Details

sample136.0ms

Algorithm

intervals

Results

52.0ms	72×	body	10240	exit
28.0ms	306×	body	80	nan
26.0ms	256×	body	80	valid

simplify1.7s

Counts

1 → 1

Iterations

Iter	Nodes
done	5019
6	1161
5	250
4	110
3	45
2	22
1	13
0	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 2 expressions with local error:

0.1b	(pow (sqrt (atan2 b b)) (- b a))
1.0b	(sqrt (atan2 b b))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity`
6×	`unpow-prod-down` `add-cube-cbrt` `sqrt-prod`
5×	`pow1` `pow-unpow`
3×	`pow-pow` `add-exp-log`
2×	`unpow-prod-up` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `add-log-exp`
1×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

2 → 41

Calls

2 calls:

6.0ms	(pow (sqrt (atan2 b b)) (- b a))
5.0ms	(sqrt (atan2 b b))

series64.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(pow (sqrt (atan2 b b)) (- b a))
19.0ms	(sqrt (atan2 b b))

simplify2.6s

Counts

47 → 47

Iterations

Iter	Nodes
done	5008
4	3205
3	966
2	335
1	153
0	60

prune248.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
0.0b	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

24×	`sqrt-prod`
20×	`add-sqr-sqrt`
18×	`unpow-prod-down` `*-un-lft-identity`
14×	`add-cube-cbrt`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`pow1/2` `add-exp-log`
4×	`unpow-prod-up` `add-cbrt-cube` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `sub-neg` `pow-exp` `sqrt-pow2` `distribute-lft-out--` `pow-sub` `difference-of-squares` `sqr-pow`

Counts

4 → 92

Calls

4 calls:

10.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
8.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series129.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
54.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
14.0ms	(sqrt (atan2 b b))
22.0ms	(sqrt (atan2 b b))

simplify3.1s

Counts

104 → 104

Iterations

Iter	Nodes
done	5002
4	3791
3	1198
2	478
1	212
0	82

prune701.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- b a))
0.5b	(* (cbrt (- b a)) (cbrt (- b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
33×	`cbrt-prod`
31×	`*-un-lft-identity`
15×	`add-cube-cbrt`
14×	`cbrt-div`
13×	`pow1`
10×	`swap-sqr`
8×	`associate-r` `associate-l`
7×	`flip3--` `pow1/3` `flip--` `distribute-lft-out--`
6×	`add-exp-log` `sqrt-prod`
5×	`difference-of-squares`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `associate-r/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 97

Calls

4 calls:

13.0ms	(cbrt (- b a))
60.0ms	(* (cbrt (- b a)) (cbrt (- b a)))
2.0ms	(sqrt (atan2 b b))
2.0ms	(sqrt (atan2 b b))

series417.0ms

Counts

4 → 12

Calls

4 calls:

208.0ms	(cbrt (- b a))
170.0ms	(* (cbrt (- b a)) (cbrt (- b a)))
19.0ms	(sqrt (atan2 b b))
20.0ms	(sqrt (atan2 b b))

simplify2.0s

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
3	1750
2	664
1	301
0	146

prune766.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize78.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (cbrt (* (+ b a) (- b a))) (cbrt (+ b a)))
1.0b	(sqrt (atan2 b b))
1.0b	(sqrt (atan2 b b))
32.9b	(cbrt (* (+ b a) (- b a)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity`
29×	`cbrt-prod`
28×	`times-frac`
26×	`add-sqr-sqrt`
24×	`add-cube-cbrt`
18×	`cbrt-div`
8×	`frac-times` `associate-/l/`
7×	`associate-/r*` `flip3-+` `flip-+`
6×	`pow1` `flip3--` `add-exp-log` `sqrt-prod` `flip--`
5×	`distribute-lft-out`
4×	`add-cbrt-cube` `associate-l/` `associate-r/` `associate-/l*` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `pow1/3` `div-exp` `div-inv`

Counts

4 → 104

Calls

4 calls:

23.0ms	(/ (cbrt (* (+ b a) (- b a))) (cbrt (+ b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
10.0ms	(cbrt (* (+ b a) (- b a)))

series441.0ms

Counts

4 → 12

Calls

4 calls:

182.0ms	(/ (cbrt (* (+ b a) (- b a))) (cbrt (+ b a)))
16.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
232.0ms	(cbrt (* (+ b a) (- b a)))

simplify2.5s

Counts

116 → 116

Iterations

Iter	Nodes
done	5000
3	3531
2	1006
1	389
0	200

prune1.0s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

simplify5.0ms

Iterations

Iter	Nodes
done	21
1	21
0	18

end0.0ms

sample5.2s

Algorithm

intervals

Results

2.5s	1870×	body	10240	exit
1.2s	9797×	body	80	nan
962.0ms	7992×	body	80	valid
5.0ms	1×	body	5120	valid
3.0ms	2×	body	640	valid
1.0ms	4×	body	160	valid
0.0ms	1×	body	320	valid