Average Error: 2.8 → 0.0
Time: 8.7s
Precision: 64
\[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
↓
\[\frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x} + x\]
x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}
↓
\frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x} + x
double f(double x, double y, double z) {
        double r532421 = x;
        double r532422 = y;
        double r532423 = 1.1283791670955126;
        double r532424 = z;
        double r532425 = exp(r532424);
        double r532426 = r532423 * r532425;
        double r532427 = r532421 * r532422;
        double r532428 = r532426 - r532427;
        double r532429 = r532422 / r532428;
        double r532430 = r532421 + r532429;
        return r532430;
}
↓
double f(double x, double y, double z) {
        double r532431 = 1.0;
        double r532432 = 1.1283791670955126;
        double r532433 = z;
        double r532434 = exp(r532433);
        double r532435 = y;
        double r532436 = r532434 / r532435;
        double r532437 = r532432 * r532436;
        double r532438 = x;
        double r532439 = r532437 - r532438;
        double r532440 = r532431 / r532439;
        double r532441 = r532440 + r532438;
        return r532441;
}

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
\[x + \frac{1}{\frac{1.12837916709551256}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.8

    \[x + \frac{y}{1.12837916709551256 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied clear-num2.8

    \[\leadsto x + \color{blue}{\frac{1}{\frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}}\]
  4. Using strategy rm

  5. Applied *-un-lft-identity2.8

    \[\leadsto x + \frac{1}{\frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{\color{blue}{1 \cdot y}}}\]

  6. Applied *-un-lft-identity2.8

    \[\leadsto x + \frac{1}{\frac{\color{blue}{1 \cdot \left(1.12837916709551256 \cdot e^{z} - x \cdot y\right)}}{1 \cdot y}}\]

  7. Applied times-frac2.8

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1}{1} \cdot \frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}}\]

  8. Simplified2.8

    \[\leadsto x + \frac{1}{\color{blue}{1} \cdot \frac{1.12837916709551256 \cdot e^{z} - x \cdot y}{y}}\]

  9. Simplified0.0

    \[\leadsto x + \frac{1}{1 \cdot \color{blue}{\left(1.12837916709551256 \cdot \frac{e^{z}}{y} - x\right)}}\]

  10. Final simplification0.0

    \[\leadsto \frac{1}{1.12837916709551256 \cdot \frac{e^{z}}{y} - x} + x\]

Reproduce

herbie shell --seed 2020047 
(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)))))