Average Error: 2.9 → 0.0
Time: 36.7s
Precision: 64
\[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
↓
\[x + \frac{1}{\frac{1.1283791670955126}{\frac{y}{e^{z}}} + \left(-x\right)}\]
x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}
↓
x + \frac{1}{\frac{1.1283791670955126}{\frac{y}{e^{z}}} + \left(-x\right)}
double f(double x, double y, double z) {
        double r25070386 = x;
        double r25070387 = y;
        double r25070388 = 1.1283791670955126;
        double r25070389 = z;
        double r25070390 = exp(r25070389);
        double r25070391 = r25070388 * r25070390;
        double r25070392 = r25070386 * r25070387;
        double r25070393 = r25070391 - r25070392;
        double r25070394 = r25070387 / r25070393;
        double r25070395 = r25070386 + r25070394;
        return r25070395;
}
↓
double f(double x, double y, double z) {
        double r25070396 = x;
        double r25070397 = 1.0;
        double r25070398 = 1.1283791670955126;
        double r25070399 = y;
        double r25070400 = z;
        double r25070401 = exp(r25070400);
        double r25070402 = r25070399 / r25070401;
        double r25070403 = r25070398 / r25070402;
        double r25070404 = -r25070396;
        double r25070405 = r25070403 + r25070404;
        double r25070406 = r25070397 / r25070405;
        double r25070407 = r25070396 + r25070406;
        return r25070407;
}

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

Original2.9
Target0.0
Herbie0.0
\[x + \frac{1.0}{\frac{1.1283791670955126}{y} \cdot e^{z} - x}\]

Derivation

  1. Initial program 2.9

    \[x + \frac{y}{1.1283791670955126 \cdot e^{z} - x \cdot y}\]
  2. Using strategy rm

  3. Applied add-log-exp3.0

    \[\leadsto x + \frac{y}{\color{blue}{\log \left(e^{1.1283791670955126 \cdot e^{z}}\right)} - x \cdot y}\]
  4. Using strategy rm

  5. Applied clear-num3.0

    \[\leadsto x + \color{blue}{\frac{1}{\frac{\log \left(e^{1.1283791670955126 \cdot e^{z}}\right) - x \cdot y}{y}}}\]

  6. Simplified0.0

    \[\leadsto x + \frac{1}{\color{blue}{\frac{1.1283791670955126}{\frac{y}{e^{z}}} + \left(-x\right)}}\]

  7. Final simplification0.0

    \[\leadsto x + \frac{1}{\frac{1.1283791670955126}{\frac{y}{e^{z}}} + \left(-x\right)}\]

Reproduce

herbie shell --seed 2019165 
(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)))))