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

46.0ms	103×	body	1280	valid
26.0ms	75×	body	640	valid
12.0ms	12×	body	2560	valid
4.0ms	24×	body	320	valid
2.0ms	15×	body	160	valid
2.0ms	27×	body	80	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune3.0ms

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: 35.4b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.6b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.7b	(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))

series15.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
6.0ms	(sin.f64 (+.f64 x eps))

simplify51.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5348	268

prune39.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	3	30

Merged error: 0.4b

Counts

30 → 3

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)))
3.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite29.0ms

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)))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series42.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(.f64 2 (.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
5.0ms	(+.f64 x (+.f64 x eps))
15.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
7.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify52.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5222	886

prune91.0ms

Filtered

53 candidates to 72 candidates (-35.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	67	8	75

Merged error: 0.4b

Counts

75 → 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)))))
0.4b	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
3.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite40.0ms

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:

8.0ms	(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))

series38.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
15.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))))
6.0ms	(log.f64 (exp.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify51.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5064	940

prune89.0ms

Filtered

54 candidates to 73 candidates (-35.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	73	8	81

Merged error: 0.4b

Counts

81 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2)))
0.4b	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) (sqrt.f64 2))
0.5b	(.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) (sqrt.f64 2)))
3.5b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`pow-prod-down_binary64` `-un-lft-identity_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `prod-exp_binary64`
6×	`sqrt-prod_binary64`
4×	`add-log-exp_binary64`
3×	`*-commutative_binary64`
1×	`unswap-sqr_binary64`

Counts

4 → 70

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2)))
8.0ms	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) (sqrt.f64 2))
11.0ms	(.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) (sqrt.f64 2)))
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series74.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2)))
25.0ms	(.f64 (.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) (sqrt.f64 2))
26.0ms	(.f64 (sqrt.f64 2) (.f64 (*.f64 (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)) (sin.f64 (/.f64 eps 2))) (sqrt.f64 2)))
6.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify63.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4975	1219
1	4975	1219

prune78.0ms

Filtered

56 candidates to 82 candidates (-46.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	82	8	90

Merged error: 0.4b

Counts

90 → 8

regimes150.0ms

Accuracy

99.4% (0.1b remaining)

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

bsearch69.0ms

Steps

Iters	Range		Point
9	1.9050947580688215e-15	2.086968805494545e-06	7.686797686493851e-09
9	-5818.371851083311	-0.0028689388283919684	-0.0029089008421326404

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

1.6s	3344×	body	1280	valid
590.0ms	611×	body	2560	valid
524.0ms	1896×	body	640	valid
134.0ms	728×	body	320	valid
78.0ms	1088×	body	80	valid
54.0ms	333×	body	160	valid

Details

analyze2.0ms

sample100.0ms

simplify8.0ms

prune3.0ms

localize8.0ms

rewrite12.0ms

series15.0ms

simplify51.0ms

prune39.0ms

localize12.0ms

rewrite29.0ms

series42.0ms

simplify52.0ms

prune91.0ms

localize16.0ms

rewrite40.0ms

series38.0ms

simplify51.0ms

prune89.0ms

localize17.0ms

rewrite35.0ms

series74.0ms

simplify63.0ms

prune78.0ms

regimes150.0ms

bsearch69.0ms

simplify2.0ms

end0.0ms

sample3.1s

Profiling