Average Error: 3.0 → 0.1
Time: 10.9s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[\frac{1}{\left(1.128379167095512558560699289955664426088 \cdot e^{z}\right) \cdot \frac{1}{y} - x} + x\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
\frac{1}{\left(1.128379167095512558560699289955664426088 \cdot e^{z}\right) \cdot \frac{1}{y} - x} + x
double f(double x, double y, double z) {
        double r314066 = x;
        double r314067 = y;
        double r314068 = 1.1283791670955126;
        double r314069 = z;
        double r314070 = exp(r314069);
        double r314071 = r314068 * r314070;
        double r314072 = r314066 * r314067;
        double r314073 = r314071 - r314072;
        double r314074 = r314067 / r314073;
        double r314075 = r314066 + r314074;
        return r314075;
}
↓
double f(double x, double y, double z) {
        double r314076 = 1.0;
        double r314077 = 1.1283791670955126;
        double r314078 = z;
        double r314079 = exp(r314078);
        double r314080 = r314077 * r314079;
        double r314081 = y;
        double r314082 = r314076 / r314081;
        double r314083 = r314080 * r314082;
        double r314084 = x;
        double r314085 = r314083 - r314084;
        double r314086 = r314076 / r314085;
        double r314087 = r314086 + r314084;
        return r314087;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original3.0
Target0.1
Herbie0.1
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 3.0

    \[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num3.0

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity3.0

    \[\leadsto x + \frac{1}{\frac{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}{\color{blue}{1 \cdot y}}}\]

  6. Applied *-un-lft-identity3.0

    \[\leadsto x + \frac{1}{\frac{\color{blue}{1 \cdot \left(1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y\right)}}{1 \cdot y}}\]

  7. Applied times-frac3.0

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{1} \cdot \frac{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}{y}}}\]

  8. Simplified3.0

    \[\leadsto x + \frac{1}{\color{blue}{1} \cdot \frac{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}{y}}\]

  9. Simplified0.0

    \[\leadsto x + \frac{1}{1 \cdot \color{blue}{\left(\frac{1.128379167095512558560699289955664426088 \cdot e^{z}}{y} - x\right)}}\]
  10. Using strategy rm

  11. Applied div-inv0.1

    \[\leadsto x + \frac{1}{1 \cdot \left(\color{blue}{\left(1.128379167095512558560699289955664426088 \cdot e^{z}\right) \cdot \frac{1}{y}} - x\right)}\]

  12. Final simplification0.1

    \[\leadsto \frac{1}{\left(1.128379167095512558560699289955664426088 \cdot e^{z}\right) \cdot \frac{1}{y} - x} + x\]

Reproduce

herbie shell --seed 2019209 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.12837916709551256 y) (exp z)) x)))

  (+ x (/ y (- (* 1.12837916709551256 (exp z)) (* x y)))))