Average Error: 0.5 → 0.6
Time: 4.4m
Precision: 64
Internal Precision: 1408
\[x1 + \left(\left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) \cdot \left(\frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 3\right) + \left(x1 \cdot x1\right) \cdot \left(4 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1} - 6\right)\right) \cdot \left(x1 \cdot x1 + 1\right) + \left(\left(3 \cdot x1\right) \cdot x1\right) \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 + 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right) + \left(x1 \cdot x1\right) \cdot x1\right) + x1\right) + 3 \cdot \frac{\left(\left(3 \cdot x1\right) \cdot x1 - 2 \cdot x2\right) - x1}{x1 \cdot x1 + 1}\right)\]
↓
\[\left(x1 + {x1}^{3}\right) + \left(\left(x1 + \left(\frac{\left(x2 - \left(x1 - x2\right)\right) + \left(x1 \cdot x1\right) \cdot 3}{1 + x1 \cdot x1} \cdot \left(\left(x1 \cdot x1\right) \cdot 3\right) + \frac{\left(x1 \cdot x1\right) \cdot 3 - \left(x1 + \left(x2 + x2\right)\right)}{\frac{1 + x1 \cdot x1}{3}}\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(\left(\frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{\frac{x1 \cdot x1 + 1}{4}} - 6\right) \cdot \left(x1 \cdot x1\right) + \frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{\frac{x1 \cdot x1 + 1}{x1 + x1}} \cdot \frac{\left(x2 - \left(x1 - x2\right)\right) + 3 \cdot \left(x1 \cdot x1\right)}{x1 \cdot x1 + 1}\right) + \frac{\left(\left(x2 - \left(x1 - x2\right)\right) + \left(x1 \cdot x1\right) \cdot 3\right) \cdot \left(x1 + x1\right)}{1 + x1 \cdot x1} \cdot \left(-3\right)\right)\right)\]

Error

Bits error versus x1

Bits error versus x2

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. Applied simplify0.6

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

  4. Applied add-cube-cbrt0.7

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

  5. Applied associate-*l*0.7

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

  7. Applied sub-neg0.7

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

  8. Applied distribute-lft-in0.7

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

  9. Applied associate-+r+0.7

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

  10. Applied simplify0.6

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

Runtime

Time bar (total: 4.4m)Debug logProfile

herbie shell --seed '#(1064173506 2580572819 2847706409 4129882574 1125180799 1845288547)' 
(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))))))