Details

analyze116.0ms (2.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	34
1	43	34
0	2	2
1	2	2

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)

sample53.0ms (1.2%)

Algorithm

1×

intervals

Results

20.0ms	70×	body	1024	valid
9.0ms	135×	body	128	valid
7.0ms	36×	body	512	valid
5.0ms	256×	pre	128	true
2.0ms	15×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify12.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

prune3.0ms (0.1%)

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

Error

0.2b

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 (cos.f64 v))
0.1b	(*.f64 e (sin.f64 v))

rewrite19.0ms (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 (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))

series157.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

88.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
39.0ms	(*.f64 e (sin.f64 v))
30.0ms	(*.f64 e (cos.f64 v))

simplify88.0ms (2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4947	920
1	4947	920

prune68.0ms (1.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Error

0.0b

Counts

69 → 7

Compiler

Compiled 1205 to 483 computations (59.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 e (cos.f64 v))
0.1b	(*.f64 e (sin.f64 v))
0.1b	(*.f64 e (pow.f64 (cos.f64 v) 2))
0.3b	(pow.f64 (cos.f64 v) 2)

rewrite24.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64_1123`
14×	`add-exp-log_binary64_1139` `associate-r_binary64_1041`
13×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
10×	`add-cbrt-cube_binary64_1137`
9×	`pow1_binary64_1162` `associate-l_binary64_1042`
7×	`unpow-prod-down_binary64_1180`
6×	`unswap-sqr_binary64_1069`
5×	`prod-exp_binary64_1150`
4×	`add-log-exp_binary64_1140`
3×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `pow-unpow_binary64_1178` `sqr-pow_binary64_1073` `unpow2_binary64_1166`
2×	`pow-exp_binary64_1169` `pow-prod-down_binary64_1172` `pow-to-exp_binary64_1170`
1×	`pow-pow_binary64_1173`

Counts

4 → 81

Calls

4 calls:

6.0ms	(*.f64 e (pow.f64 (cos.f64 v) 2))
4.0ms	(*.f64 e (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))
3.0ms	(pow.f64 (cos.f64 v) 2)

series121.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(*.f64 e (pow.f64 (cos.f64 v) 2))
36.0ms	(*.f64 e (cos.f64 v))
29.0ms	(*.f64 e (sin.f64 v))
14.0ms	(pow.f64 (cos.f64 v) 2)

simplify79.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4937	793
1	4937	793

prune104.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Error

0.0b

Counts

100 → 7

Compiler

Compiled 2454 to 1145 computations (53.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite28.0ms (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:

7.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
5.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))

series196.0ms (4.5%)

Counts

3 → 9

Calls

3 calls:

92.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
76.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
27.0ms	(*.f64 e (cos.f64 v))

simplify91.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4954	3222
1	4954	3222

prune122.0ms (2.8%)

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

Error

0.0b

Counts

133 → 8

Compiler

Compiled 2733 to 1127 computations (58.8% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 e) (+.f64 1 (*.f64 e (cos.f64 v))))
0.1b	(*.f64 e (cos.f64 v))
0.2b	(*.f64 (sin.f64 v) (sqrt.f64 e))
0.3b	(.f64 (/.f64 (sqrt.f64 e) (+.f64 1 (.f64 e (cos.f64 v)))) (*.f64 (sin.f64 v) (sqrt.f64 e)))

rewrite39.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_1123`
37×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
36×	`times-frac_binary64_1107`
30×	`associate-l_binary64_1042`
25×	`sqrt-prod_binary64_1117`
22×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
13×	`pow1_binary64_1162`
10×	`associate-r_binary64_1041`
8×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150`
6×	`associate-/l*_binary64_1046`
5×	`pow-prod-down_binary64_1172`
4×	`add-log-exp_binary64_1140` `associate-/r/_binary64_1047`
3×	`-commutative_binary64_1032` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `unswap-sqr_binary64_1069` `associate-/r_binary64_1045`
2×	`flip3-+_binary64_1104` `div-inv_binary64_1098` `flip-+_binary64_1075`
1×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-*l/_binary64_1044`

Counts

4 → 125

Calls

4 calls:

13.0ms	(.f64 (/.f64 (sqrt.f64 e) (+.f64 1 (.f64 e (cos.f64 v)))) (*.f64 (sin.f64 v) (sqrt.f64 e)))
5.0ms	(/.f64 (sqrt.f64 e) (+.f64 1 (*.f64 e (cos.f64 v))))
5.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
4.0ms	(*.f64 e (cos.f64 v))

series299.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(.f64 (/.f64 (sqrt.f64 e) (+.f64 1 (.f64 e (cos.f64 v)))) (*.f64 (sin.f64 v) (sqrt.f64 e)))
103.0ms	(/.f64 (sqrt.f64 e) (+.f64 1 (*.f64 e (cos.f64 v))))
45.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
27.0ms	(*.f64 e (cos.f64 v))

simplify109.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	5060	2891

prune131.0ms (3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	135	10	145

Error

Counts

145 → 10

Compiler

Compiled 3173 to 1181 computations (62.8% saved)

regimes215.0ms (4.9%)

Accuracy

Total 0.1b remaining (96.1%)

Threshold costs 0.1b (96.1%)

Compiler

Compiled 2201 to 1514 computations (31.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	75	34
1	75	34

end0.0ms (0%)

sample2.2s (51.3%)

Algorithm

1×

intervals

Results

589.0ms	2045×	body	1024	valid
304.0ms	4473×	body	128	valid
206.0ms	978×	body	512	valid
158.0ms	8000×	pre	128	true
68.0ms	499×	body	256	valid
3.0ms	5×	body	2048	valid

Compiler

Compiled 762 to 526 computations (31% saved)

Details

analyze116.0ms (2.7%)

sample53.0ms (1.2%)

simplify12.0ms (0.3%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite19.0ms (0.4%)

series157.0ms (3.6%)

simplify88.0ms (2%)

prune68.0ms (1.6%)

localize14.0ms (0.3%)

rewrite24.0ms (0.6%)

series121.0ms (2.8%)

simplify79.0ms (1.8%)

prune104.0ms (2.4%)

localize9.0ms (0.2%)

rewrite28.0ms (0.6%)

series196.0ms (4.5%)

simplify91.0ms (2.1%)

prune122.0ms (2.8%)

localize14.0ms (0.3%)

rewrite39.0ms (0.9%)

series299.0ms (6.9%)

simplify109.0ms (2.5%)

prune131.0ms (3%)

regimes215.0ms (4.9%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.2s (51.3%)

Profiling