Details

analyze4.0ms (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)

sample141.0ms (0.9%)

Algorithm

1×

intervals

Results

66.0ms	115×	body	1024	valid
37.0ms	42×	body	2048	valid
15.0ms	42×	body	512	valid
5.0ms	23×	body	256	valid
4.0ms	34×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify160.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune4.0ms (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

40.7b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.2b	(sin.f64 (+.f64 x eps))
1.7b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
1.7b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.2b	(sin.f64 (+.f64 x eps))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64_1403` `add-sqr-sqrt_binary64_1425`
4×	`add-log-exp_binary64_1442`
3×	`cancel-sign-sub-inv_binary64_1369` `add-cube-cbrt_binary64_1438`
2×	`sin-sum_binary64_1536` `pow1_binary64_1464` `add-exp-log_binary64_1441` `add-cbrt-cube_binary64_1439`
1×	`sub-neg_binary64_1396` `associate--l+_binary64_1340` `diff-log_binary64_1495` `flip--_binary64_1378` `difference-of-squares_binary64_1372` `diff-sin_binary64_1553` `flip3--_binary64_1407` `distribute-lft-out--_binary64_1355`

Counts

2 → 26

Calls

4 calls:

13.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
8.0ms	(sin.f64 (+.f64 x eps))
0.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
0.0ms	(sin.f64 (+.f64 x eps))

series195.0ms (1.3%)

Counts

2 → 24

Calls

2 calls:

121.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
73.0ms	(sin.f64 (+.f64 x eps))

Compiler

Compiled 368 to 288 computations (21.7% saved)

simplify109.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5023	755

prune105.0ms (0.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	46	4	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	4	51

Error

0.2b

Counts

51 → 4

Compiler

Compiled 683 to 238 computations (65.2% saved)

localize25.0ms (0.2%)

Local error

Found 8 expressions with local error:

3.1b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
0.1b	(*.f64 (cos.f64 x) (sin.f64 eps))
0.1b	(*.f64 (sin.f64 x) (cos.f64 eps))
0.1b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
0.1b	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
0.1b	(*.f64 (sin.f64 x) (cos.f64 eps))
0.1b	(*.f64 (cos.f64 x) (sin.f64 eps))
3.1b	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))

rewrite56.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_1425`
11×	`*-un-lft-identity_binary64_1403` `add-log-exp_binary64_1442`
9×	`add-cube-cbrt_binary64_1438`
8×	`pow1_binary64_1464` `add-exp-log_binary64_1441` `add-cbrt-cube_binary64_1439`
6×	`associate-l_binary64_1344` `associate-r_binary64_1343`
3×	`cancel-sign-sub-inv_binary64_1369`
2×	`unswap-sqr_binary64_1371` `prod-exp_binary64_1452` `diff-log_binary64_1495` `sum-log_binary64_1494` `pow-prod-down_binary64_1474` `*-commutative_binary64_1334` `cbrt-unprod_binary64_1436`
1×	`flip3-+_binary64_1406` `+-commutative_binary64_1333` `sub-neg_binary64_1396` `associate--l+_binary64_1340` `flip--_binary64_1378` `flip-+_binary64_1377` `difference-of-squares_binary64_1372` `sin-cos-mult_binary64_1559` `flip3--_binary64_1407` `distribute-lft-out--_binary64_1355`

Counts

4 → 66

Calls

8 calls:

17.0ms	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
11.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
9.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
9.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))
0.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))

series933.0ms (6%)

Counts

4 → 46

Calls

4 calls:

326.0ms	(-.f64 (+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps))) (sin.f64 x))
253.0ms	(+.f64 (.f64 (sin.f64 x) (cos.f64 eps)) (.f64 (cos.f64 x) (sin.f64 eps)))
183.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
168.0ms	(*.f64 (sin.f64 x) (cos.f64 eps))

Compiler

Compiled 1112 to 796 computations (28.4% saved)

simplify147.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	5212	1995

prune225.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	103	9	112
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	106	10	116

Error

0.1b

Counts

116 → 10

Compiler

Compiled 2342 to 705 computations (69.9% saved)

localize22.0ms (0.1%)

Local error

Found 8 expressions with local error:

2.2b	(+.f64 (cos.f64 eps) -1)
0.2b	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
0.1b	(*.f64 (cos.f64 x) (sin.f64 eps))
0.1b	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
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))
2.2b	(+.f64 (cos.f64 eps) -1)

rewrite47.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1425`
12×	`*-un-lft-identity_binary64_1403`
8×	`pow1_binary64_1464` `add-exp-log_binary64_1441` `add-cube-cbrt_binary64_1438` `associate-r_binary64_1343` `add-cbrt-cube_binary64_1439` `add-log-exp_binary64_1442`
6×	`associate-l_binary64_1344`
3×	`flip3-+_binary64_1406` `flip-+_binary64_1377`
2×	`unswap-sqr_binary64_1371` `prod-exp_binary64_1452` `distribute-rgt-in_binary64_1353` `distribute-lft-in_binary64_1352` `associate-r/_binary64_1345` `+-commutative_binary64_1333` `difference-of-sqr--1_binary64_1374` `associate-+r+_binary64_1335` `sum-log_binary64_1494` `pow-prod-down_binary64_1474` `-commutative_binary64_1334` `distribute-lft-out_binary64_1354` `cbrt-unprod_binary64_1436`

