Average Error: 2.8 → 0.0
Time: 13.3s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{\frac{y}{e^{z}}} + \left(-x\right)}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{\frac{y}{e^{z}}} + \left(-x\right)}
double f(double x, double y, double z) {
        double r234951 = x;
        double r234952 = y;
        double r234953 = 1.1283791670955126;
        double r234954 = z;
        double r234955 = exp(r234954);
        double r234956 = r234953 * r234955;
        double r234957 = r234951 * r234952;
        double r234958 = r234956 - r234957;
        double r234959 = r234952 / r234958;
        double r234960 = r234951 + r234959;
        return r234960;
}
↓
double f(double x, double y, double z) {
        double r234961 = x;
        double r234962 = 1.0;
        double r234963 = 1.1283791670955126;
        double r234964 = y;
        double r234965 = z;
        double r234966 = exp(r234965);
        double r234967 = r234964 / r234966;
        double r234968 = r234963 / r234967;
        double r234969 = -r234961;
        double r234970 = r234968 + r234969;
        double r234971 = r234962 / r234970;
        double r234972 = r234961 + r234971;
        return r234972;
}

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

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. Simplified0.1

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

  6. Applied fma-udef0.1

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

  7. Simplified0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 +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)))))