Average Error: 11.5 → 10.3
Time: 7.6s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -1.4523079412932612 \cdot 10^{-51}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot {\left(t \cdot \left(x \cdot a\right)\right)}^{1}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;t \le 2.9415755592289815 \cdot 10^{-52}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + -1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\\ \mathbf{elif}\;t \le 1.0660304109241224 \cdot 10^{-40}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + 0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot {\left(t \cdot \left(x \cdot a\right)\right)}^{1}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]
\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}\;t \le -1.4523079412932612 \cdot 10^{-51}:\\
\;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot {\left(t \cdot \left(x \cdot a\right)\right)}^{1}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\mathbf{elif}\;t \le 2.9415755592289815 \cdot 10^{-52}:\\
\;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + -1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\\

\mathbf{elif}\;t \le 1.0660304109241224 \cdot 10^{-40}:\\
\;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + 0\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot {\left(t \cdot \left(x \cdot a\right)\right)}^{1}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r125530 = x;
        double r125531 = y;
        double r125532 = z;
        double r125533 = r125531 * r125532;
        double r125534 = t;
        double r125535 = a;
        double r125536 = r125534 * r125535;
        double r125537 = r125533 - r125536;
        double r125538 = r125530 * r125537;
        double r125539 = b;
        double r125540 = c;
        double r125541 = r125540 * r125532;
        double r125542 = i;
        double r125543 = r125542 * r125535;
        double r125544 = r125541 - r125543;
        double r125545 = r125539 * r125544;
        double r125546 = r125538 - r125545;
        double r125547 = j;
        double r125548 = r125540 * r125534;
        double r125549 = r125542 * r125531;
        double r125550 = r125548 - r125549;
        double r125551 = r125547 * r125550;
        double r125552 = r125546 + r125551;
        return r125552;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r125553 = t;
        double r125554 = -1.4523079412932612e-51;
        bool r125555 = r125553 <= r125554;
        double r125556 = x;
        double r125557 = y;
        double r125558 = r125556 * r125557;
        double r125559 = z;
        double r125560 = r125558 * r125559;
        double r125561 = -1.0;
        double r125562 = a;
        double r125563 = r125556 * r125562;
        double r125564 = r125553 * r125563;
        double r125565 = 1.0;
        double r125566 = pow(r125564, r125565);
        double r125567 = r125561 * r125566;
        double r125568 = r125560 + r125567;
        double r125569 = b;
        double r125570 = c;
        double r125571 = r125570 * r125559;
        double r125572 = i;
        double r125573 = r125572 * r125562;
        double r125574 = r125571 - r125573;
        double r125575 = r125569 * r125574;
        double r125576 = r125568 - r125575;
        double r125577 = j;
        double r125578 = r125570 * r125553;
        double r125579 = r125572 * r125557;
        double r125580 = r125578 - r125579;
        double r125581 = r125577 * r125580;
        double r125582 = r125576 + r125581;
        double r125583 = 2.9415755592289815e-52;
        bool r125584 = r125553 <= r125583;
        double r125585 = r125557 * r125559;
        double r125586 = r125556 * r125585;
        double r125587 = r125556 * r125553;
        double r125588 = r125562 * r125587;
        double r125589 = r125561 * r125588;
        double r125590 = r125586 + r125589;
        double r125591 = r125590 - r125575;
        double r125592 = cbrt(r125581);
        double r125593 = r125592 * r125592;
        double r125594 = r125593 * r125592;
        double r125595 = r125591 + r125594;
        double r125596 = 1.0660304109241224e-40;
        bool r125597 = r125553 <= r125596;
        double r125598 = r125560 + r125589;
        double r125599 = r125598 - r125575;
        double r125600 = 0.0;
        double r125601 = r125599 + r125600;
        double r125602 = r125597 ? r125601 : r125582;
        double r125603 = r125584 ? r125595 : r125602;
        double r125604 = r125555 ? r125582 : r125603;
        return r125604;
}

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

Derivation

  1. Split input into 3 regimes

  2. if t < -1.4523079412932612e-51 or 1.0660304109241224e-40 < t

    1. Initial program 14.5

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

    3. Applied sub-neg14.5

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

    4. Applied distribute-lft-in14.5

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

    5. Taylor expanded around inf 15.3

      \[\leadsto \left(\left(x \cdot \left(y \cdot z\right) + \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot t\right)\right)}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    6. Using strategy rm

    7. Applied associate-*r*14.3

      \[\leadsto \left(\left(\color{blue}{\left(x \cdot y\right) \cdot z} + -1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    8. Using strategy rm

    9. Applied pow114.3

      \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot \left(a \cdot \left(x \cdot \color{blue}{{t}^{1}}\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    10. Applied pow114.3

      \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot \left(a \cdot \left(\color{blue}{{x}^{1}} \cdot {t}^{1}\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    11. Applied pow-prod-down14.3

      \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot \left(a \cdot \color{blue}{{\left(x \cdot t\right)}^{1}}\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    12. Applied pow114.3

      \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot \left(\color{blue}{{a}^{1}} \cdot {\left(x \cdot t\right)}^{1}\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    13. Applied pow-prod-down14.3

      \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot \color{blue}{{\left(a \cdot \left(x \cdot t\right)\right)}^{1}}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    14. Simplified11.3

      \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot {\color{blue}{\left(t \cdot \left(x \cdot a\right)\right)}}^{1}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    if -1.4523079412932612e-51 < t < 2.9415755592289815e-52

    1. Initial program 8.7

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

    3. Applied sub-neg8.7

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

    4. Applied distribute-lft-in8.7

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

    5. Taylor expanded around inf 8.8

      \[\leadsto \left(\left(x \cdot \left(y \cdot z\right) + \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot t\right)\right)}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    6. Using strategy rm

    7. Applied add-cube-cbrt9.0

      \[\leadsto \left(\left(x \cdot \left(y \cdot z\right) + -1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{\left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}}\]

    if 2.9415755592289815e-52 < t < 1.0660304109241224e-40

    1. Initial program 10.4

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

    3. Applied sub-neg10.4

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

    4. Applied distribute-lft-in10.4

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

    5. Taylor expanded around inf 10.4

      \[\leadsto \left(\left(x \cdot \left(y \cdot z\right) + \color{blue}{-1 \cdot \left(a \cdot \left(x \cdot t\right)\right)}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
    6. Using strategy rm

    7. Applied associate-*r*9.8

      \[\leadsto \left(\left(\color{blue}{\left(x \cdot y\right) \cdot z} + -1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    8. Taylor expanded around 0 28.1

      \[\leadsto \left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \color{blue}{0}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification10.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -1.4523079412932612 \cdot 10^{-51}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot {\left(t \cdot \left(x \cdot a\right)\right)}^{1}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \mathbf{elif}\;t \le 2.9415755592289815 \cdot 10^{-52}:\\ \;\;\;\;\left(\left(x \cdot \left(y \cdot z\right) + -1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \left(\sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)} \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\right) \cdot \sqrt[3]{j \cdot \left(c \cdot t - i \cdot y\right)}\\ \mathbf{elif}\;t \le 1.0660304109241224 \cdot 10^{-40}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot \left(a \cdot \left(x \cdot t\right)\right)\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + 0\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(x \cdot y\right) \cdot z + -1 \cdot {\left(t \cdot \left(x \cdot a\right)\right)}^{1}\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  :precision binary64
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))