Average Error: 5.7 → 5.9
Time: 18.6s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -2.533140772447663761050877991824058359518 \cdot 10^{144}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\sqrt[3]{t} \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right)\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;x \le -2.533140772447663761050877991824058359518 \cdot 10^{144}:\\
\;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\sqrt[3]{t} \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right)\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\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 k) {
        double r435297 = x;
        double r435298 = 18.0;
        double r435299 = r435297 * r435298;
        double r435300 = y;
        double r435301 = r435299 * r435300;
        double r435302 = z;
        double r435303 = r435301 * r435302;
        double r435304 = t;
        double r435305 = r435303 * r435304;
        double r435306 = a;
        double r435307 = 4.0;
        double r435308 = r435306 * r435307;
        double r435309 = r435308 * r435304;
        double r435310 = r435305 - r435309;
        double r435311 = b;
        double r435312 = c;
        double r435313 = r435311 * r435312;
        double r435314 = r435310 + r435313;
        double r435315 = r435297 * r435307;
        double r435316 = i;
        double r435317 = r435315 * r435316;
        double r435318 = r435314 - r435317;
        double r435319 = j;
        double r435320 = 27.0;
        double r435321 = r435319 * r435320;
        double r435322 = k;
        double r435323 = r435321 * r435322;
        double r435324 = r435318 - r435323;
        return r435324;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r435325 = x;
        double r435326 = -2.5331407724476638e+144;
        bool r435327 = r435325 <= r435326;
        double r435328 = t;
        double r435329 = 0.0;
        double r435330 = a;
        double r435331 = 4.0;
        double r435332 = r435330 * r435331;
        double r435333 = r435329 - r435332;
        double r435334 = r435328 * r435333;
        double r435335 = b;
        double r435336 = c;
        double r435337 = r435335 * r435336;
        double r435338 = r435325 * r435331;
        double r435339 = i;
        double r435340 = r435338 * r435339;
        double r435341 = j;
        double r435342 = 27.0;
        double r435343 = r435341 * r435342;
        double r435344 = k;
        double r435345 = r435343 * r435344;
        double r435346 = r435340 + r435345;
        double r435347 = r435337 - r435346;
        double r435348 = r435334 + r435347;
        double r435349 = cbrt(r435328);
        double r435350 = r435349 * r435349;
        double r435351 = 18.0;
        double r435352 = y;
        double r435353 = r435351 * r435352;
        double r435354 = r435325 * r435353;
        double r435355 = z;
        double r435356 = r435354 * r435355;
        double r435357 = r435356 - r435332;
        double r435358 = r435349 * r435357;
        double r435359 = r435350 * r435358;
        double r435360 = r435342 * r435344;
        double r435361 = r435341 * r435360;
        double r435362 = r435340 + r435361;
        double r435363 = r435337 - r435362;
        double r435364 = r435359 + r435363;
        double r435365 = r435327 ? r435348 : r435364;
        return r435365;
}

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

Bits error versus k

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.7
Target1.8
Herbie5.9
\[\begin{array}{l} \mathbf{if}\;t \lt -1.62108153975413982700795070153457058168 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \mathbf{elif}\;t \lt 165.6802794380522243500308832153677940369:\\ \;\;\;\;\left(\left(18 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) + \left(c \cdot b - 27 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4\right) - \left(\left(k \cdot j\right) \cdot 27 - c \cdot b\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -2.5331407724476638e+144

    1. Initial program 19.4

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    2. Simplified19.4

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)}\]

    3. Taylor expanded around 0 15.5

      \[\leadsto t \cdot \left(\color{blue}{0} - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\]

    if -2.5331407724476638e+144 < x

    1. Initial program 4.7

      \[\left(\left(\left(\left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4\right) \cdot i\right) - \left(j \cdot 27\right) \cdot k\]

    2. Simplified4.7

      \[\leadsto \color{blue}{t \cdot \left(\left(\left(x \cdot 18\right) \cdot y\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)}\]
    3. Using strategy rm

    4. Applied associate-*l*4.7

      \[\leadsto t \cdot \left(\color{blue}{\left(x \cdot \left(18 \cdot y\right)\right)} \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\]
    5. Using strategy rm

    6. Applied associate-*l*4.7

      \[\leadsto t \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \color{blue}{j \cdot \left(27 \cdot k\right)}\right)\right)\]
    7. Using strategy rm

    8. Applied add-cube-cbrt5.1

      \[\leadsto \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)} \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\]

    9. Applied associate-*l*5.1

      \[\leadsto \color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\sqrt[3]{t} \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right)\right)} + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification5.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -2.533140772447663761050877991824058359518 \cdot 10^{144}:\\ \;\;\;\;t \cdot \left(0 - a \cdot 4\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + \left(j \cdot 27\right) \cdot k\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(\sqrt[3]{t} \cdot \left(\left(x \cdot \left(18 \cdot y\right)\right) \cdot z - a \cdot 4\right)\right) + \left(b \cdot c - \left(\left(x \cdot 4\right) \cdot i + j \cdot \left(27 \cdot k\right)\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019298 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"
  :precision binary64

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b))) (if (< t 165.680279438052224) (+ (- (* (* 18 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4)) (- (* c b) (* 27 (* k j)))) (- (- (* (* 18 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4)) (- (* (* k j) 27) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18) y) z) t) (* (* a 4) t)) (* b c)) (* (* x 4) i)) (* (* j 27) k)))