Details

analyze2.0ms

Algorithm

Search

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

sample98.0ms

Algorithm

intervals

Results

49.0ms	110×	body	1280	valid
20.0ms	53×	body	640	valid
14.0ms	15×	body	2560	valid
4.0ms	22×	body	320	valid
2.0ms	42×	body	80	valid
2.0ms	14×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune2.0ms

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: 32.9b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

1.2b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
2.8b	(sin.f64 (+.f64 x eps))

rewrite12.0ms

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))
5.0ms	(sin.f64 (+.f64 x eps))

series14.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

simplify54.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5348	268

prune28.0ms

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 4 expressions with local error:

0.0b	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
0.0b	(+.f64 x (+.f64 x eps))
0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
2.8b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series35.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
4.0ms	(+.f64 x (+.f64 x eps))
11.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify53.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5222	886

prune63.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	68	8	76

Merged error: 0.2b

Counts

76 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
0.4b	(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)
2.8b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite25.0ms

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:

9.0ms	(*.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))
3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series40.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)))
8.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3))
14.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 3)
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify42.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4924	1255
1	4924	1255

prune67.0ms

Filtered

58 candidates to 97 candidates (-67.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	96	9	105

Merged error: 0.2b

Counts

105 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)))
0.5b	(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)
2.8b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite17.0ms

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:

3.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)))
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9))
3.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series57.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)))
15.0ms	(cbrt.f64 (pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9))
28.0ms	(pow.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) 9)
9.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify38.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5086	992

prune59.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	67	2	69
Fresh	1	5	6
Picked	1	0	1
Done	1	1	2
Total	70	8	78

Merged error: 0.2b

Counts

78 → 8

regimes116.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.4b against oracle of 0.4b and baseline of 15.4b

bsearch88.0ms

Steps

Iters	Range		Point
9	1.5014043123823452e-12	7.000548315219014e-07	1.4156913723501369e-08
11	-6428.5598610616225	-1.7374184253756152e-16	-1.1034653589771911e-08

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	51
1	47	51

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	3332×	body	1280	valid
611.0ms	629×	body	2560	valid
495.0ms	1818×	body	640	valid
140.0ms	779×	body	320	valid
65.0ms	1109×	body	80	valid
42.0ms	333×	body	160	valid

Details

analyze2.0ms

sample98.0ms

simplify8.0ms

prune2.0ms

localize7.0ms

rewrite12.0ms

series14.0ms

simplify54.0ms

prune28.0ms

localize12.0ms

rewrite31.0ms

series35.0ms

simplify53.0ms

prune63.0ms

localize15.0ms

rewrite25.0ms

series40.0ms

simplify42.0ms

prune67.0ms

localize16.0ms

rewrite17.0ms

series57.0ms

simplify38.0ms

prune59.0ms

regimes116.0ms

bsearch88.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling