Average Error: 11.7 → 11.7
Time: 30.0s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;b \le -3.929707136934608 \cdot 10^{-249}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\ \mathbf{elif}\;b \le 7.525919208168165 \cdot 10^{-236}:\\ \;\;\;\;\left(y \cdot z - t \cdot a\right) \cdot x + \left(c \cdot t - y \cdot i\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(c \cdot z - a \cdot i\right) \cdot \sqrt{b}\right) \cdot \sqrt{b}\right)\\ \end{array}\]
\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 -3.929707136934608 \cdot 10^{-249}:\\
\;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \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} - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\

\mathbf{elif}\;b \le 7.525919208168165 \cdot 10^{-236}:\\
\;\;\;\;\left(y \cdot z - t \cdot a\right) \cdot x + \left(c \cdot t - y \cdot i\right) \cdot j\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r30319191 = x;
        double r30319192 = y;
        double r30319193 = z;
        double r30319194 = r30319192 * r30319193;
        double r30319195 = t;
        double r30319196 = a;
        double r30319197 = r30319195 * r30319196;
        double r30319198 = r30319194 - r30319197;
        double r30319199 = r30319191 * r30319198;
        double r30319200 = b;
        double r30319201 = c;
        double r30319202 = r30319201 * r30319193;
        double r30319203 = i;
        double r30319204 = r30319203 * r30319196;
        double r30319205 = r30319202 - r30319204;
        double r30319206 = r30319200 * r30319205;
        double r30319207 = r30319199 - r30319206;
        double r30319208 = j;
        double r30319209 = r30319201 * r30319195;
        double r30319210 = r30319203 * r30319192;
        double r30319211 = r30319209 - r30319210;
        double r30319212 = r30319208 * r30319211;
        double r30319213 = r30319207 + r30319212;
        return r30319213;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r30319214 = b;
        double r30319215 = -3.929707136934608e-249;
        bool r30319216 = r30319214 <= r30319215;
        double r30319217 = c;
        double r30319218 = t;
        double r30319219 = r30319217 * r30319218;
        double r30319220 = y;
        double r30319221 = i;
        double r30319222 = r30319220 * r30319221;
        double r30319223 = r30319219 - r30319222;
        double r30319224 = j;
        double r30319225 = r30319223 * r30319224;
        double r30319226 = z;
        double r30319227 = r30319220 * r30319226;
        double r30319228 = a;
        double r30319229 = r30319218 * r30319228;
        double r30319230 = r30319227 - r30319229;
        double r30319231 = x;
        double r30319232 = r30319230 * r30319231;
        double r30319233 = cbrt(r30319232);
        double r30319234 = r30319233 * r30319233;
        double r30319235 = r30319234 * r30319233;
        double r30319236 = r30319217 * r30319226;
        double r30319237 = r30319228 * r30319221;
        double r30319238 = r30319236 - r30319237;
        double r30319239 = r30319214 * r30319238;
        double r30319240 = r30319235 - r30319239;
        double r30319241 = r30319225 + r30319240;
        double r30319242 = 7.525919208168165e-236;
        bool r30319243 = r30319214 <= r30319242;
        double r30319244 = r30319232 + r30319225;
        double r30319245 = sqrt(r30319214);
        double r30319246 = r30319238 * r30319245;
        double r30319247 = r30319246 * r30319245;
        double r30319248 = r30319232 - r30319247;
        double r30319249 = r30319225 + r30319248;
        double r30319250 = r30319243 ? r30319244 : r30319249;
        double r30319251 = r30319216 ? r30319241 : r30319250;
        return r30319251;
}

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

Original11.7
Target15.6
Herbie11.7
\[\begin{array}{l} \mathbf{if}\;t \lt -8.120978919195912 \cdot 10^{-33}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt -4.712553818218485 \cdot 10^{-169}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{elif}\;t \lt -7.633533346031584 \cdot 10^{-308}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \mathbf{elif}\;t \lt 1.0535888557455487 \cdot 10^{-139}:\\ \;\;\;\;\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + \frac{j \cdot \left({\left(c \cdot t\right)}^{2} - {\left(i \cdot y\right)}^{2}\right)}{c \cdot t + i \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot y - a \cdot t\right) - \left(b \cdot \left(z \cdot c - a \cdot i\right) - \left(c \cdot t - y \cdot i\right) \cdot j\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if b < -3.929707136934608e-249

    1. Initial program 10.9

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

    3. Applied add-cube-cbrt11.2

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

    if -3.929707136934608e-249 < b < 7.525919208168165e-236

    1. Initial program 18.1

      \[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    2. Taylor expanded around 0 16.7

      \[\leadsto \left(x \cdot \left(y \cdot z - t \cdot a\right) - \color{blue}{0}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]

    if 7.525919208168165e-236 < b

    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 add-sqr-sqrt10.5

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

    4. Applied associate-*l*10.5

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

  4. Final simplification11.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;b \le -3.929707136934608 \cdot 10^{-249}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(\sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x}\right) \cdot \sqrt[3]{\left(y \cdot z - t \cdot a\right) \cdot x} - b \cdot \left(c \cdot z - a \cdot i\right)\right)\\ \mathbf{elif}\;b \le 7.525919208168165 \cdot 10^{-236}:\\ \;\;\;\;\left(y \cdot z - t \cdot a\right) \cdot x + \left(c \cdot t - y \cdot i\right) \cdot j\\ \mathbf{else}:\\ \;\;\;\;\left(c \cdot t - y \cdot i\right) \cdot j + \left(\left(y \cdot z - t \cdot a\right) \cdot x - \left(\left(c \cdot z - a \cdot i\right) \cdot \sqrt{b}\right) \cdot \sqrt{b}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(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)))))