Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\frac{\sqrt{{1}^{3} - {x}^{6}}}{\sqrt{\left(1 + x \cdot x\right) \cdot 1 + {x}^{4}}}\]
\sqrt{1 - x \cdot x}
↓
\frac{\sqrt{{1}^{3} - {x}^{6}}}{\sqrt{\left(1 + x \cdot x\right) \cdot 1 + {x}^{4}}}
double f(double x) {
        double r134296 = 1.0;
        double r134297 = x;
        double r134298 = r134297 * r134297;
        double r134299 = r134296 - r134298;
        double r134300 = sqrt(r134299);
        return r134300;
}
↓
double f(double x) {
        double r134301 = 1.0;
        double r134302 = 3.0;
        double r134303 = pow(r134301, r134302);
        double r134304 = x;
        double r134305 = 6.0;
        double r134306 = pow(r134304, r134305);
        double r134307 = r134303 - r134306;
        double r134308 = sqrt(r134307);
        double r134309 = r134304 * r134304;
        double r134310 = r134301 + r134309;
        double r134311 = r134310 * r134301;
        double r134312 = 4.0;
        double r134313 = pow(r134304, r134312);
        double r134314 = r134311 + r134313;
        double r134315 = sqrt(r134314);
        double r134316 = r134308 / r134315;
        return r134316;
}

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

    \[\sqrt{1 - x \cdot x}\]
  2. Using strategy rm

  3. Applied flip3--0.0

    \[\leadsto \sqrt{\color{blue}{\frac{{1}^{3} - {\left(x \cdot x\right)}^{3}}{1 \cdot 1 + \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right) + 1 \cdot \left(x \cdot x\right)\right)}}}\]

  4. Applied sqrt-div0.0

    \[\leadsto \color{blue}{\frac{\sqrt{{1}^{3} - {\left(x \cdot x\right)}^{3}}}{\sqrt{1 \cdot 1 + \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right) + 1 \cdot \left(x \cdot x\right)\right)}}}\]

  5. Simplified0.0

    \[\leadsto \frac{\color{blue}{\sqrt{{1}^{3} - {x}^{6}}}}{\sqrt{1 \cdot 1 + \left(\left(x \cdot x\right) \cdot \left(x \cdot x\right) + 1 \cdot \left(x \cdot x\right)\right)}}\]

  6. Simplified0.0

    \[\leadsto \frac{\sqrt{{1}^{3} - {x}^{6}}}{\color{blue}{\sqrt{\left(1 + x \cdot x\right) \cdot 1 + {x}^{4}}}}\]

  7. Final simplification0.0

    \[\leadsto \frac{\sqrt{{1}^{3} - {x}^{6}}}{\sqrt{\left(1 + x \cdot x\right) \cdot 1 + {x}^{4}}}\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  :precision binary64
  (sqrt (- 1 (* x x))))