Average Error: 0.2 → 0.0
Time: 27.0s
Precision: 64
\[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
↓
\[\frac{x - 1}{4 \cdot \sqrt{x} + \left(x + 1\right)} \cdot 6\]
\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}
↓
\frac{x - 1}{4 \cdot \sqrt{x} + \left(x + 1\right)} \cdot 6
double f(double x) {
        double r42798198 = 6.0;
        double r42798199 = x;
        double r42798200 = 1.0;
        double r42798201 = r42798199 - r42798200;
        double r42798202 = r42798198 * r42798201;
        double r42798203 = r42798199 + r42798200;
        double r42798204 = 4.0;
        double r42798205 = sqrt(r42798199);
        double r42798206 = r42798204 * r42798205;
        double r42798207 = r42798203 + r42798206;
        double r42798208 = r42798202 / r42798207;
        return r42798208;
}
↓
double f(double x) {
        double r42798209 = x;
        double r42798210 = 1.0;
        double r42798211 = r42798209 - r42798210;
        double r42798212 = 4.0;
        double r42798213 = sqrt(r42798209);
        double r42798214 = r42798212 * r42798213;
        double r42798215 = r42798209 + r42798210;
        double r42798216 = r42798214 + r42798215;
        double r42798217 = r42798211 / r42798216;
        double r42798218 = 6.0;
        double r42798219 = r42798217 * r42798218;
        return r42798219;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.0
\[\frac{6}{\frac{\left(x + 1\right) + 4 \cdot \sqrt{x}}{x - 1}}\]

Derivation

  1. Initial program 0.2

    \[\frac{6 \cdot \left(x - 1\right)}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]
  2. Using strategy rm

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

    \[\leadsto \frac{6 \cdot \left(x - 1\right)}{\color{blue}{1 \cdot \left(\left(x + 1\right) + 4 \cdot \sqrt{x}\right)}}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{6}{1} \cdot \frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{6} \cdot \frac{x - 1}{\left(x + 1\right) + 4 \cdot \sqrt{x}}\]

  6. Final simplification0.0

    \[\leadsto \frac{x - 1}{4 \cdot \sqrt{x} + \left(x + 1\right)} \cdot 6\]

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)))))