Average Error: 12.0 → 11.9
Time: 29.8s
Precision: 64
\[\left(x \cdot \left(y \cdot z - t \cdot a\right) - b \cdot \left(c \cdot z - i \cdot a\right)\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -7.956534375479292996771812307974132157211 \cdot 10^{-112}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(t \cdot a\right) \cdot \left(-x\right) + \sqrt[3]{x} \cdot \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \mathbf{elif}\;x \le 8.098261062553838320818646911898221044477 \cdot 10^{-233}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(y \cdot \left(z \cdot x\right) + \left(t \cdot a\right) \cdot \left(-x\right)\right) - \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \left(z \cdot c - i \cdot a\right)\right)\right)\\ \mathbf{elif}\;x \le 1.004501937429617973047375648440637726055 \cdot 10^{-191}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(-a\right) \cdot \left(x \cdot t\right) + \left(y \cdot z\right) \cdot x\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + \left(t \cdot a\right) \cdot \left(-x\right)\right) - \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array}\]
\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}\;x \le -7.956534375479292996771812307974132157211 \cdot 10^{-112}:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(t \cdot a\right) \cdot \left(-x\right) + \sqrt[3]{x} \cdot \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\

\mathbf{elif}\;x \le 8.098261062553838320818646911898221044477 \cdot 10^{-233}:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(y \cdot \left(z \cdot x\right) + \left(t \cdot a\right) \cdot \left(-x\right)\right) - \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \left(z \cdot c - i \cdot a\right)\right)\right)\\

\mathbf{elif}\;x \le 1.004501937429617973047375648440637726055 \cdot 10^{-191}:\\
\;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(-a\right) \cdot \left(x \cdot t\right) + \left(y \cdot z\right) \cdot x\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r3946206 = x;
        double r3946207 = y;
        double r3946208 = z;
        double r3946209 = r3946207 * r3946208;
        double r3946210 = t;
        double r3946211 = a;
        double r3946212 = r3946210 * r3946211;
        double r3946213 = r3946209 - r3946212;
        double r3946214 = r3946206 * r3946213;
        double r3946215 = b;
        double r3946216 = c;
        double r3946217 = r3946216 * r3946208;
        double r3946218 = i;
        double r3946219 = r3946218 * r3946211;
        double r3946220 = r3946217 - r3946219;
        double r3946221 = r3946215 * r3946220;
        double r3946222 = r3946214 - r3946221;
        double r3946223 = j;
        double r3946224 = r3946216 * r3946210;
        double r3946225 = r3946218 * r3946207;
        double r3946226 = r3946224 - r3946225;
        double r3946227 = r3946223 * r3946226;
        double r3946228 = r3946222 + r3946227;
        return r3946228;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j) {
        double r3946229 = x;
        double r3946230 = -7.956534375479293e-112;
        bool r3946231 = r3946229 <= r3946230;
        double r3946232 = j;
        double r3946233 = t;
        double r3946234 = c;
        double r3946235 = r3946233 * r3946234;
        double r3946236 = y;
        double r3946237 = i;
        double r3946238 = r3946236 * r3946237;
        double r3946239 = r3946235 - r3946238;
        double r3946240 = r3946232 * r3946239;
        double r3946241 = a;
        double r3946242 = r3946233 * r3946241;
        double r3946243 = -r3946229;
        double r3946244 = r3946242 * r3946243;
        double r3946245 = cbrt(r3946229);
        double r3946246 = r3946245 * r3946245;
        double r3946247 = z;
        double r3946248 = r3946236 * r3946247;
        double r3946249 = r3946246 * r3946248;
        double r3946250 = r3946245 * r3946249;
        double r3946251 = r3946244 + r3946250;
        double r3946252 = b;
        double r3946253 = r3946247 * r3946234;
        double r3946254 = r3946237 * r3946241;
        double r3946255 = r3946253 - r3946254;
        double r3946256 = r3946252 * r3946255;
        double r3946257 = r3946251 - r3946256;
        double r3946258 = r3946240 + r3946257;
        double r3946259 = 8.098261062553838e-233;
        bool r3946260 = r3946229 <= r3946259;
        double r3946261 = r3946247 * r3946229;
        double r3946262 = r3946236 * r3946261;
        double r3946263 = r3946262 + r3946244;
        double r3946264 = cbrt(r3946252);
        double r3946265 = r3946264 * r3946264;
        double r3946266 = r3946264 * r3946255;
        double r3946267 = r3946265 * r3946266;
        double r3946268 = r3946263 - r3946267;
        double r3946269 = r3946240 + r3946268;
        double r3946270 = 1.004501937429618e-191;
        bool r3946271 = r3946229 <= r3946270;
        double r3946272 = -r3946241;
        double r3946273 = r3946229 * r3946233;
        double r3946274 = r3946272 * r3946273;
        double r3946275 = r3946248 * r3946229;
        double r3946276 = r3946274 + r3946275;
        double r3946277 = r3946276 - r3946256;
        double r3946278 = r3946240 + r3946277;
        double r3946279 = cbrt(r3946256);
        double r3946280 = r3946279 * r3946279;
        double r3946281 = r3946280 * r3946279;
        double r3946282 = r3946263 - r3946281;
        double r3946283 = r3946282 + r3946240;
        double r3946284 = r3946271 ? r3946278 : r3946283;
        double r3946285 = r3946260 ? r3946269 : r3946284;
        double r3946286 = r3946231 ? r3946258 : r3946285;
        return r3946286;
}

