Data.Colour.Matrix:determinant from colour-2.3.3, A

Average Error: 12.4 → 12.4

Time: 23.9s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r514215 = x;
        double r514216 = y;
        double r514217 = z;
        double r514218 = r514216 * r514217;
        double r514219 = t;
        double r514220 = a;
        double r514221 = r514219 * r514220;
        double r514222 = r514218 - r514221;
        double r514223 = r514215 * r514222;
        double r514224 = b;
        double r514225 = c;
        double r514226 = r514225 * r514217;
        double r514227 = i;
        double r514228 = r514219 * r514227;
        double r514229 = r514226 - r514228;
        double r514230 = r514224 * r514229;
        double r514231 = r514223 - r514230;
        double r514232 = j;
        double r514233 = r514225 * r514220;
        double r514234 = r514216 * r514227;
        double r514235 = r514233 - r514234;
        double r514236 = r514232 * r514235;
        double r514237 = r514231 + r514236;
        return r514237;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r514238 = x;
        double r514239 = y;
        double r514240 = z;
        double r514241 = r514239 * r514240;
        double r514242 = t;
        double r514243 = a;
        double r514244 = r514242 * r514243;
        double r514245 = r514241 - r514244;
        double r514246 = r514238 * r514245;
        double r514247 = b;
        double r514248 = c;
        double r514249 = r514248 * r514240;
        double r514250 = i;
        double r514251 = r514242 * r514250;
        double r514252 = r514249 - r514251;
        double r514253 = r514247 * r514252;
        double r514254 = r514246 - r514253;
        double r514255 = j;
        double r514256 = r514248 * r514243;
        double r514257 = r514239 * r514250;
        double r514258 = r514256 - r514257;
        double r514259 = r514255 * r514258;
        double r514260 = r514254 + r514259;
        return r514260;
}

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

Bits error versus j

Target

Original	12.4
Target	19.9
Herbie	12.4

\[\begin{array}{l} \mathbf{if}\;x \lt -1.469694296777705016266218530347997287942 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x \lt 3.21135273622268028942701600607048800714 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array}\]

Derivation

1. Initial program 12.4

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

3. Applied add-cube-cbrt 12.7

   \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \color{blue}{\left(\sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot a - y \cdot i\right)}}\]

4. Final simplification 12.4

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

Reproduce

herbie shell --seed 2019294 
(FPCore (x y z t a b c i j)
  :name "Data.Colour.Matrix:determinant from colour-2.3.3, A"
  :precision binary64

  :herbie-target
  (if (< x -1.46969429677770502e-64) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i)))) (if (< x 3.2113527362226803e-147) (- (* (- (* b i) (* x a)) t) (- (* z (* c b)) (* j (- (* c a) (* y i))))) (+ (- (* x (- (* y z) (* t a))) (/ (* b (- (pow (* c z) 2) (pow (* t i) 2))) (+ (* c z) (* t i)))) (* j (- (* c a) (* y i))))))

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