Details

analyze241.0ms (5.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
75%	25%	0%	5
75%	25%	0%	6
78.1%	21.9%	0%	7
78.1%	21.9%	0%	8
78.1%	21.9%	0%	9
78.1%	21.9%	0%	10
78.1%	21.9%	0%	11
78.1%	21.9%	0%	12
78.1%	21.9%	0%	13
78.1%	21.8%	0%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample64.0ms (1.5%)

Algorithm

1×

intervals

Results

34.0ms	77×	body	2048	valid
7.0ms	37×	body	1024	valid
7.0ms	75×	body	128	valid
6.0ms	42×	body	512	valid
2.0ms	23×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify171.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	364	12
1	364	12

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: 33.0b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.2b	(-.f64 1 (cos.f64 x))
18.7b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite19.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_77` `add-sqr-sqrt_binary64_98`
7×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
6×	`times-frac_binary64_83` `associate-/l*_binary64_24` `difference-of-squares_binary64_46`
4×	`add-log-exp_binary64_113` `add-cube-cbrt_binary64_109`
3×	`distribute-lft-out--_binary64_31`
2×	`cbrt-undiv_binary64_108` `pow1_binary64_135` `flip--_binary64_52` `div-exp_binary64_125` `flip3--_binary64_81` `associate-/l/_binary64_26`
1×	`associate-/r*_binary64_23` `cbrt-unprod_binary64_107` `div-sub_binary64_82` `sub-neg_binary64_70` `prod-exp_binary64_123` `clear-num_binary64_76` `diff-log_binary64_166` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

2 → 44

Calls

2 calls:

12.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.f64 1 (cos.f64 x))

series82.0ms (2%)

Counts

2 → 6

Calls

2 calls:

62.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
20.0ms	(-.f64 1 (cos.f64 x))

simplify53.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5002	700

prune64.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	7	51

Merged error: 0.0b

Counts

51 → 7

Compiler

Compiled 744 to 407 computations (45.3% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
0.3b	(*.f64 (sin.f64 x) (sin.f64 x))
0.3b	(+.f64 1 (cos.f64 x))
18.5b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite42.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
24×	`*-un-lft-identity_binary64_77`
22×	`times-frac_binary64_83`
16×	`add-sqr-sqrt_binary64_98`
14×	`add-cube-cbrt_binary64_109`
12×	`cbrt-undiv_binary64_108` `div-exp_binary64_125`
11×	`pow1_binary64_135` `associate-/l*_binary64_24`
7×	`cbrt-unprod_binary64_107` `prod-exp_binary64_123`
6×	`add-log-exp_binary64_113` `associate-/r/_binary64_25`
5×	`associate-/r*_binary64_23` `distribute-lft-out_binary64_30`
4×	`flip-+_binary64_51` `flip3-+_binary64_80` `div-inv_binary64_74`
3×	`associate-l_binary64_20` `div-sub_binary64_82` `sqr-sin-a_binary64_222` `swap-sqr_binary64_44` `associate-r_binary64_19`
2×	`sin-mult_binary64_229` `clear-num_binary64_76` `associate-/l/_binary64_26` `frac-2neg_binary64_88`
1×	`pow2_binary64_155` `pow-prod-down_binary64_145` `pow-sqr_binary64_50` `pow-plus_binary64_137` `pow-prod-up_binary64_144` `+-commutative_binary64_9` `unswap-sqr_binary64_45` `*-commutative_binary64_10` `sum-log_binary64_165`

Counts

4 → 111

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
8.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))

series256.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
84.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
30.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
12.0ms	(+.f64 1 (cos.f64 x))

simplify62.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4970	1781
1	4970	1781

prune111.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	122	8	130

Merged error: 0b

Counts

130 → 8

Compiler

Compiled 2188 to 1110 computations (49.3% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
0.1b	(/.f64 (sin.f64 x) x)
0.2b	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))

rewrite31.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_98`
22×	`times-frac_binary64_83`
21×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
19×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
13×	`associate-l_binary64_20`
6×	`associate-/r*_binary64_23` `cbrt-undiv_binary64_108` `div-exp_binary64_125`
5×	`pow1_binary64_135`
4×	`cbrt-unprod_binary64_107` `tan-quot_binary64_233` `associate-/l*_binary64_24` `prod-exp_binary64_123`
3×	`add-log-exp_binary64_113` `associate-/l/_binary64_26` `associate-r_binary64_19` `div-inv_binary64_74`
2×	`frac-times_binary64_87` `associate-l/_binary64_22` `associate-r/_binary64_21` `unswap-sqr_binary64_45` `clear-num_binary64_76` `frac-2neg_binary64_88`
1×	`pow-prod-down_binary64_145` `*-commutative_binary64_10`

