Details

analyze19.0ms (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)

sample48.0ms (1.2%)

Algorithm

1×

intervals

Results

17.0ms	60×	body	1024	valid
10.0ms	156×	body	128	valid
5.0ms	27×	body	512	valid
5.0ms	256×	pre	128	true
2.0ms	13×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify98.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	17
1	24	17

prune2.0ms (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

0.1b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite23.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1123`
13×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
10×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
8×	`pow1_binary64_1162`
6×	`add-log-exp_binary64_1140` `associate-r_binary64_1041` `associate-l_binary64_1042`
3×	`cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `times-frac_binary64_1107` `associate-/r*_binary64_1045`
2×	`*-commutative_binary64_1032` `flip3-+_binary64_1104` `associate-/r/_binary64_1047` `pow-prod-down_binary64_1172` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `flip-+_binary64_1075` `unswap-sqr_binary64_1069`
1×	`frac-2neg_binary64_1112` `sum-log_binary64_1192` `clear-num_binary64_1100` `div-inv_binary64_1098` `associate-/l*_binary64_1046` `+-commutative_binary64_1031`

Counts

4 → 70

Calls

4 calls:

6.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
5.0ms	(*.f64 e (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))
3.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

series184.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

90.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
33.0ms	(*.f64 e (sin.f64 v))
31.0ms	(*.f64 e (cos.f64 v))
30.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

simplify72.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5013	1100

prune74.0ms (1.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	6	83

Error

0.0b

Counts

83 → 6

Compiler

Compiled 1402 to 557 computations (60.3% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 e (cos.f64 v))
0.1b	(*.f64 e (pow.f64 (cos.f64 v) 2))
0.1b	(*.f64 e (sin.f64 v))
0.2b	(pow.f64 (cos.f64 v) 2)

rewrite25.0ms (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))
5.0ms	(*.f64 e (cos.f64 v))
4.0ms	(*.f64 e (sin.f64 v))
3.0ms	(pow.f64 (cos.f64 v) 2)

series114.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

42.0ms	(*.f64 e (pow.f64 (cos.f64 v) 2))
29.0ms	(*.f64 e (cos.f64 v))
29.0ms	(*.f64 e (sin.f64 v))
13.0ms	(pow.f64 (cos.f64 v) 2)

simplify80.0ms (2%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4937	793
1	4937	793

prune99.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	93	6	99

Error

0.0b

Counts

99 → 6

Compiler

Compiled 2434 to 1134 computations (53.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64_1107`
58×	`add-sqr-sqrt_binary64_1123`
56×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
16×	`associate-/r*_binary64_1045`
13×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
6×	`add-log-exp_binary64_1140` `pow1_binary64_1162` `div-inv_binary64_1098` `associate-/l*_binary64_1046`
4×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
3×	`associate-r_binary64_1041` `associate-l_binary64_1042`
2×	`frac-2neg_binary64_1112` `clear-num_binary64_1100` `flip3-+_binary64_1104` `associate-/l/_binary64_1048` `flip-+_binary64_1075`
1×	`*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sum-log_binary64_1192` `associate-/r/_binary64_1047` `+-commutative_binary64_1031` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069`

Counts

4 → 128

Calls

4 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))
3.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

series218.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
67.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
33.0ms	(*.f64 e (cos.f64 v))
29.0ms	(+.f64 1 (*.f64 e (cos.f64 v)))

simplify122.0ms (3%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4951	3402
1	4951	3402

prune126.0ms (3.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	140	6	146

Error

0.0b

Counts

146 → 6

Compiler

Compiled 2904 to 1193 computations (58.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite35.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

10.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
8.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))
6.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
4.0ms	(*.f64 e (cos.f64 v))

series232.0ms (5.8%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(/.f64 (.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e))) (+.f64 1 (*.f64 e (cos.f64 v))))
47.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
39.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))
29.0ms	(*.f64 e (cos.f64 v))

simplify84.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4981	1494
1	4981	1494

prune80.0ms (2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	97	7	104

Error

0.0b

Counts

104 → 7

Compiler

Compiled 1883 to 644 computations (65.8% saved)

regimes137.0ms (3.4%)

Accuracy

Total 0.1b remaining (93%)

Threshold costs 0.1b (93%)

Compiler

Compiled 1283 to 908 computations (29.2% 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%)

sample2.1s (51.6%)

Algorithm

1×

intervals

Results

571.0ms	1968×	body	1024	valid
320.0ms	4519×	body	128	valid
220.0ms	1008×	body	512	valid
172.0ms	8000×	pre	128	true
78.0ms	500×	body	256	valid
3.0ms	5×	body	2048	valid

Compiler

Compiled 456 to 324 computations (28.9% saved)

Details

analyze19.0ms (0.5%)

sample48.0ms (1.2%)

simplify98.0ms (2.4%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

rewrite23.0ms (0.6%)

series184.0ms (4.6%)

simplify72.0ms (1.8%)

prune74.0ms (1.8%)

localize14.0ms (0.4%)

rewrite25.0ms (0.6%)

series114.0ms (2.8%)

simplify80.0ms (2%)

prune99.0ms (2.5%)

localize9.0ms (0.2%)

rewrite31.0ms (0.8%)

series218.0ms (5.4%)

simplify122.0ms (3%)

prune126.0ms (3.1%)

localize11.0ms (0.3%)

rewrite35.0ms (0.9%)

series232.0ms (5.8%)

simplify84.0ms (2.1%)

prune80.0ms (2%)

regimes137.0ms (3.4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.1s (51.6%)

Profiling