Average Error: 20.7 → 5.0
Time: 20.5s
Precision: 64
\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le -4.310655787273717085626057165340673522926 \cdot 10^{307}:\\ \;\;\;\;\left(\frac{b}{c \cdot z} + \frac{x}{\frac{c \cdot z}{y}} \cdot 9\right) - 4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le -5.714617762619817600956632832341409108159 \cdot 10^{-177}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le 1.508521702468635068346725200584782078703 \cdot 10^{-260}:\\ \;\;\;\;\frac{\frac{9 \cdot \left(y \cdot x\right) + b}{z} - t \cdot \left(a \cdot 4\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le 6.624712766971525157760939835591736702834 \cdot 10^{252}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{x}{z} \cdot \frac{y}{c}\right) \cdot 9 + \frac{b}{c \cdot z}\right) - \frac{t \cdot a}{c} \cdot 4\\ \end{array}\]
\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}{c \cdot z} \le -4.310655787273717085626057165340673522926 \cdot 10^{307}:\\
\;\;\;\;\left(\frac{b}{c \cdot z} + \frac{x}{\frac{c \cdot z}{y}} \cdot 9\right) - 4 \cdot \left(t \cdot \frac{a}{c}\right)\\

\mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le -5.714617762619817600956632832341409108159 \cdot 10^{-177}:\\
\;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\

\mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le 1.508521702468635068346725200584782078703 \cdot 10^{-260}:\\
\;\;\;\;\frac{\frac{9 \cdot \left(y \cdot x\right) + b}{z} - t \cdot \left(a \cdot 4\right)}{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}{c \cdot z} \le 6.624712766971525157760939835591736702834 \cdot 10^{252}:\\
\;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r36383003 = x;
        double r36383004 = 9.0;
        double r36383005 = r36383003 * r36383004;
        double r36383006 = y;
        double r36383007 = r36383005 * r36383006;
        double r36383008 = z;
        double r36383009 = 4.0;
        double r36383010 = r36383008 * r36383009;
        double r36383011 = t;
        double r36383012 = r36383010 * r36383011;
        double r36383013 = a;
        double r36383014 = r36383012 * r36383013;
        double r36383015 = r36383007 - r36383014;
        double r36383016 = b;
        double r36383017 = r36383015 + r36383016;
        double r36383018 = c;
        double r36383019 = r36383008 * r36383018;
        double r36383020 = r36383017 / r36383019;
        return r36383020;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r36383021 = x;
        double r36383022 = 9.0;
        double r36383023 = r36383021 * r36383022;
        double r36383024 = y;
        double r36383025 = r36383023 * r36383024;
        double r36383026 = z;
        double r36383027 = 4.0;
        double r36383028 = r36383026 * r36383027;
        double r36383029 = t;
        double r36383030 = r36383028 * r36383029;
        double r36383031 = a;
        double r36383032 = r36383030 * r36383031;
        double r36383033 = r36383025 - r36383032;
        double r36383034 = b;
        double r36383035 = r36383033 + r36383034;
        double r36383036 = c;
        double r36383037 = r36383036 * r36383026;
        double r36383038 = r36383035 / r36383037;
        double r36383039 = -4.310655787273717e+307;
        bool r36383040 = r36383038 <= r36383039;
        double r36383041 = r36383034 / r36383037;
        double r36383042 = r36383037 / r36383024;
        double r36383043 = r36383021 / r36383042;
        double r36383044 = r36383043 * r36383022;
        double r36383045 = r36383041 + r36383044;
        double r36383046 = r36383031 / r36383036;
        double r36383047 = r36383029 * r36383046;
        double r36383048 = r36383027 * r36383047;
        double r36383049 = r36383045 - r36383048;
        double r36383050 = -5.714617762619818e-177;
        bool r36383051 = r36383038 <= r36383050;
        double r36383052 = 1.508521702468635e-260;
        bool r36383053 = r36383038 <= r36383052;
        double r36383054 = r36383024 * r36383021;
        double r36383055 = r36383022 * r36383054;
        double r36383056 = r36383055 + r36383034;
        double r36383057 = r36383056 / r36383026;
        double r36383058 = r36383031 * r36383027;
        double r36383059 = r36383029 * r36383058;
        double r36383060 = r36383057 - r36383059;
        double r36383061 = r36383060 / r36383036;
        double r36383062 = 6.624712766971525e+252;
        bool r36383063 = r36383038 <= r36383062;
        double r36383064 = r36383021 / r36383026;
        double r36383065 = r36383024 / r36383036;
        double r36383066 = r36383064 * r36383065;
        double r36383067 = r36383066 * r36383022;
        double r36383068 = r36383067 + r36383041;
        double r36383069 = r36383029 * r36383031;
        double r36383070 = r36383069 / r36383036;
        double r36383071 = r36383070 * r36383027;
        double r36383072 = r36383068 - r36383071;
        double r36383073 = r36383063 ? r36383038 : r36383072;
        double r36383074 = r36383053 ? r36383061 : r36383073;
        double r36383075 = r36383051 ? r36383038 : r36383074;
        double r36383076 = r36383040 ? r36383049 : r36383075;
        return r36383076;
}

