Details

analyze237.0ms (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)

sample50.0ms (1.1%)

Algorithm

1×

intervals

Results

24.0ms	59×	body	2048	valid
7.0ms	35×	body	1024	valid
5.0ms	42×	body	512	valid
3.0ms	89×	body	128	valid
2.0ms	26×	body	256	valid
2.0ms	5×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify116.0ms (2.6%)

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

29.4b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.4b	(-.f64 1 (cos.f64 x))
14.9b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite15.0ms (0.3%)

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:

8.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
4.0ms	(-.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))

simplify65.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6395	715

prune67.0ms (1.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	45	8	53
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	8	54

Error

0.0b

Counts

54 → 8

Compiler

Compiled 797 to 431 computations (45.9% saved)

localize9.0ms (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))
14.9b	(/.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))

series137.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
49.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
16.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
7.0ms	(+.f64 1 (cos.f64 x))

simplify67.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4963	1781
1	4963	1781

prune115.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	118	5	123
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	123	8	131

Error

Counts

131 → 8

Compiler

Compiled 2200 to 1113 computations (49.4% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

rewrite28.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64_100`
40×	`times-frac_binary64_84`
33×	`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` `associate-r_binary64_18`
6×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `associate-/l_binary64_23` `associate-/r_binary64_22`
5×	`pow1_binary64_139`
4×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `div-inv_binary64_75` `unswap-sqr_binary64_46`
3×	`add-log-exp_binary64_117`
2×	`frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`tan-quot_binary64_237` `-commutative_binary64_9` `frac-times_binary64_88` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-*r/_binary64_20` `associate-/l/_binary64_25`

Counts

3 → 105

Calls

3 calls:

11.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
4.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
4.0ms	(/.f64 (sin.f64 x) x)

series153.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

70.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
60.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
22.0ms	(/.f64 (sin.f64 x) x)

simplify98.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4971	1953
1	4971	1953

prune104.0ms (2.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	116	6	122

Error

Counts

122 → 6

Compiler

Compiled 2070 to 1063 computations (48.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
0.1b	(/.f64 x (sin.f64 x))
0.1b	(/.f64 (tan.f64 (/.f64 x 2)) x)
0.2b	(/.f64 1 (/.f64 x (sin.f64 x)))

rewrite61.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

185×	`times-frac_binary64_84`
137×	`add-sqr-sqrt_binary64_100`
108×	`*-un-lft-identity_binary64_78`
104×	`add-cube-cbrt_binary64_113`
64×	`add-exp-log_binary64_116`
44×	`associate-l_binary64_19`
34×	`add-cbrt-cube_binary64_114`
30×	`div-exp_binary64_129`
19×	`associate-/r*_binary64_22`
14×	`cbrt-undiv_binary64_112` `prod-exp_binary64_127`
13×	`associate-r_binary64_18`
12×	`div-inv_binary64_75`
10×	`unswap-sqr_binary64_46`
9×	`associate-/l*_binary64_23`
7×	`pow1_binary64_139`
6×	`cbrt-unprod_binary64_111` `1-exp_binary64_122` `rec-exp_binary64_128`
4×	`add-log-exp_binary64_117`
3×	`frac-2neg_binary64_89` `clear-num_binary64_77`
2×	`associate-/r/_binary64_24`
1×	`tan-quot_binary64_237` `-commutative_binary64_9` `inv-pow_binary64_163` `frac-times_binary64_88` `pow-flip_binary64_152` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-*r/_binary64_20` `associate-/l/_binary64_25`

Counts

4 → 230

Calls

4 calls:

23.0ms	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
8.0ms	(/.f64 1 (/.f64 x (sin.f64 x)))
4.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
3.0ms	(/.f64 x (sin.f64 x))

series174.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (/.f64 (tan.f64 (/.f64 x 2)) x))
61.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
28.0ms	(/.f64 x (sin.f64 x))
19.0ms	(/.f64 1 (/.f64 x (sin.f64 x)))

simplify132.0ms (3%)

Algorithm

1×	egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4955	4347
1	4955	4347

prune215.0ms (4.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	242	0	242
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	242	6	248

Error

Counts

248 → 6

Compiler

Compiled 4725 to 2369 computations (49.9% saved)

regimes140.0ms (3.2%)

Accuracy

Total 0.1b remaining (99.7%)

Threshold costs 0.1b (99.7%)

Compiler

Compiled 1431 to 1014 computations (29.1% 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%)

sample2.3s (52.7%)

Algorithm

1×

intervals

Results

851.0ms	1973×	body	2048	valid
204.0ms	1049×	body	1024	valid
202.0ms	1578×	body	512	valid
105.0ms	2582×	body	128	valid
59.0ms	714×	body	256	valid
44.0ms	104×	body	4096	valid

Compiler

Compiled 675 to 480 computations (28.9% saved)

Details

analyze237.0ms (5.4%)

sample50.0ms (1.1%)

simplify116.0ms (2.6%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite15.0ms (0.3%)

series41.0ms (0.9%)

simplify65.0ms (1.5%)

prune67.0ms (1.5%)

localize9.0ms (0.2%)

rewrite37.0ms (0.8%)

series137.0ms (3.1%)

simplify67.0ms (1.5%)

prune115.0ms (2.6%)

localize9.0ms (0.2%)

rewrite28.0ms (0.6%)

series153.0ms (3.5%)

simplify98.0ms (2.2%)

prune104.0ms (2.4%)

localize10.0ms (0.2%)

rewrite61.0ms (1.4%)

series174.0ms (3.9%)

simplify132.0ms (3%)

prune215.0ms (4.9%)

regimes140.0ms (3.2%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.3s (52.7%)

Profiling