Details

analyze18.0ms (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)

sample56.0ms (1.3%)

Algorithm

1×

intervals

Results

16.0ms	52×	body	1024	valid
15.0ms	43×	body	512	valid
10.0ms	150×	body	128	valid
5.0ms	256×	pre	128	true
2.0ms	11×	body	256	valid

Compiler

Compiled 26 to 23 computations (11.5% saved)

simplify100.0ms (2.3%)

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

0.2b

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))

rewrite25.0ms (0.6%)

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:

8.0ms	(*.f64 e (cos.f64 v))
7.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
6.0ms	(*.f64 e (sin.f64 v))

series153.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

88.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
37.0ms	(*.f64 e (sin.f64 v))
28.0ms	(*.f64 e (cos.f64 v))

simplify83.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4947	920
1	4947	920

prune70.0ms (1.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	9	69

Error

0.0b

Counts

69 → 9

Compiler

Compiled 1222 to 505 computations (58.7% saved)

localize15.0ms (0.3%)

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)

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)

series114.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

41.0ms	(*.f64 e (pow.f64 (cos.f64 v) 2))
30.0ms	(*.f64 e (sin.f64 v))
29.0ms	(*.f64 e (cos.f64 v))
13.0ms	(pow.f64 (cos.f64 v) 2)

simplify74.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4937	793
1	4937	793

prune102.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	93	9	102

Error

0.0b

Counts

102 → 9

Compiler

Compiled 2471 to 1167 computations (52.8% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite27.0ms (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))

series191.0ms (4.5%)

Counts

3 → 9

Calls

3 calls:

90.0ms	(/.f64 e (/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v)))
73.0ms	(/.f64 (+.f64 1 (*.f64 e (cos.f64 v))) (sin.f64 v))
27.0ms	(*.f64 e (cos.f64 v))

simplify87.0ms (2%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4954	3222
1	4954	3222

prune125.0ms (2.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	122	4	126
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	126	9	135

Error

Counts

135 → 9

Compiler

Compiled 2760 to 1142 computations (58.6% saved)

localize13.0ms (0.3%)

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

rewrite41.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64_1107`
47×	`add-sqr-sqrt_binary64_1123`
41×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
28×	`sqrt-prod_binary64_1117`
22×	`add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
9×	`div-inv_binary64_1098` `associate-/l_binary64_1046` `associate-r*_binary64_1041`
8×	`pow1_binary64_1162` `associate-/r*_binary64_1045`
7×	`div-exp_binary64_1152` `cbrt-undiv_binary64_1135`
6×	`associate-l_binary64_1042`
4×	`cbrt-unprod_binary64_1134` `add-log-exp_binary64_1140` `prod-exp_binary64_1150`
3×	`unswap-sqr_binary64_1069`
2×	`*-commutative_binary64_1032` `frac-2neg_binary64_1112` `clear-num_binary64_1100` `associate-/l/_binary64_1048` `pow-prod-down_binary64_1172`
1×	`flip3-+_binary64_1104` `associate-/r/_binary64_1047` `flip-+_binary64_1075`

Counts

4 → 135

Calls

4 calls:

10.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
8.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
6.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
5.0ms	(*.f64 e (cos.f64 v))

series302.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(/.f64 (sqrt.f64 e) (/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e))))
103.0ms	(/.f64 (+.f64 1 (.f64 e (cos.f64 v))) (.f64 (sin.f64 v) (sqrt.f64 e)))
46.0ms	(*.f64 (sin.f64 v) (sqrt.f64 e))
28.0ms	(*.f64 e (cos.f64 v))

simplify123.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4954	3907
1	4954	3907

prune136.0ms (3.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	147	9	156

Error

Counts

156 → 9

Compiler

Compiled 3400 to 1224 computations (64% saved)

regimes200.0ms (4.7%)

Accuracy

Total 0.1b remaining (94.2%)

Threshold costs 0.1b (94.2%)

Compiler

Compiled 2146 to 1430 computations (33.4% 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%)

sample2.2s (51%)

Algorithm

1×

intervals

Results

591.0ms	2016×	body	1024	valid
322.0ms	4520×	body	128	valid
205.0ms	981×	body	512	valid
162.0ms	8000×	pre	128	true
66.0ms	480×	body	256	valid
2.0ms	3×	body	2048	valid

Compiler

Compiled 717 to 478 computations (33.3% saved)

Details

analyze18.0ms (0.4%)

sample56.0ms (1.3%)

simplify100.0ms (2.3%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

rewrite25.0ms (0.6%)

series153.0ms (3.6%)

simplify83.0ms (1.9%)

prune70.0ms (1.6%)

localize15.0ms (0.3%)

rewrite24.0ms (0.6%)

series114.0ms (2.7%)

simplify74.0ms (1.7%)

prune102.0ms (2.4%)

localize8.0ms (0.2%)

rewrite27.0ms (0.6%)

series191.0ms (4.5%)

simplify87.0ms (2%)

prune125.0ms (2.9%)

localize13.0ms (0.3%)

rewrite41.0ms (1%)

series302.0ms (7.1%)

simplify123.0ms (2.9%)

prune136.0ms (3.2%)

regimes200.0ms (4.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.2s (51%)

Profiling