Details

analyze19.0ms (0.4%)

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)

sample59.0ms (1.2%)

Algorithm

1×

intervals

Results

17.0ms	61×	body	1024	valid
11.0ms	256×	pre	128	true
10.0ms	140×	body	128	valid
7.0ms	35×	body	512	valid
3.0ms	20×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify98.0ms (2%)

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%)

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: 0.2b

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))

rewrite21.0ms (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:

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

series157.0ms (3.1%)

Counts

3 → 9

Calls

3 calls:

93.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
36.0ms	(*.f64 e (sin.f64 v))
28.0ms	(*.f64 e (cos.f64 v))

simplify84.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4947	920
1	4947	920

prune69.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	60	9	69

Merged error: 0.0b

Counts

69 → 9

Compiler

Compiled 1227 to 499 computations (59.3% saved)

localize10.0ms (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:

8.0ms	(/.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))

series194.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

88.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
78.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
28.0ms	(*.f64 e (cos.f64 v))

simplify87.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4954	3222
1	4954	3222

prune129.0ms (2.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	125	10	135

Merged error: 0.0b

Counts

135 → 10

Compiler

Compiled 2795 to 1162 computations (58.4% saved)

localize11.0ms (0.2%)

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))
0.3b	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))
0.3b	(*.f64 (sin.f64 v) (sqrt.f64 e))

rewrite36.0ms (0.7%)

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))
5.0ms	(*.f64 e (cos.f64 v))

series236.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

121.0ms	(/.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))
37.0ms	(.f64 (sqrt.f64 e) (.f64 (sin.f64 v) (sqrt.f64 e)))
31.0ms	(*.f64 e (cos.f64 v))

simplify79.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4981	1494
1	4981	1494

prune94.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	98	10	108

Merged error: 0.0b

Counts

108 → 10

Compiler

Compiled 2073 to 765 computations (63.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite93.0ms (1.8%)

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:

39.0ms	(.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v))))
9.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
6.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
4.0ms	(*.f64 e (cos.f64 v))

series371.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

158.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
115.0ms	(.f64 (sqrt.f64 e) (/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (sin.f64 v))))
69.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
29.0ms	(*.f64 e (cos.f64 v))

simplify142.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

286 → 286

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4965	8694
1	4965	8694

prune323.0ms (6.4%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	284	2	286
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	285	11	296

Merged error: 0.0b

Counts

296 → 11

Compiler

Compiled 7830 to 2919 computations (62.7% saved)

regimes258.0ms (5.1%)

Compiler: Compiled 2851 to 1858 computations (34.8% 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%)

sample2.4s (47.8%)

Algorithm

1×

intervals

Results

585.0ms	1894×	body	1024	valid
342.0ms	4599×	body	128	valid
218.0ms	1014×	body	512	valid
158.0ms	8000×	pre	128	true
72.0ms	487×	body	256	valid
3.0ms	6×	body	2048	valid

Compiler

Compiled 944 to 618 computations (34.5% saved)

Details

analyze19.0ms (0.4%)

sample59.0ms (1.2%)

simplify98.0ms (2%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite21.0ms (0.4%)

series157.0ms (3.1%)

simplify84.0ms (1.7%)

prune69.0ms (1.4%)

localize10.0ms (0.2%)

rewrite28.0ms (0.6%)

series194.0ms (3.9%)

simplify87.0ms (1.7%)

prune129.0ms (2.6%)

localize11.0ms (0.2%)

rewrite36.0ms (0.7%)

series236.0ms (4.7%)

simplify79.0ms (1.6%)

prune94.0ms (1.9%)

localize11.0ms (0.2%)

rewrite93.0ms (1.8%)

series371.0ms (7.4%)

simplify142.0ms (2.8%)

prune323.0ms (6.4%)

regimes258.0ms (5.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.4s (47.8%)

Profiling