Average Error: 14.0 → 0.7
Time: 26.1s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.009555688743657053093976996432682877192 \cdot 10^{278}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.900141742787772715345890115335440787699 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 4.438182973596565301288302827093808047147 \cdot 10^{-272}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 3.561199608254915194562496763078682553454 \cdot 10^{97}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.009555688743657053093976996432682877192 \cdot 10^{278}:\\
\;\;\;\;y \cdot \frac{x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.900141742787772715345890115335440787699 \cdot 10^{-270}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le 4.438182973596565301288302827093808047147 \cdot 10^{-272}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 3.561199608254915194562496763078682553454 \cdot 10^{97}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r63454 = x;
        double r63455 = y;
        double r63456 = z;
        double r63457 = r63455 / r63456;
        double r63458 = t;
        double r63459 = r63457 * r63458;
        double r63460 = r63459 / r63458;
        double r63461 = r63454 * r63460;
        return r63461;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r63462 = y;
        double r63463 = z;
        double r63464 = r63462 / r63463;
        double r63465 = -1.009555688743657e+278;
        bool r63466 = r63464 <= r63465;
        double r63467 = x;
        double r63468 = r63467 / r63463;
        double r63469 = r63462 * r63468;
        double r63470 = -1.9001417427877727e-270;
        bool r63471 = r63464 <= r63470;
        double r63472 = r63463 / r63462;
        double r63473 = r63467 / r63472;
        double r63474 = 4.438182973596565e-272;
        bool r63475 = r63464 <= r63474;
        double r63476 = r63467 * r63462;
        double r63477 = r63476 / r63463;
        double r63478 = 3.561199608254915e+97;
        bool r63479 = r63464 <= r63478;
        double r63480 = 1.0;
        double r63481 = r63480 / r63462;
        double r63482 = r63468 / r63481;
        double r63483 = r63479 ? r63473 : r63482;
        double r63484 = r63475 ? r63477 : r63483;
        double r63485 = r63471 ? r63473 : r63484;
        double r63486 = r63466 ? r63469 : r63485;
        return r63486;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 4 regimes

  2. if (/ y z) < -1.009555688743657e+278

    1. Initial program 54.6

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified45.9

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x}\]
    3. Using strategy rm

    4. Applied div-inv45.9

      \[\leadsto \color{blue}{\left(y \cdot \frac{1}{z}\right)} \cdot x\]

    5. Applied associate-*l*0.4

      \[\leadsto \color{blue}{y \cdot \left(\frac{1}{z} \cdot x\right)}\]

    6. Simplified0.2

      \[\leadsto y \cdot \color{blue}{\frac{x}{z}}\]

    if -1.009555688743657e+278 < (/ y z) < -1.9001417427877727e-270 or 4.438182973596565e-272 < (/ y z) < 3.561199608254915e+97

    1. Initial program 8.2

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified0.2

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x}\]
    3. Using strategy rm

    4. Applied div-inv0.3

      \[\leadsto \color{blue}{\left(y \cdot \frac{1}{z}\right)} \cdot x\]

    5. Applied associate-*l*9.0

      \[\leadsto \color{blue}{y \cdot \left(\frac{1}{z} \cdot x\right)}\]

    6. Simplified8.9

      \[\leadsto y \cdot \color{blue}{\frac{x}{z}}\]
    7. Using strategy rm

    8. Applied *-un-lft-identity8.9

      \[\leadsto \color{blue}{\left(1 \cdot y\right)} \cdot \frac{x}{z}\]

    9. Applied associate-*l*8.9

      \[\leadsto \color{blue}{1 \cdot \left(y \cdot \frac{x}{z}\right)}\]

    10. Simplified8.7

      \[\leadsto 1 \cdot \color{blue}{\frac{x \cdot y}{z}}\]
    11. Using strategy rm

    12. Applied associate-/l*0.2

      \[\leadsto 1 \cdot \color{blue}{\frac{x}{\frac{z}{y}}}\]

    if -1.9001417427877727e-270 < (/ y z) < 4.438182973596565e-272

    1. Initial program 18.9

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified15.8

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x}\]
    3. Using strategy rm

    4. Applied div-inv15.8

      \[\leadsto \color{blue}{\left(y \cdot \frac{1}{z}\right)} \cdot x\]

    5. Applied associate-*l*0.1

      \[\leadsto \color{blue}{y \cdot \left(\frac{1}{z} \cdot x\right)}\]

    6. Simplified0.1

      \[\leadsto y \cdot \color{blue}{\frac{x}{z}}\]
    7. Using strategy rm

    8. Applied *-un-lft-identity0.1

      \[\leadsto \color{blue}{\left(1 \cdot y\right)} \cdot \frac{x}{z}\]

    9. Applied associate-*l*0.1

      \[\leadsto \color{blue}{1 \cdot \left(y \cdot \frac{x}{z}\right)}\]

    10. Simplified0.1

      \[\leadsto 1 \cdot \color{blue}{\frac{x \cdot y}{z}}\]

    if 3.561199608254915e+97 < (/ y z)

    1. Initial program 26.4

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

    2. Simplified12.8

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x}\]
    3. Using strategy rm

    4. Applied div-inv12.8

      \[\leadsto \color{blue}{\left(y \cdot \frac{1}{z}\right)} \cdot x\]

    5. Applied associate-*l*4.0

      \[\leadsto \color{blue}{y \cdot \left(\frac{1}{z} \cdot x\right)}\]

    6. Simplified4.0

      \[\leadsto y \cdot \color{blue}{\frac{x}{z}}\]
    7. Using strategy rm

    8. Applied *-un-lft-identity4.0

      \[\leadsto \color{blue}{\left(1 \cdot y\right)} \cdot \frac{x}{z}\]

    9. Applied associate-*l*4.0

      \[\leadsto \color{blue}{1 \cdot \left(y \cdot \frac{x}{z}\right)}\]

    10. Simplified4.1

      \[\leadsto 1 \cdot \color{blue}{\frac{x \cdot y}{z}}\]
    11. Using strategy rm

    12. Applied associate-/l*11.7

      \[\leadsto 1 \cdot \color{blue}{\frac{x}{\frac{z}{y}}}\]
    13. Using strategy rm

    14. Applied div-inv11.8

      \[\leadsto 1 \cdot \frac{x}{\color{blue}{z \cdot \frac{1}{y}}}\]

    15. Applied associate-/r*4.0

      \[\leadsto 1 \cdot \color{blue}{\frac{\frac{x}{z}}{\frac{1}{y}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.009555688743657053093976996432682877192 \cdot 10^{278}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.900141742787772715345890115335440787699 \cdot 10^{-270}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 4.438182973596565301288302827093808047147 \cdot 10^{-272}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 3.561199608254915194562496763078682553454 \cdot 10^{97}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  :precision binary64
  (* x (/ (* (/ y z) t) t)))