Average Error: 0.0 → 0.0
Time: 1.2s
Precision: 64
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
↓
\[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
↓
x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}
double f(double x) {
        double r69003 = x;
        double r69004 = 2.30753;
        double r69005 = 0.27061;
        double r69006 = r69003 * r69005;
        double r69007 = r69004 + r69006;
        double r69008 = 1.0;
        double r69009 = 0.99229;
        double r69010 = 0.04481;
        double r69011 = r69003 * r69010;
        double r69012 = r69009 + r69011;
        double r69013 = r69012 * r69003;
        double r69014 = r69008 + r69013;
        double r69015 = r69007 / r69014;
        double r69016 = r69003 - r69015;
        return r69016;
}
↓
double f(double x) {
        double r69017 = x;
        double r69018 = 2.30753;
        double r69019 = 0.27061;
        double r69020 = r69017 * r69019;
        double r69021 = r69018 + r69020;
        double r69022 = 1.0;
        double r69023 = 0.99229;
        double r69024 = 0.04481;
        double r69025 = r69017 * r69024;
        double r69026 = r69023 + r69025;
        double r69027 = r69026 * r69017;
        double r69028 = r69022 + r69027;
        double r69029 = r69021 / r69028;
        double r69030 = r69017 - r69029;
        return r69030;
}

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

    \[x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]

  2. Final simplification0.0

    \[\leadsto x - \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right) \cdot x}\]

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, D"
  :precision binary64
  (- x (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* (+ 0.99229 (* x 0.04481)) x)))))