Details

analyze323.0ms (10.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample30.0ms (1%)

Algorithm

1×

intervals

Results

16.0ms	104×	body	1024	valid
3.0ms	33×	body	512	valid
2.0ms	91×	body	128	valid
1.0ms	22×	body	256	valid
1.0ms	6×	body	2048	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify165.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

prune5.0ms (0.2%)

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: 42.8b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.5b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.2b	(-.f64 (exp.f64 x) 1)

rewrite19.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1123`
30×	`*-un-lft-identity_binary64_1101`
21×	`times-frac_binary64_1107`
15×	`add-cube-cbrt_binary64_1136`
10×	`difference-of-squares_binary64_1070`
7×	`associate-/r*_binary64_1045`
5×	`difference-of-sqr-1_binary64_1071` `distribute-lft-out--_binary64_1053`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
3×	`add-exp-log_binary64_1139` `associate-/l*_binary64_1046` `cancel-sign-sub-inv_binary64_1067`
2×	`pow1_binary64_1162` `flip--_binary64_1076` `flip3--_binary64_1105` `associate-/r/_binary64_1047`
1×	`diff-log_binary64_1193` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `div-inv_binary64_1098` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135`

Counts

2 → 63

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

series96.0ms (3.2%)

Counts

2 → 6

Calls

2 calls:

78.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
18.0ms	(-.f64 (exp.f64 x) 1)

simplify67.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5712	1129

prune70.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	66	3	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	3	70

Merged error: 0.0b

Counts

70 → 3

Compiler

Compiled 956 to 474 computations (50.4% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
0.4b	(*.f64 x 1/12)

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64_1140`
6×	`add-sqr-sqrt_binary64_1123`
4×	`*-un-lft-identity_binary64_1101` `add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cube-cbrt_binary64_1136` `add-cbrt-cube_binary64_1137`
3×	`sum-log_binary64_1192` `associate-r_binary64_1041` `associate-l_binary64_1042`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `associate-+r+_binary64_1033` `flip3-+_binary64_1104` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `flip-+_binary64_1075` `unswap-sqr_binary64_1069`

Counts

2 → 31

Calls

2 calls:

10.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
4.0ms	(*.f64 x 1/12)

series42.0ms (1.4%)

Counts

2 → 6

Calls

2 calls:

24.0ms	(*.f64 x 1/12)
18.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))

simplify66.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4907	417
1	4907	417

prune37.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	36	1	37
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	36	4	40

Merged error: 0.0b

Counts

40 → 4

Compiler

Compiled 525 to 421 computations (19.8% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
3.2b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite18.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
18×	`times-frac_binary64_1107`
14×	`add-cube-cbrt_binary64_1136`
10×	`difference-of-squares_binary64_1070`
6×	`add-exp-log_binary64_1139` `associate-/r*_binary64_1045`
5×	`distribute-lft-out--_binary64_1053`
4×	`add-log-exp_binary64_1140` `add-cbrt-cube_binary64_1137`
3×	`pow1_binary64_1162` `associate-/l*_binary64_1046` `cancel-sign-sub-inv_binary64_1067`
2×	`flip--_binary64_1076` `flip3--_binary64_1105` `associate-/r/_binary64_1047` `div-exp_binary64_1152`
1×	`inv-pow_binary64_1186` `diff-log_binary64_1193` `1-exp_binary64_1145` `frac-2neg_binary64_1112` `sub-neg_binary64_1094` `clear-num_binary64_1100` `div-inv_binary64_1098` `rec-exp_binary64_1151` `cbrt-undiv_binary64_1135` `pow-flip_binary64_1175`

Counts

2 → 62

Calls

2 calls:

7.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
6.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

series97.0ms (3.2%)

Counts

2 → 6

Calls

2 calls:

