Details

analyze23.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
12.5%	12.5%	75%	2
12.5%	12.5%	75%	3
18.7%	6.2%	75%	4
21.8%	3.1%	75%	5
23.4%	1.6%	75%	6
23.4%	1.6%	75%	7
24.2%	0.8%	75%	8
24.2%	0.8%	75%	9
24.6%	0.4%	75%	10
24.6%	0.4%	75%	11
24.8%	0.2%	75%	12
24.8%	0.2%	75%	13
24.9%	0.1%	75%	14

Compiler

Compiled 15 to 12 computations (20% saved)

sample52.0ms (1.1%)

Algorithm

1×

intervals

Results

19.0ms	64×	body	1024	valid
10.0ms	137×	body	128	valid
7.0ms	34×	body	512	valid
5.0ms	256×	pre	128	true
3.0ms	21×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify89.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

prune8.0ms (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: 0.1b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
0.1b	(*.f64 e (sin.f64 v))
0.1b	(*.f64 e (cos.f64 v))

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_1123`
12×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
9×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
7×	`pow1_binary64_1162`
6×	`associate-r_binary64_1041` `associate-l_binary64_1042`
3×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `prod-exp_binary64_1150` `times-frac_binary64_1107` `associate-/r*_binary64_1045`
2×	`*-commutative_binary64_1032` `associate-/r/_binary64_1047` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `unswap-sqr_binary64_1069`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip3-+_binary64_1104` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `flip-+_binary64_1075`

Counts

3 → 59

Calls

3 calls:

6.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
4.0ms	(*.f64 e (cos.f64 v))
4.0ms	(*.f64 e (sin.f64 v))

series155.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

95.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
31.0ms	(*.f64 e (sin.f64 v))
30.0ms	(*.f64 e (cos.f64 v))

simplify82.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4947	920
1	4947	920

prune62.0ms (1.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	62	6	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	6	69

Merged error: 0.0b

Counts

69 → 6

Compiler

Compiled 1166 to 464 computations (60.2% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1))
0.1b	(.f64 e (/.f64 (sin.f64 v) (+.f64 (.f64 e (cos.f64 v)) 1)))
0.1b	(*.f64 e (cos.f64 v))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64_1123`
21×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
19×	`times-frac_binary64_1107`
18×	`associate-r_binary64_1041`
12×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
7×	`pow1_binary64_1162`
6×	`associate-l_binary64_1042`
4×	`associate-/r/_binary64_1047`
3×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `prod-exp_binary64_1150` `associate-/l_binary64_1046` `unswap-sqr_binary64_1069` `associate-/r_binary64_1045`
2×	`*-commutative_binary64_1032` `flip3-+_binary64_1104` `div-inv_binary64_1098` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-*r/_binary64_1043`

Counts

3 → 81

Calls

3 calls:

11.0ms	(.f64 e (/.f64 (sin.f64 v) (+.f64 (.f64 e (cos.f64 v)) 1)))
6.0ms	(/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1))
4.0ms	(*.f64 e (cos.f64 v))

series184.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

90.0ms	(.f64 e (/.f64 (sin.f64 v) (+.f64 (.f64 e (cos.f64 v)) 1)))
65.0ms	(/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1))
29.0ms	(*.f64 e (cos.f64 v))

simplify100.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	5416	1715

prune81.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	89	7	96

Merged error: 0.0b

Counts

96 → 7

Compiler

Compiled 1781 to 778 computations (56.3% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 e (cos.f64 v))
0.1b	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
0.2b	(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64_1107`
57×	`add-sqr-sqrt_binary64_1123`
55×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
16×	`associate-/r*_binary64_1045`
12×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
6×	`div-inv_binary64_1098` `associate-/l*_binary64_1046`
5×	`pow1_binary64_1162`
4×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
3×	`add-log-exp_binary64_1140` `associate-r_binary64_1041` `associate-l_binary64_1042`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `flip3-+_binary64_1104` `associate-/r/_binary64_1047` `pow-prod-down_binary64_1172` `flip-+_binary64_1075` `unswap-sqr_binary64_1069`

Counts

3 → 117

Calls

3 calls:

8.0ms	(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
6.0ms	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))

series186.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

93.0ms	(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
65.0ms	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
28.0ms	(*.f64 e (cos.f64 v))

simplify104.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4941	3222
1	4941	3222

prune117.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	125	8	133

Merged error: 0b

Counts

133 → 8

Compiler

Compiled 2727 to 1125 computations (58.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 e (cos.f64 v))
0.1b	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
0.3b	(.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 (.f64 e (cos.f64 v)) 1) (sin.f64 v))))
0.3b	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))

rewrite92.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

294×	`times-frac_binary64_1107`
196×	`add-sqr-sqrt_binary64_1123`
162×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
93×	`sqrt-prod_binary64_1117`
86×	`associate-r_binary64_1041`
22×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
16×	`div-inv_binary64_1098` `associate-/r*_binary64_1045`
11×	`unswap-sqr_binary64_1069`
9×	`associate-/l_binary64_1046` `associate-l*_binary64_1042`
8×	`pow1_binary64_1162`
7×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
4×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `prod-exp_binary64_1150`
2×	`*-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `associate-/r/_binary64_1047` `pow-prod-down_binary64_1172`
1×	`flip3-+_binary64_1104` `associate-*r/_binary64_1043` `flip-+_binary64_1075`

Counts

4 → 274

Calls

4 calls:

31.0ms	(.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 (.f64 e (cos.f64 v)) 1) (sin.f64 v))))
9.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
6.0ms	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))

series367.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

154.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
120.0ms	(.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 (.f64 e (cos.f64 v)) 1) (sin.f64 v))))
64.0ms	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
28.0ms	(*.f64 e (cos.f64 v))

simplify143.0ms (3%)

Algorithm

1×	egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4961	8697
1	4961	8697

prune299.0ms (6.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	286	8	294

Merged error: 0b

Counts

294 → 8

Compiler

Compiled 7832 to 2920 computations (62.7% saved)

regimes146.0ms (3.1%)

Compiler: Compiled 1412 to 998 computations (29.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	17
1	14	17

end0.0ms (0%)

sample2.3s (49%)

Algorithm

1×

intervals

Results

821.0ms	2015×	body	1024	valid
330.0ms	4449×	body	128	valid
220.0ms	1007×	body	512	valid
158.0ms	8000×	pre	128	true
81.0ms	527×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 488 to 347 computations (28.9% saved)

Details

analyze23.0ms (0.5%)

sample52.0ms (1.1%)

simplify89.0ms (1.9%)

prune8.0ms (0.2%)

localize9.0ms (0.2%)

rewrite18.0ms (0.4%)

series155.0ms (3.3%)

simplify82.0ms (1.7%)

prune62.0ms (1.3%)

localize9.0ms (0.2%)

rewrite27.0ms (0.6%)

series184.0ms (3.9%)

simplify100.0ms (2.1%)

prune81.0ms (1.7%)

localize10.0ms (0.2%)

rewrite29.0ms (0.6%)

series186.0ms (3.9%)

simplify104.0ms (2.2%)

prune117.0ms (2.5%)

localize11.0ms (0.2%)

rewrite92.0ms (1.9%)

series367.0ms (7.8%)

simplify143.0ms (3%)

prune299.0ms (6.3%)

regimes146.0ms (3.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (49%)

Profiling