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 r19524097 = 3.0;
        double r19524098 = 2.0;
        double r19524099 = r;
        double r19524100 = r19524099 * r19524099;
        double r19524101 = r19524098 / r19524100;
        double r19524102 = r19524097 + r19524101;
        double r19524103 = 0.125;
        double r19524104 = v;
        double r19524105 = r19524098 * r19524104;
        double r19524106 = r19524097 - r19524105;
        double r19524107 = r19524103 * r19524106;
        double r19524108 = w;
        double r19524109 = r19524108 * r19524108;
        double r19524110 = r19524109 * r19524099;
        double r19524111 = r19524110 * r19524099;
        double r19524112 = r19524107 * r19524111;
        double r19524113 = 1.0;
        double r19524114 = r19524113 - r19524104;
        double r19524115 = r19524112 / r19524114;
        double r19524116 = r19524102 - r19524115;
        double r19524117 = 4.5;
        double r19524118 = r19524116 - r19524117;
        return r19524118;
}
↓
double f(double v, double w, double r) {
        double r19524119 = 3.0;
        double r19524120 = 2.0;
        double r19524121 = r;
        double r19524122 = r19524120 / r19524121;
        double r19524123 = r19524122 / r19524121;
        double r19524124 = r19524119 + r19524123;
        double r19524125 = 4.5;
        double r19524126 = r19524124 - r19524125;
        double r19524127 = -2.0;
        double r19524128 = v;
        double r19524129 = r19524127 * r19524128;
        double r19524130 = r19524119 + r19524129;
        double r19524131 = 1.0;
        double r19524132 = r19524131 - r19524128;
        double r19524133 = r19524130 / r19524132;
        double r19524134 = w;
        double r19524135 = r19524134 * r19524121;
        double r19524136 = 0.125;
        double r19524137 = r19524135 * r19524136;
        double r19524138 = r19524135 * r19524137;
        double r19524139 = r19524133 * r19524138;
        double r19524140 = r19524126 - r19524139;
        return r19524140;
}

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))