Counts

4 → 68

Calls

8 calls:

13.0ms	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
9.0ms	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
8.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
7.0ms	(+.f64 (cos.f64 eps) -1)
0.0ms	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))

series725.0ms (4.7%)

Counts

4 → 39

Calls

4 calls:

311.0ms	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1)))
196.0ms	(*.f64 (sin.f64 x) (+.f64 (cos.f64 eps) -1))
181.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
38.0ms	(+.f64 (cos.f64 eps) -1)

Compiler

Compiled 983 to 773 computations (21.4% saved)

simplify136.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4946	1759
1	4946	1759

prune233.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	101	6	107
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	108	9	117

Error

0.0b

Counts

117 → 9

Compiler

Compiled 2160 to 926 computations (57.1% saved)

localize23.0ms (0.2%)

Local error

Found 8 expressions with local error:

2.0b	(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x)))
0.1b	(*.f64 (cos.f64 x) (sin.f64 eps))
0.1b	(*.f64 (cos.f64 eps) (sin.f64 x))
0.1b	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x))))
0.1b	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x))))
0.1b	(*.f64 (cos.f64 eps) (sin.f64 x))
0.1b	(*.f64 (cos.f64 x) (sin.f64 eps))
2.0b	(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x)))

rewrite53.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-log-exp_binary64_1442`
12×	`add-sqr-sqrt_binary64_1425`
9×	`*-un-lft-identity_binary64_1403`
8×	`pow1_binary64_1464` `add-exp-log_binary64_1441` `add-cube-cbrt_binary64_1438` `add-cbrt-cube_binary64_1439`
7×	`sum-log_binary64_1494`
6×	`associate-l_binary64_1344` `associate-r_binary64_1343`
4×	`associate-+r-_binary64_1337`
2×	`unswap-sqr_binary64_1371` `flip3-+_binary64_1406` `prod-exp_binary64_1452` `+-commutative_binary64_1333` `neg-log_binary64_1496` `distribute-rgt-out_binary64_1356` `flip-+_binary64_1377` `pow-prod-down_binary64_1474` `*-commutative_binary64_1334` `neg-sub0_binary64_1398` `unsub-neg_binary64_1397` `cbrt-unprod_binary64_1436`
1×	`neg-mul-1_binary64_1399` `distribute-lft-neg-in_binary64_1360` `associate-+r+_binary64_1335`

Counts

4 → 68

Calls

8 calls:

16.0ms	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x))))
11.0ms	(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x)))
8.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))
8.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
0.0ms	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x))))

series934.0ms (6%)

Counts

4 → 44

Calls

4 calls:

316.0ms	(+.f64 (.f64 (cos.f64 x) (sin.f64 eps)) (+.f64 (.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x))))
248.0ms	(+.f64 (*.f64 (cos.f64 eps) (sin.f64 x)) (neg.f64 (sin.f64 x)))
186.0ms	(*.f64 (cos.f64 x) (sin.f64 eps))
183.0ms	(*.f64 (cos.f64 eps) (sin.f64 x))

Compiler

Compiled 1211 to 883 computations (27.1% saved)

simplify109.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5297	1851

prune143.0ms (0.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	112	9	121

Error

0.0b

Counts

121 → 9

Compiler

Compiled 2130 to 608 computations (71.5% saved)

simplify39.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	398	1377
1	398	1377

regimes463.0ms (3%)

Accuracy

Total 0.3b remaining (87%)

Threshold costs 0.3b (87%)

Compiler

Compiled 2499 to 1787 computations (28.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	23
1	24	23

end0.0ms (0%)

sample10.4s (67.2%)

Algorithm

1×

intervals

Results

1.9s	3451×	body	1024	valid
1.2s	1266×	body	2048	valid
478.0ms	1351×	body	512	valid
171.0ms	1299×	body	128	valid
145.0ms	629×	body	256	valid
8.0ms	4×	body	4096	valid

Compiler

Compiled 2478 to 1761 computations (28.9% saved)

Pareto

0.2545825597151521

Details

analyze4.0ms (0%)

sample141.0ms (0.9%)

simplify160.0ms (1%)

prune4.0ms (0%)

localize12.0ms (0.1%)

rewrite24.0ms (0.2%)

series195.0ms (1.3%)

simplify109.0ms (0.7%)

prune105.0ms (0.7%)

localize25.0ms (0.2%)

rewrite56.0ms (0.4%)

series933.0ms (6%)

simplify147.0ms (0.9%)

prune225.0ms (1.5%)

localize22.0ms (0.1%)

rewrite47.0ms (0.3%)

series725.0ms (4.7%)

simplify136.0ms (0.9%)

prune233.0ms (1.5%)

localize23.0ms (0.2%)

rewrite53.0ms (0.3%)

series934.0ms (6%)

simplify109.0ms (0.7%)

prune143.0ms (0.9%)

simplify39.0ms (0.3%)

regimes463.0ms (3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample10.4s (67.2%)

Profiling