Average Error: 5.3 → 3.1
Time: 21.3s
Precision: 64
\[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le -8.801409940468935 \cdot 10^{+23}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(z \cdot x\right) \cdot 18.0\right) \cdot y\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \mathbf{elif}\;t \le 4.398142218816576 \cdot 10^{+19}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot y\right) \cdot \left(z \cdot \left(18.0 \cdot x\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(\sqrt[3]{y \cdot \left(18.0 \cdot x\right)} \cdot \left(\sqrt[3]{y \cdot \left(18.0 \cdot x\right)} \cdot \sqrt[3]{y \cdot \left(18.0 \cdot x\right)}\right)\right)\right) - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\\ \end{array}\]
\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k
↓
\begin{array}{l}
\mathbf{if}\;t \le -8.801409940468935 \cdot 10^{+23}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(z \cdot x\right) \cdot 18.0\right) \cdot y\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\

\mathbf{elif}\;t \le 4.398142218816576 \cdot 10^{+19}:\\
\;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot y\right) \cdot \left(z \cdot \left(18.0 \cdot x\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(\sqrt[3]{y \cdot \left(18.0 \cdot x\right)} \cdot \left(\sqrt[3]{y \cdot \left(18.0 \cdot x\right)} \cdot \sqrt[3]{y \cdot \left(18.0 \cdot x\right)}\right)\right)\right) - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\\

\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 r40168016 = x;
        double r40168017 = 18.0;
        double r40168018 = r40168016 * r40168017;
        double r40168019 = y;
        double r40168020 = r40168018 * r40168019;
        double r40168021 = z;
        double r40168022 = r40168020 * r40168021;
        double r40168023 = t;
        double r40168024 = r40168022 * r40168023;
        double r40168025 = a;
        double r40168026 = 4.0;
        double r40168027 = r40168025 * r40168026;
        double r40168028 = r40168027 * r40168023;
        double r40168029 = r40168024 - r40168028;
        double r40168030 = b;
        double r40168031 = c;
        double r40168032 = r40168030 * r40168031;
        double r40168033 = r40168029 + r40168032;
        double r40168034 = r40168016 * r40168026;
        double r40168035 = i;
        double r40168036 = r40168034 * r40168035;
        double r40168037 = r40168033 - r40168036;
        double r40168038 = j;
        double r40168039 = 27.0;
        double r40168040 = r40168038 * r40168039;
        double r40168041 = k;
        double r40168042 = r40168040 * r40168041;
        double r40168043 = r40168037 - r40168042;
        return r40168043;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i, double j, double k) {
        double r40168044 = t;
        double r40168045 = -8.801409940468935e+23;
        bool r40168046 = r40168044 <= r40168045;
        double r40168047 = b;
        double r40168048 = c;
        double r40168049 = r40168047 * r40168048;
        double r40168050 = z;
        double r40168051 = x;
        double r40168052 = r40168050 * r40168051;
        double r40168053 = 18.0;
        double r40168054 = r40168052 * r40168053;
        double r40168055 = y;
        double r40168056 = r40168054 * r40168055;
        double r40168057 = r40168056 * r40168044;
        double r40168058 = a;
        double r40168059 = 4.0;
        double r40168060 = r40168058 * r40168059;
        double r40168061 = r40168060 * r40168044;
        double r40168062 = r40168057 - r40168061;
        double r40168063 = r40168049 + r40168062;
        double r40168064 = r40168051 * r40168059;
        double r40168065 = i;
        double r40168066 = r40168064 * r40168065;
        double r40168067 = r40168063 - r40168066;
        double r40168068 = j;
        double r40168069 = 27.0;
        double r40168070 = k;
        double r40168071 = r40168069 * r40168070;
        double r40168072 = r40168068 * r40168071;
        double r40168073 = r40168067 - r40168072;
        double r40168074 = 4.398142218816576e+19;
        bool r40168075 = r40168044 <= r40168074;
        double r40168076 = r40168044 * r40168055;
        double r40168077 = r40168053 * r40168051;
        double r40168078 = r40168050 * r40168077;
        double r40168079 = r40168076 * r40168078;
        double r40168080 = r40168079 - r40168061;
        double r40168081 = r40168049 + r40168080;
        double r40168082 = r40168081 - r40168066;
        double r40168083 = r40168082 - r40168072;
        double r40168084 = r40168055 * r40168077;
        double r40168085 = cbrt(r40168084);
        double r40168086 = r40168085 * r40168085;
        double r40168087 = r40168085 * r40168086;
        double r40168088 = r40168050 * r40168087;
        double r40168089 = r40168044 * r40168088;
        double r40168090 = r40168089 - r40168061;
        double r40168091 = r40168090 + r40168049;
        double r40168092 = r40168091 - r40168066;
        double r40168093 = r40168068 * r40168069;
        double r40168094 = r40168093 * r40168070;
        double r40168095 = r40168092 - r40168094;
        double r40168096 = r40168075 ? r40168083 : r40168095;
        double r40168097 = r40168046 ? r40168073 : r40168096;
        return r40168097;
}

