Average Error: 7.9 → 0.5
Time: 4.1s
Precision: 64
\[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t = -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le -1.570465535572884322699978790782884605691 \cdot 10^{-101} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 1.47440313991068531415406912842436761104 \cdot 10^{-267} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 6.212678920874577831195231744431104229608 \cdot 10^{275}\right)\right)\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}} - \left(4.5 \cdot t\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \frac{t \cdot z}{a}\\ \end{array}\]
\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t = -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le -1.570465535572884322699978790782884605691 \cdot 10^{-101} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 1.47440313991068531415406912842436761104 \cdot 10^{-267} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 6.212678920874577831195231744431104229608 \cdot 10^{275}\right)\right)\right):\\
\;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}} - \left(4.5 \cdot t\right) \cdot \frac{z}{a}\\

\mathbf{else}:\\
\;\;\;\;0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \frac{t \cdot z}{a}\\

\end{array}
double f(double x, double y, double z, double t, double a) {
        double r717526 = x;
        double r717527 = y;
        double r717528 = r717526 * r717527;
        double r717529 = z;
        double r717530 = 9.0;
        double r717531 = r717529 * r717530;
        double r717532 = t;
        double r717533 = r717531 * r717532;
        double r717534 = r717528 - r717533;
        double r717535 = a;
        double r717536 = 2.0;
        double r717537 = r717535 * r717536;
        double r717538 = r717534 / r717537;
        return r717538;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r717539 = x;
        double r717540 = y;
        double r717541 = r717539 * r717540;
        double r717542 = z;
        double r717543 = 9.0;
        double r717544 = r717542 * r717543;
        double r717545 = t;
        double r717546 = r717544 * r717545;
        double r717547 = r717541 - r717546;
        double r717548 = -inf.0;
        bool r717549 = r717547 <= r717548;
        double r717550 = -1.5704655355728843e-101;
        bool r717551 = r717547 <= r717550;
        double r717552 = 1.4744031399106853e-267;
        bool r717553 = r717547 <= r717552;
        double r717554 = 6.212678920874578e+275;
        bool r717555 = r717547 <= r717554;
        double r717556 = !r717555;
        bool r717557 = r717553 || r717556;
        double r717558 = !r717557;
        bool r717559 = r717551 || r717558;
        double r717560 = !r717559;
        bool r717561 = r717549 || r717560;
        double r717562 = 0.5;
        double r717563 = a;
        double r717564 = r717563 / r717540;
        double r717565 = r717539 / r717564;
        double r717566 = r717562 * r717565;
        double r717567 = 4.5;
        double r717568 = r717567 * r717545;
        double r717569 = r717542 / r717563;
        double r717570 = r717568 * r717569;
        double r717571 = r717566 - r717570;
        double r717572 = r717541 / r717563;
        double r717573 = r717562 * r717572;
        double r717574 = r717545 * r717542;
        double r717575 = r717574 / r717563;
        double r717576 = r717567 * r717575;
        double r717577 = r717573 - r717576;
        double r717578 = r717561 ? r717571 : r717577;
        return r717578;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.9
Target5.6
Herbie0.5
\[\begin{array}{l} \mathbf{if}\;a \lt -2.090464557976709043451944897028999329376 \cdot 10^{86}:\\ \;\;\;\;0.5 \cdot \frac{y \cdot x}{a} - 4.5 \cdot \frac{t}{\frac{a}{z}}\\ \mathbf{elif}\;a \lt 2.144030707833976090627817222818061808815 \cdot 10^{99}:\\ \;\;\;\;\frac{x \cdot y - z \cdot \left(9 \cdot t\right)}{a \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{a} \cdot \left(x \cdot 0.5\right) - \frac{t}{a} \cdot \left(z \cdot 4.5\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (- (* x y) (* (* z 9.0) t)) < -inf.0 or -1.5704655355728843e-101 < (- (* x y) (* (* z 9.0) t)) < 1.4744031399106853e-267 or 6.212678920874578e+275 < (- (* x y) (* (* z 9.0) t))

    1. Initial program 33.8

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]

    2. Taylor expanded around 0 33.5

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \frac{t \cdot z}{a}}\]
    3. Using strategy rm

    4. Applied *-un-lft-identity33.5

      \[\leadsto 0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \frac{t \cdot z}{\color{blue}{1 \cdot a}}\]

    5. Applied times-frac19.0

      \[\leadsto 0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \color{blue}{\left(\frac{t}{1} \cdot \frac{z}{a}\right)}\]

    6. Simplified19.0

      \[\leadsto 0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \left(\color{blue}{t} \cdot \frac{z}{a}\right)\]
    7. Using strategy rm

    8. Applied associate-*r*19.1

      \[\leadsto 0.5 \cdot \frac{x \cdot y}{a} - \color{blue}{\left(4.5 \cdot t\right) \cdot \frac{z}{a}}\]
    9. Using strategy rm

    10. Applied associate-/l*1.3

      \[\leadsto 0.5 \cdot \color{blue}{\frac{x}{\frac{a}{y}}} - \left(4.5 \cdot t\right) \cdot \frac{z}{a}\]

    if -inf.0 < (- (* x y) (* (* z 9.0) t)) < -1.5704655355728843e-101 or 1.4744031399106853e-267 < (- (* x y) (* (* z 9.0) t)) < 6.212678920874578e+275

    1. Initial program 0.3

      \[\frac{x \cdot y - \left(z \cdot 9\right) \cdot t}{a \cdot 2}\]

    2. Taylor expanded around 0 0.3

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \frac{t \cdot z}{a}}\]
    3. Using strategy rm

    4. Applied *-un-lft-identity0.3

      \[\leadsto 0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \frac{t \cdot z}{\color{blue}{1 \cdot a}}\]

    5. Applied times-frac5.4

      \[\leadsto 0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \color{blue}{\left(\frac{t}{1} \cdot \frac{z}{a}\right)}\]

    6. Simplified5.4

      \[\leadsto 0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \left(\color{blue}{t} \cdot \frac{z}{a}\right)\]
    7. Using strategy rm

    8. Applied associate-*r*5.4

      \[\leadsto 0.5 \cdot \frac{x \cdot y}{a} - \color{blue}{\left(4.5 \cdot t\right) \cdot \frac{z}{a}}\]

    9. Taylor expanded around 0 0.3

      \[\leadsto \color{blue}{0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \frac{t \cdot z}{a}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y - \left(z \cdot 9\right) \cdot t = -\infty \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le -1.570465535572884322699978790782884605691 \cdot 10^{-101} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 1.47440313991068531415406912842436761104 \cdot 10^{-267} \lor \neg \left(x \cdot y - \left(z \cdot 9\right) \cdot t \le 6.212678920874577831195231744431104229608 \cdot 10^{275}\right)\right)\right):\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{a}{y}} - \left(4.5 \cdot t\right) \cdot \frac{z}{a}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x \cdot y}{a} - 4.5 \cdot \frac{t \cdot z}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t a)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, I"
  :precision binary64

  :herbie-target
  (if (< a -2.090464557976709e+86) (- (* 0.5 (/ (* y x) a)) (* 4.5 (/ t (/ a z)))) (if (< a 2.144030707833976e+99) (/ (- (* x y) (* z (* 9 t))) (* a 2)) (- (* (/ y a) (* x 0.5)) (* (/ t a) (* z 4.5)))))

  (/ (- (* x y) (* (* z 9) t)) (* a 2)))