Details

analyze117.0ms (1.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	117	22
1	117	22
0	2	2
1	2	2

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)

sample83.0ms (0.8%)

Algorithm

1×

intervals

Results

33.0ms	113×	body	1024	valid
19.0ms	34×	body	2048	valid
9.0ms	19×	body	256	valid
6.0ms	35×	body	512	valid
3.0ms	55×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

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

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	(sin.f64 (+.f64 x eps))
2.2b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))

rewrite63.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

20.9b

Rules

5×	`add-sqr-sqrt_binary64_1805` `*-un-lft-identity_binary64_1783`
4×	`add-log-exp_binary64_1822`
3×	`add-cube-cbrt_binary64_1818` `cancel-sign-sub-inv_binary64_1749`
2×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `sin-sum_binary64_1916`
1×	`diff-sin_binary64_1933` `diff-log_binary64_1875` `flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `associate--l+_binary64_1720`

Counts

2 → 26

Calls

2 calls:

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

Compiler

Compiled 382 to 101 computations (73.6% saved)

series168.0ms (1.6%)

Error

12.4b

Counts

2 → 24

Calls

2 calls:

95.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
42.0ms	(sin.f64 (+.f64 x eps))

Compiler

Compiled 680 to 408 computations (40% saved)

simplify69.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5023	755

prune69.0ms (0.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	45	5	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	5	51

Error

0.3b

Counts

51 → 5

Compiler

Compiled 693 to 254 computations (63.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
0.1b	(*.f64 (sin.f64 eps) (cos.f64 x))
0.2b	(*.f64 (cos.f64 eps) (sin.f64 x))
3.4b	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))

rewrite115.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

15×	`add-sqr-sqrt_binary64_1805`
11×	`add-log-exp_binary64_1822` `*-un-lft-identity_binary64_1783`
9×	`add-cube-cbrt_binary64_1818`
8×	`pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819`
6×	`associate-l_binary64_1724` `associate-r_binary64_1723`
3×	`cancel-sign-sub-inv_binary64_1749`
2×	`sum-log_binary64_1874` `diff-log_binary64_1875` `pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714`
1×	`flip3--_binary64_1787` `sub-neg_binary64_1776` `flip--_binary64_1758` `difference-of-squares_binary64_1752` `distribute-lft-out--_binary64_1735` `associate--l+_binary64_1720` `sin-cos-mult_binary64_1939` `flip3-+_binary64_1786` `flip-+_binary64_1757` `+-commutative_binary64_1713`

Counts

4 → 66

Calls

4 calls:

16.0ms	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
5.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))
5.0ms	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
5.0ms	(*.f64 (sin.f64 eps) (cos.f64 x))

Compiler

Compiled 1495 to 285 computations (80.9% saved)

series703.0ms (6.8%)

Error

0.3b

Counts

4 → 47

Calls

4 calls:

215.0ms	(-.f64 (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x))) (sin.f64 x))
197.0ms	(+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (.f64 (sin.f64 eps) (cos.f64 x)))
125.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))
110.0ms	(*.f64 (sin.f64 eps) (cos.f64 x))

Compiler

Compiled 1960 to 1078 computations (45% saved)

simplify112.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4928	2028
1	4928	2028

prune145.0ms (1.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	103	10	113
Fresh	2	2	4
Picked	1	0	1
Done	0	0	0
Total	106	12	118

Error

0.1b

Counts

118 → 12

Compiler

Compiled 2414 to 758 computations (68.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
0.1b	(*.f64 (cos.f64 x) (sin.f64 eps))
0.2b	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
1.7b	(+.f64 (cos.f64 eps) -1)

rewrite125.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.1b

Rules

14×	`add-sqr-sqrt_binary64_1805`
12×	`*-un-lft-identity_binary64_1783`
8×	`add-log-exp_binary64_1822` `pow1_binary64_1844` `add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `add-cube-cbrt_binary64_1818` `associate-r_binary64_1723`
6×	`associate-l_binary64_1724`
3×	`flip3-+_binary64_1786` `flip-+_binary64_1757`
2×	`sum-log_binary64_1874` `difference-of-sqr--1_binary64_1754` `distribute-lft-out_binary64_1734` `+-commutative_binary64_1713` `pow-prod-down_binary64_1854` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `unswap-sqr_binary64_1751` `distribute-rgt-in_binary64_1733` `distribute-lft-in_binary64_1732` `associate-r/_binary64_1725` `-commutative_binary64_1714` `associate-+r+_binary64_1715`

Counts

4 → 68

Calls

4 calls:

