Error

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 simplify 0.5

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

4. Applied sub-neg 0.5

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

5. Applied distribute-rgt-in 0.5

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

6. Applied associate-+r+ 0.5

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

7. Applied simplify 0.6

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

8. Applied simplify 0.6

   \[\leadsto \left(\left(x1 + \left(\frac{\left(\left(x2 + \left(x2 - x1\right)\right) + \left(x1 \cdot x1\right) \cdot 3\right) \cdot \left(\left(x1 \cdot x1\right) \cdot 3\right)}{1 + x1 \cdot x1} + \frac{3}{1 + x1 \cdot x1} \cdot \left(\left(x1 \cdot x1\right) \cdot 3 - \left(x1 + \left(x2 + x2\right)\right)\right)\right)\right) + \left(1 + x1 \cdot x1\right) \cdot \left(\left(\frac{\frac{x1 + x1}{{x1}^2 + 1} \cdot \left(\left(3 \cdot x1\right) \cdot x1 + \left(x2 + \left(x2 - x1\right)\right)\right)}{\frac{{x1}^2 + 1}{\left(3 \cdot x1\right) \cdot x1 + \left(x2 + \left(x2 - x1\right)\right)}} + \color{blue}{\left(\left(\left(x2 - \left(x1 - x2\right)\right) + {x1}^2 \cdot 3\right) \cdot \frac{4}{1 + {x1}^2} - 6\right) \cdot {x1}^2}\right) + \left(-3\right) \cdot \frac{x1 + x1}{\frac{1 + x1 \cdot x1}{\left(x2 + \left(x2 - x1\right)\right) + \left(x1 \cdot x1\right) \cdot 3}}\right)\right) + \left(x1 + {x1}^3\right)\]
9. Removed slow pow expressions

Runtime

Time bar (total: 58.3s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(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))))))