Average Error: 19.6 → 7.1
Time: 18.0s
Precision: 64
\[\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le -1.5906234503561492 \cdot 10^{-156}:\\ \;\;\;\;\left(\frac{b}{c \cdot z} + \frac{x}{\frac{c \cdot z}{y}} \cdot 9.0\right) - 4.0 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le 1.4789431977947666 \cdot 10^{+196}:\\ \;\;\;\;\frac{\left(9.0 \cdot \frac{y \cdot x}{z} + \frac{b}{z}\right) - \left(4.0 \cdot t\right) \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{c \cdot z} + \frac{x}{\frac{c \cdot z}{y}} \cdot 9.0\right) - \left(a \cdot \frac{t}{c}\right) \cdot 4.0\\ \end{array}\]
\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}
↓
\begin{array}{l}
\mathbf{if}\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le -1.5906234503561492 \cdot 10^{-156}:\\
\;\;\;\;\left(\frac{b}{c \cdot z} + \frac{x}{\frac{c \cdot z}{y}} \cdot 9.0\right) - 4.0 \cdot \frac{a}{\frac{c}{t}}\\

\mathbf{elif}\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le 1.4789431977947666 \cdot 10^{+196}:\\
\;\;\;\;\frac{\left(9.0 \cdot \frac{y \cdot x}{z} + \frac{b}{z}\right) - \left(4.0 \cdot t\right) \cdot a}{c}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{b}{c \cdot z} + \frac{x}{\frac{c \cdot z}{y}} \cdot 9.0\right) - \left(a \cdot \frac{t}{c}\right) \cdot 4.0\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r36127013 = x;
        double r36127014 = 9.0;
        double r36127015 = r36127013 * r36127014;
        double r36127016 = y;
        double r36127017 = r36127015 * r36127016;
        double r36127018 = z;
        double r36127019 = 4.0;
        double r36127020 = r36127018 * r36127019;
        double r36127021 = t;
        double r36127022 = r36127020 * r36127021;
        double r36127023 = a;
        double r36127024 = r36127022 * r36127023;
        double r36127025 = r36127017 - r36127024;
        double r36127026 = b;
        double r36127027 = r36127025 + r36127026;
        double r36127028 = c;
        double r36127029 = r36127018 * r36127028;
        double r36127030 = r36127027 / r36127029;
        return r36127030;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r36127031 = x;
        double r36127032 = 9.0;
        double r36127033 = r36127031 * r36127032;
        double r36127034 = y;
        double r36127035 = r36127033 * r36127034;
        double r36127036 = z;
        double r36127037 = 4.0;
        double r36127038 = r36127036 * r36127037;
        double r36127039 = t;
        double r36127040 = r36127038 * r36127039;
        double r36127041 = a;
        double r36127042 = r36127040 * r36127041;
        double r36127043 = r36127035 - r36127042;
        double r36127044 = b;
        double r36127045 = r36127043 + r36127044;
        double r36127046 = c;
        double r36127047 = r36127046 * r36127036;
        double r36127048 = r36127045 / r36127047;
        double r36127049 = -1.5906234503561492e-156;
        bool r36127050 = r36127048 <= r36127049;
        double r36127051 = r36127044 / r36127047;
        double r36127052 = r36127047 / r36127034;
        double r36127053 = r36127031 / r36127052;
        double r36127054 = r36127053 * r36127032;
        double r36127055 = r36127051 + r36127054;
        double r36127056 = r36127046 / r36127039;
        double r36127057 = r36127041 / r36127056;
        double r36127058 = r36127037 * r36127057;
        double r36127059 = r36127055 - r36127058;
        double r36127060 = 1.4789431977947666e+196;
        bool r36127061 = r36127048 <= r36127060;
        double r36127062 = r36127034 * r36127031;
        double r36127063 = r36127062 / r36127036;
        double r36127064 = r36127032 * r36127063;
        double r36127065 = r36127044 / r36127036;
        double r36127066 = r36127064 + r36127065;
        double r36127067 = r36127037 * r36127039;
        double r36127068 = r36127067 * r36127041;
        double r36127069 = r36127066 - r36127068;
        double r36127070 = r36127069 / r36127046;
        double r36127071 = r36127039 / r36127046;
        double r36127072 = r36127041 * r36127071;
        double r36127073 = r36127072 * r36127037;
        double r36127074 = r36127055 - r36127073;
        double r36127075 = r36127061 ? r36127070 : r36127074;
        double r36127076 = r36127050 ? r36127059 : r36127075;
        return r36127076;
}

