Average Error: 0.0 → 0.0
Time: 1.2s
Precision: 64
\[\tan^{-1} \left(x \cdot x - 1\right)\]
\[\tan^{-1} \left(x \cdot x - 1\right)\]
\tan^{-1} \left(x \cdot x - 1\right)
\tan^{-1} \left(x \cdot x - 1\right)
double f(double x) {
        double r55686311 = x;
        double r55686312 = r55686311 * r55686311;
        double r55686313 = 1.0;
        double r55686314 = r55686312 - r55686313;
        double r55686315 = atan(r55686314);
        return r55686315;
}

double f(double x) {
        double r55686316 = x;
        double r55686317 = r55686316 * r55686316;
        double r55686318 = 1.0;
        double r55686319 = r55686317 - r55686318;
        double r55686320 = atan(r55686319);
        return r55686320;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.0

    \[\tan^{-1} \left(x \cdot x - 1\right)\]
  2. Final simplification0.0

    \[\leadsto \tan^{-1} \left(x \cdot x - 1\right)\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "atan(x*x - 1)"
  (atan (- (* x x) 1.0)))