Average Error: 0.5 → 0.6
Time: 59.0s
Precision: 64
\[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
↓
\[\left(\frac{\left(x1 \cdot x1\right) \cdot 3}{\frac{x1 \cdot x1 + 1}{\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)}} + x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{\left(\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)\right) \cdot \left(x1 \cdot \left(\left(\frac{\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)}{x1 \cdot x1 + 1} - 3\right) \cdot 2\right) + \left(x1 \cdot x1\right) \cdot 4\right)}{x1 \cdot x1 + 1} + \left(x1 + \left(\sqrt[3]{-6 \cdot \left(x1 \cdot x1\right)} \cdot \sqrt[3]{-6 \cdot \left(x1 \cdot x1\right)}\right) \cdot \sqrt[3]{-6 \cdot \left(x1 \cdot x1\right)}\right)\right) + \frac{-2 \cdot x2 + \left(\left(x1 \cdot x1\right) \cdot 3 - x1\right)}{x1 \cdot x1 + 1} \cdot 3\right)\]
x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)
↓
\left(\frac{\left(x1 \cdot x1\right) \cdot 3}{\frac{x1 \cdot x1 + 1}{\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)}} + x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{\left(\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)\right) \cdot \left(x1 \cdot \left(\left(\frac{\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)}{x1 \cdot x1 + 1} - 3\right) \cdot 2\right) + \left(x1 \cdot x1\right) \cdot 4\right)}{x1 \cdot x1 + 1} + \left(x1 + \left(\sqrt[3]{-6 \cdot \left(x1 \cdot x1\right)} \cdot \sqrt[3]{-6 \cdot \left(x1 \cdot x1\right)}\right) \cdot \sqrt[3]{-6 \cdot \left(x1 \cdot x1\right)}\right)\right) + \frac{-2 \cdot x2 + \left(\left(x1 \cdot x1\right) \cdot 3 - x1\right)}{x1 \cdot x1 + 1} \cdot 3\right)
double f(double x1, double x2) {
        double r3028214 = x1;
        double r3028215 = 2.0;
        double r3028216 = r3028215 * r3028214;
        double r3028217 = 3.0;
        double r3028218 = r3028217 * r3028214;
        double r3028219 = r3028218 * r3028214;
        double r3028220 = x2;
        double r3028221 = r3028215 * r3028220;
        double r3028222 = r3028219 + r3028221;
        double r3028223 = r3028222 - r3028214;
        double r3028224 = r3028214 * r3028214;
        double r3028225 = 1.0;
        double r3028226 = r3028224 + r3028225;
        double r3028227 = r3028223 / r3028226;
        double r3028228 = r3028216 * r3028227;
        double r3028229 = r3028227 - r3028217;
        double r3028230 = r3028228 * r3028229;
        double r3028231 = 4.0;
        double r3028232 = r3028231 * r3028227;
        double r3028233 = 6.0;
        double r3028234 = r3028232 - r3028233;
        double r3028235 = r3028224 * r3028234;
        double r3028236 = r3028230 + r3028235;
        double r3028237 = r3028236 * r3028226;
        double r3028238 = r3028219 * r3028227;
        double r3028239 = r3028237 + r3028238;
        double r3028240 = r3028224 * r3028214;
        double r3028241 = r3028239 + r3028240;
        double r3028242 = r3028241 + r3028214;
        double r3028243 = r3028219 - r3028221;
        double r3028244 = r3028243 - r3028214;
        double r3028245 = r3028244 / r3028226;
        double r3028246 = r3028217 * r3028245;
        double r3028247 = r3028242 + r3028246;
        double r3028248 = r3028214 + r3028247;
        return r3028248;
}
↓
double f(double x1, double x2) {
        double r3028249 = x1;
        double r3028250 = r3028249 * r3028249;
        double r3028251 = 3.0;
        double r3028252 = r3028250 * r3028251;
        double r3028253 = 1.0;
        double r3028254 = r3028250 + r3028253;
        double r3028255 = x2;
        double r3028256 = 2.0;
        double r3028257 = r3028255 * r3028256;
        double r3028258 = r3028257 - r3028249;
        double r3028259 = r3028252 + r3028258;
        double r3028260 = r3028254 / r3028259;
        double r3028261 = r3028252 / r3028260;
        double r3028262 = r3028261 + r3028249;
        double r3028263 = r3028259 / r3028254;
        double r3028264 = r3028263 - r3028251;
        double r3028265 = r3028264 * r3028256;
        double r3028266 = r3028249 * r3028265;
        double r3028267 = 4.0;
        double r3028268 = r3028250 * r3028267;
        double r3028269 = r3028266 + r3028268;
        double r3028270 = r3028259 * r3028269;
        double r3028271 = r3028270 / r3028254;
        double r3028272 = -6.0;
        double r3028273 = r3028272 * r3028250;
        double r3028274 = cbrt(r3028273);
        double r3028275 = r3028274 * r3028274;
        double r3028276 = r3028275 * r3028274;
        double r3028277 = r3028249 + r3028276;
        double r3028278 = r3028271 + r3028277;
        double r3028279 = r3028254 * r3028278;
        double r3028280 = -2.0;
        double r3028281 = r3028280 * r3028255;
        double r3028282 = r3028252 - r3028249;
        double r3028283 = r3028281 + r3028282;
        double r3028284 = r3028283 / r3028254;
        double r3028285 = r3028284 * r3028251;
        double r3028286 = r3028279 + r3028285;
        double r3028287 = r3028262 + r3028286;
        return r3028287;
}

