Details

analyze2.0ms

Algorithm

Search

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

sample100.0ms

Algorithm

intervals

Results

53.0ms	107×	body	1280	valid
18.0ms	69×	body	640	valid
15.0ms	16×	body	2560	valid
3.0ms	20×	body	320	valid
2.0ms	32×	body	80	valid
1.0ms	12×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	73	11
1	73	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: 36.7b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

1.6b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.0b	(sin.f64 (+.f64 x eps))

rewrite11.0ms

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:

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

series51.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
16.0ms	(sin.f64 (+.f64 x eps))

simplify101.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	5213	426

prune26.0ms

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: 0.4b

Counts

30 → 4

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.9b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`add-sqr-sqrt_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`distribute-lft-out_binary64` `associate-r_binary64` `associate-l_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-cos-mult_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64` `*-commutative_binary64`

Counts

3 → 41

Calls

3 calls:

6.0ms	(+.f64 x (+.f64 x eps))
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))

series83.0ms

Counts

3 → 9

Calls

3 calls:

15.0ms	(+.f64 x (+.f64 x eps))
47.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
21.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify94.0ms

Algorithm

egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5170	830

prune57.0ms

Filtered

38 candidates to 50 candidates (-31.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	44	6	50
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	45	9	54

Merged error: 0.3b

Counts

54 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.5b	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
0.5b	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
2.9b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
15×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
10×	`unpow-prod-down_binary64` `cube-prod_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-unpow_binary64` `associate-l_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

8.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
2.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series141.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
20.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
61.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
17.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify76.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4835	1942
1	4835	1942

prune80.0ms

Filtered

55 candidates to 97 candidates (-76.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	98	8	106

Merged error: 0.3b

Counts

106 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9))
0.5b	(cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)))
1.1b	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)
2.9b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-prod_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `sqr-pow_binary64`
2×	`pow1/3_binary64`
1×	`pow-to-exp_binary64` `pow-pow_binary64` `pow-exp_binary64`

Counts

4 → 57

Calls

4 calls:

2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9))
2.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)))
2.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series238.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9))
19.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)))
137.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)
19.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify90.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4897	1555
1	4897	1555

prune77.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	69	8	77

Merged error: 0.3b

Counts

77 → 8

regimes71.0ms

Accuracy

98.7% (0.2b remaining)

Error of 0.6b against oracle of 0.4b and baseline of 15.0b

bsearch78.0ms

Steps

Iters	Range		Point
10	1.3822887250355968e-26	2.1021009564248895e-16	2.0837649780091063e-16
8	-1.9460658352402853	-0.0007004325775336613	-0.000711410875641239

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	60
1	47	60

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	3286×	body	1280	valid
589.0ms	605×	body	2560	valid
526.0ms	1849×	body	640	valid
153.0ms	810×	body	320	valid
64.0ms	1103×	body	80	valid
47.0ms	347×	body	160	valid

Details

analyze2.0ms

sample100.0ms

simplify15.0ms

prune1.0ms

localize7.0ms

rewrite11.0ms

series51.0ms

simplify101.0ms

prune26.0ms

localize12.0ms

rewrite20.0ms

series83.0ms

simplify94.0ms

prune57.0ms

localize14.0ms

rewrite23.0ms

series141.0ms

simplify76.0ms

prune80.0ms

localize16.0ms

rewrite16.0ms

series238.0ms

simplify90.0ms

prune77.0ms

regimes71.0ms

bsearch78.0ms

simplify4.0ms

end0.0ms

sample3.1s

Profiling