Average Error: 0.2 → 0.0
Time: 12.6s
Precision: 64
\[\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]
↓
\[\frac{x - 1.0}{4.0 \cdot \sqrt{x} + \left(x + 1.0\right)} \cdot 6.0\]
\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}
↓
\frac{x - 1.0}{4.0 \cdot \sqrt{x} + \left(x + 1.0\right)} \cdot 6.0
double f(double x) {
        double r39173307 = 6.0;
        double r39173308 = x;
        double r39173309 = 1.0;
        double r39173310 = r39173308 - r39173309;
        double r39173311 = r39173307 * r39173310;
        double r39173312 = r39173308 + r39173309;
        double r39173313 = 4.0;
        double r39173314 = sqrt(r39173308);
        double r39173315 = r39173313 * r39173314;
        double r39173316 = r39173312 + r39173315;
        double r39173317 = r39173311 / r39173316;
        return r39173317;
}
↓
double f(double x) {
        double r39173318 = x;
        double r39173319 = 1.0;
        double r39173320 = r39173318 - r39173319;
        double r39173321 = 4.0;
        double r39173322 = sqrt(r39173318);
        double r39173323 = r39173321 * r39173322;
        double r39173324 = r39173318 + r39173319;
        double r39173325 = r39173323 + r39173324;
        double r39173326 = r39173320 / r39173325;
        double r39173327 = 6.0;
        double r39173328 = r39173326 * r39173327;
        return r39173328;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.0
\[\frac{6.0}{\frac{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}{x - 1.0}}\]

Derivation

  1. Initial program 0.2

    \[\frac{6.0 \cdot \left(x - 1.0\right)}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.2

    \[\leadsto \frac{6.0 \cdot \left(x - 1.0\right)}{\color{blue}{1 \cdot \left(\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}\right)}}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{6.0}{1} \cdot \frac{x - 1.0}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{6.0} \cdot \frac{x - 1.0}{\left(x + 1.0\right) + 4.0 \cdot \sqrt{x}}\]

  6. Final simplification0.0

    \[\leadsto \frac{x - 1.0}{4.0 \cdot \sqrt{x} + \left(x + 1.0\right)} \cdot 6.0\]

Reproduce

herbie shell --seed 2019168 
(FPCore (x)
  :name "Data.Approximate.Numerics:blog from approximate-0.2.2.1"

  :herbie-target
  (/ 6.0 (/ (+ (+ x 1.0) (* 4.0 (sqrt x))) (- x 1.0)))

  (/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x)))))