Average Error: 12.3 → 0.3
Time: 3.3m
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - 4.5\right) - \frac{3 + -2 \cdot v}{1 - v} \cdot \left(\left(w \cdot r\right) \cdot \left(\left(w \cdot r\right) \cdot 0.125\right)\right)\]
\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5
↓
\left(\left(3 + \frac{\frac{2}{r}}{r}\right) - 4.5\right) - \frac{3 + -2 \cdot v}{1 - v} \cdot \left(\left(w \cdot r\right) \cdot \left(\left(w \cdot r\right) \cdot 0.125\right)\right)
double f(double v, double w, double r) {
        double r19524092 = 3.0;
        double r19524093 = 2.0;
        double r19524094 = r;
        double r19524095 = r19524094 * r19524094;
        double r19524096 = r19524093 / r19524095;
        double r19524097 = r19524092 + r19524096;
        double r19524098 = 0.125;
        double r19524099 = v;
        double r19524100 = r19524093 * r19524099;
        double r19524101 = r19524092 - r19524100;
        double r19524102 = r19524098 * r19524101;
        double r19524103 = w;
        double r19524104 = r19524103 * r19524103;
        double r19524105 = r19524104 * r19524094;
        double r19524106 = r19524105 * r19524094;
        double r19524107 = r19524102 * r19524106;
        double r19524108 = 1.0;
        double r19524109 = r19524108 - r19524099;
        double r19524110 = r19524107 / r19524109;
        double r19524111 = r19524097 - r19524110;
        double r19524112 = 4.5;
        double r19524113 = r19524111 - r19524112;
        return r19524113;
}
↓
double f(double v, double w, double r) {
        double r19524114 = 3.0;
        double r19524115 = 2.0;
        double r19524116 = r;
        double r19524117 = r19524115 / r19524116;
        double r19524118 = r19524117 / r19524116;
        double r19524119 = r19524114 + r19524118;
        double r19524120 = 4.5;
        double r19524121 = r19524119 - r19524120;
        double r19524122 = -2.0;
        double r19524123 = v;
        double r19524124 = r19524122 * r19524123;
        double r19524125 = r19524114 + r19524124;
        double r19524126 = 1.0;
        double r19524127 = r19524126 - r19524123;
        double r19524128 = r19524125 / r19524127;
        double r19524129 = w;
        double r19524130 = r19524129 * r19524116;
        double r19524131 = 0.125;
        double r19524132 = r19524130 * r19524131;
        double r19524133 = r19524130 * r19524132;
        double r19524134 = r19524128 * r19524133;
        double r19524135 = r19524121 - r19524134;
        return r19524135;
}

Error

Bits error versus v

Bits error versus w

Bits error versus r

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 12.3

    \[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]

  2. Simplified0.4

    \[\leadsto \color{blue}{\left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \frac{0.125}{\frac{\frac{1 - v}{3 - 2 \cdot v}}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}}}\]
  3. Using strategy rm

  4. Applied div-inv0.4

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \frac{0.125}{\color{blue}{\frac{1 - v}{3 - 2 \cdot v} \cdot \frac{1}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}}}\]

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

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \frac{\color{blue}{1 \cdot 0.125}}{\frac{1 - v}{3 - 2 \cdot v} \cdot \frac{1}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}}\]

  6. Applied times-frac0.4

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \color{blue}{\frac{1}{\frac{1 - v}{3 - 2 \cdot v}} \cdot \frac{0.125}{\frac{1}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}}}\]

  7. Simplified0.4

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \color{blue}{\frac{v \cdot -2 + 3}{1 - v}} \cdot \frac{0.125}{\frac{1}{\left(w \cdot r\right) \cdot \left(w \cdot r\right)}}\]

  8. Simplified0.3

    \[\leadsto \left(\left(3 + \frac{2}{r \cdot r}\right) - 4.5\right) - \frac{v \cdot -2 + 3}{1 - v} \cdot \color{blue}{\left(\left(\left(w \cdot r\right) \cdot 0.125\right) \cdot \left(w \cdot r\right)\right)}\]
  9. Using strategy rm

  10. Applied associate-/r*0.3

    \[\leadsto \left(\left(3 + \color{blue}{\frac{\frac{2}{r}}{r}}\right) - 4.5\right) - \frac{v \cdot -2 + 3}{1 - v} \cdot \left(\left(\left(w \cdot r\right) \cdot 0.125\right) \cdot \left(w \cdot r\right)\right)\]

  11. Final simplification0.3

    \[\leadsto \left(\left(3 + \frac{\frac{2}{r}}{r}\right) - 4.5\right) - \frac{3 + -2 \cdot v}{1 - v} \cdot \left(\left(w \cdot r\right) \cdot \left(\left(w \cdot r\right) \cdot 0.125\right)\right)\]

Reproduce

herbie shell --seed 2019107 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))