Details

Time bar (total: 14.9s)

sample201.0ms

Algorithm
intervals
Results
24.0ms344×body80valid

simplify44.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
067
197
2167
3267
4337
done337

prune42.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(- (* x x) y)

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
3×add-log-exp
2×add-sqr-sqrt
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- *-un-lft-identity diff-log add-cbrt-cube flip-- difference-of-squares
Counts
1 → 13
Calls
1 calls:
11.0ms
(- (* x x) y)

series32.0ms

Counts
1 → 3
Calls
1 calls:
32.0ms
(- (* x x) y)

simplify2.1s

Counts
16 → 16
Iterations

Useful iterations: 2 (41.0ms)

IterNodesCost
032136
173133
2163113
3332113
4769113
52422113
done5000113

prune59.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (- (* x x) y))
0.0b
(- (* x x) y)
0.0b
(- (* x x) y)
0.2b
(* (sqrt (- (* x x) y)) (sqrt (- (* x x) y)))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
26×sqrt-prod
20×pow1
14×sqrt-div
13×add-cube-cbrt *-un-lft-identity
9×flip3-- sqrt-pow1 pow1/2 swap-sqr flip--
8×add-log-exp
7×associate-*r* associate-*l* difference-of-squares
6×add-exp-log add-cbrt-cube
5×pow-prod-up
4×frac-times unswap-sqr
3×pow-prod-down pow-sqr
2×sub-neg diff-log associate-*r/ associate-*l/
1×pow2 rem-sqrt-square pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 102
Calls
4 calls:
21.0ms
(sqrt (- (* x x) y))
19.0ms
(- (* x x) y)
17.0ms
(- (* x x) y)
94.0ms
(* (sqrt (- (* x x) y)) (sqrt (- (* x x) y)))

series138.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(sqrt (- (* x x) y))
27.0ms
(- (* x x) y)
24.0ms
(- (* x x) y)
35.0ms
(* (sqrt (- (* x x) y)) (sqrt (- (* x x) y)))

simplify3.9s

Counts
114 → 114
Iterations

Useful iterations: done (3.9s)

IterNodesCost
01121614
12071144
2522992
31298963
43862938
done5001926

prune377.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (- (* x x) y)))
0.1b
(sqrt (sqrt (- (* x x) y)))
0.2b
(* (sqrt (- (* x x) y)) (* (sqrt (sqrt (- (* x x) y))) (sqrt (sqrt (- (* x x) y)))))
0.4b
(* (sqrt (sqrt (- (* x x) y))) (sqrt (sqrt (- (* x x) y))))

rewrite366.0ms

Algorithm
rewrite-expression-head
Rules
122×sqrt-div
104×sqrt-prod
91×sqrt-pow1
69×pow1
67×add-sqr-sqrt
47×pow1/2
39×pow-prod-up
35×flip3-- flip--
32×frac-times
22×add-cube-cbrt *-un-lft-identity
18×swap-sqr
17×associate-*l*
16×associate-*r/
12×pow-prod-down
11×add-exp-log associate-*r* pow-sqr add-cbrt-cube unswap-sqr
10×associate-*l/
7×difference-of-squares
4×rem-sqrt-square prod-exp cbrt-unprod add-log-exp
3×sqrt-unprod
2×*-commutative
1×pow2 pow-plus rem-square-sqrt
Counts
4 → 203
Calls
4 calls:
16.0ms
(sqrt (sqrt (- (* x x) y)))
25.0ms
(sqrt (sqrt (- (* x x) y)))
209.0ms
(* (sqrt (- (* x x) y)) (* (sqrt (sqrt (- (* x x) y))) (sqrt (sqrt (- (* x x) y)))))
105.0ms
(* (sqrt (sqrt (- (* x x) y))) (sqrt (sqrt (- (* x x) y))))

series315.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(sqrt (sqrt (- (* x x) y)))
105.0ms
(sqrt (sqrt (- (* x x) y)))
32.0ms
(* (sqrt (- (* x x) y)) (* (sqrt (sqrt (- (* x x) y))) (sqrt (sqrt (- (* x x) y)))))
68.0ms
(* (sqrt (sqrt (- (* x x) y))) (sqrt (sqrt (- (* x x) y))))

simplify2.8s

Counts
215 → 215
Iterations

Useful iterations: done (2.8s)

IterNodesCost
02294808
14712979
211442503
330752405
done50002378

prune629.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (sqrt y))
0.0b
(- x (sqrt y))
0.1b
(* (+ x (sqrt y)) (- x (sqrt y)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
13×*-un-lft-identity
7×add-log-exp
6×associate-*r*
5×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
4×frac-times flip3-- flip3-+ associate-*l* flip-- flip-+ difference-of-squares
3×sub-neg
2×distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/ sqrt-prod distribute-lft-out distribute-lft-out--
1×+-commutative diff-log pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
3 → 61
Calls
3 calls:
13.0ms
(+ x (sqrt y))
21.0ms
(- x (sqrt y))
64.0ms
(* (+ x (sqrt y)) (- x (sqrt y)))

series192.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(+ x (sqrt y))
63.0ms
(- x (sqrt y))
83.0ms
(* (+ x (sqrt y)) (- x (sqrt y)))

simplify3.2s

Counts
70 → 70
Iterations

Useful iterations: 3 (1.6s)

IterNodesCost
091833
1238699
2923631
34141625
done5001625

prune213.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes3.0ms