Average Error: 20.9 → 9.7
Time: 5.8s
Precision: 64
\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \le -1.357514912910746 \cdot 10^{204}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le -6.0000007604735773 \cdot 10^{-298}:\\ \;\;\;\;\left(\frac{\frac{b}{z}}{c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.60900812742176 \cdot 10^{-122}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z \cdot c}{y}}\right) - 4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 9.42548597114718612 \cdot 10^{142}:\\ \;\;\;\;\left(\frac{\frac{b}{z}}{c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]
\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 -1.357514912910746 \cdot 10^{204}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\

\mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le -6.0000007604735773 \cdot 10^{-298}:\\
\;\;\;\;\left(\frac{\frac{b}{z}}{c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\

\mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.60900812742176 \cdot 10^{-122}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z \cdot c}{y}}\right) - 4 \cdot \frac{a}{\frac{c}{t}}\\

\mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 9.42548597114718612 \cdot 10^{142}:\\
\;\;\;\;\left(\frac{\frac{b}{z}}{c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r721708 = x;
        double r721709 = 9.0;
        double r721710 = r721708 * r721709;
        double r721711 = y;
        double r721712 = r721710 * r721711;
        double r721713 = z;
        double r721714 = 4.0;
        double r721715 = r721713 * r721714;
        double r721716 = t;
        double r721717 = r721715 * r721716;
        double r721718 = a;
        double r721719 = r721717 * r721718;
        double r721720 = r721712 - r721719;
        double r721721 = b;
        double r721722 = r721720 + r721721;
        double r721723 = c;
        double r721724 = r721713 * r721723;
        double r721725 = r721722 / r721724;
        return r721725;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r721726 = x;
        double r721727 = 9.0;
        double r721728 = r721726 * r721727;
        double r721729 = y;
        double r721730 = r721728 * r721729;
        double r721731 = -1.357514912910746e+204;
        bool r721732 = r721730 <= r721731;
        double r721733 = b;
        double r721734 = z;
        double r721735 = c;
        double r721736 = r721734 * r721735;
        double r721737 = r721733 / r721736;
        double r721738 = r721726 / r721734;
        double r721739 = r721729 / r721735;
        double r721740 = r721738 * r721739;
        double r721741 = r721727 * r721740;
        double r721742 = r721737 + r721741;
        double r721743 = 4.0;
        double r721744 = a;
        double r721745 = t;
        double r721746 = r721744 * r721745;
        double r721747 = r721746 / r721735;
        double r721748 = r721743 * r721747;
        double r721749 = r721742 - r721748;
        double r721750 = -6.000000760473577e-298;
        bool r721751 = r721730 <= r721750;
        double r721752 = r721733 / r721734;
        double r721753 = r721752 / r721735;
        double r721754 = r721726 * r721729;
        double r721755 = r721754 / r721736;
        double r721756 = r721727 * r721755;
        double r721757 = r721753 + r721756;
        double r721758 = r721757 - r721748;
        double r721759 = 1.60900812742176e-122;
        bool r721760 = r721730 <= r721759;
        double r721761 = r721736 / r721729;
        double r721762 = r721726 / r721761;
        double r721763 = r721727 * r721762;
        double r721764 = r721737 + r721763;
        double r721765 = r721735 / r721745;
        double r721766 = r721744 / r721765;
        double r721767 = r721743 * r721766;
        double r721768 = r721764 - r721767;
        double r721769 = 9.425485971147186e+142;
        bool r721770 = r721730 <= r721769;
        double r721771 = r721770 ? r721758 : r721749;
        double r721772 = r721760 ? r721768 : r721771;
        double r721773 = r721751 ? r721758 : r721772;
        double r721774 = r721732 ? r721749 : r721773;
        return r721774;
}

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

Original20.9
Target15.0
Herbie9.7
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -1.10015674080410512 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -0.0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.17088779117474882 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 2.8768236795461372 \cdot 10^{130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.3838515042456319 \cdot 10^{158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (* (* x 9.0) y) < -1.357514912910746e+204 or 9.425485971147186e+142 < (* (* x 9.0) y)

    1. Initial program 36.5

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

    2. Taylor expanded around 0 29.6

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

    4. Applied times-frac14.3

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

    if -1.357514912910746e+204 < (* (* x 9.0) y) < -6.000000760473577e-298 or 1.60900812742176e-122 < (* (* x 9.0) y) < 9.425485971147186e+142

    1. Initial program 16.5

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

    2. Taylor expanded around 0 7.2

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

    4. Applied associate-/r*8.6

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

    if -6.000000760473577e-298 < (* (* x 9.0) y) < 1.60900812742176e-122

    1. Initial program 18.7

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

    2. Taylor expanded around 0 9.0

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

    4. Applied associate-/l*9.3

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

    6. Applied associate-/l*8.9

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

  4. Final simplification9.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \le -1.357514912910746 \cdot 10^{204}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le -6.0000007604735773 \cdot 10^{-298}:\\ \;\;\;\;\left(\frac{\frac{b}{z}}{c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.60900812742176 \cdot 10^{-122}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{\frac{z \cdot c}{y}}\right) - 4 \cdot \frac{a}{\frac{c}{t}}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 9.42548597114718612 \cdot 10^{142}:\\ \;\;\;\;\left(\frac{\frac{b}{z}}{c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 
(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)))