Details

analyze233.0ms (4.5%)

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)

sample58.0ms (1.1%)

Algorithm

1×

intervals

Results

28.0ms	68×	body	2048	valid
6.0ms	30×	body	1024	valid
6.0ms	2×	body	4096	valid
6.0ms	46×	body	512	valid
4.0ms	90×	body	128	valid
2.0ms	20×	body	256	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify180.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

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: 29.5b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.0b	(-.f64 1 (cos.f64 x))
16.3b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_101` `*-un-lft-identity_binary64_79`
7×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
6×	`times-frac_binary64_85` `associate-/l*_binary64_24` `difference-of-squares_binary64_48`
5×	`add-cube-cbrt_binary64_114`
4×	`add-log-exp_binary64_118`
3×	`distribute-lft-out--_binary64_31` `cancel-sign-sub-inv_binary64_45`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `flip--_binary64_54` `flip3--_binary64_83` `associate-/l/_binary64_26` `pow1_binary64_140`
1×	`associate-/r*_binary64_23` `div-sub_binary64_84` `div-inv_binary64_76` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `diff-log_binary64_171` `clear-num_binary64_78` `sub-neg_binary64_72` `frac-2neg_binary64_90`

Counts

2 → 47

Calls

2 calls:

13.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
5.0ms	(-.f64 1 (cos.f64 x))

series78.0ms (1.5%)

Counts

2 → 6

Calls

2 calls:

57.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
20.0ms	(-.f64 1 (cos.f64 x))

simplify63.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4925	715
1	4925	715

prune205.0ms (4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	46	7	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	7	54

Merged error: 0.0b

Counts

54 → 7

Compiler

Compiled 2889 to 1925 computations (33.4% saved)

localize11.0ms (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))
0.5b	(+.f64 1 (cos.f64 x))
16.5b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite41.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
24×	`*-un-lft-identity_binary64_79`
22×	`times-frac_binary64_85`
16×	`add-sqr-sqrt_binary64_101`
14×	`add-cube-cbrt_binary64_114`
12×	`cbrt-undiv_binary64_113` `div-exp_binary64_130`
11×	`associate-/l*_binary64_24` `pow1_binary64_140`
7×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128`
6×	`associate-/r/_binary64_25` `add-log-exp_binary64_118`
5×	`associate-/r*_binary64_23` `distribute-lft-out_binary64_30`
4×	`flip-+_binary64_53` `div-inv_binary64_76` `flip3-+_binary64_82`
3×	`associate-l_binary64_20` `div-sub_binary64_84` `sqr-sin-a_binary64_227` `swap-sqr_binary64_46` `associate-r_binary64_19`
2×	`sin-mult_binary64_234` `clear-num_binary64_78` `associate-/l/_binary64_26` `frac-2neg_binary64_90`
1×	`sum-log_binary64_170` `+-commutative_binary64_9` `pow-prod-up_binary64_149` `unswap-sqr_binary64_47` `pow-sqr_binary64_52` `*-commutative_binary64_10` `pow-prod-down_binary64_150` `pow-plus_binary64_142` `pow2_binary64_160`

Counts

4 → 111

Calls

4 calls:

12.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
9.0ms	(/.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))

series245.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
85.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
25.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
11.0ms	(+.f64 1 (cos.f64 x))

simplify68.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4973	1781
1	4973	1781

prune181.0ms (3.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	3	123
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	123	7	130

Merged error: 0b

Counts

130 → 7

Compiler

Compiled 3259 to 1867 computations (42.7% 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)))

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_101`
22×	`times-frac_binary64_85`
21×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
19×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
13×	`associate-l_binary64_20`
6×	`associate-/r*_binary64_23` `cbrt-undiv_binary64_113` `div-exp_binary64_130`
5×	`pow1_binary64_140`
4×	`associate-/l*_binary64_24` `tan-quot_binary64_238` `cbrt-unprod_binary64_112` `prod-exp_binary64_128`
3×	`div-inv_binary64_76` `add-log-exp_binary64_118` `associate-/l/_binary64_26` `associate-r_binary64_19`
2×	`frac-times_binary64_89` `associate-l/_binary64_22` `associate-r/_binary64_21` `unswap-sqr_binary64_47` `clear-num_binary64_78` `frac-2neg_binary64_90`
1×	`*-commutative_binary64_10` `pow-prod-down_binary64_150`

