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

Average Error: 6.4 → 1.9

Time: 7.2s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r654135 = 2.0;
        double r654136 = x;
        double r654137 = y;
        double r654138 = r654136 * r654137;
        double r654139 = z;
        double r654140 = t;
        double r654141 = r654139 * r654140;
        double r654142 = r654138 + r654141;
        double r654143 = a;
        double r654144 = b;
        double r654145 = c;
        double r654146 = r654144 * r654145;
        double r654147 = r654143 + r654146;
        double r654148 = r654147 * r654145;
        double r654149 = i;
        double r654150 = r654148 * r654149;
        double r654151 = r654142 - r654150;
        double r654152 = r654135 * r654151;
        return r654152;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r654153 = 2.0;
        double r654154 = x;
        double r654155 = y;
        double r654156 = r654154 * r654155;
        double r654157 = z;
        double r654158 = t;
        double r654159 = r654157 * r654158;
        double r654160 = r654156 + r654159;
        double r654161 = a;
        double r654162 = b;
        double r654163 = c;
        double r654164 = r654162 * r654163;
        double r654165 = r654161 + r654164;
        double r654166 = i;
        double r654167 = r654163 * r654166;
        double r654168 = r654165 * r654167;
        double r654169 = r654160 - r654168;
        double r654170 = r654153 * r654169;
        return r654170;
}

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	6.4
Target	1.9
Herbie	1.9

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

Derivation

1. Initial program 6.4

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

3. Applied associate-*l* 1.9

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

4. Final simplification 1.9

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

Reproduce

herbie shell --seed 2020064 
(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))))