Average Error: 11.6 → 10.8
Time: 8.6s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;j \le -7.3496665066932727 \cdot 10^{-160} \lor \neg \left(j \le 1.91780152691440701 \cdot 10^{93}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(\sqrt[3]{c \cdot z - t \cdot i} \cdot \sqrt[3]{c \cdot z - t \cdot i}\right) \cdot \sqrt[3]{c \cdot z - t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-j\right) \cdot \left(y \cdot i\right)\right)\\ \end{array}\]
\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)
↓
\begin{array}{l}
\mathbf{if}\;j \le -7.3496665066932727 \cdot 10^{-160} \lor \neg \left(j \le 1.91780152691440701 \cdot 10^{93}\right):\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(\sqrt[3]{c \cdot z - t \cdot i} \cdot \sqrt[3]{c \cdot z - t \cdot i}\right) \cdot \sqrt[3]{c \cdot z - t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\

\mathbf{else}:\\
\;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-j\right) \cdot \left(y \cdot i\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r922239 = x;
        double r922240 = y;
        double r922241 = z;
        double r922242 = r922240 * r922241;
        double r922243 = t;
        double r922244 = a;
        double r922245 = r922243 * r922244;
        double r922246 = r922242 - r922245;
        double r922247 = r922239 * r922246;
        double r922248 = b;
        double r922249 = c;
        double r922250 = r922249 * r922241;
        double r922251 = i;
        double r922252 = r922243 * r922251;
        double r922253 = r922250 - r922252;
        double r922254 = r922248 * r922253;
        double r922255 = r922247 - r922254;
        double r922256 = j;
        double r922257 = r922249 * r922244;
        double r922258 = r922240 * r922251;
        double r922259 = r922257 - r922258;
        double r922260 = r922256 * r922259;
        double r922261 = r922255 + r922260;
        return r922261;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r922262 = j;
        double r922263 = -7.349666506693273e-160;
        bool r922264 = r922262 <= r922263;
        double r922265 = 1.917801526914407e+93;
        bool r922266 = r922262 <= r922265;
        double r922267 = !r922266;
        bool r922268 = r922264 || r922267;
        double r922269 = x;
        double r922270 = y;
        double r922271 = z;
        double r922272 = r922270 * r922271;
        double r922273 = t;
        double r922274 = a;
        double r922275 = r922273 * r922274;
        double r922276 = r922272 - r922275;
        double r922277 = r922269 * r922276;
        double r922278 = b;
        double r922279 = c;
        double r922280 = r922279 * r922271;
        double r922281 = i;
        double r922282 = r922273 * r922281;
        double r922283 = r922280 - r922282;
        double r922284 = cbrt(r922283);
        double r922285 = r922284 * r922284;
        double r922286 = r922285 * r922284;
        double r922287 = r922278 * r922286;
        double r922288 = r922277 - r922287;
        double r922289 = r922279 * r922274;
        double r922290 = r922270 * r922281;
        double r922291 = r922289 - r922290;
        double r922292 = r922262 * r922291;
        double r922293 = r922288 + r922292;
        double r922294 = r922278 * r922283;
        double r922295 = r922277 - r922294;
        double r922296 = r922262 * r922279;
        double r922297 = r922274 * r922296;
        double r922298 = -r922262;
        double r922299 = r922298 * r922290;
        double r922300 = r922297 + r922299;
        double r922301 = r922295 + r922300;
        double r922302 = r922268 ? r922293 : r922301;
        return r922302;
}

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

Original11.6
Target19.5
Herbie10.8
\[\begin{array}{l} \mathbf{if}\;x \lt -1.46969429677770502 \cdot 10^{-64}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{elif}\;x \lt 3.2113527362226803 \cdot 10^{-147}:\\ \;\;\;\;\left(b \cdot i - x \cdot a\right) \cdot t - \left(z \cdot \left(c \cdot b\right) - j \cdot \left(c \cdot a - y \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - \frac{b \cdot \left({\left(c \cdot z\right)}^{2} - {\left(t \cdot i\right)}^{2}\right)}{c \cdot z + t \cdot i}\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if j < -7.349666506693273e-160 or 1.917801526914407e+93 < j

    1. Initial program 9.2

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

    3. Applied add-cube-cbrt9.5

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

    if -7.349666506693273e-160 < j < 1.917801526914407e+93

    1. Initial program 13.7

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

    3. Applied add-cube-cbrt13.9

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

    4. Applied associate-*l*13.9

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

    6. Applied sub-neg13.9

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

    7. Applied distribute-lft-in13.9

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

    8. Applied distribute-lft-in13.9

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

    9. Simplified12.1

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

    10. Simplified12.0

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(a \cdot \left(j \cdot c\right) + \color{blue}{\left(-j\right) \cdot \left(y \cdot i\right)}\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification10.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;j \le -7.3496665066932727 \cdot 10^{-160} \lor \neg \left(j \le 1.91780152691440701 \cdot 10^{93}\right):\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(\left(\sqrt[3]{c \cdot z - t \cdot i} \cdot \sqrt[3]{c \cdot z - t \cdot i}\right) \cdot \sqrt[3]{c \cdot z - t \cdot i}\right)\right) + j \cdot \left(c \cdot a - y \cdot i\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - t \cdot i\right)\right) + \left(a \cdot \left(j \cdot c\right) + \left(-j\right) \cdot \left(y \cdot i\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020027 
(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)))))