Average Error: 0.2 → 0.0
Time: 8.7s
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 r17279649 = 6.0;
        double r17279650 = x;
        double r17279651 = 1.0;
        double r17279652 = r17279650 - r17279651;
        double r17279653 = r17279649 * r17279652;
        double r17279654 = r17279650 + r17279651;
        double r17279655 = 4.0;
        double r17279656 = sqrt(r17279650);
        double r17279657 = r17279655 * r17279656;
        double r17279658 = r17279654 + r17279657;
        double r17279659 = r17279653 / r17279658;
        return r17279659;
}
↓
double f(double x) {
        double r17279660 = x;
        double r17279661 = 1.0;
        double r17279662 = r17279660 - r17279661;
        double r17279663 = 4.0;
        double r17279664 = sqrt(r17279660);
        double r17279665 = r17279663 * r17279664;
        double r17279666 = r17279660 + r17279661;
        double r17279667 = r17279665 + r17279666;
        double r17279668 = r17279662 / r17279667;
        double r17279669 = 6.0;
        double r17279670 = r17279668 * r17279669;
        return r17279670;
}

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

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 2019156 
(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)))))