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)

sample57.0ms (1.2%)

Algorithm

1×

intervals

Results

18.0ms	63×	body	1024	valid
12.0ms	32×	body	512	valid
10.0ms	143×	body	128	valid
5.0ms	256×	pre	128	true
3.0ms	18×	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

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

0.1b

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))

rewrite24.0ms (0.5%)

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:

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

series244.0ms (5%)

Counts

3 → 23

Calls

3 calls:

123.0ms	(/.f64 (.f64 e (sin.f64 v)) (+.f64 1 (.f64 e (cos.f64 v))))
61.0ms	(*.f64 e (sin.f64 v))
59.0ms	(*.f64 e (cos.f64 v))

Compiler

Compiled 585 to 460 computations (21.4% saved)

simplify88.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4954	1070
1	4954	1070

prune76.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Error

0.0b

Counts

83 → 8

Compiler

Compiled 1333 to 529 computations (60.3% saved)

localize8.0ms (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))

rewrite28.0ms (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:

10.0ms	(.f64 e (/.f64 (sin.f64 v) (+.f64 (.f64 e (cos.f64 v)) 1)))
7.0ms	(/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1))
4.0ms	(*.f64 e (cos.f64 v))

series300.0ms (6.1%)

Counts

3 → 26

Calls

3 calls:

127.0ms	(.f64 e (/.f64 (sin.f64 v) (+.f64 (.f64 e (cos.f64 v)) 1)))
106.0ms	(/.f64 (sin.f64 v) (+.f64 (*.f64 e (cos.f64 v)) 1))
68.0ms	(*.f64 e (cos.f64 v))

Compiler

Compiled 710 to 543 computations (23.5% saved)

simplify100.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4946	1932
1	4946	1932

prune96.0ms (2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	104	3	107
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	106	9	115

Error

0.0b

Counts

115 → 9

Compiler

Compiled 2005 to 886 computations (55.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 e (.f64 (/.f64 (sin.f64 v) (+.f64 (.f64 e (.f64 e (pow.f64 (cos.f64 v) 2))) -1)) (-.f64 (*.f64 e (cos.f64 v)) 1)))
0.1b	(*.f64 e (cos.f64 v))
0.1b	(*.f64 e (pow.f64 (cos.f64 v) 2))
0.3b	(pow.f64 (cos.f64 v) 2)

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_1123`
21×	`add-exp-log_binary64_1139`
17×	`add-cbrt-cube_binary64_1137`
16×	`*-un-lft-identity_binary64_1101` `distribute-lft-in_binary64_1050` `add-cube-cbrt_binary64_1136` `distribute-rgt-in_binary64_1051`
12×	`pow1_binary64_1162` `associate-r_binary64_1041` `cancel-sign-sub-inv_binary64_1067`
9×	`prod-exp_binary64_1150` `associate-l_binary64_1042`
7×	`cbrt-unprod_binary64_1134` `unpow-prod-down_binary64_1180` `associate-*r/_binary64_1043`
5×	`unswap-sqr_binary64_1069`
4×	`add-log-exp_binary64_1140` `sub-neg_binary64_1094` `pow-prod-down_binary64_1172`
3×	`*-commutative_binary64_1032` `pow-unpow_binary64_1178` `sqr-pow_binary64_1073` `unpow2_binary64_1166`
2×	`pow-exp_binary64_1169` `frac-times_binary64_1111` `flip--_binary64_1076` `flip3--_binary64_1105` `pow-to-exp_binary64_1170`
1×	`pow-pow_binary64_1173` `div-exp_binary64_1152` `cbrt-undiv_binary64_1135` `associate-*l/_binary64_1044`

Counts

4 → 104

Calls

4 calls:

16.0ms	(.f64 e (.f64 (/.f64 (sin.f64 v) (+.f64 (.f64 e (.f64 e (pow.f64 (cos.f64 v) 2))) -1)) (-.f64 (*.f64 e (cos.f64 v)) 1)))
6.0ms	(*.f64 e (pow.f64 (cos.f64 v) 2))
4.0ms	(*.f64 e (cos.f64 v))
3.0ms	(pow.f64 (cos.f64 v) 2)

series445.0ms (9.1%)

Counts

4 → 25

Calls

4 calls:

272.0ms	(.f64 e (.f64 (/.f64 (sin.f64 v) (+.f64 (.f64 e (.f64 e (pow.f64 (cos.f64 v) 2))) -1)) (-.f64 (*.f64 e (cos.f64 v)) 1)))
92.0ms	(*.f64 e (pow.f64 (cos.f64 v) 2))
62.0ms	(*.f64 e (cos.f64 v))
20.0ms	(pow.f64 (cos.f64 v) 2)

Compiler

Compiled 1141 to 859 computations (24.7% saved)

simplify57.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5097	2402

prune138.0ms (2.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	129	9	138

Error

0.0b

Counts

138 → 9

Compiler

Compiled 3388 to 1674 computations (50.6% saved)

localize9.0ms (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)))

rewrite31.0ms (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)))
7.0ms	(*.f64 e (cos.f64 v))
6.0ms	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))

series342.0ms (7%)

Counts

3 → 26

Calls

3 calls:

150.0ms	(/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v))
127.0ms	(/.f64 e (/.f64 (+.f64 (*.f64 e (cos.f64 v)) 1) (sin.f64 v)))
65.0ms	(*.f64 e (cos.f64 v))

Compiler

Compiled 632 to 489 computations (22.6% saved)

simplify74.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5050	3434

prune129.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	140	3	143
Fresh	2	5	7
Picked	1	0	1
Done	1	0	1
Total	144	8	152

Error

0.0b

Counts

152 → 8

Compiler

Compiled 2785 to 1113 computations (60% saved)

regimes190.0ms (3.9%)

Accuracy

Total 0.1b remaining (95.5%)

Threshold costs 0.1b (95.5%)

Compiler

Compiled 1862 to 1313 computations (29.5% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	34
1	26	34

end0.0ms (0%)

sample2.3s (46.3%)

Algorithm

1×

intervals

Results

634.0ms	2034×	body	1024	valid
311.0ms	4471×	body	128	valid
216.0ms	1007×	body	512	valid
155.0ms	8000×	pre	128	true
73.0ms	481×	body	256	valid
4.0ms	7×	body	2048	valid

Compiler

Compiled 649 to 459 computations (29.3% saved)

Details

analyze19.0ms (0.4%)

sample57.0ms (1.2%)

simplify98.0ms (2%)

prune3.0ms (0.1%)

localize9.0ms (0.2%)

rewrite24.0ms (0.5%)

series244.0ms (5%)

simplify88.0ms (1.8%)

prune76.0ms (1.6%)

localize8.0ms (0.2%)

rewrite28.0ms (0.6%)

series300.0ms (6.1%)

simplify100.0ms (2.1%)

prune96.0ms (2%)

localize16.0ms (0.3%)

rewrite39.0ms (0.8%)

series445.0ms (9.1%)

simplify57.0ms (1.2%)

prune138.0ms (2.8%)

localize9.0ms (0.2%)

rewrite31.0ms (0.6%)

series342.0ms (7%)

simplify74.0ms (1.5%)

prune129.0ms (2.6%)

regimes190.0ms (3.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample2.3s (46.3%)

Profiling