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

Original5.3
Target1.6
Herbie3.1
\[\begin{array}{l} \mathbf{if}\;t \lt -1.6210815397541398 \cdot 10^{-69}:\\ \;\;\;\;\left(\left(18.0 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4.0\right) - \left(\left(k \cdot j\right) \cdot 27.0 - c \cdot b\right)\\ \mathbf{elif}\;t \lt 165.68027943805222:\\ \;\;\;\;\left(\left(18.0 \cdot y\right) \cdot \left(x \cdot \left(z \cdot t\right)\right) - \left(a \cdot t + i \cdot x\right) \cdot 4.0\right) + \left(c \cdot b - 27.0 \cdot \left(k \cdot j\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(18.0 \cdot t\right) \cdot \left(\left(x \cdot y\right) \cdot z\right) - \left(a \cdot t + i \cdot x\right) \cdot 4.0\right) - \left(\left(k \cdot j\right) \cdot 27.0 - c \cdot b\right)\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if t < -8.801409940468935e+23

    1. Initial program 1.3

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*1.4

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{j \cdot \left(27.0 \cdot k\right)}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity1.4

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot \color{blue}{\left(1 \cdot t\right)} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\]

    6. Applied associate-*r*1.4

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot 1\right) \cdot t} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\]

    7. Simplified1.6

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(18.0 \cdot x\right) \cdot z\right) \cdot y\right)} \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\]
    8. Using strategy rm

    9. Applied *-un-lft-identity1.6

      \[\leadsto \left(\left(\left(\left(\left(\left(18.0 \cdot x\right) \cdot z\right) \cdot \color{blue}{\left(1 \cdot y\right)}\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\]

    10. Applied associate-*r*1.6

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(\left(18.0 \cdot x\right) \cdot z\right) \cdot 1\right) \cdot y\right)} \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\]

    11. Simplified1.7

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(\left(z \cdot x\right) \cdot 18.0\right)} \cdot y\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\]

    if -8.801409940468935e+23 < t < 4.398142218816576e+19

    1. Initial program 7.1

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    2. Using strategy rm

    3. Applied associate-*l*7.1

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \color{blue}{j \cdot \left(27.0 \cdot k\right)}\]
    4. Using strategy rm

    5. Applied *-un-lft-identity7.1

      \[\leadsto \left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot \color{blue}{\left(1 \cdot t\right)} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\]

    6. Applied associate-*r*7.1

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot 1\right) \cdot t} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\]

    7. Simplified7.1

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(\left(18.0 \cdot x\right) \cdot z\right) \cdot y\right)} \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\]
    8. Using strategy rm

    9. Applied associate-*l*3.7

      \[\leadsto \left(\left(\left(\color{blue}{\left(\left(18.0 \cdot x\right) \cdot z\right) \cdot \left(y \cdot t\right)} - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\]

    if 4.398142218816576e+19 < t

    1. Initial program 1.9

      \[\left(\left(\left(\left(\left(\left(x \cdot 18.0\right) \cdot y\right) \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
    2. Using strategy rm

    3. Applied add-cube-cbrt2.1

      \[\leadsto \left(\left(\left(\left(\color{blue}{\left(\left(\sqrt[3]{\left(x \cdot 18.0\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot 18.0\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot 18.0\right) \cdot y}\right)} \cdot z\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\]
  3. Recombined 3 regimes into one program.

  4. Final simplification3.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -8.801409940468935 \cdot 10^{+23}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(\left(\left(z \cdot x\right) \cdot 18.0\right) \cdot y\right) \cdot t - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \mathbf{elif}\;t \le 4.398142218816576 \cdot 10^{+19}:\\ \;\;\;\;\left(\left(b \cdot c + \left(\left(t \cdot y\right) \cdot \left(z \cdot \left(18.0 \cdot x\right)\right) - \left(a \cdot 4.0\right) \cdot t\right)\right) - \left(x \cdot 4.0\right) \cdot i\right) - j \cdot \left(27.0 \cdot k\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(t \cdot \left(z \cdot \left(\sqrt[3]{y \cdot \left(18.0 \cdot x\right)} \cdot \left(\sqrt[3]{y \cdot \left(18.0 \cdot x\right)} \cdot \sqrt[3]{y \cdot \left(18.0 \cdot x\right)}\right)\right)\right) - \left(a \cdot 4.0\right) \cdot t\right) + b \cdot c\right) - \left(x \cdot 4.0\right) \cdot i\right) - \left(j \cdot 27.0\right) \cdot k\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t a b c i j k)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, E"

  :herbie-target
  (if (< t -1.6210815397541398e-69) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b))) (if (< t 165.68027943805222) (+ (- (* (* 18.0 y) (* x (* z t))) (* (+ (* a t) (* i x)) 4.0)) (- (* c b) (* 27.0 (* k j)))) (- (- (* (* 18.0 t) (* (* x y) z)) (* (+ (* a t) (* i x)) 4.0)) (- (* (* k j) 27.0) (* c b)))))

  (- (- (+ (- (* (* (* (* x 18.0) y) z) t) (* (* a 4.0) t)) (* b c)) (* (* x 4.0) i)) (* (* j 27.0) k)))