Average Error: 14.2 → 0.6
Time: 8.8s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.89968713120227716200243957970138180903 \cdot 10^{210}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.674553152877029983261934607928478862346 \cdot 10^{-163}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.288243228157504650577480569870560524088 \cdot 10^{170}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -2.89968713120227716200243957970138180903 \cdot 10^{210}:\\
\;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\

\mathbf{elif}\;\frac{y}{z} \le -2.674553152877029983261934607928478862346 \cdot 10^{-163}:\\
\;\;\;\;\frac{y}{z} \cdot x\\

\mathbf{elif}\;\frac{y}{z} \le -0.0:\\
\;\;\;\;\frac{y \cdot x}{z}\\

\mathbf{elif}\;\frac{y}{z} \le 1.288243228157504650577480569870560524088 \cdot 10^{170}:\\
\;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\

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

\end{array}
double f(double x, double y, double z, double t) {
        double r411473 = x;
        double r411474 = y;
        double r411475 = z;
        double r411476 = r411474 / r411475;
        double r411477 = t;
        double r411478 = r411476 * r411477;
        double r411479 = r411478 / r411477;
        double r411480 = r411473 * r411479;
        return r411480;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r411481 = y;
        double r411482 = z;
        double r411483 = r411481 / r411482;
        double r411484 = -2.899687131202277e+210;
        bool r411485 = r411483 <= r411484;
        double r411486 = 1.0;
        double r411487 = x;
        double r411488 = r411482 / r411487;
        double r411489 = r411488 / r411481;
        double r411490 = r411486 / r411489;
        double r411491 = -2.67455315287703e-163;
        bool r411492 = r411483 <= r411491;
        double r411493 = r411483 * r411487;
        double r411494 = -0.0;
        bool r411495 = r411483 <= r411494;
        double r411496 = r411481 * r411487;
        double r411497 = r411496 / r411482;
        double r411498 = 1.2882432281575047e+170;
        bool r411499 = r411483 <= r411498;
        double r411500 = r411486 / r411487;
        double r411501 = r411483 / r411500;
        double r411502 = r411487 / r411482;
        double r411503 = r411481 * r411502;
        double r411504 = r411499 ? r411501 : r411503;
        double r411505 = r411495 ? r411497 : r411504;
        double r411506 = r411492 ? r411493 : r411505;
        double r411507 = r411485 ? r411490 : r411506;
        return r411507;
}

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

Original14.2
Target1.5
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \lt -1.206722051230450047215521150762600712224 \cdot 10^{245}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt -5.90752223693390632993316700759382836344 \cdot 10^{-275}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 5.658954423153415216825328199697215652986 \cdot 10^{-65}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \lt 2.008718050240713347941382056648619307142 \cdot 10^{217}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 5 regimes

  2. if (/ y z) < -2.899687131202277e+210

    1. Initial program 42.0

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

    2. Simplified0.7

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

    4. Applied associate-/l*1.1

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

    6. Applied clear-num1.2

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

    if -2.899687131202277e+210 < (/ y z) < -2.67455315287703e-163

    1. Initial program 7.5

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

    2. Simplified10.1

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

    4. Applied associate-/l*10.1

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

    6. Applied associate-/r/0.2

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

    if -2.67455315287703e-163 < (/ y z) < -0.0

    1. Initial program 16.9

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

    2. Simplified0.8

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

    if -0.0 < (/ y z) < 1.2882432281575047e+170

    1. Initial program 10.2

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

    2. Simplified7.5

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

    4. Applied associate-/l*6.7

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

    6. Applied div-inv6.7

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

    7. Applied associate-/r*3.5

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

    if 1.2882432281575047e+170 < (/ y z)

    1. Initial program 37.2

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

    2. Simplified2.2

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

    4. Applied *-un-lft-identity2.2

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

    5. Applied times-frac1.8

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

    6. Simplified1.8

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

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.89968713120227716200243957970138180903 \cdot 10^{210}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.674553152877029983261934607928478862346 \cdot 10^{-163}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.288243228157504650577480569870560524088 \cdot 10^{170}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019209 
(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) -1.20672205123045005e245) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) -5.90752223693390633e-275) (* x (/ y z)) (if (< (/ (* (/ y z) t) t) 5.65895442315341522e-65) (/ y (/ z x)) (if (< (/ (* (/ y z) t) t) 2.0087180502407133e217) (* x (/ y z)) (/ (* y x) z)))))

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