Details

analyze225.0ms (3.2%)

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 (0.8%)

Algorithm

1×

intervals

Results

34.0ms	71×	body	2048	valid
7.0ms	35×	body	1024	valid
5.0ms	43×	body	512	valid
4.0ms	92×	body	128	valid
1.0ms	14×	body	256	valid
1.0ms	1×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify109.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

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

Merged error: 30.5b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.1b	(-.f64 1 (cos.f64 x))
16.5b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite16.0ms (0.2%)

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))
4.0ms	(-.f64 1 (cos.f64 x))

series47.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

35.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
12.0ms	(-.f64 1 (cos.f64 x))

simplify66.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	6395	715

prune64.0ms (0.9%)

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

Merged error: 0.0b

Counts

54 → 8

Compiler

Compiled 801 to 436 computations (45.6% saved)

localize10.0ms (0.1%)

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))
16.3b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite40.0ms (0.6%)

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))

series138.0ms (2%)

Counts

4 → 12

Calls

4 calls:

71.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
45.0ms	(/.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%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4963	1781
1	4963	1781

prune106.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	121	2	123
Fresh	5	2	7
Picked	0	1	1
Done	0	0	0
Total	126	5	131

Merged error: 0b

Counts

131 → 5

Compiler

Compiled 2141 to 1075 computations (49.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite28.0ms (0.4%)

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))
5.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
4.0ms	(/.f64 (sin.f64 x) x)

series149.0ms (2.1%)

Counts

3 → 9

Calls

3 calls:

75.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
54.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
19.0ms	(/.f64 (sin.f64 x) x)

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4971	1953
1	4971	1953

prune99.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	114	5	119

Merged error: 0b

Counts

119 → 5

Compiler

Compiled 2043 to 1050 computations (48.6% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
0.2b	(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 x (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))
1.1b	(-.f64 1 (cos.f64 x))
1.1b	(-.f64 1 (cos.f64 x))

rewrite292.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Rules

2649×	`times-frac_binary64_84`
1607×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
1158×	`sqrt-prod_binary64_94`
1022×	`add-cube-cbrt_binary64_113`
390×	`difference-of-squares_binary64_47`
195×	`distribute-lft-out--_binary64_30`
101×	`associate-/r*_binary64_22`
42×	`div-inv_binary64_75`
18×	`associate-/l*_binary64_23`
15×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
11×	`associate-/r/_binary64_24`
8×	`add-log-exp_binary64_117`
7×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
6×	`cancel-sign-sub-inv_binary64_44`
4×	`flip3--_binary64_82` `flip--_binary64_53` `sqrt-div_binary64_95` `associate-/l/_binary64_25` `pow1_binary64_139`
2×	`diff-log_binary64_170` `frac-2neg_binary64_89` `clear-num_binary64_77` `sub-neg_binary64_71`

Counts

4 → 1095

Calls

4 calls:

46.0ms	(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 x (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))
7.0ms	(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
4.0ms	(-.f64 1 (cos.f64 x))
4.0ms	(-.f64 1 (cos.f64 x))

series101.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

50.0ms	(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)
28.0ms	(/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) (/.f64 x (/.f64 (sqrt.f64 (-.f64 1 (cos.f64 x))) x)))
12.0ms	(-.f64 1 (cos.f64 x))
11.0ms	(-.f64 1 (cos.f64 x))

simplify463.0ms (6.6%)

Algorithm

1×	egg-herbie

Counts

1107 → 1107

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4985	48971
1	4985	48971

prune2.5s (35.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	1107	0	1107
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	1107	5	1112

Merged error: 0b

Counts

1112 → 5

Compiler

Compiled 32896 to 18380 computations (44.1% saved)

regimes113.0ms (1.6%)

Compiler: Compiled 1137 to 832 computations (26.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	10	17

end0.0ms (0%)

sample2.2s (31.3%)

Algorithm

1×

intervals

Results

865.0ms	1966×	body	2048	valid
224.0ms	1136×	body	1024	valid
189.0ms	1488×	body	512	valid
102.0ms	2556×	body	128	valid
62.0ms	747×	body	256	valid
41.0ms	107×	body	4096	valid

Compiler

Compiled 533 to 393 computations (26.3% saved)

Details

analyze225.0ms (3.2%)

sample58.0ms (0.8%)

simplify109.0ms (1.6%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite16.0ms (0.2%)

series47.0ms (0.7%)

simplify66.0ms (0.9%)

prune64.0ms (0.9%)

localize10.0ms (0.1%)

rewrite40.0ms (0.6%)

series138.0ms (2%)

simplify67.0ms (1%)

prune106.0ms (1.5%)

localize10.0ms (0.1%)

rewrite28.0ms (0.4%)

series149.0ms (2.1%)

simplify89.0ms (1.3%)

prune99.0ms (1.4%)

localize8.0ms (0.1%)

rewrite292.0ms (4.2%)

series101.0ms (1.4%)

simplify463.0ms (6.6%)

prune2.5s (35.7%)

regimes113.0ms (1.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.2s (31.3%)

Profiling