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 4 regimes

  2. if x < -7.956534375479293e-112

    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-rgt-in8.7

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

    6. Applied add-cube-cbrt8.9

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

    7. Applied associate-*r*8.9

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

    if -7.956534375479293e-112 < x < 8.098261062553838e-233

    1. Initial program 17.1

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

    3. Applied sub-neg17.1

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

    4. Applied distribute-rgt-in17.1

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

    6. Applied associate-*l*13.9

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

    8. Applied add-cube-cbrt14.3

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

    9. Applied associate-*l*14.3

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

    if 8.098261062553838e-233 < x < 1.004501937429618e-191

    1. Initial program 17.1

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

    3. Applied sub-neg17.1

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

    4. Applied distribute-rgt-in17.1

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

    5. Taylor expanded around inf 13.5

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

    6. Simplified13.5

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

    if 1.004501937429618e-191 < x

    1. Initial program 10.3

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

    3. Applied sub-neg10.3

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

    4. Applied distribute-rgt-in10.3

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

    6. Applied associate-*l*12.2

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

    8. Applied add-cube-cbrt12.4

      \[\leadsto \left(\left(y \cdot \left(z \cdot x\right) + \left(-t \cdot a\right) \cdot x\right) - \color{blue}{\left(\sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(c \cdot z - i \cdot a\right)}}\right) + j \cdot \left(c \cdot t - i \cdot y\right)\]
  3. Recombined 4 regimes into one program.

  4. Final simplification11.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -7.956534375479292996771812307974132157211 \cdot 10^{-112}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(t \cdot a\right) \cdot \left(-x\right) + \sqrt[3]{x} \cdot \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(y \cdot z\right)\right)\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \mathbf{elif}\;x \le 8.098261062553838320818646911898221044477 \cdot 10^{-233}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(y \cdot \left(z \cdot x\right) + \left(t \cdot a\right) \cdot \left(-x\right)\right) - \left(\sqrt[3]{b} \cdot \sqrt[3]{b}\right) \cdot \left(\sqrt[3]{b} \cdot \left(z \cdot c - i \cdot a\right)\right)\right)\\ \mathbf{elif}\;x \le 1.004501937429617973047375648440637726055 \cdot 10^{-191}:\\ \;\;\;\;j \cdot \left(t \cdot c - y \cdot i\right) + \left(\left(\left(-a\right) \cdot \left(x \cdot t\right) + \left(y \cdot z\right) \cdot x\right) - b \cdot \left(z \cdot c - i \cdot a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y \cdot \left(z \cdot x\right) + \left(t \cdot a\right) \cdot \left(-x\right)\right) - \left(\sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)} \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right) \cdot \sqrt[3]{b \cdot \left(z \cdot c - i \cdot a\right)}\right) + j \cdot \left(t \cdot c - y \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019172 
(FPCore (x y z t a b c i j)
  :name "Linear.Matrix:det33 from linear-1.19.1.3"
  (+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))) (* j (- (* c t) (* i y)))))