Average Error: 12.1 → 12.4
Time: 8.4s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]
↓
\[\left(x \cdot \left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]
\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)
↓
\left(x \cdot \left(\left(\sqrt[3]{y \cdot z - t \cdot a} \cdot \sqrt[3]{y \cdot z - t \cdot a}\right) \cdot \sqrt[3]{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)
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r940452 = x;
        double r940453 = y;
        double r940454 = z;
        double r940455 = r940453 * r940454;
        double r940456 = t;
        double r940457 = a;
        double r940458 = r940456 * r940457;
        double r940459 = r940455 - r940458;
        double r940460 = r940452 * r940459;
        double r940461 = b;
        double r940462 = c;
        double r940463 = r940462 * r940454;
        double r940464 = i;
        double r940465 = r940456 * r940464;
        double r940466 = r940463 - r940465;
        double r940467 = r940461 * r940466;
        double r940468 = r940460 - r940467;
        double r940469 = j;
        double r940470 = r940462 * r940457;
        double r940471 = r940453 * r940464;
        double r940472 = r940470 - r940471;
        double r940473 = r940469 * r940472;
        double r940474 = r940468 + r940473;
        return r940474;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r940475 = x;
        double r940476 = y;
        double r940477 = z;
        double r940478 = r940476 * r940477;
        double r940479 = t;
        double r940480 = a;
        double r940481 = r940479 * r940480;
        double r940482 = r940478 - r940481;
        double r940483 = cbrt(r940482);
        double r940484 = r940483 * r940483;
        double r940485 = r940484 * r940483;
        double r940486 = r940475 * r940485;
        double r940487 = b;
        double r940488 = c;
        double r940489 = r940488 * r940477;
        double r940490 = i;
        double r940491 = r940479 * r940490;
        double r940492 = r940489 - r940491;
        double r940493 = r940487 * r940492;
        double r940494 = r940486 - r940493;
        double r940495 = j;
        double r940496 = r940488 * r940480;
        double r940497 = r940476 * r940490;
        double r940498 = r940496 - r940497;
        double r940499 = r940495 * r940498;
        double r940500 = r940494 + r940499;
        return r940500;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original12.1
Target19.8
Herbie12.4
\[\begin{array}{l} \mathbf{if}\;x \lt -1.46969429677770502 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x \lt 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array}\]

Derivation

  1. Initial program 12.1

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

  3. Applied add-cube-cbrt12.4

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

  4. Final simplification12.4

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

Reproduce

herbie shell --seed 2020021 
(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 -1.469694296777705e-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)))))