Details

analyze133.0ms (1.2%)

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)

sample115.0ms (1.1%)

Algorithm

1×

intervals

Results

53.0ms	67×	body	2048	valid
37.0ms	124×	body	1024	valid
10.0ms	42×	body	512	valid
2.0ms	17×	body	256	valid
0.0ms	6×	body	128	valid

Compiler

Compiled 15 to 15 computations (0% saved)

simplify10.0ms (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

39.9b

Counts

2 → 1

Compiler

Compiled 14 to 12 computations (14.3% saved)

localize12.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.4b	(cos.f64 (+.f64 x eps))
1.5b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))

rewrite53.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Error

17.7b

Rules

5×	`add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
4×	`add-log-exp_binary64_458`
3×	`add-cube-cbrt_binary64_454` `cancel-sign-sub-inv_binary64_385`
2×	`pow1_binary64_480` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `cos-sum_binary64_553`
1×	`diff-cos_binary64_570` `diff-log_binary64_511` `flip3--_binary64_423` `sub-neg_binary64_412` `flip--_binary64_394` `difference-of-squares_binary64_388` `distribute-lft-out--_binary64_371` `associate--l-_binary64_357`

Counts

2 → 26

Calls

2 calls:

11.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 382 to 101 computations (73.6% saved)

series187.0ms (1.7%)

Error

12.7b

Counts

2 → 24

Calls

2 calls:

93.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
48.0ms	(cos.f64 (+.f64 x eps))

Compiler

Compiled 702 to 440 computations (37.3% saved)

simplify77.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5016	764

prune66.0ms (0.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	43	7	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	7	51

Error

0.2b

Counts

51 → 7

Compiler

Compiled 716 to 267 computations (62.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
0.0b	(+.f64 x (+.f64 eps x))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
1.4b	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

rewrite162.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

12×	`*-un-lft-identity_binary64_419`
11×	`pow1_binary64_480` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
9×	`add-log-exp_binary64_458` `add-sqr-sqrt_binary64_441`
7×	`add-cube-cbrt_binary64_454`
6×	`associate-l_binary64_360`
4×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-r_binary64_359`
3×	`sum-log_binary64_510` `distribute-lft-out_binary64_370`
2×	`sin-mult_binary64_574` `*-commutative_binary64_350`
1×	`unswap-sqr_binary64_387` `flip3-+_binary64_422` `flip-+_binary64_393` `associate-+r+_binary64_351` `+-commutative_binary64_349` `associate-*r/_binary64_361`

Counts

4 → 60

Calls

4 calls:

24.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
14.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
11.0ms	(+.f64 x (+.f64 eps x))
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

Compiler

Compiled 1452 to 895 computations (38.4% saved)

series501.0ms (4.6%)

Error

0.2b

Counts

4 → 48

Calls

4 calls:

162.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))))
127.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2)))
84.0ms	(+.f64 x (+.f64 eps x))
64.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 eps x)) 2))

Compiler

Compiled 2082 to 1744 computations (16.2% saved)

simplify99.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4912	2057
1	4912	2057

prune154.0ms (1.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	6	108
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	104	11	115

Error

0.2b

Counts

115 → 11

Compiler

Compiled 2270 to 1522 computations (33% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
6.9b	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
6.9b	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
6.9b	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))

rewrite177.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

4×	`pow1_binary64_480` `add-log-exp_binary64_458` `add-exp-log_binary64_457` `add-cbrt-cube_binary64_455` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441` `*-un-lft-identity_binary64_419`
3×	`pow1/3_binary64_501` `sin-mult_binary64_574` `associate-*r/_binary64_361` `cbrt-div_binary64_451` `cbrt-prod_binary64_450`

Counts

4 → 37

Calls

4 calls:

21.0ms	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
15.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
12.0ms	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
12.0ms	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))

Compiler

Compiled 2257 to 1462 computations (35.2% saved)

series1.7s (15.7%)

Error

0.2b

Counts

4 → 36

Calls

4 calls:

