Details

analyze242.0ms (5.4%)

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)

sample57.0ms (1.3%)

Algorithm

1×

intervals

Results

27.0ms	64×	body	2048	valid
11.0ms	32×	body	1024	valid
5.0ms	42×	body	512	valid
4.0ms	94×	body	128	valid
2.0ms	22×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify104.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	366	12
1	366	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

Error

28.8b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.5b	(-.f64 1 (cos.f64 x))
15.3b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
7×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`times-frac_binary64_84` `associate-/l*_binary64_23` `difference-of-squares_binary64_47`
5×	`add-cube-cbrt_binary64_113`
4×	`add-log-exp_binary64_117`
3×	`distribute-lft-out--_binary64_30` `cancel-sign-sub-inv_binary64_44`
2×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip3--_binary64_82` `flip--_binary64_53` `associate-/l/_binary64_25` `pow1_binary64_139`
1×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `diff-log_binary64_170` `frac-2neg_binary64_89` `div-inv_binary64_75` `associate-/r*_binary64_22` `clear-num_binary64_77` `div-sub_binary64_83` `sub-neg_binary64_71`

Counts

2 → 47

Calls

2 calls:

9.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
5.0ms	(-.f64 1 (cos.f64 x))

series41.0ms (0.9%)

Counts

2 → 6

Calls

2 calls:

30.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
11.0ms	(-.f64 1 (cos.f64 x))

simplify69.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	6395	715

prune67.0ms (1.5%)

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

Error

0.0b

Counts

54 → 7

Compiler

Compiled 783 to 422 computations (46.1% 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))
0.5b	(+.f64 1 (cos.f64 x))
15.5b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite37.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
24×	`*-un-lft-identity_binary64_78`
22×	`times-frac_binary64_84`
16×	`add-sqr-sqrt_binary64_100`
14×	`add-cube-cbrt_binary64_113`
12×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
11×	`associate-/l*_binary64_23` `pow1_binary64_139`
7×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
6×	`add-log-exp_binary64_117` `associate-/r/_binary64_24`
5×	`associate-/r*_binary64_22` `distribute-lft-out_binary64_29`
4×	`flip-+_binary64_52` `div-inv_binary64_75` `flip3-+_binary64_81`
3×	`associate-l_binary64_19` `swap-sqr_binary64_45` `associate-r_binary64_18` `sqr-sin-a_binary64_226` `div-sub_binary64_83`
2×	`frac-2neg_binary64_89` `sin-mult_binary64_233` `clear-num_binary64_77` `associate-/l/_binary64_25`
1×	`+-commutative_binary64_8` `pow2_binary64_159` `*-commutative_binary64_9` `pow-sqr_binary64_51` `pow-prod-up_binary64_148` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `pow-plus_binary64_141` `sum-log_binary64_169`

Counts

4 → 111

Calls

4 calls:

11.0ms	(/.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))

series144.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

70.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
51.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
15.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
7.0ms	(+.f64 1 (cos.f64 x))

simplify66.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4963	1781
1	4963	1781

prune114.0ms (2.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	122	8	130

Error

Counts

130 → 8

Compiler

Compiled 2191 to 1110 computations (49.3% saved)

localize11.0ms (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)))

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_100`
22×	`times-frac_binary64_84`
21×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
19×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
13×	`associate-l_binary64_19`
6×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-/r*_binary64_22`
5×	`pow1_binary64_139`
4×	`tan-quot_binary64_237` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `associate-/l*_binary64_23`
3×	`add-log-exp_binary64_117` `div-inv_binary64_75` `associate-r_binary64_18` `associate-/l/_binary64_25`
2×	`frac-2neg_binary64_89` `frac-times_binary64_88` `associate-l/_binary64_21` `unswap-sqr_binary64_46` `associate-r/_binary64_20` `clear-num_binary64_77`
1×	`*-commutative_binary64_9` `pow-prod-down_binary64_149`

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)

series165.0ms (3.7%)

Counts

3 → 9

Calls

3 calls:

76.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
68.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
20.0ms	(/.f64 (sin.f64 x) x)

simplify86.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4932	1539
1	4932	1539

prune82.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	2	4	6
Picked	0	1	1
Done	0	1	1
Total	96	8	104

Error

Counts

104 → 8

Compiler

Compiled 1663 to 839 computations (49.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite58.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

461×	`times-frac_binary64_84`
222×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
32×	`div-inv_binary64_75`
20×	`associate-/r*_binary64_22`
19×	`add-cbrt-cube_binary64_114` `associate-/l*_binary64_23` `add-exp-log_binary64_116`
16×	`associate-/r/_binary64_24`
15×	`tan-quot_binary64_237`
10×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
3×	`add-log-exp_binary64_117` `frac-2neg_binary64_89` `clear-num_binary64_77` `pow1_binary64_139`
1×	`associate-/l/_binary64_25`

Counts

3 → 284

Calls

3 calls:

13.0ms	(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (/.f64 x 2))))
7.0ms	(/.f64 x (tan.f64 (/.f64 x 2)))
4.0ms	(/.f64 (sin.f64 x) x)

series160.0ms (3.6%)

Counts

3 → 9

Calls

3 calls:

74.0ms	(/.f64 x (tan.f64 (/.f64 x 2)))
66.0ms	(/.f64 (/.f64 (sin.f64 x) x) (/.f64 x (tan.f64 (/.f64 x 2))))
19.0ms	(/.f64 (sin.f64 x) x)

simplify156.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

293 → 293

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5020	9205

prune319.0ms (7.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	291	2	293
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	294	7	301

Error

Counts

301 → 7

Compiler

Compiled 6645 to 3374 computations (49.2% saved)

regimes131.0ms (2.9%)

Accuracy

Total 0.1b remaining (99.5%)

Threshold costs 0.1b (99.5%)

Compiler

Compiled 1391 to 982 computations (29.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	17
1	9	17

end0.0ms (0%)

sample2.3s (51.3%)

Algorithm

1×

intervals

Results

873.0ms	1975×	body	2048	valid
223.0ms	1109×	body	1024	valid
188.0ms	1497×	body	512	valid
108.0ms	2564×	body	128	valid
63.0ms	747×	body	256	valid
42.0ms	108×	body	4096	valid

Compiler

Compiled 655 to 464 computations (29.2% saved)

Details

analyze242.0ms (5.4%)

sample57.0ms (1.3%)

simplify104.0ms (2.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite17.0ms (0.4%)

series41.0ms (0.9%)

simplify69.0ms (1.5%)

prune67.0ms (1.5%)

localize10.0ms (0.2%)

rewrite37.0ms (0.8%)

series144.0ms (3.2%)

simplify66.0ms (1.5%)

prune114.0ms (2.5%)

localize11.0ms (0.2%)

rewrite28.0ms (0.6%)

series165.0ms (3.7%)

simplify86.0ms (1.9%)

prune82.0ms (1.8%)

localize9.0ms (0.2%)

rewrite58.0ms (1.3%)

series160.0ms (3.6%)

simplify156.0ms (3.5%)

prune319.0ms (7.1%)

regimes131.0ms (2.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (51.3%)

Profiling