Details

sample142.0ms

Algorithm

intervals

Results

55.0ms	72×	body	10240	exit
31.0ms	306×	body	80	nan
28.0ms	256×	body	80	valid

simplify1.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	1114
5	256
4	110
3	45
2	22
1	13
0	7

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize30.0ms

Local error

Found 2 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
12×	`add-cube-cbrt`
11×	`unpow-prod-up`
9×	`prod-diff`
6×	`unpow-prod-down` `sqrt-prod`
5×	`pow1` `pow-unpow`
3×	`pow-pow` `add-exp-log`
2×	`expm1-log1p-u` `sqrt-pow1` `add-cbrt-cube` `pow1/2` `log1p-expm1-u` `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 → 54

Calls

2 calls:

13.0ms	(pow (sqrt (atan2 b b)) (- b a))
6.0ms	(sqrt (atan2 b b))

series75.0ms

Counts

2 → 6

Calls

2 calls:

44.0ms	(pow (sqrt (atan2 b b)) (- b a))
31.0ms	(sqrt (atan2 b b))

simplify1.8s

Counts

60 → 60

Iterations

Iter	Nodes
done	5001
3	1525
2	610
1	277
0	100

prune254.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

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))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
26×	`add-cube-cbrt`
24×	`sqrt-prod`
22×	`unpow-prod-up`
18×	`unpow-prod-down` `prod-diff`
12×	`pow1`
10×	`pow-unpow` `pow-pow` `sqrt-pow1`
6×	`pow1/2` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `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 → 118

Calls

4 calls:

8.0ms	(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))

series116.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
55.0ms	(pow (sqrt (sqrt (atan2 b b))) (- b a))
11.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))

simplify1.8s

Counts

130 → 130

Iterations

Iter	Nodes
done	5002
3	2010
2	761
1	338
0	122

prune762.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize50.0ms

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))

rewrite72.0ms

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×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `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 → 105

Calls

4 calls:

6.0ms	(cbrt (- b a))
60.0ms	(* (cbrt (- b a)) (cbrt (- b a)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))

series397.0ms

Counts

4 → 12

Calls

4 calls:

221.0ms	(cbrt (- b a))
152.0ms	(* (cbrt (- b a)) (cbrt (- b a)))
11.0ms	(sqrt (atan2 b b))
12.0ms	(sqrt (atan2 b b))

simplify1.8s

Counts

117 → 117

Iterations

Iter	Nodes
done	5001
3	2084
2	723
1	312
0	152

prune843.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

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×	`expm1-log1p-u` `add-cbrt-cube` `associate-l/` `associate-r/` `log1p-expm1-u` `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 → 112

Calls

4 calls:

21.0ms	(/ (cbrt (* (- b a) (+ a b))) (cbrt (+ a b)))
1.0ms	(sqrt (atan2 b b))
1.0ms	(sqrt (atan2 b b))
10.0ms	(cbrt (* (- b a) (+ a b)))

series847.0ms

Counts

4 → 12

Calls

4 calls:

223.0ms	(/ (cbrt (* (- b a) (+ a b))) (cbrt (+ a b)))
15.0ms	(sqrt (atan2 b b))
11.0ms	(sqrt (atan2 b b))
597.0ms	(cbrt (* (- b a) (+ a b)))

simplify1.4s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	1227
1	437
0	212

prune1.1s

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0.0b

simplify3.0ms

Iterations

Iter	Nodes
done	21
1	21
0	18

end0.0ms

sample5.3s

Algorithm

intervals

Results

2.3s	1870×	body	10240	exit
1.5s	9797×	body	80	nan
920.0ms	7992×	body	80	valid
5.0ms	1×	body	5120	valid
1.0ms	2×	body	640	valid
1.0ms	4×	body	160	valid
0.0ms	1×	body	320	valid