Average Error: 12.3 → 12.6
Time: 8.3s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]
↓
\[\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(y \cdot z - t \cdot a\right)\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]
\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(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \left(y \cdot z - t \cdot a\right)\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 r767397 = x;
        double r767398 = y;
        double r767399 = z;
        double r767400 = r767398 * r767399;
        double r767401 = t;
        double r767402 = a;
        double r767403 = r767401 * r767402;
        double r767404 = r767400 - r767403;
        double r767405 = r767397 * r767404;
        double r767406 = b;
        double r767407 = c;
        double r767408 = r767407 * r767399;
        double r767409 = i;
        double r767410 = r767401 * r767409;
        double r767411 = r767408 - r767410;
        double r767412 = r767406 * r767411;
        double r767413 = r767405 - r767412;
        double r767414 = j;
        double r767415 = r767407 * r767402;
        double r767416 = r767398 * r767409;
        double r767417 = r767415 - r767416;
        double r767418 = r767414 * r767417;
        double r767419 = r767413 + r767418;
        return r767419;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r767420 = x;
        double r767421 = cbrt(r767420);
        double r767422 = r767421 * r767421;
        double r767423 = y;
        double r767424 = z;
        double r767425 = r767423 * r767424;
        double r767426 = t;
        double r767427 = a;
        double r767428 = r767426 * r767427;
        double r767429 = r767425 - r767428;
        double r767430 = r767421 * r767429;
        double r767431 = r767422 * r767430;
        double r767432 = b;
        double r767433 = c;
        double r767434 = r767433 * r767424;
        double r767435 = i;
        double r767436 = r767426 * r767435;
        double r767437 = r767434 - r767436;
        double r767438 = r767432 * r767437;
        double r767439 = r767431 - r767438;
        double r767440 = j;
        double r767441 = r767433 * r767427;
        double r767442 = r767423 * r767435;
        double r767443 = r767441 - r767442;
        double r767444 = r767440 * r767443;
        double r767445 = r767439 + r767444;
        return r767445;
}

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

Original12.3
Target19.7
Herbie12.6
\[\begin{array}{l} \mathbf{if}\;x \lt -1.46969429677770502 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x \lt 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array}\]

Derivation

  1. Initial program 12.3

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

  3. Applied add-cube-cbrt12.6

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

  4. Applied associate-*l*12.6

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

  5. Final simplification12.6

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

Reproduce

herbie shell --seed 2020036 
(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)))))