Average Error: 13.9 → 11.0
Time: 42.4s
Precision: 64
\[\left(-x \cdot \frac{1}{\tan B}\right) + \frac{F}{\sin B} \cdot {\left(\left(F \cdot F + 2\right) + 2 \cdot x\right)}^{\left(-\frac{1}{2}\right)}\]
↓
\[\frac{{\left({\left(\left(2 \cdot x + F \cdot F\right) + 2\right)}^{\frac{-1}{2}}\right)}^{\frac{1}{2}} \cdot \frac{{\left(\left(2 \cdot x + F \cdot F\right) + 2\right)}^{\frac{-1}{4}}}{\sin B}}{\frac{1}{F}} - \frac{x}{\tan B}\]
\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)}
↓
\frac{{\left({\left(\left(2 \cdot x + F \cdot F\right) + 2\right)}^{\frac{-1}{2}}\right)}^{\frac{1}{2}} \cdot \frac{{\left(\left(2 \cdot x + F \cdot F\right) + 2\right)}^{\frac{-1}{4}}}{\sin B}}{\frac{1}{F}} - \frac{x}{\tan B}
double f(double F, double B, double x) {
        double r1172295 = x;
        double r1172296 = 1.0;
        double r1172297 = B;
        double r1172298 = tan(r1172297);
        double r1172299 = r1172296 / r1172298;
        double r1172300 = r1172295 * r1172299;
        double r1172301 = -r1172300;
        double r1172302 = F;
        double r1172303 = sin(r1172297);
        double r1172304 = r1172302 / r1172303;
        double r1172305 = r1172302 * r1172302;
        double r1172306 = 2.0;
        double r1172307 = r1172305 + r1172306;
        double r1172308 = r1172306 * r1172295;
        double r1172309 = r1172307 + r1172308;
        double r1172310 = r1172296 / r1172306;
        double r1172311 = -r1172310;
        double r1172312 = pow(r1172309, r1172311);
        double r1172313 = r1172304 * r1172312;
        double r1172314 = r1172301 + r1172313;
        return r1172314;
}
↓
double f(double F, double B, double x) {
        double r1172315 = 2.0;
        double r1172316 = x;
        double r1172317 = r1172315 * r1172316;
        double r1172318 = F;
        double r1172319 = r1172318 * r1172318;
        double r1172320 = r1172317 + r1172319;
        double r1172321 = r1172320 + r1172315;
        double r1172322 = -0.5;
        double r1172323 = pow(r1172321, r1172322);
        double r1172324 = 0.5;
        double r1172325 = pow(r1172323, r1172324);
        double r1172326 = -0.25;
        double r1172327 = pow(r1172321, r1172326);
        double r1172328 = B;
        double r1172329 = sin(r1172328);
        double r1172330 = r1172327 / r1172329;
        double r1172331 = r1172325 * r1172330;
        double r1172332 = 1.0;
        double r1172333 = r1172332 / r1172318;
        double r1172334 = r1172331 / r1172333;
        double r1172335 = tan(r1172328);
        double r1172336 = r1172316 / r1172335;
        double r1172337 = r1172334 - r1172336;
        return r1172337;
}

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 13.9

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

  2. Simplified13.4

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

  4. Applied div-inv13.4

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

  5. Applied associate-/r*11.0

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

  7. Applied *-un-lft-identity11.0

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

  8. Applied sqr-pow11.0

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

  9. Applied times-frac11.0

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

  11. Applied div-inv11.0

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

  12. Applied pow-unpow11.0

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

  13. Final simplification11.0

    \[\leadsto \frac{{\left({\left(\left(2 \cdot x + F \cdot F\right) + 2\right)}^{\frac{-1}{2}}\right)}^{\frac{1}{2}} \cdot \frac{{\left(\left(2 \cdot x + F \cdot F\right) + 2\right)}^{\frac{-1}{4}}}{\sin B}}{\frac{1}{F}} - \frac{x}{\tan B}\]

Reproduce

herbie shell --seed 2019152 
(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))))))