Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 8 to 7 computations (12.5% saved)

sample72.0ms (1.1%)

Algorithm

1×

intervals

Results

31.0ms	112×	body	1024	valid
20.0ms	41×	body	2048	valid
8.0ms	40×	body	512	valid
3.0ms	26×	body	256	valid
2.0ms	37×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify110.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

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: 35.2b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.4b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.7b	(sin.f64 (+.f64 x eps))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
4×	`add-log-exp_binary64_1140`
3×	`add-cube-cbrt_binary64_1136` `cancel-sign-sub-inv_binary64_1067`
2×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137` `sin-sum_binary64_1234`
1×	`diff-log_binary64_1193` `difference-of-squares_binary64_1070` `sub-neg_binary64_1094` `distribute-lft-out--_binary64_1053` `associate--l+_binary64_1038` `flip--_binary64_1076` `diff-sin_binary64_1251` `flip3--_binary64_1105`

Counts

2 → 26

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
4.0ms	(sin.f64 (+.f64 x eps))

series74.0ms (1.1%)

Counts

2 → 12

Calls

2 calls:

59.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
15.0ms	(sin.f64 (+.f64 x eps))

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4894	499
1	4894	499

prune33.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	35	3	38
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	36	3	39

Merged error: 0.2b

Counts

39 → 3

Compiler

Compiled 469 to 126 computations (73.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
0.1b	(*.f64 (cos.f64 x) (sin.f64 eps))
0.2b	(*.f64 (sin.f64 x) (cos.f64 eps))
2.8b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))

rewrite30.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1123`
11×	`add-log-exp_binary64_1140`
10×	`*-un-lft-identity_binary64_1101` `add-cube-cbrt_binary64_1136`
8×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `add-cbrt-cube_binary64_1137`
6×	`associate-r_binary64_1041` `associate-l_binary64_1042` `cancel-sign-sub-inv_binary64_1067`
4×	`associate-+r+_binary64_1033`
3×	`sin-cos-mult_binary64_1257`
2×	`diff-log_binary64_1193` `*-commutative_binary64_1032` `cbrt-unprod_binary64_1134` `prod-exp_binary64_1150` `sum-log_binary64_1192` `sub-neg_binary64_1094` `flip--_binary64_1076` `flip3--_binary64_1105` `pow-prod-down_binary64_1172` `unswap-sqr_binary64_1069` `frac-add_binary64_1109`
1×	`associate-+r-_binary64_1035` `flip3-+_binary64_1104` `+-commutative_binary64_1031` `flip-+_binary64_1075`

Counts

4 → 70

Calls

4 calls:

10.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
5.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
5.0ms	(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
5.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))

series506.0ms (7.4%)

Counts

4 → 24

Calls

4 calls:

217.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (-.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x)))
115.0ms	(-.f64 (*.f64 (cos.f64 x) (sin.f64 eps)) (sin.f64 x))
91.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))
82.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5411	1606

prune88.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	86	8	94
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	87	10	97

Merged error: 0.1b

Counts

97 → 10

Compiler

Compiled 2033 to 515 computations (74.7% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
1.5b	(+.f64 (cos.f64 eps) -1)
1.5b	(+.f64 (cos.f64 eps) -1)
1.5b	(+.f64 (cos.f64 eps) -1)

rewrite24.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_1101`
10×	`add-log-exp_binary64_1140`
8×	`add-sqr-sqrt_binary64_1123`
5×	`add-cube-cbrt_binary64_1136`
4×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `flip-+_binary64_1075`
3×	`distribute-lft-out_binary64_1052` `sum-log_binary64_1192` `+-commutative_binary64_1031` `difference-of-sqr--1_binary64_1072` `cbrt-prod_binary64_1132`
2×	`cbrt-div_binary64_1133`
1×	`pow1/3_binary64_1183`

Counts

4 → 52

Calls

4 calls:

4.0ms	(+.f64 (cos.f64 eps) -1)
4.0ms	(+.f64 (cos.f64 eps) -1)
4.0ms	(+.f64 (cos.f64 eps) -1)
4.0ms	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))

series556.0ms (8.1%)

Counts

4 → 15

Calls

4 calls:

532.0ms	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
8.0ms	(+.f64 (cos.f64 eps) -1)
8.0ms	(+.f64 (cos.f64 eps) -1)
7.0ms	(+.f64 (cos.f64 eps) -1)

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5215	1112

prune127.0ms (1.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	67	10	77

Merged error: 0.1b

Counts

77 → 10

Compiler

Compiled 3560 to 1542 computations (56.7% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
0.7b	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) 2)) (+.f64 (cos.f64 eps) 1)))))
1.5b	(+.f64 (cos.f64 eps) -1)
1.5b	(+.f64 (cos.f64 eps) -1)

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_1101`
8×	`add-sqr-sqrt_binary64_1123` `add-log-exp_binary64_1140`
6×	`add-cube-cbrt_binary64_1136` `cbrt-prod_binary64_1132`
4×	`add-exp-log_binary64_1139` `pow1_binary64_1162` `flip3-+_binary64_1104` `add-cbrt-cube_binary64_1137` `flip-+_binary64_1075` `cbrt-div_binary64_1133`
2×	`pow1/3_binary64_1183` `distribute-lft-out_binary64_1052` `sum-log_binary64_1192` `+-commutative_binary64_1031` `difference-of-sqr--1_binary64_1072`

Counts

4 → 52

Calls

4 calls:

4.0ms	(+.f64 (cos.f64 eps) -1)
4.0ms	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) 2)) (+.f64 (cos.f64 eps) 1)))))
4.0ms	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
4.0ms	(+.f64 (cos.f64 eps) -1)

series1.3s (18.6%)

Counts

4 → 18

Calls

4 calls:

739.0ms	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (/.f64 (neg.f64 (pow.f64 (sin.f64 eps) 2)) (+.f64 (cos.f64 eps) 1)))))
520.0ms	(cbrt.f64 (+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))))
8.0ms	(+.f64 (cos.f64 eps) -1)
7.0ms	(+.f64 (cos.f64 eps) -1)

simplify61.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5150	1706

prune133.0ms (1.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	68	12	80

Merged error: 0.1b

Counts

80 → 12

Compiler

Compiled 3959 to 1744 computations (55.9% saved)

regimes198.0ms (2.9%)

Compiler: Compiled 2307 to 1457 computations (36.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	21
1	16	21

end0.0ms (0%)

sample3.2s (47.5%)

Algorithm

1×

intervals

Results

1.2s	3443×	body	1024	valid
649.0ms	1245×	body	2048	valid
264.0ms	1335×	body	512	valid
94.0ms	1336×	body	128	valid
82.0ms	637×	body	256	valid
4.0ms	4×	body	4096	valid

Compiler

Compiled 797 to 511 computations (35.9% saved)

Details

analyze2.0ms (0%)

sample72.0ms (1.1%)

simplify110.0ms (1.6%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite12.0ms (0.2%)

series74.0ms (1.1%)

simplify66.0ms (1%)

prune33.0ms (0.5%)

localize11.0ms (0.2%)

rewrite30.0ms (0.4%)

series506.0ms (7.4%)

simplify73.0ms (1.1%)

prune88.0ms (1.3%)

localize19.0ms (0.3%)

rewrite24.0ms (0.4%)

series556.0ms (8.1%)

simplify61.0ms (0.9%)

prune127.0ms (1.9%)

localize24.0ms (0.3%)

rewrite27.0ms (0.4%)

series1.3s (18.6%)

simplify61.0ms (0.9%)

prune133.0ms (1.9%)

regimes198.0ms (2.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample3.2s (47.5%)

Profiling