Average Error: 2.8 → 0.1
Time: 13.5s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{e^{z}}{y} \cdot 1.128379167095512558560699289955664426088 + \left(-x\right)}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{e^{z}}{y} \cdot 1.128379167095512558560699289955664426088 + \left(-x\right)}
double f(double x, double y, double z) {
        double r276185 = x;
        double r276186 = y;
        double r276187 = 1.1283791670955126;
        double r276188 = z;
        double r276189 = exp(r276188);
        double r276190 = r276187 * r276189;
        double r276191 = r276185 * r276186;
        double r276192 = r276190 - r276191;
        double r276193 = r276186 / r276192;
        double r276194 = r276185 + r276193;
        return r276194;
}
↓
double f(double x, double y, double z) {
        double r276195 = x;
        double r276196 = 1.0;
        double r276197 = z;
        double r276198 = exp(r276197);
        double r276199 = y;
        double r276200 = r276198 / r276199;
        double r276201 = 1.1283791670955126;
        double r276202 = r276200 * r276201;
        double r276203 = -r276195;
        double r276204 = r276202 + r276203;
        double r276205 = r276196 / r276204;
        double r276206 = r276195 + r276205;
        return r276206;
}

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

Original2.8
Target0.0
Herbie0.1
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.8

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

  3. Applied clear-num2.8

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

  4. Simplified0.0

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

  6. Applied fma-udef0.0

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ x (/ 1 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

  (+ x (/ y (- (* 1.1283791670955126 (exp z)) (* x y)))))