Average Error: 2.3 → 2.4
Time: 4.2s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\begin{array}{l} \mathbf{if}\;t \le 8.74690451588153372 \cdot 10^{-269}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{elif}\;t \le 3.5231411634558426 \cdot 10^{-34}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array}\]
\frac{x - y}{z - y} \cdot t
↓
\begin{array}{l}
\mathbf{if}\;t \le 8.74690451588153372 \cdot 10^{-269}:\\
\;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\

\mathbf{elif}\;t \le 3.5231411634558426 \cdot 10^{-34}:\\
\;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\

\mathbf{else}:\\
\;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r437028 = x;
        double r437029 = y;
        double r437030 = r437028 - r437029;
        double r437031 = z;
        double r437032 = r437031 - r437029;
        double r437033 = r437030 / r437032;
        double r437034 = t;
        double r437035 = r437033 * r437034;
        return r437035;
}
↓
double f(double x, double y, double z, double t) {
        double r437036 = t;
        double r437037 = 8.746904515881534e-269;
        bool r437038 = r437036 <= r437037;
        double r437039 = x;
        double r437040 = y;
        double r437041 = r437039 - r437040;
        double r437042 = 1.0;
        double r437043 = z;
        double r437044 = r437043 - r437040;
        double r437045 = r437042 / r437044;
        double r437046 = r437041 * r437045;
        double r437047 = r437046 * r437036;
        double r437048 = 3.5231411634558426e-34;
        bool r437049 = r437036 <= r437048;
        double r437050 = r437041 * r437036;
        double r437051 = r437050 / r437044;
        double r437052 = r437036 / r437044;
        double r437053 = r437041 * r437052;
        double r437054 = r437049 ? r437051 : r437053;
        double r437055 = r437038 ? r437047 : r437054;
        return r437055;
}

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

Original2.3
Target2.3
Herbie2.4
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Split input into 3 regimes

  2. if t < 8.746904515881534e-269

    1. Initial program 2.6

      \[\frac{x - y}{z - y} \cdot t\]
    2. Using strategy rm

    3. Applied div-inv2.7

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

    if 8.746904515881534e-269 < t < 3.5231411634558426e-34

    1. Initial program 1.8

      \[\frac{x - y}{z - y} \cdot t\]
    2. Using strategy rm

    3. Applied add-cube-cbrt3.0

      \[\leadsto \frac{x - y}{z - y} \cdot \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\]

    4. Applied associate-*r*3.0

      \[\leadsto \color{blue}{\left(\frac{x - y}{z - y} \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t}}\]
    5. Using strategy rm

    6. Applied associate-*l/2.2

      \[\leadsto \color{blue}{\frac{\left(x - y\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)}{z - y}} \cdot \sqrt[3]{t}\]

    7. Applied associate-*l/2.6

      \[\leadsto \color{blue}{\frac{\left(\left(x - y\right) \cdot \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) \cdot \sqrt[3]{t}}{z - y}}\]

    8. Simplified1.5

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

    if 3.5231411634558426e-34 < t

    1. Initial program 1.9

      \[\frac{x - y}{z - y} \cdot t\]
    2. Using strategy rm

    3. Applied div-inv2.1

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

    4. Applied associate-*l*2.5

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

    5. Simplified2.4

      \[\leadsto \left(x - y\right) \cdot \color{blue}{\frac{t}{z - y}}\]
  3. Recombined 3 regimes into one program.

  4. Final simplification2.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;t \le 8.74690451588153372 \cdot 10^{-269}:\\ \;\;\;\;\left(\left(x - y\right) \cdot \frac{1}{z - y}\right) \cdot t\\ \mathbf{elif}\;t \le 3.5231411634558426 \cdot 10^{-34}:\\ \;\;\;\;\frac{\left(x - y\right) \cdot t}{z - y}\\ \mathbf{else}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{t}{z - y}\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

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