Average Error: 12.7 → 0.6
Time: 9.0s
Precision: 64
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{\left(0.125 \cdot \left(3 - 2 \cdot v\right)\right) \cdot \left(\left(\left(w \cdot w\right) \cdot r\right) \cdot r\right)}{1 - v}\right) - 4.5\]
↓
\[\left(\left(3 + \frac{2}{r \cdot r}\right) - \frac{1}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{\sqrt[3]{{\left(\left|w \cdot r\right|\right)}^{2}} \cdot \sqrt[3]{{\left(\left|w \cdot r\right|\right)}^{2}}}} \cdot \frac{1}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{\sqrt[3]{{\left(\left|w \cdot r\right|\right)}^{2}}}}\right) - 4.5\]
\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{2}{r \cdot r}\right) - \frac{1}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{\sqrt[3]{{\left(\left|w \cdot r\right|\right)}^{2}} \cdot \sqrt[3]{{\left(\left|w \cdot r\right|\right)}^{2}}}} \cdot \frac{1}{\frac{\sqrt{\frac{1 - v}{0.125 \cdot \left(3 - 2 \cdot v\right)}}}{\sqrt[3]{{\left(\left|w \cdot r\right|\right)}^{2}}}}\right) - 4.5
double f(double v, double w, double r) {
        double r29164 = 3.0;
        double r29165 = 2.0;
        double r29166 = r;
        double r29167 = r29166 * r29166;
        double r29168 = r29165 / r29167;
        double r29169 = r29164 + r29168;
        double r29170 = 0.125;
        double r29171 = v;
        double r29172 = r29165 * r29171;
        double r29173 = r29164 - r29172;
        double r29174 = r29170 * r29173;
        double r29175 = w;
        double r29176 = r29175 * r29175;
        double r29177 = r29176 * r29166;
        double r29178 = r29177 * r29166;
        double r29179 = r29174 * r29178;
        double r29180 = 1.0;
        double r29181 = r29180 - r29171;
        double r29182 = r29179 / r29181;
        double r29183 = r29169 - r29182;
        double r29184 = 4.5;
        double r29185 = r29183 - r29184;
        return r29185;
}
↓
double f(double v, double w, double r) {
        double r29186 = 3.0;
        double r29187 = 2.0;
        double r29188 = r;
        double r29189 = r29188 * r29188;
        double r29190 = r29187 / r29189;
        double r29191 = r29186 + r29190;
        double r29192 = 1.0;
        double r29193 = 1.0;
        double r29194 = v;
        double r29195 = r29193 - r29194;
        double r29196 = 0.125;
        double r29197 = r29187 * r29194;
        double r29198 = r29186 - r29197;
        double r29199 = r29196 * r29198;
        double r29200 = r29195 / r29199;
        double r29201 = sqrt(r29200);
        double r29202 = w;
        double r29203 = r29202 * r29188;
        double r29204 = fabs(r29203);
        double r29205 = 2.0;
        double r29206 = pow(r29204, r29205);
        double r29207 = cbrt(r29206);
        double r29208 = r29207 * r29207;
        double r29209 = r29201 / r29208;
        double r29210 = r29192 / r29209;
        double r29211 = r29201 / r29207;
        double r29212 = r29192 / r29211;
        double r29213 = r29210 * r29212;
        double r29214 = r29191 - r29213;
        double r29215 = 4.5;
        double r29216 = r29214 - r29215;
        return r29216;
}

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 12.7

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

  3. Applied add-sqr-sqrt12.7

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

  4. Simplified12.7

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

  5. Simplified6.6

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

  7. Applied clear-num6.6

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

  8. Simplified0.4

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

  10. Applied add-cube-cbrt0.6

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

  11. Applied add-sqr-sqrt0.6

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

  12. Applied times-frac0.6

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

  13. Applied *-un-lft-identity0.6

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

  14. Applied times-frac0.6

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

  15. Final simplification0.6

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

Reproduce

herbie shell --seed 2020001 
(FPCore (v w r)
  :name "Rosa's TurbineBenchmark"
  :precision binary64
  (- (- (+ 3 (/ 2 (* r r))) (/ (* (* 0.125 (- 3 (* 2 v))) (* (* (* w w) r) r)) (- 1 v))) 4.5))