Counts

3 → 87

Calls

3 calls:

9.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
9.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
4.0ms	(/.f64 (sin.f64 x) x)

series320.0ms (7.7%)

Counts

3 → 9

Calls

3 calls:

143.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
142.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
34.0ms	(/.f64 (sin.f64 x) x)

simplify82.0ms (2%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4993	1539
1	4993	1539

prune85.0ms (2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	97	7	104

Merged error: 0b

Counts

104 → 7

Compiler

Compiled 1664 to 841 computations (49.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) x) x)
0.2b	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))
17.9b	(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) x)

rewrite28.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64_83`
25×	`add-sqr-sqrt_binary64_98`
23×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
19×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
8×	`associate-/l*_binary64_24`
7×	`cbrt-undiv_binary64_108` `div-exp_binary64_125`
6×	`associate-/r*_binary64_23` `div-inv_binary64_74`
5×	`pow1_binary64_135`
3×	`associate-l_binary64_20` `add-log-exp_binary64_113` `cbrt-unprod_binary64_107` `prod-exp_binary64_123` `associate-r_binary64_19`
2×	`tan-quot_binary64_233` `associate-*r/_binary64_21` `clear-num_binary64_76` `associate-/l/_binary64_26` `frac-2neg_binary64_88`
1×	`pow-prod-down_binary64_145` `unswap-sqr_binary64_45` `*-commutative_binary64_10`

Counts

3 → 89

Calls

3 calls:

7.0ms	(/.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) x) x)
7.0ms	(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) x)
6.0ms	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

series378.0ms (9.1%)

Counts

3 → 9

Calls

3 calls:

147.0ms	(/.f64 (/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) x) x)
144.0ms	(/.f64 (*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2))) x)
86.0ms	(*.f64 (sin.f64 x) (tan.f64 (/.f64 x 2)))

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4998	1938
1	4998	1938

prune82.0ms (2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	1	4	5
Picked	0	1	1
Done	1	0	1
Total	99	6	105

Merged error: 0b

Counts

105 → 6

Compiler

Compiled 1652 to 936 computations (43.3% saved)

regimes30.0ms (0.7%)

Compiler: Compiled 79 to 59 computations (25.3% saved)

bsearch50.0ms (1.2%)

Steps

Iters	Range		Point
8	1.1071107221452794e-70	1.6704130574323723e-67	5.530578574506921e-70
7	-0.2986504883839154	-0.0018931643806128877	-0.010529840751750804

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	67	65
1	67	65

end0.0ms (0%)

sample1.8s (43.2%)

Algorithm

1×

intervals

Results

845.0ms	1954×	body	2048	valid
228.0ms	1113×	body	1024	valid
214.0ms	1483×	body	512	valid
103.0ms	2570×	body	128	valid
70.0ms	768×	body	256	valid
46.0ms	112×	body	4096	valid

Compiler

Compiled 129 to 94 computations (27.1% saved)

Details

analyze241.0ms (5.8%)

sample64.0ms (1.5%)

simplify171.0ms (4.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite19.0ms (0.5%)

series82.0ms (2%)

simplify53.0ms (1.3%)

prune64.0ms (1.5%)

localize10.0ms (0.2%)

rewrite42.0ms (1%)

series256.0ms (6.2%)

simplify62.0ms (1.5%)

prune111.0ms (2.7%)

localize9.0ms (0.2%)

rewrite31.0ms (0.8%)

series320.0ms (7.7%)

simplify82.0ms (2%)

prune85.0ms (2%)

localize9.0ms (0.2%)

rewrite28.0ms (0.7%)

series378.0ms (9.1%)

simplify66.0ms (1.6%)

prune82.0ms (2%)

regimes30.0ms (0.7%)

bsearch50.0ms (1.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.8s (43.2%)

Profiling