Details

analyze2.0ms

Algorithm

Search

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

sample96.0ms

Algorithm

intervals

Results

48.0ms	123×	body	1024	valid
28.0ms	39×	body	2048	valid
8.0ms	40×	body	512	valid
2.0ms	41×	body	128	valid
2.0ms	13×	body	256	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	72	11
1	72	11

prune1.0ms

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: 36.3b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.1b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.7b	(sin.f64 (+.f64 x eps))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `sin-sum_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `diff-sin_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

2 → 23

Calls

2 calls:

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

series96.0ms

Counts

2 → 6

Calls

2 calls:

68.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
28.0ms	(sin.f64 (+.f64 x eps))

simplify93.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4896	426
1	4896	426

prune25.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	25	4	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	26	4	30

Merged error: 0.3b

Counts

30 → 4

localize12.0ms

Local error

Found 2 expressions with local error:

0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`add-log-exp_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`

Counts

2 → 26

Calls

2 calls:

6.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series121.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
37.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify68.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4984	659
1	4984	659

prune45.0ms

Filtered

27 candidates to 32 candidates (-18.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	27	5	32
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	28	8	36

Merged error: 0.3b

Counts

36 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
0.5b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
2.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`log-prod_binary64` `exp-prod_binary64`
8×	`pow1_binary64` `log-pow_binary64`
7×	`associate-r_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`add-log-exp_binary64`
3×	`distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 61

Calls

4 calls:

9.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
14.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
9.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series359.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
168.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
96.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
33.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify48.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4990	1478
1	4990	1478

prune77.0ms

Filtered

52 candidates to 73 candidates (-40.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	72	9	81

Merged error: 0.3b

Counts

81 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.8b	(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
0.8b	(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
2.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
2.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

12×	`log-prod_binary64` `log-pow_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`pow1_binary64` `sqrt-pow1_binary64`
6×	`add-exp-log_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
2×	`pow1/2_binary64` `rem-log-exp_binary64`

Counts

4 → 54

Calls

4 calls:

10.0ms	(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
10.0ms	(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series363.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
153.0ms	(log.f64 (sqrt.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
29.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))
30.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify83.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5000	1292

prune89.0ms

Filtered

50 candidates to 66 candidates (-32.0%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	66	9	75

Merged error: 0.3b

Counts

75 → 9

regimes91.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 15.0b

bsearch84.0ms

Steps

Iters	Range		Point
9	8.905256041694157e-13	8.84181087252949e-05	8.388280414749377e-09
10	-3.8556134819774685e-06	-1.3497901026008548e-17	-1.2684541137945322e-08

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	60
1	47	60

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.3s	3489×	body	1024	valid
935.0ms	1238×	body	2048	valid
296.0ms	1398×	body	512	valid
80.0ms	1309×	body	128	valid
73.0ms	563×	body	256	valid
6.0ms	3×	body	4096	valid

Details

analyze2.0ms

sample96.0ms

simplify10.0ms

prune1.0ms

localize8.0ms

rewrite13.0ms

series96.0ms

simplify93.0ms

prune25.0ms

localize12.0ms

rewrite16.0ms

series121.0ms

simplify68.0ms

prune45.0ms

localize16.0ms

rewrite45.0ms

series359.0ms

simplify48.0ms

prune77.0ms

localize20.0ms

rewrite42.0ms

series363.0ms

simplify83.0ms

prune89.0ms

regimes91.0ms

bsearch84.0ms

simplify3.0ms

end0.0ms

sample2.8s

Profiling