Average Error: 0.0 → 0.0
Time: 3.5s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\log \left(e^{\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\log \left(e^{\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r276714 = 2.0;
        double r276715 = sqrt(r276714);
        double r276716 = 4.0;
        double r276717 = r276715 / r276716;
        double r276718 = 1.0;
        double r276719 = 3.0;
        double r276720 = v;
        double r276721 = r276720 * r276720;
        double r276722 = r276719 * r276721;
        double r276723 = r276718 - r276722;
        double r276724 = sqrt(r276723);
        double r276725 = r276717 * r276724;
        double r276726 = r276718 - r276721;
        double r276727 = r276725 * r276726;
        return r276727;
}
↓
double f(double v) {
        double r276728 = 2.0;
        double r276729 = sqrt(r276728);
        double r276730 = 4.0;
        double r276731 = r276729 / r276730;
        double r276732 = 1.0;
        double r276733 = 3.0;
        double r276734 = v;
        double r276735 = r276734 * r276734;
        double r276736 = r276733 * r276735;
        double r276737 = r276732 - r276736;
        double r276738 = sqrt(r276737);
        double r276739 = r276731 * r276738;
        double r276740 = exp(r276739);
        double r276741 = log(r276740);
        double r276742 = r276732 - r276735;
        double r276743 = r276741 * r276742;
        return r276743;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
  2. Using strategy rm

  3. Applied add-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right)} \cdot \left(1 - v \cdot v\right)\]

  4. Final simplification0.0

    \[\leadsto \log \left(e^{\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right) \cdot \left(1 - v \cdot v\right)\]

Reproduce

herbie shell --seed 2020062 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))