Error

Bits error versus x1

Bits error versus x2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]

  2. Simplified0.5

    \[\leadsto \color{blue}{\left(3 \cdot \frac{x2 \cdot -2 + \left(\left(x1 \cdot x1\right) \cdot 3 - x1\right)}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\frac{\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)}{1 + x1 \cdot x1} \cdot \left(x1 \cdot \left(\left(\frac{\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)}{1 + x1 \cdot x1} - 3\right) \cdot 2\right) + \left(x1 \cdot x1\right) \cdot 4\right) + \left(-6 \cdot \left(x1 \cdot x1\right) + x1\right)\right)\right) + \left(\frac{\left(x1 \cdot x1\right) \cdot 3}{\frac{1 + x1 \cdot x1}{\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)}} + x1\right)}\]
  3. Using strategy rm

  4. Applied associate-*l/0.5

    \[\leadsto \left(3 \cdot \frac{x2 \cdot -2 + \left(\left(x1 \cdot x1\right) \cdot 3 - x1\right)}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\color{blue}{\frac{\left(\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)\right) \cdot \left(x1 \cdot \left(\left(\frac{\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)}{1 + x1 \cdot x1} - 3\right) \cdot 2\right) + \left(x1 \cdot x1\right) \cdot 4\right)}{1 + x1 \cdot x1}} + \left(-6 \cdot \left(x1 \cdot x1\right) + x1\right)\right)\right) + \left(\frac{\left(x1 \cdot x1\right) \cdot 3}{\frac{1 + x1 \cdot x1}{\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)}} + x1\right)\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.6

    \[\leadsto \left(3 \cdot \frac{x2 \cdot -2 + \left(\left(x1 \cdot x1\right) \cdot 3 - x1\right)}{1 + x1 \cdot x1} + \left(1 + x1 \cdot x1\right) \cdot \left(\frac{\left(\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)\right) \cdot \left(x1 \cdot \left(\left(\frac{\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)}{1 + x1 \cdot x1} - 3\right) \cdot 2\right) + \left(x1 \cdot x1\right) \cdot 4\right)}{1 + x1 \cdot x1} + \left(\color{blue}{\left(\sqrt[3]{-6 \cdot \left(x1 \cdot x1\right)} \cdot \sqrt[3]{-6 \cdot \left(x1 \cdot x1\right)}\right) \cdot \sqrt[3]{-6 \cdot \left(x1 \cdot x1\right)}} + x1\right)\right)\right) + \left(\frac{\left(x1 \cdot x1\right) \cdot 3}{\frac{1 + x1 \cdot x1}{\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)}} + x1\right)\]

  7. Final simplification0.6

    \[\leadsto \left(\frac{\left(x1 \cdot x1\right) \cdot 3}{\frac{x1 \cdot x1 + 1}{\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)}} + x1\right) + \left(\left(x1 \cdot x1 + 1\right) \cdot \left(\frac{\left(\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)\right) \cdot \left(x1 \cdot \left(\left(\frac{\left(x1 \cdot x1\right) \cdot 3 + \left(x2 \cdot 2 - x1\right)}{x1 \cdot x1 + 1} - 3\right) \cdot 2\right) + \left(x1 \cdot x1\right) \cdot 4\right)}{x1 \cdot x1 + 1} + \left(x1 + \left(\sqrt[3]{-6 \cdot \left(x1 \cdot x1\right)} \cdot \sqrt[3]{-6 \cdot \left(x1 \cdot x1\right)}\right) \cdot \sqrt[3]{-6 \cdot \left(x1 \cdot x1\right)}\right)\right) + \frac{-2 \cdot x2 + \left(\left(x1 \cdot x1\right) \cdot 3 - x1\right)}{x1 \cdot x1 + 1} \cdot 3\right)\]

Reproduce

herbie shell --seed 2019139 
(FPCore (x1 x2)
  :name "Rosa's FloatVsDoubleBenchmark"
  (+ x1 (+ (+ (+ (+ (* (+ (* (* (* 2 x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) (- (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)) 3)) (* (* x1 x1) (- (* 4 (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))) 6))) (+ (* x1 x1) 1)) (* (* (* 3 x1) x1) (/ (- (+ (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1)))) (* (* x1 x1) x1)) x1) (* 3 (/ (- (- (* (* 3 x1) x1) (* 2 x2)) x1) (+ (* x1 x1) 1))))))