Average Error: 20.3 → 8.1
Time: 7.1s
Precision: 64
\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \le -1.2280089963750865 \cdot 10^{182}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(x \cdot \left(\frac{1}{z} \cdot \frac{y}{c}\right)\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le -6.0836397381801304 \cdot 10^{-281}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.24275387751464733 \cdot 10^{-83}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(x \cdot \left(\frac{1}{z} \cdot \frac{y}{c}\right)\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.04800748302761941 \cdot 10^{208}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\sqrt[3]{b} \cdot \sqrt[3]{b}}{z} \cdot \frac{\sqrt[3]{b}}{c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\ \end{array}\]
\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}\;\left(x \cdot 9\right) \cdot y \le -1.2280089963750865 \cdot 10^{182}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(x \cdot \left(\frac{1}{z} \cdot \frac{y}{c}\right)\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\

\mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le -6.0836397381801304 \cdot 10^{-281}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)\\

\mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.24275387751464733 \cdot 10^{-83}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(x \cdot \left(\frac{1}{z} \cdot \frac{y}{c}\right)\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\

\mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.04800748302761941 \cdot 10^{208}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{\sqrt[3]{b} \cdot \sqrt[3]{b}}{z} \cdot \frac{\sqrt[3]{b}}{c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r596966 = x;
        double r596967 = 9.0;
        double r596968 = r596966 * r596967;
        double r596969 = y;
        double r596970 = r596968 * r596969;
        double r596971 = z;
        double r596972 = 4.0;
        double r596973 = r596971 * r596972;
        double r596974 = t;
        double r596975 = r596973 * r596974;
        double r596976 = a;
        double r596977 = r596975 * r596976;
        double r596978 = r596970 - r596977;
        double r596979 = b;
        double r596980 = r596978 + r596979;
        double r596981 = c;
        double r596982 = r596971 * r596981;
        double r596983 = r596980 / r596982;
        return r596983;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r596984 = x;
        double r596985 = 9.0;
        double r596986 = r596984 * r596985;
        double r596987 = y;
        double r596988 = r596986 * r596987;
        double r596989 = -1.2280089963750865e+182;
        bool r596990 = r596988 <= r596989;
        double r596991 = b;
        double r596992 = z;
        double r596993 = c;
        double r596994 = r596992 * r596993;
        double r596995 = r596991 / r596994;
        double r596996 = 1.0;
        double r596997 = r596996 / r596992;
        double r596998 = r596987 / r596993;
        double r596999 = r596997 * r596998;
        double r597000 = r596984 * r596999;
        double r597001 = r596985 * r597000;
        double r597002 = r596995 + r597001;
        double r597003 = 4.0;
        double r597004 = a;
        double r597005 = cbrt(r596993);
        double r597006 = r597005 * r597005;
        double r597007 = r597004 / r597006;
        double r597008 = t;
        double r597009 = r597008 / r597005;
        double r597010 = r597007 * r597009;
        double r597011 = r597003 * r597010;
        double r597012 = r597002 - r597011;
        double r597013 = -6.08363973818013e-281;
        bool r597014 = r596988 <= r597013;
        double r597015 = r596984 * r596987;
        double r597016 = r597015 / r596994;
        double r597017 = r596985 * r597016;
        double r597018 = r596995 + r597017;
        double r597019 = r597004 * r597008;
        double r597020 = r596996 / r596993;
        double r597021 = r597019 * r597020;
        double r597022 = r597003 * r597021;
        double r597023 = r597018 - r597022;
        double r597024 = 1.2427538775146473e-83;
        bool r597025 = r596988 <= r597024;
        double r597026 = 1.0480074830276194e+208;
        bool r597027 = r596988 <= r597026;
        double r597028 = r597008 / r596993;
        double r597029 = r597004 * r597028;
        double r597030 = r597003 * r597029;
        double r597031 = r597018 - r597030;
        double r597032 = cbrt(r596991);
        double r597033 = r597032 * r597032;
        double r597034 = r597033 / r596992;
        double r597035 = r597032 / r596993;
        double r597036 = r597034 * r597035;
        double r597037 = r596984 / r596992;
        double r597038 = r597037 * r596998;
        double r597039 = r596985 * r597038;
        double r597040 = r597036 + r597039;
        double r597041 = r597040 - r597011;
        double r597042 = r597027 ? r597031 : r597041;
        double r597043 = r597025 ? r597012 : r597042;
        double r597044 = r597014 ? r597023 : r597043;
        double r597045 = r596990 ? r597012 : r597044;
        return r597045;
}

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

Original20.3
Target14.9
Herbie8.1
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -1.10015674080410512 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -0.0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.17088779117474882 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 2.8768236795461372 \cdot 10^{130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.3838515042456319 \cdot 10^{158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (* (* x 9.0) y) < -1.2280089963750865e+182 or -6.08363973818013e-281 < (* (* x 9.0) y) < 1.2427538775146473e-83

    1. Initial program 21.2

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

    2. Taylor expanded around 0 13.0

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

    4. Applied add-cube-cbrt13.4

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

    5. Applied times-frac12.4

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

    7. Applied times-frac9.4

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

    9. Applied div-inv9.4

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \left(\color{blue}{\left(x \cdot \frac{1}{z}\right)} \cdot \frac{y}{c}\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\]

    10. Applied associate-*l*8.8

      \[\leadsto \left(\frac{b}{z \cdot c} + 9 \cdot \color{blue}{\left(x \cdot \left(\frac{1}{z} \cdot \frac{y}{c}\right)\right)}\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\]

    if -1.2280089963750865e+182 < (* (* x 9.0) y) < -6.08363973818013e-281

    1. Initial program 16.8

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

    2. Taylor expanded around 0 7.3

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

    4. Applied div-inv7.3

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

    if 1.2427538775146473e-83 < (* (* x 9.0) y) < 1.0480074830276194e+208

    1. Initial program 16.7

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

    2. Taylor expanded around 0 8.2

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

    4. Applied *-un-lft-identity8.2

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

    5. Applied times-frac6.9

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

    6. Simplified6.9

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

    if 1.0480074830276194e+208 < (* (* x 9.0) y)

    1. Initial program 41.1

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

    2. Taylor expanded around 0 36.2

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

    4. Applied add-cube-cbrt36.2

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

    5. Applied times-frac34.3

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

    7. Applied times-frac11.5

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

    9. Applied add-cube-cbrt11.6

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

    10. Applied times-frac11.3

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

  4. Final simplification8.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \le -1.2280089963750865 \cdot 10^{182}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(x \cdot \left(\frac{1}{z} \cdot \frac{y}{c}\right)\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le -6.0836397381801304 \cdot 10^{-281}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(\left(a \cdot t\right) \cdot \frac{1}{c}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.24275387751464733 \cdot 10^{-83}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(x \cdot \left(\frac{1}{z} \cdot \frac{y}{c}\right)\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.04800748302761941 \cdot 10^{208}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{\sqrt[3]{b} \cdot \sqrt[3]{b}}{z} \cdot \frac{\sqrt[3]{b}}{c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020035 
(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)) -1.1001567408041051e-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)))