Average Error: 20.7 → 7.5
Time: 20.5s
Precision: 64
\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le -1.020674458090830407540978412360813821868 \cdot 10^{302}:\\ \;\;\;\;\frac{\frac{b}{z} - \left(a \cdot 4\right) \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le -3.223871194353012928756684221546116408409 \cdot 10^{-287}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 0.0:\\ \;\;\;\;\frac{\frac{\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \left(a \cdot 4\right) \cdot t}{\sqrt[3]{c} \cdot \sqrt[3]{c}}}{\sqrt[3]{c}}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 9.015864611909133506028130612168974390184 \cdot 10^{300}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - \left(a \cdot 4\right) \cdot t}{c}\\ \end{array}\]
\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}\;\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 -1.020674458090830407540978412360813821868 \cdot 10^{302}:\\
\;\;\;\;\frac{\frac{b}{z} - \left(a \cdot 4\right) \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} \le -3.223871194353012928756684221546116408409 \cdot 10^{-287}:\\
\;\;\;\;\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 0.0:\\
\;\;\;\;\frac{\frac{\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \left(a \cdot 4\right) \cdot t}{\sqrt[3]{c} \cdot \sqrt[3]{c}}}{\sqrt[3]{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 9.015864611909133506028130612168974390184 \cdot 10^{300}:\\
\;\;\;\;\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{\frac{b}{z} - \left(a \cdot 4\right) \cdot t}{c}\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r478618 = x;
        double r478619 = 9.0;
        double r478620 = r478618 * r478619;
        double r478621 = y;
        double r478622 = r478620 * r478621;
        double r478623 = z;
        double r478624 = 4.0;
        double r478625 = r478623 * r478624;
        double r478626 = t;
        double r478627 = r478625 * r478626;
        double r478628 = a;
        double r478629 = r478627 * r478628;
        double r478630 = r478622 - r478629;
        double r478631 = b;
        double r478632 = r478630 + r478631;
        double r478633 = c;
        double r478634 = r478623 * r478633;
        double r478635 = r478632 / r478634;
        return r478635;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r478636 = x;
        double r478637 = 9.0;
        double r478638 = r478636 * r478637;
        double r478639 = y;
        double r478640 = r478638 * r478639;
        double r478641 = z;
        double r478642 = 4.0;
        double r478643 = r478641 * r478642;
        double r478644 = t;
        double r478645 = r478643 * r478644;
        double r478646 = a;
        double r478647 = r478645 * r478646;
        double r478648 = r478640 - r478647;
        double r478649 = b;
        double r478650 = r478648 + r478649;
        double r478651 = c;
        double r478652 = r478641 * r478651;
        double r478653 = r478650 / r478652;
        double r478654 = -1.0206744580908304e+302;
        bool r478655 = r478653 <= r478654;
        double r478656 = r478649 / r478641;
        double r478657 = r478646 * r478642;
        double r478658 = r478657 * r478644;
        double r478659 = r478656 - r478658;
        double r478660 = r478659 / r478651;
        double r478661 = -3.223871194353013e-287;
        bool r478662 = r478653 <= r478661;
        double r478663 = 0.0;
        bool r478664 = r478653 <= r478663;
        double r478665 = r478649 + r478640;
        double r478666 = r478665 / r478641;
        double r478667 = r478666 - r478658;
        double r478668 = cbrt(r478651);
        double r478669 = r478668 * r478668;
        double r478670 = r478667 / r478669;
        double r478671 = r478670 / r478668;
        double r478672 = 9.015864611909134e+300;
        bool r478673 = r478653 <= r478672;
        double r478674 = r478673 ? r478653 : r478660;
        double r478675 = r478664 ? r478671 : r478674;
        double r478676 = r478662 ? r478653 : r478675;
        double r478677 = r478655 ? r478660 : r478676;
        return r478677;
}

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
Target14.6
Herbie7.5
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -1.100156740804104887233830094663413900721 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -0.0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.170887791174748819600820354912645756062 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 2.876823679546137226963937101710277849382 \cdot 10^{130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.383851504245631860711731716196098366993 \cdot 10^{158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < -1.0206744580908304e+302 or 9.015864611909134e+300 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c))

    1. Initial program 62.1

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

    2. Simplified25.6

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

    4. Applied clear-num25.6

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

    5. Taylor expanded around 0 27.0

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

    if -1.0206744580908304e+302 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < -3.223871194353013e-287 or 0.0 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < 9.015864611909134e+300

    1. Initial program 3.7

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

    if -3.223871194353013e-287 < (/ (+ (- (* (* x 9.0) y) (* (* (* z 4.0) t) a)) b) (* z c)) < 0.0

    1. Initial program 37.1

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

    2. Simplified0.6

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

    4. Applied add-cube-cbrt1.2

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

    5. Applied associate-/r*1.2

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

  4. Final simplification7.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le -1.020674458090830407540978412360813821868 \cdot 10^{302}:\\ \;\;\;\;\frac{\frac{b}{z} - \left(a \cdot 4\right) \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le -3.223871194353012928756684221546116408409 \cdot 10^{-287}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 0.0:\\ \;\;\;\;\frac{\frac{\frac{b + \left(x \cdot 9\right) \cdot y}{z} - \left(a \cdot 4\right) \cdot t}{\sqrt[3]{c} \cdot \sqrt[3]{c}}}{\sqrt[3]{c}}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \le 9.015864611909133506028130612168974390184 \cdot 10^{300}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{b}{z} - \left(a \cdot 4\right) \cdot t}{c}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(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)) -1.100156740804105e-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)))