Average Error: 2.2 → 1.3
Time: 14.5s
Precision: 64
\[\sin^{-1} \left(x + 1\right) - 2\]
\[\frac{\sin^{-1} \left(x + 1\right) \cdot \left(\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right)\right) - 2 \cdot \left(2 \cdot 2\right)}{\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right) + \left(2 \cdot 2 + \sin^{-1} \left(x + 1\right) \cdot 2\right)}\]
\sin^{-1} \left(x + 1\right) - 2
\frac{\sin^{-1} \left(x + 1\right) \cdot \left(\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right)\right) - 2 \cdot \left(2 \cdot 2\right)}{\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right) + \left(2 \cdot 2 + \sin^{-1} \left(x + 1\right) \cdot 2\right)}
double f(double x) {
        double r22373301 = x;
        double r22373302 = 1.0;
        double r22373303 = r22373301 + r22373302;
        double r22373304 = asin(r22373303);
        double r22373305 = 2.0;
        double r22373306 = r22373304 - r22373305;
        return r22373306;
}

double f(double x) {
        double r22373307 = x;
        double r22373308 = 1.0;
        double r22373309 = r22373307 + r22373308;
        double r22373310 = asin(r22373309);
        double r22373311 = r22373310 * r22373310;
        double r22373312 = r22373310 * r22373311;
        double r22373313 = 2.0;
        double r22373314 = r22373313 * r22373313;
        double r22373315 = r22373313 * r22373314;
        double r22373316 = r22373312 - r22373315;
        double r22373317 = r22373310 * r22373313;
        double r22373318 = r22373314 + r22373317;
        double r22373319 = r22373311 + r22373318;
        double r22373320 = r22373316 / r22373319;
        return r22373320;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.2

    \[\sin^{-1} \left(x + 1\right) - 2\]
  2. Using strategy rm
  3. Applied flip3--1.3

    \[\leadsto \color{blue}{\frac{{\left(\sin^{-1} \left(x + 1\right)\right)}^{3} - {2}^{3}}{\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right) + \left(2 \cdot 2 + \sin^{-1} \left(x + 1\right) \cdot 2\right)}}\]
  4. Simplified1.3

    \[\leadsto \frac{\color{blue}{\left(\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right)\right) \cdot \sin^{-1} \left(x + 1\right) - \left(2 \cdot 2\right) \cdot 2}}{\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right) + \left(2 \cdot 2 + \sin^{-1} \left(x + 1\right) \cdot 2\right)}\]
  5. Final simplification1.3

    \[\leadsto \frac{\sin^{-1} \left(x + 1\right) \cdot \left(\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right)\right) - 2 \cdot \left(2 \cdot 2\right)}{\sin^{-1} \left(x + 1\right) \cdot \sin^{-1} \left(x + 1\right) + \left(2 \cdot 2 + \sin^{-1} \left(x + 1\right) \cdot 2\right)}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "asin(x+1)-2"
  (- (asin (+ x 1.0)) 2.0))