Details

analyze331.0ms (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)

sample59.0ms (1%)

Algorithm

1×

intervals

Results

25.0ms	53×	body	2048	valid
8.0ms	39×	body	1024	valid
7.0ms	49×	body	512	valid
4.0ms	31×	body	256	valid
3.0ms	81×	body	128	valid
1.0ms	3×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify113.0ms (2%)

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

32.9b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

3.2b	(-.f64 1 (cos.f64 x))
13.6b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite68.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

32.0b

Rules

14×	`add-sqr-sqrt_binary64_100` `*-un-lft-identity_binary64_78`
7×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
6×	`times-frac_binary64_84` `difference-of-squares_binary64_47` `associate-/l*_binary64_23`
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×	`pow1_binary64_139` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `flip3--_binary64_82` `associate-/l/_binary64_25` `flip--_binary64_53`
1×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `div-sub_binary64_83` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/r*_binary64_22` `diff-log_binary64_170` `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))

Compiler

Compiled 708 to 357 computations (49.6% saved)

series73.0ms (1.3%)

Error

0.4b

Counts

2 → 12

Calls

2 calls:

42.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
19.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 320 to 251 computations (21.6% saved)

simplify68.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	6299	811

prune59.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	50	9	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	9	60

Error

0.0b

Counts

60 → 9

Compiler

Compiled 886 to 490 computations (44.7% 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))
0.3b	(+.f64 1 (cos.f64 x))
13.4b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite153.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

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))

Compiler

Compiled 2503 to 957 computations (61.8% saved)

series204.0ms (3.6%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

81.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
60.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
29.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
14.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 870 to 613 computations (29.5% saved)

simplify88.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4936	1964
1	4936	1964

prune121.0ms (2.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	135	9	144

Error

Counts

144 → 9

Compiler

Compiled 2390 to 1220 computations (49% saved)

localize8.0ms (0.1%)

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)))

rewrite99.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Error

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-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
13×	`associate-l_binary64_19`
6×	`div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-/r*_binary64_22`
5×	`pow1_binary64_139`
4×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111` `tan-quot_binary64_237` `associate-/l*_binary64_23`
3×	`add-log-exp_binary64_117` `div-inv_binary64_75` `associate-r_binary64_18` `associate-/l/_binary64_25`
2×	`frac-times_binary64_88` `unswap-sqr_binary64_46` `associate-l/_binary64_21` `associate-r/_binary64_20` `frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`pow-prod-down_binary64_149` `*-commutative_binary64_9`

Counts

3 → 87

Calls

3 calls:

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

Compiler

Compiled 1623 to 756 computations (53.4% saved)

series225.0ms (3.9%)

Error

Counts

3 → 18

Calls

3 calls:

99.0ms	(*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2)))
82.0ms	(/.f64 (*.f64 (/.f64 (sin.f64 x) x) (tan.f64 (/.f64 x 2))) x)
31.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 586 to 459 computations (21.7% saved)

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4937	1665
1	4937	1665

prune86.0ms (1.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	107	7	114

Error

Counts

114 → 7

Compiler

Compiled 1779 to 921 computations (48.2% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite280.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Error

Rules

159×	`times-frac_binary64_84`
106×	`add-sqr-sqrt_binary64_100`
94×	`*-un-lft-identity_binary64_78`
92×	`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×	`prod-exp_binary64_127` `cbrt-undiv_binary64_112`
11×	`div-inv_binary64_75`
7×	`pow1_binary64_139` `associate-/l*_binary64_23`
6×	`1-exp_binary64_122` `rec-exp_binary64_128` `cbrt-unprod_binary64_111`
5×	`unswap-sqr_binary64_46`
4×	`add-log-exp_binary64_117` `tan-quot_binary64_237`
3×	`associate-r_binary64_18` `frac-2neg_binary64_89` `clear-num_binary64_77` `associate-/l/_binary64_25`
2×	`frac-times_binary64_88` `associate-l/_binary64_21` `associate-r/_binary64_20` `associate-/r/_binary64_24`
1×	`pow-prod-down_binary64_149` `*-commutative_binary64_9` `inv-pow_binary64_163` `pow-flip_binary64_152`

Counts

4 → 209

Calls

4 calls:

17.0ms	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (tan.f64 (/.f64 x 2)))
13.0ms	(/.f64 (*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (tan.f64 (/.f64 x 2))) x)
6.0ms	(/.f64 1 (/.f64 x (sin.f64 x)))
3.0ms	(/.f64 x (sin.f64 x))

Compiler

Compiled 4722 to 2491 computations (47.2% saved)

series263.0ms (4.6%)

Error

Counts

4 → 24

Calls

4 calls:

97.0ms	(*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (tan.f64 (/.f64 x 2)))
81.0ms	(/.f64 (*.f64 (/.f64 1 (/.f64 x (sin.f64 x))) (tan.f64 (/.f64 x 2))) x)
41.0ms	(/.f64 x (sin.f64 x))
26.0ms	(/.f64 1 (/.f64 x (sin.f64 x)))

Compiler

Compiled 816 to 642 computations (21.3% saved)

simplify115.0ms (2%)

Algorithm

1×	egg-herbie

Counts

233 → 233

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4931	3841
1	4931	3841

prune200.0ms (3.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	231	2	233
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	233	7	240

Error

Counts

240 → 7

Compiler

Compiled 4337 to 2176 computations (49.8% saved)

regimes233.0ms (4.1%)

Accuracy

Total 0.1b remaining (99.4%)

Threshold costs 0.1b (99.4%)

Compiler

Compiled 2599 to 1779 computations (31.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	9	17

end0.0ms (0%)

sample2.8s (48.5%)

Algorithm

1×

intervals

Results

805.0ms	1916×	body	2048	valid
210.0ms	1115×	body	1024	valid
183.0ms	1485×	body	512	valid
120.0ms	2648×	body	128	valid
63.0ms	739×	body	256	valid
37.0ms	97×	body	4096	valid

Compiler

Compiled 1245 to 854 computations (31.4% saved)

Details

analyze331.0ms (5.8%)

sample59.0ms (1%)

simplify113.0ms (2%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite68.0ms (1.2%)

series73.0ms (1.3%)

simplify68.0ms (1.2%)

prune59.0ms (1%)

localize9.0ms (0.2%)

rewrite153.0ms (2.7%)

series204.0ms (3.6%)

simplify88.0ms (1.5%)

prune121.0ms (2.1%)

localize8.0ms (0.1%)

rewrite99.0ms (1.7%)

series225.0ms (3.9%)

simplify85.0ms (1.5%)

prune86.0ms (1.5%)

localize9.0ms (0.2%)

rewrite280.0ms (4.9%)

series263.0ms (4.6%)

simplify115.0ms (2%)

prune200.0ms (3.5%)

regimes233.0ms (4.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (48.5%)

Profiling