Details

analyze2.0ms

Algorithm

Search

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

sample95.0ms

Algorithm

intervals

Results

52.0ms	147×	body	1280	valid
14.0ms	64×	body	640	valid
12.0ms	14×	body	2560	valid
3.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	4×	body	80	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune10.0ms

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: 39.1b

Counts

2 → 1

localize12.0ms

Local error

Found 2 expressions with local error:

0.8b	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0b	(cos.f64 (+.f64 x eps))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64_574` `add-sqr-sqrt_binary64_559` `add-log-exp_binary64_539`
2×	`add-cube-cbrt_binary64_545` `pow1_binary64_520` `add-cbrt-cube_binary64_546` `cos-sum_binary64_424` `add-exp-log_binary64_538`
1×	`flip3--_binary64_573` `associate--l-_binary64_631` `distribute-lft-out--_binary64_619` `diff-log_binary64_490` `sub-neg_binary64_578` `flip--_binary64_600` `difference-of-squares_binary64_603` `diff-cos_binary64_441`

Counts

2 → 23

Calls

2 calls:

6.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
4.0ms	(cos.f64 (+.f64 x eps))

series54.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(-.f64 (cos.f64 (+.f64 x eps)) (cos.f64 x))
15.0ms	(cos.f64 (+.f64 x eps))

simplify45.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5087	429

prune158.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	20	9	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	21	9	30

Merged error: 0.6b

Counts

30 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.0b	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
4.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64_574`
11×	`pow1_binary64_520` `add-cbrt-cube_binary64_546` `add-exp-log_binary64_538`
9×	`add-sqr-sqrt_binary64_559` `add-log-exp_binary64_539`
7×	`add-cube-cbrt_binary64_545`
6×	`associate-l_binary64_634`
4×	`cbrt-unprod_binary64_543` `associate-r_binary64_633` `pow-prod-down_binary64_501` `prod-exp_binary64_525`
3×	`distribute-lft-out_binary64_618` `sum-log_binary64_489`
2×	`sin-mult_binary64_445` `*-commutative_binary64_642`
1×	`associate-+r+_binary64_625` `+-commutative_binary64_641` `unswap-sqr_binary64_602` `flip3-+_binary64_572` `flip-+_binary64_599` `associate-*r/_binary64_635`

Counts

4 → 60

Calls

4 calls:

6.0ms	(+.f64 x (+.f64 x eps))
18.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
13.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
7.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series142.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+.f64 x (+.f64 x eps))
56.0ms	(.f64 -2 (.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
46.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
23.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify100.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4886	1363
1	4886	1363

prune360.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	61	11	72
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	66	15	81

Merged error: 0.5b

Counts

81 → 15

localize33.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
0.6b	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
4.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod_binary64_541`
7×	`*-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545` `add-sqr-sqrt_binary64_559`
4×	`pow1_binary64_520` `add-cbrt-cube_binary64_546` `add-exp-log_binary64_538` `add-log-exp_binary64_539`
3×	`pow1/3_binary64_512`

Counts

4 → 40

Calls

4 calls:

2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
2.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
8.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series267.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
82.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
84.0ms	(cbrt.f64 (sin.f64 (/.f64 eps 2)))
22.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify50.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5317	695

prune365.0ms

Filtered

45 candidates to 52 candidates (-15.6%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	50	2	52
Fresh	0	13	13
Picked	0	1	1
Done	0	1	1
Total	50	17	67

Merged error: 0.5b

Counts

67 → 17

localize25.0ms

Local error

Found 4 expressions with local error:

4.0b	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
6.2b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
6.2b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
6.2b	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64_574` `add-cube-cbrt_binary64_545` `pow1_binary64_520` `add-cbrt-cube_binary64_546` `add-sqr-sqrt_binary64_559` `add-exp-log_binary64_538` `add-log-exp_binary64_539`
3×	`pow1/3_binary64_512` `cbrt-div_binary64_542` `cbrt-prod_binary64_541` `sin-mult_binary64_445`

Counts

4 → 37

Calls

4 calls:

11.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
9.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
8.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
8.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
145.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
143.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))
144.0ms	(cbrt.f64 (*.f64 (sin.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))))

simplify107.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5335	1133

prune282.0ms

Filtered

42 candidates to 49 candidates (-16.7%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	48	1	49
Fresh	1	13	14
Picked	0	1	1
Done	0	2	2
Total	49	17	66

Merged error: 0.5b

Counts

66 → 17

regimes384.0ms

Accuracy

97.7% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 15.1b

bsearch87.0ms

Steps

Iters	Range		Point
8	6408568851553929/288230376151711744	1740752582515861/70368744177664	0.027486047656807233
8	-341604615952879/1180591620717411303424	-4328019243294623/19342813113834066795298816	-2.8455796645710814e-07

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	81
1	83	81

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	4569×	body	1280	valid
566.0ms	623×	body	2560	valid
420.0ms	1765×	body	640	valid
112.0ms	685×	body	320	valid
37.0ms	293×	body	160	valid
4.0ms	65×	body	80	valid

Details

analyze2.0ms

sample95.0ms

simplify14.0ms

prune10.0ms

localize12.0ms

rewrite11.0ms

series54.0ms

simplify45.0ms

prune158.0ms

localize19.0ms

rewrite45.0ms

series142.0ms

simplify100.0ms

prune360.0ms

localize33.0ms

rewrite16.0ms

series267.0ms

simplify50.0ms

prune365.0ms

localize25.0ms

rewrite37.0ms

series452.0ms

simplify107.0ms

prune282.0ms

regimes384.0ms

bsearch87.0ms

simplify4.0ms

end0.0ms

sample3.1s

Profiling