Average Error: 20.7 → 3.7
Time: 27.7s
Precision: 64
\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le -4.310655787273717085626057165340673522926 \cdot 10^{307}:\\ \;\;\;\;\frac{\frac{b}{z}}{c} + \left(\left(9 \cdot \frac{y}{\frac{z}{x}}\right) \cdot \frac{1}{c} - 4 \cdot \frac{t}{\frac{c}{a}}\right)\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le -5.714617762619817600956632832341409108159 \cdot 10^{-177}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le 1.671805885893177383054106113137405111152 \cdot 10^{-158}:\\ \;\;\;\;\left(\frac{9}{c} \cdot \left(\frac{y}{z} \cdot x\right) - \frac{t \cdot a}{c} \cdot 4\right) + \frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le 4.27457595021274958730075869238930553966 \cdot 10^{305}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c} + \left(\left(9 \cdot \frac{y}{\frac{z}{x}}\right) \cdot \frac{1}{c} - 4 \cdot \frac{t}{\frac{c}{a}}\right)\\ \end{array}\]
\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}\;\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}:\\
\;\;\;\;\frac{\frac{b}{z}}{c} + \left(\left(9 \cdot \frac{y}{\frac{z}{x}}\right) \cdot \frac{1}{c} - 4 \cdot \frac{t}{\frac{c}{a}}\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 1.671805885893177383054106113137405111152 \cdot 10^{-158}:\\
\;\;\;\;\left(\frac{9}{c} \cdot \left(\frac{y}{z} \cdot x\right) - \frac{t \cdot a}{c} \cdot 4\right) + \frac{\frac{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}{c \cdot z} \le 4.27457595021274958730075869238930553966 \cdot 10^{305}:\\
\;\;\;\;\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}:\\
\;\;\;\;\frac{\frac{b}{z}}{c} + \left(\left(9 \cdot \frac{y}{\frac{z}{x}}\right) \cdot \frac{1}{c} - 4 \cdot \frac{t}{\frac{c}{a}}\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r606021 = x;
        double r606022 = 9.0;
        double r606023 = r606021 * r606022;
        double r606024 = y;
        double r606025 = r606023 * r606024;
        double r606026 = z;
        double r606027 = 4.0;
        double r606028 = r606026 * r606027;
        double r606029 = t;
        double r606030 = r606028 * r606029;
        double r606031 = a;
        double r606032 = r606030 * r606031;
        double r606033 = r606025 - r606032;
        double r606034 = b;
        double r606035 = r606033 + r606034;
        double r606036 = c;
        double r606037 = r606026 * r606036;
        double r606038 = r606035 / r606037;
        return r606038;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r606039 = x;
        double r606040 = 9.0;
        double r606041 = r606039 * r606040;
        double r606042 = y;
        double r606043 = r606041 * r606042;
        double r606044 = z;
        double r606045 = 4.0;
        double r606046 = r606044 * r606045;
        double r606047 = t;
        double r606048 = r606046 * r606047;
        double r606049 = a;
        double r606050 = r606048 * r606049;
        double r606051 = r606043 - r606050;
        double r606052 = b;
        double r606053 = r606051 + r606052;
        double r606054 = c;
        double r606055 = r606054 * r606044;
        double r606056 = r606053 / r606055;
        double r606057 = -4.310655787273717e+307;
        bool r606058 = r606056 <= r606057;
        double r606059 = r606052 / r606044;
        double r606060 = r606059 / r606054;
        double r606061 = r606044 / r606039;
        double r606062 = r606042 / r606061;
        double r606063 = r606040 * r606062;
        double r606064 = 1.0;
        double r606065 = r606064 / r606054;
        double r606066 = r606063 * r606065;
        double r606067 = r606054 / r606049;
        double r606068 = r606047 / r606067;
        double r606069 = r606045 * r606068;
        double r606070 = r606066 - r606069;
        double r606071 = r606060 + r606070;
        double r606072 = -5.714617762619818e-177;
        bool r606073 = r606056 <= r606072;
        double r606074 = 1.6718058858931774e-158;
        bool r606075 = r606056 <= r606074;
        double r606076 = r606040 / r606054;
        double r606077 = r606042 / r606044;
        double r606078 = r606077 * r606039;
        double r606079 = r606076 * r606078;
        double r606080 = r606047 * r606049;
        double r606081 = r606080 / r606054;
        double r606082 = r606081 * r606045;
        double r606083 = r606079 - r606082;
        double r606084 = r606083 + r606060;
        double r606085 = 4.2745759502127496e+305;
        bool r606086 = r606056 <= r606085;
        double r606087 = r606086 ? r606056 : r606071;
        double r606088 = r606075 ? r606084 : r606087;
        double r606089 = r606073 ? r606056 : r606088;
        double r606090 = r606058 ? r606071 : r606089;
        return r606090;
}

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
Herbie3.7
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -1.100156740804104887233830094663413900721 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -0.0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.170887791174748819600820354912645756062 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 2.876823679546137226963937101710277849382 \cdot 10^{130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.383851504245631860711731716196098366993 \cdot 10^{158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < -4.310655787273717e+307 or 4.2745759502127496e+305 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))

    1. Initial program 63.4

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

    2. Simplified27.5

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

    3. Taylor expanded around 0 31.7

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

    4. Simplified17.3

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

    6. Applied div-inv17.4

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

    7. Applied associate-*r*17.4

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

    8. Simplified17.4

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

    10. Applied associate-/l*11.8

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

    if -4.310655787273717e+307 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < -5.714617762619818e-177 or 1.6718058858931774e-158 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < 4.2745759502127496e+305

    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)) < 1.6718058858931774e-158

    1. Initial program 26.4

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

    2. Simplified0.9

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

    3. Taylor expanded around 0 16.1

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

    4. Simplified1.7

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

    6. Applied div-inv1.7

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

    7. Applied associate-*l*1.8

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

    8. Simplified1.7

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

  4. Final simplification3.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le -4.310655787273717085626057165340673522926 \cdot 10^{307}:\\ \;\;\;\;\frac{\frac{b}{z}}{c} + \left(\left(9 \cdot \frac{y}{\frac{z}{x}}\right) \cdot \frac{1}{c} - 4 \cdot \frac{t}{\frac{c}{a}}\right)\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le -5.714617762619817600956632832341409108159 \cdot 10^{-177}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le 1.671805885893177383054106113137405111152 \cdot 10^{-158}:\\ \;\;\;\;\left(\frac{9}{c} \cdot \left(\frac{y}{z} \cdot x\right) - \frac{t \cdot a}{c} \cdot 4\right) + \frac{\frac{b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le 4.27457595021274958730075869238930553966 \cdot 10^{305}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{c \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z}}{c} + \left(\left(9 \cdot \frac{y}{\frac{z}{x}}\right) \cdot \frac{1}{c} - 4 \cdot \frac{t}{\frac{c}{a}}\right)\\ \end{array}\]

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)))