Average Error: 11.9 → 10.8
Time: 24.3s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -1.0730045135916517 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(\sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} - \left(b \cdot \left(c \cdot z\right) + \left(i \cdot a\right) \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(i \cdot \left(\left(-a\right) \cdot b\right) + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\left(c \cdot b\right) \cdot \sqrt[3]{z}\right)\right)\right)\\ \end{array}\]
\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)
↓
\begin{array}{l}
\mathbf{if}\;b \le -1.0730045135916517 \cdot 10^{+126}:\\
\;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(\sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} - \left(b \cdot \left(c \cdot z\right) + \left(i \cdot a\right) \cdot \left(-b\right)\right)\right)\\

\mathbf{else}:\\
\;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(i \cdot \left(\left(-a\right) \cdot b\right) + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\left(c \cdot b\right) \cdot \sqrt[3]{z}\right)\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 r29066232 = x;
        double r29066233 = y;
        double r29066234 = z;
        double r29066235 = r29066233 * r29066234;
        double r29066236 = t;
        double r29066237 = a;
        double r29066238 = r29066236 * r29066237;
        double r29066239 = r29066235 - r29066238;
        double r29066240 = r29066232 * r29066239;
        double r29066241 = b;
        double r29066242 = c;
        double r29066243 = r29066242 * r29066234;
        double r29066244 = i;
        double r29066245 = r29066244 * r29066237;
        double r29066246 = r29066243 - r29066245;
        double r29066247 = r29066241 * r29066246;
        double r29066248 = r29066240 - r29066247;
        double r29066249 = j;
        double r29066250 = r29066242 * r29066236;
        double r29066251 = r29066244 * r29066233;
        double r29066252 = r29066250 - r29066251;
        double r29066253 = r29066249 * r29066252;
        double r29066254 = r29066248 + r29066253;
        return r29066254;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r29066255 = b;
        double r29066256 = -1.0730045135916517e+126;
        bool r29066257 = r29066255 <= r29066256;
        double r29066258 = j;
        double r29066259 = c;
        double r29066260 = t;
        double r29066261 = r29066259 * r29066260;
        double r29066262 = y;
        double r29066263 = i;
        double r29066264 = r29066262 * r29066263;
        double r29066265 = r29066261 - r29066264;
        double r29066266 = r29066258 * r29066265;
        double r29066267 = z;
        double r29066268 = r29066262 * r29066267;
        double r29066269 = a;
        double r29066270 = r29066260 * r29066269;
        double r29066271 = r29066268 - r29066270;
        double r29066272 = x;
        double r29066273 = r29066271 * r29066272;
        double r29066274 = cbrt(r29066273);
        double r29066275 = r29066274 * r29066274;
        double r29066276 = r29066275 * r29066274;
        double r29066277 = r29066259 * r29066267;
        double r29066278 = r29066255 * r29066277;
        double r29066279 = r29066263 * r29066269;
        double r29066280 = -r29066255;
        double r29066281 = r29066279 * r29066280;
        double r29066282 = r29066278 + r29066281;
        double r29066283 = r29066276 - r29066282;
        double r29066284 = r29066266 + r29066283;
        double r29066285 = -r29066269;
        double r29066286 = r29066285 * r29066255;
        double r29066287 = r29066263 * r29066286;
        double r29066288 = cbrt(r29066267);
        double r29066289 = r29066288 * r29066288;
        double r29066290 = r29066259 * r29066255;
        double r29066291 = r29066290 * r29066288;
        double r29066292 = r29066289 * r29066291;
        double r29066293 = r29066287 + r29066292;
        double r29066294 = r29066273 - r29066293;
        double r29066295 = r29066266 + r29066294;
        double r29066296 = r29066257 ? r29066284 : r29066295;
        return r29066296;
}

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

Original11.9
Target15.3
Herbie10.8
\[\begin{array}{l} \mathbf{if}\;t \lt -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{elif}\;t \lt -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if b < -1.0730045135916517e+126

    1. Initial program 6.6

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

    3. Applied sub-neg6.6

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

    4. Applied distribute-rgt-in6.6

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

    6. Applied add-cube-cbrt6.7

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

    if -1.0730045135916517e+126 < b

    1. Initial program 12.4

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

    3. Applied sub-neg12.4

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

    4. Applied distribute-rgt-in12.4

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

    6. Applied distribute-rgt-neg-in12.4

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

    7. Applied associate-*l*11.9

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

    8. Taylor expanded around inf 11.1

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

    10. Applied add-cube-cbrt11.2

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

    11. Applied associate-*l*11.2

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

  4. Final simplification10.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -1.0730045135916517 \cdot 10^{+126}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(\sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} - \left(b \cdot \left(c \cdot z\right) + \left(i \cdot a\right) \cdot \left(-b\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;j \cdot \left(c \cdot t - y \cdot i\right) + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(i \cdot \left(\left(-a\right) \cdot b\right) + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\left(c \cdot b\right) \cdot \sqrt[3]{z}\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"

  :herbie-target
  (if (< t -8.120978919195912e-33) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t -4.712553818218485e-169) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (if (< t -7.633533346031584e-308) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j))) (if (< t 1.0535888557455487e-139) (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (/ (* j (- (pow (* c t) 2) (pow (* i y) 2))) (+ (* c t) (* i y)))) (- (* x (- (* z y) (* a t))) (- (* b (- (* z c) (* a i))) (* (- (* c t) (* y i)) j)))))))

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