Average Error: 20.7 → 7.4
Time: 20.4s
Precision: 64
\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} = -\infty:\\ \;\;\;\;\frac{1}{\frac{c}{\left(b + \left(x \cdot 9\right) \cdot y\right) \cdot \frac{1}{z} - \left(a \cdot 4\right) \cdot t}}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le -7.871356618472160089166896848678735709787 \cdot 10^{-243}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 1.01445260762466640003481055345419026939 \cdot 10^{85}:\\ \;\;\;\;\left(\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \left(a \cdot 4\right) \cdot t\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 3.764994856652344411432804749280478465856 \cdot 10^{301}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c}{\left(b + \left(x \cdot 9\right) \cdot y\right) \cdot \frac{1}{z} - \left(a \cdot 4\right) \cdot t}}\\ \end{array}\]
\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} = -\infty:\\
\;\;\;\;\frac{1}{\frac{c}{\left(b + \left(x \cdot 9\right) \cdot y\right) \cdot \frac{1}{z} - \left(a \cdot 4\right) \cdot 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 -7.871356618472160089166896848678735709787 \cdot 10^{-243}:\\
\;\;\;\;\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{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 1.01445260762466640003481055345419026939 \cdot 10^{85}:\\
\;\;\;\;\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 3.764994856652344411432804749280478465856 \cdot 10^{301}:\\
\;\;\;\;\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}:\\
\;\;\;\;\frac{1}{\frac{c}{\left(b + \left(x \cdot 9\right) \cdot y\right) \cdot \frac{1}{z} - \left(a \cdot 4\right) \cdot t}}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r467940 = x;
        double r467941 = 9.0;
        double r467942 = r467940 * r467941;
        double r467943 = y;
        double r467944 = r467942 * r467943;
        double r467945 = z;
        double r467946 = 4.0;
        double r467947 = r467945 * r467946;
        double r467948 = t;
        double r467949 = r467947 * r467948;
        double r467950 = a;
        double r467951 = r467949 * r467950;
        double r467952 = r467944 - r467951;
        double r467953 = b;
        double r467954 = r467952 + r467953;
        double r467955 = c;
        double r467956 = r467945 * r467955;
        double r467957 = r467954 / r467956;
        return r467957;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r467958 = x;
        double r467959 = 9.0;
        double r467960 = r467958 * r467959;
        double r467961 = y;
        double r467962 = r467960 * r467961;
        double r467963 = z;
        double r467964 = 4.0;
        double r467965 = r467963 * r467964;
        double r467966 = t;
        double r467967 = r467965 * r467966;
        double r467968 = a;
        double r467969 = r467967 * r467968;
        double r467970 = r467962 - r467969;
        double r467971 = b;
        double r467972 = r467970 + r467971;
        double r467973 = c;
        double r467974 = r467963 * r467973;
        double r467975 = r467972 / r467974;
        double r467976 = -inf.0;
        bool r467977 = r467975 <= r467976;
        double r467978 = 1.0;
        double r467979 = r467971 + r467962;
        double r467980 = r467978 / r467963;
        double r467981 = r467979 * r467980;
        double r467982 = r467968 * r467964;
        double r467983 = r467982 * r467966;
        double r467984 = r467981 - r467983;
        double r467985 = r467973 / r467984;
        double r467986 = r467978 / r467985;
        double r467987 = -7.87135661847216e-243;
        bool r467988 = r467975 <= r467987;
        double r467989 = 1.0144526076246664e+85;
        bool r467990 = r467975 <= r467989;
        double r467991 = r467979 / r467963;
        double r467992 = r467991 - r467983;
        double r467993 = r467978 / r467973;
        double r467994 = r467992 * r467993;
        double r467995 = 3.7649948566523444e+301;
        bool r467996 = r467975 <= r467995;
        double r467997 = r467996 ? r467975 : r467986;
        double r467998 = r467990 ? r467994 : r467997;
        double r467999 = r467988 ? r467975 : r467998;
        double r468000 = r467977 ? r467986 : r467999;
        return r468000;
}

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
Target14.4
Herbie7.4
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -1.100156740804104887233830094663413900721 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -0.0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.170887791174748819600820354912645756062 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 2.876823679546137226963937101710277849382 \cdot 10^{130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.383851504245631860711731716196098366993 \cdot 10^{158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < -inf.0 or 3.7649948566523444e+301 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))

    1. Initial program 63.0

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

    2. Simplified25.1

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

    4. Applied clear-num25.2

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

    6. Applied div-inv25.2

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

    if -inf.0 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < -7.87135661847216e-243 or 1.0144526076246664e+85 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < 3.7649948566523444e+301

    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 -7.87135661847216e-243 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < 1.0144526076246664e+85

    1. Initial program 14.5

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

    2. Simplified1.9

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

    4. Applied div-inv1.9

      \[\leadsto \color{blue}{\left(\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \left(a \cdot 4\right) \cdot t\right) \cdot \frac{1}{c}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification7.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} = -\infty:\\ \;\;\;\;\frac{1}{\frac{c}{\left(b + \left(x \cdot 9\right) \cdot y\right) \cdot \frac{1}{z} - \left(a \cdot 4\right) \cdot t}}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le -7.871356618472160089166896848678735709787 \cdot 10^{-243}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 1.01445260762466640003481055345419026939 \cdot 10^{85}:\\ \;\;\;\;\left(\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \left(a \cdot 4\right) \cdot t\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 3.764994856652344411432804749280478465856 \cdot 10^{301}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{c}{\left(b + \left(x \cdot 9\right) \cdot y\right) \cdot \frac{1}{z} - \left(a \cdot 4\right) \cdot t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(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)) -1.1001567408041049e-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)) 1.17088779117474882e-53) (/ (+ (- (* (* x 9) y) (* (* z 4) (* t a))) b) (* z c)) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 2.8768236795461372e130) (- (+ (* (* 9 (/ y c)) (/ x z)) (/ b (* c z))) (* 4 (/ (* a t) c))) (if (< (/ (+ (- (* (* x 9) y) (* (* (* z 4) t) a)) b) (* z c)) 1.3838515042456319e158) (/ (+ (- (* (* 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)))