Average Error: 13.3 → 10.4
Time: 50.9s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
↓
\[\left({\left(\left(2 \cdot x + F \cdot F\right) + 2\right)}^{\frac{-1}{2}} \cdot F\right) \cdot \frac{1}{\sin B} - \frac{x}{\tan B}\]
\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}
↓
\left({\left(\left(2 \cdot x + F \cdot F\right) + 2\right)}^{\frac{-1}{2}} \cdot F\right) \cdot \frac{1}{\sin B} - \frac{x}{\tan B}
double f(double F, double B, double x) {
        double r2172522 = x;
        double r2172523 = 1.0;
        double r2172524 = B;
        double r2172525 = tan(r2172524);
        double r2172526 = r2172523 / r2172525;
        double r2172527 = r2172522 * r2172526;
        double r2172528 = -r2172527;
        double r2172529 = F;
        double r2172530 = sin(r2172524);
        double r2172531 = r2172529 / r2172530;
        double r2172532 = r2172529 * r2172529;
        double r2172533 = 2.0;
        double r2172534 = r2172532 + r2172533;
        double r2172535 = r2172533 * r2172522;
        double r2172536 = r2172534 + r2172535;
        double r2172537 = r2172523 / r2172533;
        double r2172538 = -r2172537;
        double r2172539 = pow(r2172536, r2172538);
        double r2172540 = r2172531 * r2172539;
        double r2172541 = r2172528 + r2172540;
        return r2172541;
}
↓
double f(double F, double B, double x) {
        double r2172542 = 2.0;
        double r2172543 = x;
        double r2172544 = r2172542 * r2172543;
        double r2172545 = F;
        double r2172546 = r2172545 * r2172545;
        double r2172547 = r2172544 + r2172546;
        double r2172548 = r2172547 + r2172542;
        double r2172549 = -0.5;
        double r2172550 = pow(r2172548, r2172549);
        double r2172551 = r2172550 * r2172545;
        double r2172552 = 1.0;
        double r2172553 = B;
        double r2172554 = sin(r2172553);
        double r2172555 = r2172552 / r2172554;
        double r2172556 = r2172551 * r2172555;
        double r2172557 = tan(r2172553);
        double r2172558 = r2172543 / r2172557;
        double r2172559 = r2172556 - r2172558;
        return r2172559;
}

Error

Bits error versus F

Bits error versus B

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.3

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

  2. Simplified10.4

    \[\leadsto \color{blue}{\frac{{\left(2 + \left(2 \cdot x + F \cdot F\right)\right)}^{\frac{-1}{2}} \cdot F}{\sin B} - \frac{x}{\tan B}}\]
  3. Using strategy rm

  4. Applied div-inv10.4

    \[\leadsto \color{blue}{\left({\left(2 + \left(2 \cdot x + F \cdot F\right)\right)}^{\frac{-1}{2}} \cdot F\right) \cdot \frac{1}{\sin B}} - \frac{x}{\tan B}\]

  5. Final simplification10.4

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

Reproduce

herbie shell --seed 2019141 
(FPCore (F B x)
  :name "VandenBroeck and Keller, Equation (23)"
  (+ (- (* x (/ 1 (tan B)))) (* (/ F (sin B)) (pow (+ (+ (* F F) 2) (* 2 x)) (- (/ 1 2))))))