Average Error: 2.7 → 0.0
Time: 9.0s
Precision: 64
\[x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{e^{z}}{\frac{y}{1.128379167095512558560699289955664426088}} + \left(-x\right)}\]
x + \frac{y}{1.128379167095512558560699289955664426088 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{e^{z}}{\frac{y}{1.128379167095512558560699289955664426088}} + \left(-x\right)}
double f(double x, double y, double z) {
        double r291349 = x;
        double r291350 = y;
        double r291351 = 1.1283791670955126;
        double r291352 = z;
        double r291353 = exp(r291352);
        double r291354 = r291351 * r291353;
        double r291355 = r291349 * r291350;
        double r291356 = r291354 - r291355;
        double r291357 = r291350 / r291356;
        double r291358 = r291349 + r291357;
        return r291358;
}
↓
double f(double x, double y, double z) {
        double r291359 = x;
        double r291360 = 1.0;
        double r291361 = z;
        double r291362 = exp(r291361);
        double r291363 = y;
        double r291364 = 1.1283791670955126;
        double r291365 = r291363 / r291364;
        double r291366 = r291362 / r291365;
        double r291367 = -r291359;
        double r291368 = r291366 + r291367;
        double r291369 = r291360 / r291368;
        double r291370 = r291359 + r291369;
        return r291370;
}

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

Original2.7
Target0.0
Herbie0.0
\[x + \frac{1}{\frac{1.128379167095512558560699289955664426088}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.7

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

  3. Applied clear-num2.7

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

  4. Simplified2.7

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

  5. Taylor expanded around inf 0.1

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

  6. Simplified0.1

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

  8. Applied fma-udef0.1

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, A"

  :herbie-target
  (+ x (/ 1.0 (- (* (/ 1.1283791670955126 y) (exp z)) x)))

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