Average Error: 5.8 → 1.1
Time: 27.5s
Precision: 64
\[2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(c \cdot b + a\right) \cdot c \le -7.711821572914459 \cdot 10^{+111}:\\ \;\;\;\;2.0 \cdot \left(\left(x \cdot y + t \cdot z\right) + \left(-c\right) \cdot \left(a \cdot i + \left(i \cdot c\right) \cdot b\right)\right)\\ \mathbf{elif}\;\left(c \cdot b + a\right) \cdot c \le 5.793851923347976 \cdot 10^{+108}:\\ \;\;\;\;\left(\left(x \cdot y + t \cdot z\right) - \left(\left(c \cdot b + a\right) \cdot c\right) \cdot i\right) \cdot 2.0\\ \mathbf{else}:\\ \;\;\;\;2.0 \cdot \left(\left(x \cdot y + t \cdot z\right) - \left(c \cdot b + a\right) \cdot \left(i \cdot c\right)\right)\\ \end{array}\]
2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)
↓
\begin{array}{l}
\mathbf{if}\;\left(c \cdot b + a\right) \cdot c \le -7.711821572914459 \cdot 10^{+111}:\\
\;\;\;\;2.0 \cdot \left(\left(x \cdot y + t \cdot z\right) + \left(-c\right) \cdot \left(a \cdot i + \left(i \cdot c\right) \cdot b\right)\right)\\

\mathbf{elif}\;\left(c \cdot b + a\right) \cdot c \le 5.793851923347976 \cdot 10^{+108}:\\
\;\;\;\;\left(\left(x \cdot y + t \cdot z\right) - \left(\left(c \cdot b + a\right) \cdot c\right) \cdot i\right) \cdot 2.0\\

\mathbf{else}:\\
\;\;\;\;2.0 \cdot \left(\left(x \cdot y + t \cdot z\right) - \left(c \cdot b + a\right) \cdot \left(i \cdot c\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r30197449 = 2.0;
        double r30197450 = x;
        double r30197451 = y;
        double r30197452 = r30197450 * r30197451;
        double r30197453 = z;
        double r30197454 = t;
        double r30197455 = r30197453 * r30197454;
        double r30197456 = r30197452 + r30197455;
        double r30197457 = a;
        double r30197458 = b;
        double r30197459 = c;
        double r30197460 = r30197458 * r30197459;
        double r30197461 = r30197457 + r30197460;
        double r30197462 = r30197461 * r30197459;
        double r30197463 = i;
        double r30197464 = r30197462 * r30197463;
        double r30197465 = r30197456 - r30197464;
        double r30197466 = r30197449 * r30197465;
        return r30197466;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r30197467 = c;
        double r30197468 = b;
        double r30197469 = r30197467 * r30197468;
        double r30197470 = a;
        double r30197471 = r30197469 + r30197470;
        double r30197472 = r30197471 * r30197467;
        double r30197473 = -7.711821572914459e+111;
        bool r30197474 = r30197472 <= r30197473;
        double r30197475 = 2.0;
        double r30197476 = x;
        double r30197477 = y;
        double r30197478 = r30197476 * r30197477;
        double r30197479 = t;
        double r30197480 = z;
        double r30197481 = r30197479 * r30197480;
        double r30197482 = r30197478 + r30197481;
        double r30197483 = -r30197467;
        double r30197484 = i;
        double r30197485 = r30197470 * r30197484;
        double r30197486 = r30197484 * r30197467;
        double r30197487 = r30197486 * r30197468;
        double r30197488 = r30197485 + r30197487;
        double r30197489 = r30197483 * r30197488;
        double r30197490 = r30197482 + r30197489;
        double r30197491 = r30197475 * r30197490;
        double r30197492 = 5.793851923347976e+108;
        bool r30197493 = r30197472 <= r30197492;
        double r30197494 = r30197472 * r30197484;
        double r30197495 = r30197482 - r30197494;
        double r30197496 = r30197495 * r30197475;
        double r30197497 = r30197471 * r30197486;
        double r30197498 = r30197482 - r30197497;
        double r30197499 = r30197475 * r30197498;
        double r30197500 = r30197493 ? r30197496 : r30197499;
        double r30197501 = r30197474 ? r30197491 : r30197500;
        return r30197501;
}

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

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.8
Target1.9
Herbie1.1
\[2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Split input into 3 regimes

  2. if (* (+ a (* b c)) c) < -7.711821572914459e+111

    1. Initial program 19.0

      \[2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
    2. Using strategy rm

    3. Applied associate-*l*4.4

      \[\leadsto 2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]

    4. Taylor expanded around inf 24.6

      \[\leadsto 2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(i \cdot \left(b \cdot {c}^{2}\right) + a \cdot \left(i \cdot c\right)\right)}\right)\]

    5. Simplified19.0

      \[\leadsto 2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\left(c \cdot c\right) \cdot \left(i \cdot b\right) + \left(c \cdot i\right) \cdot a\right)}\right)\]
    6. Using strategy rm

    7. Applied sub-neg19.0

      \[\leadsto 2.0 \cdot \color{blue}{\left(\left(x \cdot y + z \cdot t\right) + \left(-\left(\left(c \cdot c\right) \cdot \left(i \cdot b\right) + \left(c \cdot i\right) \cdot a\right)\right)\right)}\]

    8. Simplified2.6

      \[\leadsto 2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) + \color{blue}{\left(-c\right) \cdot \left(i \cdot a + \left(c \cdot i\right) \cdot b\right)}\right)\]

    if -7.711821572914459e+111 < (* (+ a (* b c)) c) < 5.793851923347976e+108

    1. Initial program 0.3

      \[2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]

    if 5.793851923347976e+108 < (* (+ a (* b c)) c)

    1. Initial program 19.2

      \[2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
    2. Using strategy rm

    3. Applied associate-*l*3.5

      \[\leadsto 2.0 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(a + b \cdot c\right) \cdot \left(c \cdot i\right)}\right)\]
  3. Recombined 3 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(c \cdot b + a\right) \cdot c \le -7.711821572914459 \cdot 10^{+111}:\\ \;\;\;\;2.0 \cdot \left(\left(x \cdot y + t \cdot z\right) + \left(-c\right) \cdot \left(a \cdot i + \left(i \cdot c\right) \cdot b\right)\right)\\ \mathbf{elif}\;\left(c \cdot b + a\right) \cdot c \le 5.793851923347976 \cdot 10^{+108}:\\ \;\;\;\;\left(\left(x \cdot y + t \cdot z\right) - \left(\left(c \cdot b + a\right) \cdot c\right) \cdot i\right) \cdot 2.0\\ \mathbf{else}:\\ \;\;\;\;2.0 \cdot \left(\left(x \cdot y + t \cdot z\right) - \left(c \cdot b + a\right) \cdot \left(i \cdot c\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a b c i)
  :name "Diagrams.ThreeD.Shapes:frustum from diagrams-lib-1.3.0.3, A"

  :herbie-target
  (* 2.0 (- (+ (* x y) (* z t)) (* (+ a (* b c)) (* c i))))

  (* 2.0 (- (+ (* x y) (* z t)) (* (* (+ a (* b c)) c) i))))