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

Average Error: 6.5 → 1.8

Time: 19.4s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r509034 = 2.0;
        double r509035 = x;
        double r509036 = y;
        double r509037 = r509035 * r509036;
        double r509038 = z;
        double r509039 = t;
        double r509040 = r509038 * r509039;
        double r509041 = r509037 + r509040;
        double r509042 = a;
        double r509043 = b;
        double r509044 = c;
        double r509045 = r509043 * r509044;
        double r509046 = r509042 + r509045;
        double r509047 = r509046 * r509044;
        double r509048 = i;
        double r509049 = r509047 * r509048;
        double r509050 = r509041 - r509049;
        double r509051 = r509034 * r509050;
        return r509051;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r509052 = 2.0;
        double r509053 = x;
        double r509054 = y;
        double r509055 = r509053 * r509054;
        double r509056 = z;
        double r509057 = t;
        double r509058 = r509056 * r509057;
        double r509059 = r509055 + r509058;
        double r509060 = a;
        double r509061 = b;
        double r509062 = c;
        double r509063 = r509061 * r509062;
        double r509064 = r509060 + r509063;
        double r509065 = i;
        double r509066 = r509065 * r509062;
        double r509067 = r509064 * r509066;
        double r509068 = r509059 - r509067;
        double r509069 = r509052 * r509068;
        return r509069;
}

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	1.8
Herbie	1.8

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

Derivation

1. Initial program 6.5

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

3. Applied associate-*l* 1.8

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

4. Simplified 1.8

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

5. Final simplification 1.8

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

Reproduce

herbie shell --seed 2019212 
(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))))