Average Error: 19.9 → 7.9
Time: 11.2s
Precision: 64
\[\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c}\]
↓
\[\begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \le -1.07259742585831686 \cdot 10^{192}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le -1.85155038842901986 \cdot 10^{-269}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.8069570257286407 \cdot 10^{-259}:\\ \;\;\;\;\left(\frac{b + \left(x \cdot 9\right) \cdot y}{z} - 4 \cdot \left(t \cdot a\right)\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.9905307423898903 \cdot 10^{-159}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{c \cdot \frac{z}{y}}\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.33211823861849885 \cdot 10^{145}:\\ \;\;\;\;\left(\frac{1}{z} \cdot \frac{b}{c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\ \end{array}\]
\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}\;\left(x \cdot 9\right) \cdot y \le -1.07259742585831686 \cdot 10^{192}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\

\mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le -1.85155038842901986 \cdot 10^{-269}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\

\mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.8069570257286407 \cdot 10^{-259}:\\
\;\;\;\;\left(\frac{b + \left(x \cdot 9\right) \cdot y}{z} - 4 \cdot \left(t \cdot a\right)\right) \cdot \frac{1}{c}\\

\mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.9905307423898903 \cdot 10^{-159}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{c \cdot \frac{z}{y}}\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\

\mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.33211823861849885 \cdot 10^{145}:\\
\;\;\;\;\left(\frac{1}{z} \cdot \frac{b}{c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\

\mathbf{else}:\\
\;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r637452 = x;
        double r637453 = 9.0;
        double r637454 = r637452 * r637453;
        double r637455 = y;
        double r637456 = r637454 * r637455;
        double r637457 = z;
        double r637458 = 4.0;
        double r637459 = r637457 * r637458;
        double r637460 = t;
        double r637461 = r637459 * r637460;
        double r637462 = a;
        double r637463 = r637461 * r637462;
        double r637464 = r637456 - r637463;
        double r637465 = b;
        double r637466 = r637464 + r637465;
        double r637467 = c;
        double r637468 = r637457 * r637467;
        double r637469 = r637466 / r637468;
        return r637469;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c) {
        double r637470 = x;
        double r637471 = 9.0;
        double r637472 = r637470 * r637471;
        double r637473 = y;
        double r637474 = r637472 * r637473;
        double r637475 = -1.0725974258583169e+192;
        bool r637476 = r637474 <= r637475;
        double r637477 = b;
        double r637478 = z;
        double r637479 = c;
        double r637480 = r637478 * r637479;
        double r637481 = r637477 / r637480;
        double r637482 = r637470 / r637478;
        double r637483 = r637473 / r637479;
        double r637484 = r637482 * r637483;
        double r637485 = r637471 * r637484;
        double r637486 = r637481 + r637485;
        double r637487 = 4.0;
        double r637488 = a;
        double r637489 = cbrt(r637479);
        double r637490 = r637489 * r637489;
        double r637491 = r637488 / r637490;
        double r637492 = t;
        double r637493 = r637492 / r637489;
        double r637494 = r637491 * r637493;
        double r637495 = r637487 * r637494;
        double r637496 = r637486 - r637495;
        double r637497 = -1.85155038842902e-269;
        bool r637498 = r637474 <= r637497;
        double r637499 = r637470 * r637473;
        double r637500 = r637499 / r637480;
        double r637501 = r637471 * r637500;
        double r637502 = r637481 + r637501;
        double r637503 = r637492 / r637479;
        double r637504 = r637488 * r637503;
        double r637505 = r637487 * r637504;
        double r637506 = r637502 - r637505;
        double r637507 = 1.8069570257286407e-259;
        bool r637508 = r637474 <= r637507;
        double r637509 = r637477 + r637474;
        double r637510 = r637509 / r637478;
        double r637511 = r637492 * r637488;
        double r637512 = r637487 * r637511;
        double r637513 = r637510 - r637512;
        double r637514 = 1.0;
        double r637515 = r637514 / r637479;
        double r637516 = r637513 * r637515;
        double r637517 = 1.9905307423898903e-159;
        bool r637518 = r637474 <= r637517;
        double r637519 = r637478 / r637473;
        double r637520 = r637479 * r637519;
        double r637521 = r637470 / r637520;
        double r637522 = r637471 * r637521;
        double r637523 = r637481 + r637522;
        double r637524 = r637523 - r637495;
        double r637525 = 1.3321182386184989e+145;
        bool r637526 = r637474 <= r637525;
        double r637527 = r637514 / r637478;
        double r637528 = r637477 / r637479;
        double r637529 = r637527 * r637528;
        double r637530 = r637529 + r637501;
        double r637531 = r637488 * r637492;
        double r637532 = r637531 / r637479;
        double r637533 = r637487 * r637532;
        double r637534 = r637530 - r637533;
        double r637535 = r637526 ? r637534 : r637496;
        double r637536 = r637518 ? r637524 : r637535;
        double r637537 = r637508 ? r637516 : r637536;
        double r637538 = r637498 ? r637506 : r637537;
        double r637539 = r637476 ? r637496 : r637538;
        return r637539;
}

