Average Error: 20.7 → 4.9
Time: 17.8s
Precision: 64
\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le -2.049750915246272776707763168040883621167 \cdot 10^{-94}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z \cdot c}{y}}\right) - 4 \cdot \frac{1}{\frac{\frac{c}{a}}{t}}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 3.971157461644661283027653876483402071819 \cdot 10^{51}:\\ \;\;\;\;\left(\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \left(a \cdot 4\right) \cdot t\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 4.994986043275433565391109757715461612213 \cdot 10^{297}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z}{y} \cdot c}\right) - 4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array}\]
\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le -2.049750915246272776707763168040883621167 \cdot 10^{-94}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z \cdot c}{y}}\right) - 4 \cdot \frac{1}{\frac{\frac{c}{a}}{t}}\\

\mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 3.971157461644661283027653876483402071819 \cdot 10^{51}:\\
\;\;\;\;\left(\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \left(a \cdot 4\right) \cdot t\right) \cdot \frac{1}{c}\\

\mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 4.994986043275433565391109757715461612213 \cdot 10^{297}:\\
\;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z}{y} \cdot c}\right) - 4 \cdot \frac{t}{\frac{c}{a}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r461885 = x;
        double r461886 = 9.0;
        double r461887 = r461885 * r461886;
        double r461888 = y;
        double r461889 = r461887 * r461888;
        double r461890 = z;
        double r461891 = 4.0;
        double r461892 = r461890 * r461891;
        double r461893 = t;
        double r461894 = r461892 * r461893;
        double r461895 = a;
        double r461896 = r461894 * r461895;
        double r461897 = r461889 - r461896;
        double r461898 = b;
        double r461899 = r461897 + r461898;
        double r461900 = c;
        double r461901 = r461890 * r461900;
        double r461902 = r461899 / r461901;
        return r461902;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r461903 = x;
        double r461904 = 9.0;
        double r461905 = r461903 * r461904;
        double r461906 = y;
        double r461907 = r461905 * r461906;
        double r461908 = z;
        double r461909 = 4.0;
        double r461910 = r461908 * r461909;
        double r461911 = t;
        double r461912 = r461910 * r461911;
        double r461913 = a;
        double r461914 = r461912 * r461913;
        double r461915 = r461907 - r461914;
        double r461916 = b;
        double r461917 = r461915 + r461916;
        double r461918 = c;
        double r461919 = r461908 * r461918;
        double r461920 = r461917 / r461919;
        double r461921 = -2.0497509152462728e-94;
        bool r461922 = r461920 <= r461921;
        double r461923 = r461916 / r461919;
        double r461924 = r461919 / r461906;
        double r461925 = r461903 / r461924;
        double r461926 = r461904 * r461925;
        double r461927 = r461923 + r461926;
        double r461928 = 1.0;
        double r461929 = r461918 / r461913;
        double r461930 = r461929 / r461911;
        double r461931 = r461928 / r461930;
        double r461932 = r461909 * r461931;
        double r461933 = r461927 - r461932;
        double r461934 = 3.971157461644661e+51;
        bool r461935 = r461920 <= r461934;
        double r461936 = r461916 + r461907;
        double r461937 = r461936 / r461908;
        double r461938 = r461913 * r461909;
        double r461939 = r461938 * r461911;
        double r461940 = r461937 - r461939;
        double r461941 = r461928 / r461918;
        double r461942 = r461940 * r461941;
        double r461943 = 4.9949860432754336e+297;
        bool r461944 = r461920 <= r461943;
        double r461945 = r461908 / r461906;
        double r461946 = r461945 * r461918;
        double r461947 = r461903 / r461946;
        double r461948 = r461904 * r461947;
        double r461949 = r461923 + r461948;
        double r461950 = r461911 / r461929;
        double r461951 = r461909 * r461950;
        double r461952 = r461949 - r461951;
        double r461953 = r461944 ? r461920 : r461952;
        double r461954 = r461935 ? r461942 : r461953;
        double r461955 = r461922 ? r461933 : r461954;
        return r461955;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original20.7
Target14.7
Herbie4.9
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -1.100156740804104887233830094663413900721 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -0.0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.170887791174748819600820354912645756062 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 2.876823679546137226963937101710277849382 \cdot 10^{130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.383851504245631860711731716196098366993 \cdot 10^{158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < -2.0497509152462728e-94

    1. Initial program 14.4

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

    2. Simplified14.0

      \[\leadsto \color{blue}{\frac{\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \left(a \cdot 4\right) \cdot t}{c}}\]

    3. Taylor expanded around 0 8.6

      \[\leadsto \color{blue}{\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{t \cdot a}{c}}\]
    4. Using strategy rm

    5. Applied associate-/l*7.9

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \color{blue}{\frac{t}{\frac{c}{a}}}\]
    6. Using strategy rm

    7. Applied associate-/l*6.6

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\frac{x}{\frac{z \cdot c}{y}}}\right) - 4 \cdot \frac{t}{\frac{c}{a}}\]
    8. Using strategy rm

    9. Applied clear-num6.6

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z \cdot c}{y}}\right) - 4 \cdot \color{blue}{\frac{1}{\frac{\frac{c}{a}}{t}}}\]

    if -2.0497509152462728e-94 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < 3.971157461644661e+51

    1. Initial program 14.2

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

    2. Simplified1.3

      \[\leadsto \color{blue}{\frac{\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \left(a \cdot 4\right) \cdot t}{c}}\]
    3. Using strategy rm

    4. Applied div-inv1.4

      \[\leadsto \color{blue}{\left(\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \left(a \cdot 4\right) \cdot t\right) \cdot \frac{1}{c}}\]

    if 3.971157461644661e+51 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < 4.9949860432754336e+297

    1. Initial program 0.7

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

    if 4.9949860432754336e+297 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))

    1. Initial program 61.3

      \[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

    2. Simplified28.2

      \[\leadsto \color{blue}{\frac{\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \left(a \cdot 4\right) \cdot t}{c}}\]

    3. Taylor expanded around 0 30.7

      \[\leadsto \color{blue}{\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{t \cdot a}{c}}\]
    4. Using strategy rm

    5. Applied associate-/l*25.4

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \color{blue}{\frac{t}{\frac{c}{a}}}\]
    6. Using strategy rm

    7. Applied associate-/l*15.6

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\frac{x}{\frac{z \cdot c}{y}}}\right) - 4 \cdot \frac{t}{\frac{c}{a}}\]

    8. Taylor expanded around 0 15.6

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\color{blue}{\frac{z \cdot c}{y}}}\right) - 4 \cdot \frac{t}{\frac{c}{a}}\]

    9. Simplified11.3

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\color{blue}{\frac{z}{y} \cdot c}}\right) - 4 \cdot \frac{t}{\frac{c}{a}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification4.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le -2.049750915246272776707763168040883621167 \cdot 10^{-94}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z \cdot c}{y}}\right) - 4 \cdot \frac{1}{\frac{\frac{c}{a}}{t}}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 3.971157461644661283027653876483402071819 \cdot 10^{51}:\\ \;\;\;\;\left(\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \left(a \cdot 4\right) \cdot t\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 4.994986043275433565391109757715461612213 \cdot 10^{297}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z}{y} \cdot c}\right) - 4 \cdot \frac{t}{\frac{c}{a}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"
  :precision binary64

  :herbie-target
  (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) -0.0) (/ (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (- (+ (* 9 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)))