74.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
22.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

simplify76.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4913	1052
1	4913	1052

prune52.0ms (1.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	68	4	72

Merged error: 0.0b

Counts

72 → 4

Compiler

Compiled 889 to 570 computations (35.9% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(/.f64 1 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
0.5b	(*.f64 (/.f64 1 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (+.f64 (exp.f64 x) 1))
3.2b	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite54.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64_1123`
48×	`*-un-lft-identity_binary64_1101`
38×	`times-frac_binary64_1107`
27×	`add-cube-cbrt_binary64_1136`
24×	`associate-l_binary64_1042`
17×	`add-exp-log_binary64_1139`
11×	`add-cbrt-cube_binary64_1137`
8×	`difference-of-squares_binary64_1070` `add-log-exp_binary64_1140` `distribute-lft-out--_binary64_1053` `sinh-undef_binary64_1294`
7×	`pow1_binary64_1162`
6×	`associate-/r*_binary64_1045`
4×	`prod-exp_binary64_1150` `associate-/r/_binary64_1047` `associate-r_binary64_1041` `div-exp_binary64_1152`
3×	`flip--_binary64_1076` `flip3--_binary64_1105` `flip3-+_binary64_1104` `associate-/l*_binary64_1046` `flip-+_binary64_1075` `unswap-sqr_binary64_1069` `cancel-sign-sub-inv_binary64_1067`
2×	`1-exp_binary64_1145` `cbrt-unprod_binary64_1134` `frac-times_binary64_1111` `distribute-lft-out_binary64_1052` `associate-*r/_binary64_1043` `div-inv_binary64_1098` `rec-exp_binary64_1151` `cbrt-undiv_binary64_1135`
1×	`inv-pow_binary64_1186` `diff-log_binary64_1193` `-commutative_binary64_1032` `frac-2neg_binary64_1112` `sum-log_binary64_1192` `sub-neg_binary64_1094` `distribute-lft-in_binary64_1050` `clear-num_binary64_1100` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `associate-l/_binary64_1044` `distribute-rgt-in_binary64_1051` `pow-flip_binary64_1175`

Counts

4 → 127

Calls

4 calls:

22.0ms	(*.f64 (/.f64 1 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (+.f64 (exp.f64 x) 1))
8.0ms	(/.f64 1 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
6.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
5.0ms	(+.f64 (exp.f64 x) 1)

series251.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(*.f64 (/.f64 1 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))) (+.f64 (exp.f64 x) 1))
98.0ms	(/.f64 1 (-.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
39.0ms	(-.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
11.0ms	(+.f64 (exp.f64 x) 1)

simplify84.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5985	2504

prune123.0ms (4.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	1	0	1
Picked	1	0	1
Done	1	1	2
Total	140	3	143

Merged error: 0.0b

Counts

143 → 3

Compiler

Compiled 2617 to 1128 computations (56.9% saved)

regimes110.0ms (3.7%)

Compiler: Compiled 993 to 703 computations (29.2% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	14	17

end0.0ms (0%)

sample1.2s (39.1%)

Algorithm

1×

intervals

Results

421.0ms	2654×	body	1024	valid
114.0ms	1329×	body	512	valid
78.0ms	3126×	body	128	valid
56.0ms	274×	body	2048	valid
36.0ms	617×	body	256	valid

Compiler

Compiled 284 to 210 computations (26.1% saved)

Details

analyze323.0ms (10.8%)

sample30.0ms (1%)

simplify165.0ms (5.5%)

prune5.0ms (0.2%)

localize4.0ms (0.1%)

rewrite19.0ms (0.6%)

series96.0ms (3.2%)

simplify67.0ms (2.2%)

prune70.0ms (2.3%)

localize6.0ms (0.2%)

rewrite17.0ms (0.6%)

series42.0ms (1.4%)

simplify66.0ms (2.2%)

prune37.0ms (1.3%)

localize5.0ms (0.2%)

rewrite18.0ms (0.6%)

series97.0ms (3.2%)

simplify76.0ms (2.5%)

prune52.0ms (1.7%)

localize8.0ms (0.3%)

rewrite54.0ms (1.8%)

series251.0ms (8.4%)

simplify84.0ms (2.8%)

prune123.0ms (4.1%)

regimes110.0ms (3.7%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.2s (39.1%)

Profiling