Details

analyze41.0ms (1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
50%	50%	0.1%	3
50%	50%	0.1%	4
62.4%	37.5%	0.1%	5
62.4%	31.2%	6.3%	6
68.7%	21.9%	9.5%	7
68.7%	17.2%	14.1%	8
71.8%	11.7%	16.5%	9
71.8%	9%	19.2%	10
73.4%	6%	20.6%	11
73.4%	4.6%	22%	12
74.1%	3.1%	22.8%	13
74.1%	2.3%	23.5%	14

Compiler

Compiled 7 to 7 computations (0% saved)

sample42.0ms (1.1%)

Algorithm

1×

intervals

Results

17.0ms	53×	body	2048	valid
7.0ms	48×	body	1024	valid
6.0ms	32×	body	512	valid
3.0ms	98×	body	128	valid
1.0ms	25×	body	256	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 13 to 15 computations (-15.4% saved)

simplify225.0ms (5.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5029	9

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 27.5b

Counts

2 → 1

Compiler

Compiled 12 to 12 computations (0% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(exp.f64 (*.f64 a x))
4.5b	(-.f64 (exp.f64 (*.f64 a x)) 1)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64_1133`
6×	`*-un-lft-identity_binary64_1111` `add-log-exp_binary64_1150`
3×	`cancel-sign-sub-inv_binary64_1077` `add-cube-cbrt_binary64_1146`
2×	`add-cbrt-cube_binary64_1147` `difference-of-squares_binary64_1080` `pow1_binary64_1172` `add-exp-log_binary64_1149`
1×	`flip3--_binary64_1115` `diff-log_binary64_1203` `exp-to-pow_binary64_1173` `difference-of-sqr-1_binary64_1081` `rem-exp-log_binary64_1151` `exp-prod_binary64_1163` `sub-neg_binary64_1104` `distribute-lft-out--_binary64_1063` `flip--_binary64_1086`

Counts

2 → 28

Calls

2 calls:

5.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
2.0ms	(exp.f64 (*.f64 a x))

series72.0ms (1.8%)

Counts

2 → 6

Calls

2 calls:

49.0ms	(-.f64 (exp.f64 (*.f64 a x)) 1)
23.0ms	(exp.f64 (*.f64 a x))

simplify48.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

34 → 34

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5005	377

prune64.0ms (1.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	29	5	34
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	5	35

Merged error: 4.9b

Counts

35 → 5

Compiler

Compiled 862 to 551 computations (36.1% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 1/6 (pow.f64 a 3))
5.9b	(.f64 x (.f64 1/6 (pow.f64 a 3)))
6.3b	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
7.9b	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))

rewrite44.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`add-exp-log_binary64_1149`
20×	`add-sqr-sqrt_binary64_1133`
16×	`associate-r_binary64_1051`
13×	`add-cbrt-cube_binary64_1147`
11×	`prod-exp_binary64_1160` `*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
9×	`associate-l_binary64_1052`
8×	`pow1_binary64_1172`
6×	`add-log-exp_binary64_1150`
5×	`cbrt-unprod_binary64_1144` `unswap-sqr_binary64_1079`
4×	`unpow-prod-down_binary64_1190` `cube-prod_binary64_1139`
3×	`*-commutative_binary64_1042`
2×	`flip-+_binary64_1085` `flip3-+_binary64_1114` `pow-exp_binary64_1179` `pow-prod-down_binary64_1182` `sqr-pow_binary64_1083` `pow-to-exp_binary64_1180` `associate-*r/_binary64_1053`
1×	`cube-mult_binary64_1141` `distribute-lft-in_binary64_1060` `+-commutative_binary64_1041` `unpow3_binary64_1177` `distribute-rgt-in_binary64_1061` `sum-log_binary64_1202`

Counts

4 → 83

Calls

4 calls:

11.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
8.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
8.0ms	(*.f64 1/6 (pow.f64 a 3))
7.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))

series409.0ms (10.4%)

Counts

4 → 12

Calls

4 calls:

