Average Error: 19.6 → 7.1
Time: 17.9s
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 r36771757 = x;
        double r36771758 = 9.0;
        double r36771759 = r36771757 * r36771758;
        double r36771760 = y;
        double r36771761 = r36771759 * r36771760;
        double r36771762 = z;
        double r36771763 = 4.0;
        double r36771764 = r36771762 * r36771763;
        double r36771765 = t;
        double r36771766 = r36771764 * r36771765;
        double r36771767 = a;
        double r36771768 = r36771766 * r36771767;
        double r36771769 = r36771761 - r36771768;
        double r36771770 = b;
        double r36771771 = r36771769 + r36771770;
        double r36771772 = c;
        double r36771773 = r36771762 * r36771772;
        double r36771774 = r36771771 / r36771773;
        return r36771774;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r36771775 = x;
        double r36771776 = 9.0;
        double r36771777 = r36771775 * r36771776;
        double r36771778 = y;
        double r36771779 = r36771777 * r36771778;
        double r36771780 = z;
        double r36771781 = 4.0;
        double r36771782 = r36771780 * r36771781;
        double r36771783 = t;
        double r36771784 = r36771782 * r36771783;
        double r36771785 = a;
        double r36771786 = r36771784 * r36771785;
        double r36771787 = r36771779 - r36771786;
        double r36771788 = b;
        double r36771789 = r36771787 + r36771788;
        double r36771790 = c;
        double r36771791 = r36771790 * r36771780;
        double r36771792 = r36771789 / r36771791;
        double r36771793 = -1.5906234503561492e-156;
        bool r36771794 = r36771792 <= r36771793;
        double r36771795 = r36771788 / r36771791;
        double r36771796 = r36771791 / r36771778;
        double r36771797 = r36771775 / r36771796;
        double r36771798 = r36771797 * r36771776;
        double r36771799 = r36771795 + r36771798;
        double r36771800 = r36771790 / r36771783;
        double r36771801 = r36771785 / r36771800;
        double r36771802 = r36771781 * r36771801;
        double r36771803 = r36771799 - r36771802;
        double r36771804 = 1.4789431977947666e+196;
        bool r36771805 = r36771792 <= r36771804;
        double r36771806 = r36771778 * r36771775;
        double r36771807 = r36771806 / r36771780;
        double r36771808 = r36771776 * r36771807;
        double r36771809 = r36771788 / r36771780;
        double r36771810 = r36771808 + r36771809;
        double r36771811 = r36771781 * r36771783;
        double r36771812 = r36771811 * r36771785;
        double r36771813 = r36771810 - r36771812;
        double r36771814 = r36771813 / r36771790;
        double r36771815 = r36771783 / r36771790;
        double r36771816 = r36771785 * r36771815;
        double r36771817 = r36771816 * r36771781;
        double r36771818 = r36771799 - r36771817;
        double r36771819 = r36771805 ? r36771814 : r36771818;
        double r36771820 = r36771794 ? r36771803 : r36771819;
        return r36771820;
}

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)))