Average Error: 14.2 → 0.6
Time: 10.8s
Precision: 64
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.89968713120227716200243957970138180903 \cdot 10^{210}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.674553152877029983261934607928478862346 \cdot 10^{-163}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.288243228157504650577480569870560524088 \cdot 10^{170}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]
x \cdot \frac{\frac{y}{z} \cdot t}{t}
↓
\begin{array}{l}
\mathbf{if}\;\frac{y}{z} \le -2.89968713120227716200243957970138180903 \cdot 10^{210}:\\
\;\;\;\;\frac{y}{\frac{z}{x}}\\

\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 r491947 = x;
        double r491948 = y;
        double r491949 = z;
        double r491950 = r491948 / r491949;
        double r491951 = t;
        double r491952 = r491950 * r491951;
        double r491953 = r491952 / r491951;
        double r491954 = r491947 * r491953;
        return r491954;
}
↓
double f(double x, double y, double z, double __attribute__((unused)) t) {
        double r491955 = y;
        double r491956 = z;
        double r491957 = r491955 / r491956;
        double r491958 = -2.899687131202277e+210;
        bool r491959 = r491957 <= r491958;
        double r491960 = x;
        double r491961 = r491956 / r491960;
        double r491962 = r491955 / r491961;
        double r491963 = -2.67455315287703e-163;
        bool r491964 = r491957 <= r491963;
        double r491965 = r491957 * r491960;
        double r491966 = -0.0;
        bool r491967 = r491957 <= r491966;
        double r491968 = r491955 * r491960;
        double r491969 = r491968 / r491956;
        double r491970 = 1.2882432281575047e+170;
        bool r491971 = r491957 <= r491970;
        double r491972 = 1.0;
        double r491973 = r491972 / r491960;
        double r491974 = r491957 / r491973;
        double r491975 = r491960 / r491956;
        double r491976 = r491955 * r491975;
        double r491977 = r491971 ? r491974 : r491976;
        double r491978 = r491967 ? r491969 : r491977;
        double r491979 = r491964 ? r491965 : r491978;
        double r491980 = r491959 ? r491962 : r491979;
        return r491980;
}

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

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

    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

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(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)))