Details

Time bar (total: 11.3s)

sample79.0ms

Algorithm
intervals
Results
56.0ms678×body80valid

simplify6.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
019696
153696
2159696
3449696
41319696
53532696
done5000696

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b
(* (* a a) (+ 1.0 a))
0.3b
(pow (+ (* a a) (* b b)) 2.0)
1.2b
(* (* b b) (- 1.0 (* 3.0 a)))

rewrite159.0ms

Algorithm
rewrite-expression-head
Rules
15×pow1 add-exp-log
14×add-cbrt-cube
10×add-sqr-sqrt *-un-lft-identity
8×add-cube-cbrt
7×associate-*r*
6×pow-prod-down prod-exp cbrt-unprod add-log-exp
4×distribute-rgt-in distribute-lft-in associate-*r/
3×pow-unpow unpow-prod-down
2×associate-+r+ sub-neg flip3-+ associate-*l* *-commutative flip-+ unswap-sqr
1×pow-to-exp +-commutative sum-log pow-pow flip3-- pow-exp flip-- distribute-lft-out sqr-pow
Counts
4 → 79
Calls
4 calls:
74.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
33.0ms
(* (* a a) (+ 1.0 a))
16.0ms
(pow (+ (* a a) (* b b)) 2.0)
35.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

series435.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
73.0ms
(* (* a a) (+ 1.0 a))
148.0ms
(pow (+ (* a a) (* b b)) 2.0)
66.0ms
(* (* b b) (- 1.0 (* 3.0 a)))

simplify2.3s

Counts
91 → 91
Iterations

Useful iterations: done (2.3s)

IterNodesCost
017534981
151929087
2193328647
done500128567

prune634.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize91.0ms

Local error

Found 4 expressions with local error:

1.2b
(* (* b b) (- 1.0 (* 3.0 a)))
1.2b
(* (* b b) (- 1.0 (* 3.0 a)))
10.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
10.4b
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

rewrite204.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
14×add-cbrt-cube add-exp-log
12×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
6×associate-*r* pow-prod-down prod-exp sqrt-prod cbrt-unprod
4×distribute-rgt-in sub-neg distribute-lft-in sqrt-div associate-*r/ add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ flip3-- pow1/2 associate-*l* *-commutative flip-+ flip-- unswap-sqr
Counts
4 → 80
Calls
4 calls:
23.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
25.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
64.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
90.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

series681.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
72.0ms
(* (* b b) (- 1.0 (* 3.0 a)))
259.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))
280.0ms
(sqrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a)))))))

simplify97.0ms

Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
012143668