Average Error: 14.8 → 0.4
Time: 1.9s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.6183489977482823 \cdot 10^{236}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -6.8792362608384231 \cdot 10^{-264}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.06689610291439 \cdot 10^{-310}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le 8.69850988828769301 \cdot 10^{221}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -4.6183489977482823 \cdot 10^{236}:\\
\;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\

\mathbf{elif}\;\frac{y}{z} \le -6.8792362608384231 \cdot 10^{-264}:\\
\;\;\;\;x \cdot \frac{y}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 1.06689610291439 \cdot 10^{-310}:\\
\;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\

\mathbf{elif}\;\frac{y}{z} \le 8.69850988828769301 \cdot 10^{221}:\\
\;\;\;\;\frac{x}{\frac{z}{y}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r598516 = x;
        double r598517 = y;
        double r598518 = z;
        double r598519 = r598517 / r598518;
        double r598520 = t;
        double r598521 = r598519 * r598520;
        double r598522 = r598521 / r598520;
        double r598523 = r598516 * r598522;
        return r598523;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r598524 = y;
        double r598525 = z;
        double r598526 = r598524 / r598525;
        double r598527 = -4.618348997748282e+236;
        bool r598528 = r598526 <= r598527;
        double r598529 = x;
        double r598530 = r598529 * r598524;
        double r598531 = 1.0;
        double r598532 = r598531 / r598525;
        double r598533 = r598530 * r598532;
        double r598534 = -6.879236260838423e-264;
        bool r598535 = r598526 <= r598534;
        double r598536 = r598529 * r598526;
        double r598537 = 1.0668961029144e-310;
        bool r598538 = r598526 <= r598537;
        double r598539 = r598525 / r598530;
        double r598540 = r598531 / r598539;
        double r598541 = 8.698509888287693e+221;
        bool r598542 = r598526 <= r598541;
        double r598543 = r598525 / r598524;
        double r598544 = r598529 / r598543;
        double r598545 = r598525 / r598529;
        double r598546 = r598545 / r598524;
        double r598547 = r598531 / r598546;
        double r598548 = r598542 ? r598544 : r598547;
        double r598549 = r598538 ? r598540 : r598548;
        double r598550 = r598535 ? r598536 : r598549;
        double r598551 = r598528 ? r598533 : r598550;
        return r598551;
}

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

Original14.8
Target1.7
Herbie0.4
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.20672205123045005 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390633 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.65895442315341522 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.0087180502407133 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 5 regimes

  2. if (/ y z) < -4.618348997748282e+236

    1. Initial program 47.2

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

    2. Simplified36.9

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

    4. Applied div-inv36.9

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

    5. Applied associate-*r*1.2

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

    if -4.618348997748282e+236 < (/ y z) < -6.879236260838423e-264

    1. Initial program 9.7

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

    2. Simplified0.2

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

    if -6.879236260838423e-264 < (/ y z) < 1.0668961029144e-310

    1. Initial program 19.2

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

    2. Simplified16.5

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

    4. Applied associate-*r/0.1

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

    6. Applied clear-num0.9

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

    if 1.0668961029144e-310 < (/ y z) < 8.698509888287693e+221

    1. Initial program 9.0

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

    2. Simplified0.2

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

    4. Applied associate-*r/8.6

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

    6. Applied associate-/l*0.3

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

    if 8.698509888287693e+221 < (/ y z)

    1. Initial program 44.5

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

    2. Simplified29.9

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

    4. Applied associate-*r/0.8

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

    6. Applied clear-num0.9

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

    8. Applied associate-/r*0.6

      \[\leadsto \frac{1}{\color{blue}{\frac{\frac{z}{x}}{y}}}\]
  3. Recombined 5 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.6183489977482823 \cdot 10^{236}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -6.8792362608384231 \cdot 10^{-264}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.06689610291439 \cdot 10^{-310}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;\frac{y}{z} \le 8.69850988828769301 \cdot 10^{221}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020064 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1, B"
  :precision binary64

  :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)))