Average Error: 2.0 → 2.0
Time: 10.3s
Precision: 64
\[\frac{x - y}{z - y} \cdot t\]
↓
\[\frac{t}{\frac{z - y}{x - y}}\]
\frac{x - y}{z - y} \cdot t
↓
\frac{t}{\frac{z - y}{x - y}}
double f(double x, double y, double z, double t) {
        double r1990 = x;
        double r1991 = y;
        double r1992 = r1990 - r1991;
        double r1993 = z;
        double r1994 = r1993 - r1991;
        double r1995 = r1992 / r1994;
        double r1996 = t;
        double r1997 = r1995 * r1996;
        return r1997;
}
↓
double f(double x, double y, double z, double t) {
        double r1998 = t;
        double r1999 = z;
        double r2000 = y;
        double r2001 = r1999 - r2000;
        double r2002 = x;
        double r2003 = r2002 - r2000;
        double r2004 = r2001 / r2003;
        double r2005 = r1998 / r2004;
        return r2005;
}

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

Original2.0
Target2.0
Herbie2.0
\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

  1. Initial program 2.0

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

  3. Applied clear-num2.2

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

  5. Applied pow12.2

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

  6. Applied pow12.2

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

  7. Applied pow-prod-down2.2

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

  8. Simplified2.0

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

  9. Final simplification2.0

    \[\leadsto \frac{t}{\frac{z - y}{x - y}}\]

Reproduce

herbie shell --seed 2020025 +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))