Details

analyze334.0ms (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)

sample55.0ms (1.1%)

Algorithm

1×

intervals

Results

26.0ms	62×	body	2048	valid
9.0ms	51×	body	1024	valid
5.0ms	42×	body	512	valid
3.0ms	74×	body	128	valid
2.0ms	25×	body	256	valid
1.0ms	2×	body	4096	valid

Compiler

Compiled 17 to 14 computations (17.6% saved)

simplify22.0ms (0.4%)

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

32.5b

Counts

2 → 1

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

2.0b	(-.f64 1 (cos.f64 x))
15.3b	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))

rewrite70.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Error

31.1b

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:

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

Compiler

Compiled 708 to 357 computations (49.6% saved)

series48.0ms (1%)

Error

1.0b

Counts

2 → 6

Calls

2 calls:

32.0ms	(/.f64 (-.f64 1 (cos.f64 x)) (*.f64 x x))
12.0ms	(-.f64 1 (cos.f64 x))

Compiler

Compiled 138 to 105 computations (23.9% saved)

simplify59.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4903	679
1	4903	679

prune51.0ms (1%)

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 750 to 399 computations (46.8% 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))
15.3b	(/.f64 (/.f64 (.f64 (sin.f64 x) (sin.f64 x)) (+.f64 1 (cos.f64 x))) (.f64 x x))

rewrite143.0ms (2.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

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:

12.0ms	(/.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)

series160.0ms (3.2%)

Error

0.0b

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)))
20.0ms	(*.f64 (sin.f64 x) (sin.f64 x))
10.0ms	(+.f64 1 (cos.f64 x))

Compiler

Compiled 441 to 298 computations (32.4% saved)

simplify64.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5801	1709

prune105.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	119	4	123
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	126	5	131

Error

Counts

131 → 5

Compiler

Compiled 2098 to 1029 computations (51% saved)

localize8.0ms (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)
0.1b	(/.f64 (sin.f64 x) x)

rewrite117.0ms (2.3%)

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×	`tan-quot_binary64_237` `associate-/l/_binary64_25` `pow-prod-down_binary64_149` `frac-times_binary64_88` `associate-l/_binary64_21` `associate-r/_binary64_20` `*-commutative_binary64_9`

Counts

3 → 105

Calls

3 calls:

12.0ms	(*.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)

Compiler

Compiled 2058 to 1010 computations (50.9% saved)

series165.0ms (3.3%)

Error

Counts

3 → 10

Calls

3 calls:

67.0ms	(*.f64 (/.f64 (sin.f64 x) x) (/.f64 (tan.f64 (/.f64 x 2)) x))
60.0ms	(/.f64 (tan.f64 (/.f64 x 2)) x)
28.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 355 to 265 computations (25.4% saved)

simplify78.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4967	1909
1	4967	1909

prune97.0ms (1.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	116	4	120

Error

Counts

120 → 4

Compiler

Compiled 2017 to 1031 computations (48.9% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite161.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

34×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
32×	`add-sqr-sqrt_binary64_100`
25×	`add-cube-cbrt_binary64_113` `times-frac_binary64_84` `*-un-lft-identity_binary64_78`
16×	`associate-l_binary64_19`
10×	`prod-exp_binary64_127` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `cbrt-unprod_binary64_111` `associate-r_binary64_18`
8×	`pow1_binary64_139`
6×	`associate-/l*_binary64_23`
4×	`add-log-exp_binary64_117` `div-inv_binary64_75` `associate-/r*_binary64_22`
3×	`unswap-sqr_binary64_46`
2×	`frac-2neg_binary64_89` `clear-num_binary64_77` `pow-prod-down_binary64_149` `*-commutative_binary64_9`
1×	`frac-times_binary64_88` `associate-l/_binary64_21` `associate-r/_binary64_20`

Counts

4 → 112

Calls

4 calls:

12.0ms	(.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 x (cos.f64 (.f64 x 1/2)))))
6.0ms	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 x (cos.f64 (*.f64 x 1/2))))
5.0ms	(.f64 x (cos.f64 (.f64 x 1/2)))
4.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 2823 to 1622 computations (42.5% saved)

series176.0ms (3.5%)

Error

Counts

4 → 14

Calls

4 calls:

59.0ms	(.f64 (/.f64 (sin.f64 x) x) (/.f64 (sin.f64 (.f64 x 1/2)) (.f64 x (cos.f64 (.f64 x 1/2)))))
47.0ms	(/.f64 (sin.f64 (.f64 x 1/2)) (.f64 x (cos.f64 (*.f64 x 1/2))))
30.0ms	(.f64 x (cos.f64 (.f64 x 1/2)))
29.0ms	(/.f64 (sin.f64 x) x)

Compiler

Compiled 585 to 429 computations (26.7% saved)

simplify74.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5304	2350

prune124.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	126	4	130

Error

Counts

130 → 4

Compiler

Compiled 2649 to 1542 computations (41.8% saved)

regimes201.0ms (4%)

Accuracy

Total 0.1b remaining (99.6%)

Threshold costs 0.1b (99.6%)

Compiler

Compiled 2199 to 1503 computations (31.7% 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%)

sample2.7s (53.4%)

Algorithm

1×

intervals

Results

878.0ms	2006×	body	2048	valid
208.0ms	1093×	body	1024	valid
184.0ms	1495×	body	512	valid
98.0ms	2537×	body	128	valid
62.0ms	753×	body	256	valid
44.0ms	116×	body	4096	valid

Compiler

Compiled 1040 to 712 computations (31.5% saved)

Details

analyze334.0ms (6.7%)

sample55.0ms (1.1%)

simplify22.0ms (0.4%)

prune2.0ms (0%)

localize5.0ms (0.1%)

rewrite70.0ms (1.4%)

series48.0ms (1%)

simplify59.0ms (1.2%)

prune51.0ms (1%)

localize9.0ms (0.2%)

rewrite143.0ms (2.8%)

series160.0ms (3.2%)

simplify64.0ms (1.3%)

prune105.0ms (2.1%)

localize8.0ms (0.2%)

rewrite117.0ms (2.3%)

series165.0ms (3.3%)

simplify78.0ms (1.5%)

prune97.0ms (1.9%)

localize10.0ms (0.2%)

rewrite161.0ms (3.2%)

series176.0ms (3.5%)

simplify74.0ms (1.5%)

prune124.0ms (2.5%)

regimes201.0ms (4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.7s (53.4%)

Profiling