (* (+ a (* b c)) c) i) < 4.4752237138994016e+290

   1. Initial program 0.3

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

   if 4.4752237138994016e+290 < (* (* (+ a (* b c)) c) i)

   1. Initial program 54.1

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

   3. Applied associate-*l* 9.5

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

   5. Applied add-sqr-sqrt 9.7

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

4. Final simplification 1.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i = -\infty:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{elif}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le 4.4752237138994016 \cdot 10^{290}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \sqrt{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)} \cdot \sqrt{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020100 
(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 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

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