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

Original19.9
Target14.4
Herbie7.9
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -1.10015674080410512 \cdot 10^{-171}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt -0.0:\\ \;\;\;\;\frac{\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z}}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.17088779117474882 \cdot 10^{-53}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 2.8768236795461372 \cdot 10^{130}:\\ \;\;\;\;\left(\left(9 \cdot \frac{y}{c}\right) \cdot \frac{x}{z} + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{elif}\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(\left(z \cdot 4\right) \cdot t\right) \cdot a\right) + b}{z \cdot c} \lt 1.3838515042456319 \cdot 10^{158}:\\ \;\;\;\;\frac{\left(\left(x \cdot 9\right) \cdot y - \left(z \cdot 4\right) \cdot \left(t \cdot a\right)\right) + b}{z \cdot c}\\ \mathbf{else}:\\ \;\;\;\;\left(9 \cdot \left(\frac{y}{c \cdot z} \cdot x\right) + \frac{b}{c \cdot z}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \end{array}\]

Derivation

  1. Split input into 5 regimes

  2. if (* (* x 9.0) y) < -1.0725974258583169e+192 or 1.3321182386184989e+145 < (* (* x 9.0) y)

    1. Initial program 36.4

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

    2. Simplified34.7

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

    3. Taylor expanded around 0 31.0

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

    5. Applied add-cube-cbrt31.1

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

    6. Applied times-frac29.1

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

    8. Applied times-frac11.8

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

    if -1.0725974258583169e+192 < (* (* x 9.0) y) < -1.85155038842902e-269

    1. Initial program 14.9

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

    2. Simplified9.1

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

    3. Taylor expanded around 0 7.2

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

    5. Applied *-un-lft-identity7.2

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

    6. Applied times-frac6.7

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

    7. Simplified6.7

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

    if -1.85155038842902e-269 < (* (* x 9.0) y) < 1.8069570257286407e-259

    1. Initial program 18.4

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

    2. Simplified7.4

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

    4. Applied div-inv7.5

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

    if 1.8069570257286407e-259 < (* (* x 9.0) y) < 1.9905307423898903e-159

    1. Initial program 15.5

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

    2. Simplified8.0

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

    3. Taylor expanded around 0 7.5

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

    5. Applied add-cube-cbrt7.9

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

    6. Applied times-frac6.9

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

    8. Applied associate-/l*7.3

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

    9. Simplified7.5

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

    if 1.9905307423898903e-159 < (* (* x 9.0) y) < 1.3321182386184989e+145

    1. Initial program 16.3

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

    2. Simplified8.8

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

    3. Taylor expanded around 0 6.3

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

    5. Applied *-un-lft-identity6.3

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

    6. Applied times-frac7.0

      \[\leadsto \left(\color{blue}{\frac{1}{z} \cdot \frac{b}{c}} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification7.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;\left(x \cdot 9\right) \cdot y \le -1.07259742585831686 \cdot 10^{192}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le -1.85155038842901986 \cdot 10^{-269}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \left(a \cdot \frac{t}{c}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.8069570257286407 \cdot 10^{-259}:\\ \;\;\;\;\left(\frac{b + \left(x \cdot 9\right) \cdot y}{z} - 4 \cdot \left(t \cdot a\right)\right) \cdot \frac{1}{c}\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.9905307423898903 \cdot 10^{-159}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \frac{x}{c \cdot \frac{z}{y}}\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\ \mathbf{elif}\;\left(x \cdot 9\right) \cdot y \le 1.33211823861849885 \cdot 10^{145}:\\ \;\;\;\;\left(\frac{1}{z} \cdot \frac{b}{c} + 9 \cdot \frac{x \cdot y}{z \cdot c}\right) - 4 \cdot \frac{a \cdot t}{c}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{b}{z \cdot c} + 9 \cdot \left(\frac{x}{z} \cdot \frac{y}{c}\right)\right) - 4 \cdot \left(\frac{a}{\sqrt[3]{c} \cdot \sqrt[3]{c}} \cdot \frac{t}{\sqrt[3]{c}}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020045 
(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)) -1.1001567408041051e-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)))