Counts

3 → 87

Calls

3 calls:

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

series324.0ms (6.3%)

Counts

3 → 9

Calls

3 calls:

152.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
135.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
37.0ms	(/.f64 (sin.f64 x) x)

simplify84.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4937	1539
1	4937	1539

prune79.0ms (1.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	96	7	103

Merged error: 0b

Counts

103 → 7

Compiler

Compiled 1645 to 828 computations (49.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x))))
0.5b	(+.f64 1 (cos.f64 x))
0.5b	(+.f64 1 (cos.f64 x))
0.6b	(*.f64 (/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) x) (/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) x))

rewrite241.0ms (4.7%)

Algorithm

1×	rewrite-expression-head

Rules

781×	`times-frac_binary64_85`
486×	`*-un-lft-identity_binary64_79`
456×	`add-sqr-sqrt_binary64_101`
348×	`add-cube-cbrt_binary64_114`
222×	`sqrt-prod_binary64_95`
121×	`swap-sqr_binary64_46`
85×	`associate-l_binary64_20` `associate-r_binary64_19`
60×	`distribute-lft-out_binary64_30`
42×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
26×	`associate-/r/_binary64_25` `sqrt-div_binary64_96`
19×	`cbrt-undiv_binary64_113` `div-exp_binary64_130`
17×	`div-inv_binary64_76`
16×	`unswap-sqr_binary64_47`
15×	`flip-+_binary64_53` `flip3-+_binary64_82`
11×	`pow1_binary64_140`
9×	`cbrt-unprod_binary64_112` `prod-exp_binary64_128`
8×	`add-log-exp_binary64_118`
7×	`associate-/r*_binary64_23`
3×	`associate-/l*_binary64_24`
2×	`sum-log_binary64_170` `+-commutative_binary64_9`
1×	`frac-times_binary64_89` `associate-l/_binary64_22` `pow-prod-up_binary64_149` `associate-r/_binary64_21` `pow-sqr_binary64_52` `*-commutative_binary64_10` `pow-prod-down_binary64_150` `clear-num_binary64_78` `pow-plus_binary64_142` `frac-2neg_binary64_90` `pow2_binary64_160`

Counts

4 → 410

Calls

4 calls:

131.0ms	(*.f64 (/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) x) (/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) x))
10.0ms	(/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x))))
4.0ms	(+.f64 1 (cos.f64 x))
4.0ms	(+.f64 1 (cos.f64 x))

series251.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(*.f64 (/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) x) (/.f64 (/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x)))) x))
112.0ms	(/.f64 (sin.f64 x) (sqrt.f64 (+.f64 1 (cos.f64 x))))
12.0ms	(+.f64 1 (cos.f64 x))
12.0ms	(+.f64 1 (cos.f64 x))

simplify199.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

422 → 422

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5021	18084

prune776.0ms (15.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	422	0	422
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	422	7	429

Merged error: 0b

Counts

429 → 7

Compiler

Compiled 14950 to 7432 computations (50.3% saved)

regimes18.0ms (0.4%)

Compiler: Compiled 99 to 73 computations (26.3% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	17
1	10	17

end0.0ms (0%)

sample1.7s (33.6%)

Algorithm

1×

intervals

Results

821.0ms	1928×	body	2048	valid
217.0ms	1093×	body	1024	valid
194.0ms	1479×	body	512	valid
106.0ms	2651×	body	128	valid
64.0ms	749×	body	256	valid
40.0ms	100×	body	4096	valid

Compiler

Compiled 117 to 87 computations (25.6% saved)

Details

analyze233.0ms (4.5%)

sample58.0ms (1.1%)

simplify180.0ms (3.5%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite21.0ms (0.4%)

series78.0ms (1.5%)

simplify63.0ms (1.2%)

prune205.0ms (4%)

localize11.0ms (0.2%)

rewrite41.0ms (0.8%)

series245.0ms (4.8%)

simplify68.0ms (1.3%)

prune181.0ms (3.5%)

localize9.0ms (0.2%)

rewrite29.0ms (0.6%)

series324.0ms (6.3%)

simplify84.0ms (1.6%)

prune79.0ms (1.5%)

localize10.0ms (0.2%)

rewrite241.0ms (4.7%)

series251.0ms (4.9%)

simplify199.0ms (3.9%)

prune776.0ms (15.1%)

regimes18.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.7s (33.6%)

Profiling