Average Error: 0.0 → 0.1
Time: 12.2s
Precision: 64
\[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
↓
\[\frac{1}{\sqrt{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}} \cdot \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{\sqrt{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}} - x\]
\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x
↓
\frac{1}{\sqrt{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}} \cdot \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{\sqrt{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)}} - x
double f(double x) {
        double r66570 = 2.30753;
        double r66571 = x;
        double r66572 = 0.27061;
        double r66573 = r66571 * r66572;
        double r66574 = r66570 + r66573;
        double r66575 = 1.0;
        double r66576 = 0.99229;
        double r66577 = 0.04481;
        double r66578 = r66571 * r66577;
        double r66579 = r66576 + r66578;
        double r66580 = r66571 * r66579;
        double r66581 = r66575 + r66580;
        double r66582 = r66574 / r66581;
        double r66583 = r66582 - r66571;
        return r66583;
}
↓
double f(double x) {
        double r66584 = 1.0;
        double r66585 = 1.0;
        double r66586 = x;
        double r66587 = 0.99229;
        double r66588 = 0.04481;
        double r66589 = r66586 * r66588;
        double r66590 = r66587 + r66589;
        double r66591 = r66586 * r66590;
        double r66592 = r66585 + r66591;
        double r66593 = sqrt(r66592);
        double r66594 = r66584 / r66593;
        double r66595 = 2.30753;
        double r66596 = 0.27061;
        double r66597 = r66586 * r66596;
        double r66598 = r66595 + r66597;
        double r66599 = r66598 / r66593;
        double r66600 = r66594 * r66599;
        double r66601 = r66600 - r66586;
        return r66601;
}

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

    \[\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.1

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

  4. Applied *-un-lft-identity0.1

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

  5. Applied times-frac0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(FPCore (x)
  :name "Numeric.SpecFunctions:invIncompleteGamma from math-functions-0.1.5.2, C"
  :precision binary64
  (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x))