Details

analyze400.0ms (6.7%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	366	12
1	366	12
0	1	1
1	1	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)

sample62.0ms (1%)

Algorithm

1×

intervals

Results

32.0ms	74×	body	2048	valid
8.0ms	37×	body	1024	valid
6.0ms	50×	body	512	valid
2.0ms	67×	body	128	valid
2.0ms	24×	body	256	valid
2.0ms	4×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify29.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	366	12
1	366	12

prune4.0ms (0.1%)

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

33.6b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

2.5b	(-.f64 1 (cos.f64 x))
17.2b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite91.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

32.5b

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:

15.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
7.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 708 to 357 computations (49.6% saved)

series56.0ms (0.9%)

Error

0.5b

Counts

2 → 8

Calls

2 calls:

34.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
16.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 194 to 150 computations (22.7% saved)

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4996	705
1	4996	705

prune59.0ms (1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	47	8	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	8	56

Error

0.0b

Counts

56 → 8

Compiler

Compiled 804 to 432 computations (46.3% 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)))
0.2b	(*.f64 (sin.f64 x) (sin.f64 x))
0.4b	(+.f64 1 (cos.f64 x))
17.2b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite157.0ms (2.6%)

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:

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))

Compiler

Compiled 2503 to 957 computations (61.8% saved)

series222.0ms (3.7%)

Error

0.0b

Counts

4 → 16

Calls

4 calls:

97.0ms	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))
72.0ms	(/.f64 (*.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x)))
29.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
12.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 579 to 398 computations (31.3% saved)

simplify97.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4986	1758
1	4986	1758

prune143.0ms (2.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	126	9	135

Error

Counts

135 → 9

Compiler

Compiled 2196 to 1087 computations (50.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite152.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Error

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-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
13×	`associate-l_binary64_19` `associate-r_binary64_18`
6×	`div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-/l_binary64_23` `associate-/r_binary64_22`
5×	`pow1_binary64_139`
4×	`div-inv_binary64_75` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `unswap-sqr_binary64_46`
3×	`add-log-exp_binary64_117`
2×	`frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`pow-prod-down_binary64_149` `frac-times_binary64_88` `associate-l/_binary64_21` `associate-r/_binary64_20` `*-commutative_binary64_9` `tan-quot_binary64_237` `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))
7.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
4.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 2058 to 1010 computations (50.9% saved)

series200.0ms (3.3%)

Error

Counts

3 → 12

Calls

3 calls:

106.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
59.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
26.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 405 to 305 computations (24.7% saved)

simplify109.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4973	1929
1	4973	1929

prune119.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	120	6	126

Error

Counts

126 → 6

Compiler

Compiled 2039 to 1040 computations (49% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(.f64 (.f64 x x) (cos.f64 (*.f64 x 1/2)))
0.1b	(.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2)))
17.1b	(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) (.f64 (.f64 x x) (cos.f64 (*.f64 x 1/2))))

rewrite125.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

31×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
13×	`prod-exp_binary64_127` `cbrt-unprod_binary64_111`
10×	`pow1_binary64_139`
9×	`add-sqr-sqrt_binary64_100`
6×	`div-exp_binary64_129` `add-cube-cbrt_binary64_113` `cbrt-undiv_binary64_112` `-un-lft-identity_binary64_78` `associate-r*_binary64_18`
4×	`pow-prod-down_binary64_149` `associate-l_binary64_19`
3×	`add-log-exp_binary64_117`
2×	`sin-mult_binary64_233` `unswap-sqr_binary64_46` `*-commutative_binary64_9`
1×	`frac-2neg_binary64_89` `times-frac_binary64_84` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l/_binary64_25` `associate-/l_binary64_23` `associate-/r_binary64_22`

Counts

3 → 64

Calls

3 calls:

12.0ms	(.f64 (.f64 x x) (cos.f64 (*.f64 x 1/2)))
10.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) (.f64 (.f64 x x) (cos.f64 (*.f64 x 1/2))))
8.0ms	(.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2)))

Compiler

Compiled 1645 to 980 computations (40.4% saved)

series144.0ms (2.4%)

Error

Counts

3 → 12

Calls

3 calls:

74.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2))) (.f64 (.f64 x x) (cos.f64 (*.f64 x 1/2))))
35.0ms	(.f64 (.f64 x x) (cos.f64 (*.f64 x 1/2)))
27.0ms	(.f64 (sin.f64 x) (sin.f64 (.f64 x 1/2)))

Compiler

Compiled 490 to 377 computations (23.1% saved)

simplify100.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4970	1373
1	4970	1373

prune81.0ms (1.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	76	6	82

Error

Counts

82 → 6

Compiler

Compiled 1484 to 905 computations (39% saved)

regimes247.0ms (4.1%)

Accuracy

Total 0.1b remaining (99.2%)

Threshold costs 0.1b (99.2%)

Compiler

Compiled 2053 to 1429 computations (30.4% 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%)

sample3.3s (55.4%)

Algorithm

1×

intervals

Results

1.1s	2038×	body	2048	valid
272.0ms	1079×	body	1024	valid
234.0ms	1498×	body	512	valid
120.0ms	2521×	body	128	valid
80.0ms	753×	body	256	valid
54.0ms	111×	body	4096	valid

Compiler

Compiled 982 to 687 computations (30% saved)

Details

analyze400.0ms (6.7%)

sample62.0ms (1%)

simplify29.0ms (0.5%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite91.0ms (1.5%)

series56.0ms (0.9%)

simplify42.0ms (0.7%)

prune59.0ms (1%)

localize9.0ms (0.2%)

rewrite157.0ms (2.6%)

series222.0ms (3.7%)

simplify97.0ms (1.6%)

prune143.0ms (2.4%)

localize8.0ms (0.1%)

rewrite152.0ms (2.5%)

series200.0ms (3.3%)

simplify109.0ms (1.8%)

prune119.0ms (2%)

localize10.0ms (0.2%)

rewrite125.0ms (2.1%)

series144.0ms (2.4%)

simplify100.0ms (1.7%)

prune81.0ms (1.4%)

regimes247.0ms (4.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.3s (55.4%)

Profiling