Details

sample103.0ms

Algorithm

intervals

Results

28.0ms	510×	body	80	nan
28.0ms	235×	body	160	nan
23.0ms	256×	body	80	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	1825
6	472
5	156
4	60
3	35
2	19
1	16
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ x (sqrt (- (* x x) 1))))
0.0b	(- (* x x) 1)
0.0b	(+ x (sqrt (- (* x x) 1)))
32.5b	(sqrt (- (* x x) 1))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity`
9×	`add-sqr-sqrt`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
5×	`add-exp-log`
4×	`log-prod` `add-cbrt-cube` `insert-posit16` `difference-of-squares`
2×	`log-div` `flip3-+` `flip3--` `sqrt-div` `difference-of-sqr-1` `flip-+` `flip--` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `rem-log-exp` `log-pow`

Counts

4 → 64

Calls

4 calls:

11.0ms	(log (+ x (sqrt (- (* x x) 1))))
9.0ms	(- (* x x) 1)
12.0ms	(+ x (sqrt (- (* x x) 1)))
8.0ms	(sqrt (- (* x x) 1))

series347.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(log (+ x (sqrt (- (* x x) 1))))
64.0ms	(- (* x x) 1)
73.0ms	(+ x (sqrt (- (* x x) 1)))
40.0ms	(sqrt (- (* x x) 1))

simplify2.0s

Counts

76 → 76

Iterations

Iter	Nodes
done	5008
3	2554
2	832
1	323
0	145

prune331.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
0.0b	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
0.0b	(sqrt (+ x 1))
0.5b	(* (sqrt (+ x 1)) (sqrt (- x 1)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`sqrt-prod`
17×	`*-un-lft-identity`
14×	`sqrt-div`
10×	`pow1` `associate-r` `add-cube-cbrt`
7×	`associate-l` `add-exp-log`
6×	`flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
4×	`frac-times` `insert-posit16` `unswap-sqr`
3×	`log-prod` `sqrt-pow1` `flip3--` `pow1/2` `pow-prod-down` `flip--`
2×	`log-div` `associate-l/` `associate-r/` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `sqrt-unprod` `difference-of-sqr-1` `rem-log-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 88

Calls

4 calls:

5.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
10.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
9.0ms	(sqrt (+ x 1))
52.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(log (+ x (* (sqrt (+ x 1)) (sqrt (- x 1)))))
70.0ms	(+ x (* (sqrt (+ x 1)) (sqrt (- x 1))))
37.0ms	(sqrt (+ x 1))
103.0ms	(* (sqrt (+ x 1)) (sqrt (- x 1)))

simplify2.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	5002
3	3321
2	996
1	412
0	185

prune473.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ x 1)))
0.1b	(sqrt (sqrt (+ x 1)))
0.5b	(* (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt (- x 1)))
0.6b	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

122×	`sqrt-div`
114×	`sqrt-prod`
62×	`add-sqr-sqrt`
43×	`*-un-lft-identity` `sqrt-pow1`
39×	`pow1`
32×	`frac-times`
26×	`flip3-+` `flip-+`
23×	`pow1/2`
22×	`add-cube-cbrt`
20×	`associate-r`
18×	`swap-sqr`
16×	`associate-*l/`
12×	`pow-prod-down`
11×	`add-cbrt-cube` `associate-l` `add-exp-log` `unswap-sqr`
10×	`associate-*r/`
9×	`flip3--` `pow-prod-up` `flip--`
8×	`distribute-lft-out`
5×	`pow-sqr`
4×	`rem-sqrt-square` `prod-exp` `cbrt-unprod` `insert-posit16` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative` `difference-of-squares`
1×	`pow2` `rem-square-sqrt` `pow-plus` `difference-of-sqr-1` `distribute-lft-out--`

Counts

4 → 192

Calls

4 calls:

5.0ms	(sqrt (sqrt (+ x 1)))
7.0ms	(sqrt (sqrt (+ x 1)))
85.0ms	(* (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt (- x 1)))
30.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

series207.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(sqrt (sqrt (+ x 1)))
38.0ms	(sqrt (sqrt (+ x 1)))
91.0ms	(* (* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1)))) (sqrt (- x 1)))
28.0ms	(* (sqrt (sqrt (+ x 1))) (sqrt (sqrt (+ x 1))))

simplify3.0s

Counts

204 → 204

Iterations

Iter	Nodes
done	5004
3	3756
2	1380
1	603
0	245

prune773.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify3.0ms

Iterations

Iter	Nodes
done	16
1	16
0	11

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.4s	7610×	body	160	nan
954.0ms	16024×	body	80	nan
646.0ms	8000×	body	80	valid