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

Average Error: 6.7 → 1.7

Time: 21.6s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le -3.293636657081936215052546669040792345465 \cdot 10^{297} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le 5.773020174715613141848109214938053438756 \cdot 10^{-291}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r736930 = 2.0;
        double r736931 = x;
        double r736932 = y;
        double r736933 = r736931 * r736932;
        double r736934 = z;
        double r736935 = t;
        double r736936 = r736934 * r736935;
        double r736937 = r736933 + r736936;
        double r736938 = a;
        double r736939 = b;
        double r736940 = c;
        double r736941 = r736939 * r736940;
        double r736942 = r736938 + r736941;
        double r736943 = r736942 * r736940;
        double r736944 = i;
        double r736945 = r736943 * r736944;
        double r736946 = r736937 - r736945;
        double r736947 = r736930 * r736946;
        return r736947;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r736948 = a;
        double r736949 = b;
        double r736950 = c;
        double r736951 = r736949 * r736950;
        double r736952 = r736948 + r736951;
        double r736953 = r736952 * r736950;
        double r736954 = i;
        double r736955 = r736953 * r736954;
        double r736956 = -3.293636657081936e+297;
        bool r736957 = r736955 <= r736956;
        double r736958 = 5.773020174715613e-291;
        bool r736959 = r736955 <= r736958;
        double r736960 = !r736959;
        bool r736961 = r736957 || r736960;
        double r736962 = 2.0;
        double r736963 = x;
        double r736964 = y;
        double r736965 = r736963 * r736964;
        double r736966 = z;
        double r736967 = t;
        double r736968 = r736966 * r736967;
        double r736969 = r736965 + r736968;
        double r736970 = r736954 * r736950;
        double r736971 = r736952 * r736970;
        double r736972 = r736969 - r736971;
        double r736973 = r736962 * r736972;
        double r736974 = r736969 - r736955;
        double r736975 = r736962 * r736974;
        double r736976 = r736961 ? r736973 : r736975;
        return r736976;
}

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	6.7
Target	1.9
Herbie	1.7

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

Derivation

1. Split input into 2 regimes

2. if (* (* (+ a (* b c)) c) i) < -3.293636657081936e+297 or 5.773020174715613e-291 < (* (* (+ a (* b c)) c) i)

   1. Initial program 14.4

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

   3. Applied associate-*l* 3.3

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

   4. Simplified 3.3

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

   if -3.293636657081936e+297 < (* (* (+ a (* b c)) c) i) < 5.773020174715613e-291

   1. Initial program 0.4

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

4. Final simplification 1.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le -3.293636657081936215052546669040792345465 \cdot 10^{297} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le 5.773020174715613141848109214938053438756 \cdot 10^{-291}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(i \cdot c\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 
(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))))