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

Average Error: 6.5 → 1.2

Time: 7.7s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c = -\infty \lor \neg \left(\left(a + b \cdot c\right) \cdot c \le 1.86415285528346707 \cdot 10^{263}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r811193 = 2.0;
        double r811194 = x;
        double r811195 = y;
        double r811196 = r811194 * r811195;
        double r811197 = z;
        double r811198 = t;
        double r811199 = r811197 * r811198;
        double r811200 = r811196 + r811199;
        double r811201 = a;
        double r811202 = b;
        double r811203 = c;
        double r811204 = r811202 * r811203;
        double r811205 = r811201 + r811204;
        double r811206 = r811205 * r811203;
        double r811207 = i;
        double r811208 = r811206 * r811207;
        double r811209 = r811200 - r811208;
        double r811210 = r811193 * r811209;
        return r811210;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r811211 = a;
        double r811212 = b;
        double r811213 = c;
        double r811214 = r811212 * r811213;
        double r811215 = r811211 + r811214;
        double r811216 = r811215 * r811213;
        double r811217 = -inf.0;
        bool r811218 = r811216 <= r811217;
        double r811219 = 1.864152855283467e+263;
        bool r811220 = r811216 <= r811219;
        double r811221 = !r811220;
        bool r811222 = r811218 || r811221;
        double r811223 = 2.0;
        double r811224 = x;
        double r811225 = y;
        double r811226 = r811224 * r811225;
        double r811227 = z;
        double r811228 = t;
        double r811229 = r811227 * r811228;
        double r811230 = r811226 + r811229;
        double r811231 = i;
        double r811232 = r811213 * r811231;
        double r811233 = r811215 * r811232;
        double r811234 = r811230 - r811233;
        double r811235 = r811223 * r811234;
        double r811236 = r811216 * r811231;
        double r811237 = r811230 - r811236;
        double r811238 = r811223 * r811237;
        double r811239 = r811222 ? r811235 : r811238;
        return r811239;
}

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	6.5
Target	1.7
Herbie	1.2

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

Derivation

1. Split input into 2 regimes

2. if (* (+ a (* b c)) c) < -inf.0 or 1.864152855283467e+263 < (* (+ a (* b c)) c)

   1. Initial program 54.0

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

   3. Applied associate-*l* 8.4

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

   if -inf.0 < (* (+ a (* b c)) c) < 1.864152855283467e+263

   1. Initial program 0.3

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

4. Final simplification 1.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(a + b \cdot c\right) \cdot c = -\infty \lor \neg \left(\left(a + b \cdot c\right) \cdot c \le 1.86415285528346707 \cdot 10^{263}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020065 
(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))))