Average Error: 15.1 → 0.7
Time: 30.2s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.167382686214397895425941397509630236779 \cdot 10^{231}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.827587823355642407973457381841440310715 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.053250369059781787110723173910298691639 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 1.111565981439738552177075156972483526402 \cdot 10^{232}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -1.167382686214397895425941397509630236779 \cdot 10^{231}:\\
\;\;\;\;\frac{x \cdot y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -1.827587823355642407973457381841440310715 \cdot 10^{-156}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le 1.053250369059781787110723173910298691639 \cdot 10^{-123}:\\
\;\;\;\;\frac{x}{z} \cdot y\\

\mathbf{elif}\;\frac{y}{z} \le 1.111565981439738552177075156972483526402 \cdot 10^{232}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r23554393 = x;
        double r23554394 = y;
        double r23554395 = z;
        double r23554396 = r23554394 / r23554395;
        double r23554397 = t;
        double r23554398 = r23554396 * r23554397;
        double r23554399 = r23554398 / r23554397;
        double r23554400 = r23554393 * r23554399;
        return r23554400;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r23554401 = y;
        double r23554402 = z;
        double r23554403 = r23554401 / r23554402;
        double r23554404 = -1.1673826862143979e+231;
        bool r23554405 = r23554403 <= r23554404;
        double r23554406 = x;
        double r23554407 = r23554406 * r23554401;
        double r23554408 = r23554407 / r23554402;
        double r23554409 = -1.8275878233556424e-156;
        bool r23554410 = r23554403 <= r23554409;
        double r23554411 = r23554403 * r23554406;
        double r23554412 = 1.0532503690597818e-123;
        bool r23554413 = r23554403 <= r23554412;
        double r23554414 = r23554406 / r23554402;
        double r23554415 = r23554414 * r23554401;
        double r23554416 = 1.1115659814397386e+232;
        bool r23554417 = r23554403 <= r23554416;
        double r23554418 = r23554417 ? r23554411 : r23554415;
        double r23554419 = r23554413 ? r23554415 : r23554418;
        double r23554420 = r23554410 ? r23554411 : r23554419;
        double r23554421 = r23554405 ? r23554408 : r23554420;
        return r23554421;
}

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

Target

Original15.1
Target1.5
Herbie0.7
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 3 regimes

  2. if (/ y z) < -1.1673826862143979e+231

    1. Initial program 50.5

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

    2. Simplified0.8

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

    3. Taylor expanded around 0 0.7

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

    if -1.1673826862143979e+231 < (/ y z) < -1.8275878233556424e-156 or 1.0532503690597818e-123 < (/ y z) < 1.1115659814397386e+232

    1. Initial program 8.2

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

    2. Simplified11.2

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

    3. Taylor expanded around 0 9.7

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

    5. Applied *-un-lft-identity9.7

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

    6. Applied times-frac0.3

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

    7. Simplified0.3

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

    if -1.8275878233556424e-156 < (/ y z) < 1.0532503690597818e-123 or 1.1115659814397386e+232 < (/ y z)

    1. Initial program 20.2

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

    2. Simplified1.3

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

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.167382686214397895425941397509630236779 \cdot 10^{231}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.827587823355642407973457381841440310715 \cdot 10^{-156}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.053250369059781787110723173910298691639 \cdot 10^{-123}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 1.111565981439738552177075156972483526402 \cdot 10^{232}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"

  :herbie-target
  (if (< (/ (* (/ y z) t) t) -1.20672205123045e+245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.907522236933906e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.658954423153415e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e+217) (* x (/ y z)) (/ (* y x) z)))))

  (* x (/ (* (/ y z) t) t)))