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

Original19.6
Target13.7
Herbie7.1
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -1.100156740804105 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(z \cdot 4.0\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -0.0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.1708877911747488 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(z \cdot 4.0\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 2.876823679546137 \cdot 10^{+130}:\\ \;\;\;\;\left(\left(9.0 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4.0 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.3838515042456319 \cdot 10^{+158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(z \cdot 4.0\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9.0 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4.0 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < -1.5906234503561492e-156

    1. Initial program 12.3

      \[\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

    2. Simplified12.5

      \[\leadsto \color{blue}{\frac{\frac{b + \left(x \cdot 9.0\right) \cdot y}{z} - \left(t \cdot 4.0\right) \cdot a}{c}}\]

    3. Taylor expanded around 0 7.1

      \[\leadsto \color{blue}{\left(9.0 \cdot \frac{x \cdot y}{z \cdot c} + \frac{b}{z \cdot c}\right) - 4.0 \cdot \frac{a \cdot t}{c}}\]
    4. Using strategy rm

    5. Applied associate-/l*6.9

      \[\leadsto \left(9.0 \cdot \color{blue}{\frac{x}{\frac{z \cdot c}{y}}} + \frac{b}{z \cdot c}\right) - 4.0 \cdot \frac{a \cdot t}{c}\]
    6. Using strategy rm

    7. Applied associate-/l*6.2

      \[\leadsto \left(9.0 \cdot \frac{x}{\frac{z \cdot c}{y}} + \frac{b}{z \cdot c}\right) - 4.0 \cdot \color{blue}{\frac{a}{\frac{c}{t}}}\]

    if -1.5906234503561492e-156 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < 1.4789431977947666e+196

    1. Initial program 10.7

      \[\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

    2. Simplified4.5

      \[\leadsto \color{blue}{\frac{\frac{b + \left(x \cdot 9.0\right) \cdot y}{z} - \left(t \cdot 4.0\right) \cdot a}{c}}\]

    3. Taylor expanded around 0 4.5

      \[\leadsto \frac{\color{blue}{\left(9.0 \cdot \frac{x \cdot y}{z} + \frac{b}{z}\right)} - \left(t \cdot 4.0\right) \cdot a}{c}\]

    if 1.4789431977947666e+196 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))

    1. Initial program 43.1

      \[\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]

    2. Simplified24.4

      \[\leadsto \color{blue}{\frac{\frac{b + \left(x \cdot 9.0\right) \cdot y}{z} - \left(t \cdot 4.0\right) \cdot a}{c}}\]

    3. Taylor expanded around 0 22.5

      \[\leadsto \color{blue}{\left(9.0 \cdot \frac{x \cdot y}{z \cdot c} + \frac{b}{z \cdot c}\right) - 4.0 \cdot \frac{a \cdot t}{c}}\]
    4. Using strategy rm

    5. Applied associate-/l*17.9

      \[\leadsto \left(9.0 \cdot \color{blue}{\frac{x}{\frac{z \cdot c}{y}}} + \frac{b}{z \cdot c}\right) - 4.0 \cdot \frac{a \cdot t}{c}\]
    6. Using strategy rm

    7. Applied *-un-lft-identity17.9

      \[\leadsto \left(9.0 \cdot \frac{x}{\frac{z \cdot c}{y}} + \frac{b}{z \cdot c}\right) - 4.0 \cdot \frac{a \cdot t}{\color{blue}{1 \cdot c}}\]

    8. Applied times-frac12.0

      \[\leadsto \left(9.0 \cdot \frac{x}{\frac{z \cdot c}{y}} + \frac{b}{z \cdot c}\right) - 4.0 \cdot \color{blue}{\left(\frac{a}{1} \cdot \frac{t}{c}\right)}\]

    9. Simplified12.0

      \[\leadsto \left(9.0 \cdot \frac{x}{\frac{z \cdot c}{y}} + \frac{b}{z \cdot c}\right) - 4.0 \cdot \left(\color{blue}{a} \cdot \frac{t}{c}\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplification7.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le -1.5906234503561492 \cdot 10^{-156}:\\ \;\;\;\;\left(\frac{b}{c \cdot z} + \frac{x}{\frac{c \cdot z}{y}} \cdot 9.0\right) - 4.0 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9.0\right) \cdot y - \left(\left(z \cdot 4.0\right) \cdot t\right) \cdot a\right) + b}{c \cdot z} \le 1.4789431977947666 \cdot 10^{+196}:\\ \;\;\;\;\frac{\left(9.0 \cdot \frac{y \cdot x}{z} + \frac{b}{z}\right) - \left(4.0 \cdot t\right) \cdot a}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{c \cdot z} + \frac{x}{\frac{c \cdot z}{y}} \cdot 9.0\right) - \left(a \cdot \frac{t}{c}\right) \cdot 4.0\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(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)))