7.0ms	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
5.0ms	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
5.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
4.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 1405 to 554 computations (60.6% saved)

series566.0ms (5.5%)

Error

0.1b

Counts

4 → 39

Calls

4 calls:

226.0ms	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
142.0ms	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
133.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
22.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 1782 to 1159 computations (35% saved)

simplify94.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4949	1792
1	4949	1792

prune121.0ms (1.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	101	6	107
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	109	10	119

Error

0.0b

Counts

119 → 10

Compiler

Compiled 2191 to 949 computations (56.7% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1))
0.2b	(.f64 (sin.f64 x) (/.f64 (.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1)))
0.3b	(*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps)))
0.3b	(+.f64 (cos.f64 eps) 1)

rewrite195.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

21×	`*-un-lft-identity_binary64_1783`
20×	`add-exp-log_binary64_1821` `add-cbrt-cube_binary64_1819` `associate-r_binary64_1723`
17×	`add-sqr-sqrt_binary64_1805`
13×	`add-cube-cbrt_binary64_1818`
8×	`pow1_binary64_1844` `times-frac_binary64_1789`
6×	`add-log-exp_binary64_1822` `prod-exp_binary64_1832` `cbrt-unprod_binary64_1816` `associate-l_binary64_1724`
4×	`distribute-lft-out_binary64_1734` `distribute-rgt-neg-out_binary64_1743` `div-exp_binary64_1834` `cbrt-undiv_binary64_1817` `associate-/r/_binary64_1729` `associate-/r*_binary64_1727`
3×	`flip3-+_binary64_1786` `flip-+_binary64_1757` `distribute-rgt-neg-in_binary64_1741` `distribute-lft-neg-in_binary64_1740`
2×	`pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `*-commutative_binary64_1714` `distribute-frac-neg_binary64_1746` `div-inv_binary64_1780`
1×	`sum-log_binary64_1874` `+-commutative_binary64_1713` `neg-mul-1_binary64_1779` `associate-r/_binary64_1725` `frac-2neg_binary64_1794` `clear-num_binary64_1782` `associate-/l_binary64_1728`

Counts

4 → 95

Calls

4 calls:

12.0ms	(*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps)))
12.0ms	(.f64 (sin.f64 x) (/.f64 (.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1)))
9.0ms	(/.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1))
7.0ms	(+.f64 (cos.f64 eps) 1)

Compiler

Compiled 2664 to 872 computations (67.3% saved)

series524.0ms (5.1%)

Error

0.0b

Counts

4 → 26

Calls

4 calls:

323.0ms	(.f64 (sin.f64 x) (/.f64 (.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1)))
94.0ms	(/.f64 (*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps))) (+.f64 (cos.f64 eps) 1))
52.0ms	(*.f64 (sin.f64 eps) (neg.f64 (sin.f64 eps)))
27.0ms	(+.f64 (cos.f64 eps) 1)

Compiler

Compiled 1613 to 1081 computations (33% saved)

simplify84.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4924	1792
1	4924	1792

prune168.0ms (1.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	121	10	131

Error

0.0b

Counts

131 → 10

Compiler

Compiled 2761 to 1166 computations (57.8% saved)

regimes879.0ms (8.5%)

Accuracy

Total 0.2b remaining (82.5%)

Threshold costs 0.2b (82.5%)

Compiler

Compiled 7825 to 4902 computations (37.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	28
1	32	28

end0.0ms (0%)

sample5.9s (56.7%)

Algorithm

1×

intervals

Results

1.2s	3550×	body	1024	valid
984.0ms	1159×	body	2048	valid
315.0ms	1333×	body	512	valid
99.0ms	1387×	body	128	valid
82.0ms	567×	body	256	valid
8.0ms	4×	body	4096	valid

Compiler

Compiled 2608 to 1644 computations (37% saved)

Details

analyze117.0ms (1.1%)

sample83.0ms (0.8%)

simplify14.0ms (0.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite63.0ms (0.6%)

series168.0ms (1.6%)

simplify69.0ms (0.7%)

prune69.0ms (0.7%)

localize17.0ms (0.2%)

rewrite115.0ms (1.1%)

series703.0ms (6.8%)

simplify112.0ms (1.1%)

prune145.0ms (1.4%)

localize16.0ms (0.2%)

rewrite125.0ms (1.2%)

series566.0ms (5.5%)

simplify94.0ms (0.9%)

prune121.0ms (1.2%)

localize15.0ms (0.1%)

rewrite195.0ms (1.9%)

series524.0ms (5.1%)

simplify84.0ms (0.8%)

prune168.0ms (1.6%)

regimes879.0ms (8.5%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample5.9s (56.7%)

Profiling