192.0ms	(.f64 x (+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (*.f64 1/6 (pow.f64 a 3)))))
91.0ms	(.f64 x (.f64 1/6 (pow.f64 a 3)))
77.0ms	(+.f64 (.f64 1/2 (.f64 a a)) (.f64 x (.f64 1/6 (pow.f64 a 3))))
49.0ms	(*.f64 1/6 (pow.f64 a 3))

simplify90.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4932	1404
1	4932	1404

prune124.0ms (3.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	95	5	100

Merged error: 2.5b

Counts

100 → 5

Compiler

Compiled 2490 to 1532 computations (38.5% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6)))))))
0.4b	(*.f64 x 1/6)
0.7b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))
6.3b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))

rewrite39.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cbrt-cube_binary64_1147` `pow1_binary64_1172` `add-exp-log_binary64_1149`
15×	`add-sqr-sqrt_binary64_1133`
11×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `pow-prod-down_binary64_1182`
10×	`-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146` `associate-r_binary64_1051` `associate-l*_binary64_1052`
8×	`associate-*r/_binary64_1053`
6×	`distribute-lft-in_binary64_1060` `distribute-rgt-in_binary64_1061`
4×	`*-commutative_binary64_1042` `add-log-exp_binary64_1150`
3×	`flip-+_binary64_1085` `flip3-+_binary64_1114` `unswap-sqr_binary64_1079`

Counts

4 → 90

Calls

4 calls:

12.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))
9.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))
7.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6)))))))
4.0ms	(*.f64 x 1/6)

series391.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(.f64 x (+.f64 a (.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6)))))))
142.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))
67.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))
21.0ms	(*.f64 x 1/6)

simplify45.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5675	1933

prune114.0ms (2.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	101	1	102
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	101	6	107

Merged error: 2.5b

Counts

107 → 6

Compiler

Compiled 2607 to 1531 computations (41.3% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.7b	(.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))
6.3b	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))

rewrite32.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-cbrt-cube_binary64_1147` `pow1_binary64_1172` `add-exp-log_binary64_1149`
9×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `add-sqr-sqrt_binary64_1133` `pow-prod-down_binary64_1182`
8×	`*-un-lft-identity_binary64_1111` `add-cube-cbrt_binary64_1146`
6×	`cbrt-prod_binary64_1142` `associate-*r/_binary64_1053`
5×	`distribute-lft-in_binary64_1060` `distribute-rgt-in_binary64_1061`
4×	`associate-r_binary64_1051` `associate-l_binary64_1052` `add-log-exp_binary64_1150`
2×	`*-commutative_binary64_1042` `pow1/3_binary64_1193` `flip-+_binary64_1085` `flip3-+_binary64_1114`
1×	`unswap-sqr_binary64_1079`

Counts

4 → 72

Calls

4 calls:

14.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))
9.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series509.0ms (12.9%)

Counts

4 → 12

Calls

4 calls:

151.0ms	(cbrt.f64 x)
144.0ms	(.f64 x (.f64 (.f64 a a) (+.f64 1/2 (.f64 a (*.f64 x 1/6)))))
141.0ms	(cbrt.f64 x)
72.0ms	(.f64 (.f64 a a) (+.f64 1/2 (.f64 a (.f64 x 1/6))))

simplify67.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4966	1264
1	4966	1264

prune88.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	84	6	90

Merged error: 2.5b

Counts

90 → 6

Compiler

Compiled 2397 to 1130 computations (52.9% saved)

regimes138.0ms (3.5%)

Compiler: Compiled 594 to 437 computations (26.4% saved)

bsearch1.0ms (0%)

Compiler: Compiled 3 to 3 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	47
1	41	47

end0.0ms (0%)

sample1.3s (33%)

Algorithm

1×

intervals

Results

468.0ms	1438×	body	2048	valid
277.0ms	1708×	body	1024	valid
103.0ms	1132×	body	512	valid
82.0ms	3083×	body	128	valid
37.0ms	639×	body	256	valid
4.0ms	118×	body	128	invalid

Compiler

Compiled 162 to 115 computations (29% saved)

Details

analyze41.0ms (1%)

sample42.0ms (1.1%)

simplify225.0ms (5.7%)

prune2.0ms (0%)

localize4.0ms (0.1%)

rewrite9.0ms (0.2%)

series72.0ms (1.8%)

simplify48.0ms (1.2%)

prune64.0ms (1.6%)

localize12.0ms (0.3%)

rewrite44.0ms (1.1%)

series409.0ms (10.4%)

simplify90.0ms (2.3%)

prune124.0ms (3.1%)

localize10.0ms (0.3%)

rewrite39.0ms (1%)

series391.0ms (9.9%)

simplify45.0ms (1.1%)

prune114.0ms (2.9%)

localize14.0ms (0.4%)

rewrite32.0ms (0.8%)

series509.0ms (12.9%)

simplify67.0ms (1.7%)

prune88.0ms (2.2%)

regimes138.0ms (3.5%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.3s (33%)

Profiling