Average Error: 6.2 → 0.8
Time: 32.1s
Precision: 64
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le -3.90679311301216179 \cdot 10^{306} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le 5.7811419947610468 \cdot 10^{298}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(\left(i \cdot b\right) \cdot c + a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]
2 \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(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le -3.90679311301216179 \cdot 10^{306} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le 5.7811419947610468 \cdot 10^{298}\right):\\
\;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(\left(i \cdot b\right) \cdot c + a \cdot i\right)\right)\\

\mathbf{else}:\\
\;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1250347 = 2.0;
        double r1250348 = x;
        double r1250349 = y;
        double r1250350 = r1250348 * r1250349;
        double r1250351 = z;
        double r1250352 = t;
        double r1250353 = r1250351 * r1250352;
        double r1250354 = r1250350 + r1250353;
        double r1250355 = a;
        double r1250356 = b;
        double r1250357 = c;
        double r1250358 = r1250356 * r1250357;
        double r1250359 = r1250355 + r1250358;
        double r1250360 = r1250359 * r1250357;
        double r1250361 = i;
        double r1250362 = r1250360 * r1250361;
        double r1250363 = r1250354 - r1250362;
        double r1250364 = r1250347 * r1250363;
        return r1250364;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1250365 = a;
        double r1250366 = b;
        double r1250367 = c;
        double r1250368 = r1250366 * r1250367;
        double r1250369 = r1250365 + r1250368;
        double r1250370 = r1250369 * r1250367;
        double r1250371 = i;
        double r1250372 = r1250370 * r1250371;
        double r1250373 = -3.906793113012162e+306;
        bool r1250374 = r1250372 <= r1250373;
        double r1250375 = 5.781141994761047e+298;
        bool r1250376 = r1250372 <= r1250375;
        double r1250377 = !r1250376;
        bool r1250378 = r1250374 || r1250377;
        double r1250379 = 2.0;
        double r1250380 = x;
        double r1250381 = y;
        double r1250382 = r1250380 * r1250381;
        double r1250383 = z;
        double r1250384 = t;
        double r1250385 = r1250383 * r1250384;
        double r1250386 = r1250382 + r1250385;
        double r1250387 = r1250371 * r1250366;
        double r1250388 = r1250387 * r1250367;
        double r1250389 = r1250365 * r1250371;
        double r1250390 = r1250388 + r1250389;
        double r1250391 = r1250367 * r1250390;
        double r1250392 = r1250386 - r1250391;
        double r1250393 = r1250379 * r1250392;
        double r1250394 = r1250386 - r1250372;
        double r1250395 = r1250379 * r1250394;
        double r1250396 = r1250378 ? r1250393 : r1250395;
        return r1250396;
}

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

Original6.2
Target1.8
Herbie0.8
\[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \left(c \cdot i\right)\right)\]

Derivation

  1. Split input into 2 regimes

  2. if (* (* (+ a (* b c)) c) i) < -3.906793113012162e+306 or 5.781141994761047e+298 < (* (* (+ a (* b c)) c) i)

    1. Initial program 60.6

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

    3. Applied associate-*l*10.4

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

    4. Simplified10.4

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(a + b \cdot c\right) \cdot \color{blue}{\left(i \cdot c\right)}\right)\]
    5. Using strategy rm

    6. Applied add-cube-cbrt10.9

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \sqrt[3]{a + b \cdot c}\right)} \cdot \left(i \cdot c\right)\right)\]

    7. Applied associate-*l*10.9

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \color{blue}{\left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \left(\sqrt[3]{a + b \cdot c} \cdot \left(i \cdot c\right)\right)}\right)\]
    8. Using strategy rm

    9. Applied associate-*r*11.1

      \[\leadsto 2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\sqrt[3]{a + b \cdot c} \cdot \sqrt[3]{a + b \cdot c}\right) \cdot \color{blue}{\left(\left(\sqrt[3]{a + b \cdot c} \cdot i\right) \cdot c\right)}\right)\]

    10. Taylor expanded around inf 53.6

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

    11. Simplified5.5

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

    if -3.906793113012162e+306 < (* (* (+ a (* b c)) c) i) < 5.781141994761047e+298

    1. Initial program 0.3

      \[2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le -3.90679311301216179 \cdot 10^{306} \lor \neg \left(\left(\left(a + b \cdot c\right) \cdot c\right) \cdot i \le 5.7811419947610468 \cdot 10^{298}\right):\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - c \cdot \left(\left(i \cdot b\right) \cdot c + a \cdot i\right)\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\left(x \cdot y + z \cdot t\right) - \left(\left(a + b \cdot c\right) \cdot c\right) \cdot i\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019199 
(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))))