Average Error: 0.0 → 0.0
Time: 15.9s
Precision: 64
\[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
↓
\[0.70711 \cdot \left(\frac{1}{\frac{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}{x \cdot 0.27061 + 2.30753}} - x\right)\]
0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)
↓
0.70711 \cdot \left(\frac{1}{\frac{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}{x \cdot 0.27061 + 2.30753}} - x\right)
double f(double x) {
        double r5164281 = 0.70711;
        double r5164282 = 2.30753;
        double r5164283 = x;
        double r5164284 = 0.27061;
        double r5164285 = r5164283 * r5164284;
        double r5164286 = r5164282 + r5164285;
        double r5164287 = 1.0;
        double r5164288 = 0.99229;
        double r5164289 = 0.04481;
        double r5164290 = r5164283 * r5164289;
        double r5164291 = r5164288 + r5164290;
        double r5164292 = r5164283 * r5164291;
        double r5164293 = r5164287 + r5164292;
        double r5164294 = r5164286 / r5164293;
        double r5164295 = r5164294 - r5164283;
        double r5164296 = r5164281 * r5164295;
        return r5164296;
}
↓
double f(double x) {
        double r5164297 = 0.70711;
        double r5164298 = 1.0;
        double r5164299 = x;
        double r5164300 = 0.04481;
        double r5164301 = r5164299 * r5164300;
        double r5164302 = 0.99229;
        double r5164303 = r5164301 + r5164302;
        double r5164304 = r5164299 * r5164303;
        double r5164305 = 1.0;
        double r5164306 = r5164304 + r5164305;
        double r5164307 = 0.27061;
        double r5164308 = r5164299 * r5164307;
        double r5164309 = 2.30753;
        double r5164310 = r5164308 + r5164309;
        double r5164311 = r5164306 / r5164310;
        double r5164312 = r5164298 / r5164311;
        double r5164313 = r5164312 - r5164299;
        double r5164314 = r5164297 * r5164313;
        return r5164314;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[0.70711 \cdot \left(\frac{2.30753 + x \cdot 0.27061}{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)} - x\right)\]
  2. Using strategy rm

  3. Applied clear-num0.0

    \[\leadsto 0.70711 \cdot \left(\color{blue}{\frac{1}{\frac{1.0 + x \cdot \left(0.99229 + x \cdot 0.04481\right)}{2.30753 + x \cdot 0.27061}}} - x\right)\]

  4. Final simplification0.0

    \[\leadsto 0.70711 \cdot \left(\frac{1}{\frac{x \cdot \left(x \cdot 0.04481 + 0.99229\right) + 1.0}{x \cdot 0.27061 + 2.30753}} - x\right)\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))