Average Error: 2.8 → 0.0
Time: 11.9s
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 r312005 = x;
        double r312006 = y;
        double r312007 = 1.1283791670955126;
        double r312008 = z;
        double r312009 = exp(r312008);
        double r312010 = r312007 * r312009;
        double r312011 = r312005 * r312006;
        double r312012 = r312010 - r312011;
        double r312013 = r312006 / r312012;
        double r312014 = r312005 + r312013;
        return r312014;
}
↓
double f(double x, double y, double z) {
        double r312015 = x;
        double r312016 = 1.0;
        double r312017 = 1.1283791670955126;
        double r312018 = y;
        double r312019 = z;
        double r312020 = exp(r312019);
        double r312021 = r312018 / r312020;
        double r312022 = r312017 / r312021;
        double r312023 = -r312015;
        double r312024 = r312022 + r312023;
        double r312025 = r312016 / r312024;
        double r312026 = r312015 + r312025;
        return r312026;
}

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)))))