Average Error: 0.0 → 0.0
Time: 8.9s
Precision: 64
\[\sqrt{1 - x \cdot x}\]
↓
\[\sqrt{\frac{1 \cdot \left(1 \cdot 1\right) - \left(x \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)}{\left(x \cdot x\right) \cdot \left(1 + x \cdot x\right) + 1 \cdot 1}}\]
\sqrt{1 - x \cdot x}
↓
\sqrt{\frac{1 \cdot \left(1 \cdot 1\right) - \left(x \cdot \left(x \cdot x\right)\right) \cdot \left(x \cdot \left(x \cdot x\right)\right)}{\left(x \cdot x\right) \cdot \left(1 + x \cdot x\right) + 1 \cdot 1}}
double f(double x) {
        double r9016112 = 1.0;
        double r9016113 = x;
        double r9016114 = r9016113 * r9016113;
        double r9016115 = r9016112 - r9016114;
        double r9016116 = sqrt(r9016115);
        return r9016116;
}
↓
double f(double x) {
        double r9016117 = 1.0;
        double r9016118 = r9016117 * r9016117;
        double r9016119 = r9016117 * r9016118;
        double r9016120 = x;
        double r9016121 = r9016120 * r9016120;
        double r9016122 = r9016120 * r9016121;
        double r9016123 = r9016122 * r9016122;
        double r9016124 = r9016119 - r9016123;
        double r9016125 = r9016117 + r9016121;
        double r9016126 = r9016121 * r9016125;
        double r9016127 = r9016126 + r9016118;
        double r9016128 = r9016124 / r9016127;
        double r9016129 = sqrt(r9016128);
        return r9016129;
}

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. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019170 
(FPCore (x)
  :name "Diagrams.TwoD.Ellipse:ellipse from diagrams-lib-1.3.0.3"
  (sqrt (- 1.0 (* x x))))