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
Target14.5
Herbie5.0
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -1.100156740804104887233830094663413900721 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -0.0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.170887791174748819600820354912645756062 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 2.876823679546137226963937101710277849382 \cdot 10^{130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.383851504245631860711731716196098366993 \cdot 10^{158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Derivation

  1. Split input into 4 regimes

  2. if (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < -4.310655787273717e+307

    1. Initial program 63.5

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

    2. Simplified28.8

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

    3. Taylor expanded around 0 34.3

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

    5. Applied associate-/l*15.6

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

    7. Applied *-un-lft-identity15.6

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

    8. Applied times-frac9.0

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

    9. Simplified9.0

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

    if -4.310655787273717e+307 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < -5.714617762619818e-177 or 1.508521702468635e-260 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < 6.624712766971525e+252

    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 -5.714617762619818e-177 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < 1.508521702468635e-260

    1. Initial program 30.8

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

    2. Simplified0.7

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

    3. Taylor expanded around 0 0.8

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

    if 6.624712766971525e+252 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))

    1. Initial program 53.7

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

    2. Simplified26.4

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

    3. Taylor expanded around 0 26.8

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

    5. Applied times-frac17.2

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

  4. Final simplification5.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le -4.310655787273717085626057165340673522926 \cdot 10^{307}:\\ \;\;\;\;\left(\frac{b}{c \cdot z} + \frac{x}{\frac{c \cdot z}{y}} \cdot 9\right) - 4 \cdot \left(t \cdot \frac{a}{c}\right)\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le -5.714617762619817600956632832341409108159 \cdot 10^{-177}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le 1.508521702468635068346725200584782078703 \cdot 10^{-260}:\\ \;\;\;\;\frac{\frac{9 \cdot \left(y \cdot x\right) + b}{z} - t \cdot \left(a \cdot 4\right)}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le 6.624712766971525157760939835591736702834 \cdot 10^{252}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\frac{x}{z} \cdot \frac{y}{c}\right) \cdot 9 + \frac{b}{c \cdot z}\right) - \frac{t \cdot a}{c} \cdot 4\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, J"

  :herbie-target
  (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -1.100156740804105e-171) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) -0.0) (/ (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) z) c) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.1708877911747488e-53) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 2.876823679546137e+130) (- (+ (* (* 9.0 (/ y c)) (/ x z)) (/ b (* c z))) (* 4.0 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) 1.3838515042456319e+158) (/ (+ (- (* (* x 9.0) y) (* (* z 4.0) (* t a))) b) (* z c)) (- (+ (* 9.0 (* (/ y (* c z)) x)) (/ b (* c z))) (* 4.0 (/ (* a t) c))))))))

  (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)))