534.0ms	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
502.0ms	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
491.0ms	(cbrt.f64 (.f64 -2 (.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) (sin.f64 (/.f64 eps 2)))))
82.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 5496 to 4152 computations (24.5% saved)

simplify153.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4933	1835
1	4933	1835

prune264.0ms (2.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	73	11	84

Error

0.2b

Counts

84 → 11

Compiler

Compiled 4170 to 2806 computations (32.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)))
0.5b	(pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)
1.4b	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
8.6b	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3))

rewrite217.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

0.2b

Rules

28×	`cbrt-prod_binary64_450`
24×	`add-sqr-sqrt_binary64_441`
15×	`add-cube-cbrt_binary64_454` `-un-lft-identity_binary64_419` `associate-r*_binary64_359`
10×	`unpow-prod-down_binary64_498` `cube-prod_binary64_447`
7×	`pow1_binary64_480` `add-exp-log_binary64_457`
6×	`add-cbrt-cube_binary64_455`
5×	`unswap-sqr_binary64_387`
4×	`add-log-exp_binary64_458` `sqr-pow_binary64_391`
3×	`unpow3_binary64_485` `cube-mult_binary64_449` `pow-unpow_binary64_496` `associate-l_binary64_360`
1×	`pow1/3_binary64_501` `rem-cbrt-cube_binary64_443` `pow-pow_binary64_491` `pow-to-exp_binary64_488` `pow-exp_binary64_487` `rem-cube-cbrt_binary64_442` `pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `*-commutative_binary64_350`

Counts

4 → 85

Calls

4 calls:

17.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)))
15.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3))
14.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))
12.0ms	(pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)

Compiler

Compiled 2536 to 1670 computations (34.1% saved)

series541.0ms (5%)

Error

0.2b

Counts

4 → 48

Calls

4 calls:

197.0ms	(pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)
135.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3)))
57.0ms	(cbrt.f64 (pow.f64 (sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2)) 3))
56.0ms	(sin.f64 (/.f64 (+.f64 eps (+.f64 x x)) 2))

Compiler

Compiled 2668 to 2207 computations (17.3% saved)

simplify102.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5009	2959

prune205.0ms (1.9%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	132	12	144

Error

0.2b

Counts

144 → 12

Compiler

Compiled 3173 to 2144 computations (32.4% saved)

regimes821.0ms (7.5%)

Accuracy

Total 0.3b remaining (60.7%)

Threshold costs 0.3b (60.7%)

Compiler

Compiled 4984 to 3597 computations (27.8% saved)

bsearch85.0ms (0.8%)

Steps

Iters	Range		Point
10	5.363314581432124e-09	29339.173542895947	0.0028201086254281693
6	-0.008932345422473816	-0.0019506233314318347	-0.003094156930413806

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	157	106
1	157	106

end0.0ms (0%)

sample5.0s (45.8%)

Algorithm

1×

intervals

Results

1.3s	2052×	body	2048	valid
1.2s	3912×	body	1024	valid
265.0ms	1293×	body	512	valid
73.0ms	511×	body	256	valid
16.0ms	228×	body	128	valid
5.0ms	4×	body	4096	valid

Compiler

Compiled 1698 to 1221 computations (28.1% saved)

Details

analyze133.0ms (1.2%)

sample115.0ms (1.1%)

simplify10.0ms (0.1%)

prune2.0ms (0%)

localize12.0ms (0.1%)

rewrite53.0ms (0.5%)

series187.0ms (1.7%)

simplify77.0ms (0.7%)

prune66.0ms (0.6%)

localize14.0ms (0.1%)

rewrite162.0ms (1.5%)

series501.0ms (4.6%)

simplify99.0ms (0.9%)

prune154.0ms (1.4%)

localize26.0ms (0.2%)

rewrite177.0ms (1.6%)

series1.7s (15.7%)

simplify153.0ms (1.4%)

prune264.0ms (2.4%)

localize14.0ms (0.1%)

rewrite217.0ms (2%)

series541.0ms (5%)

simplify102.0ms (0.9%)

prune205.0ms (1.9%)

regimes821.0ms (7.5%)

bsearch85.0ms (0.8%)

simplify4.0ms (0%)

end0.0ms (0%)

sample5.0s (45.8%)

Profiling