Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	49.7%	50.3%	0
0%	49.7%	50.3%	1
0%	49.7%	50.3%	2
24.8%	24.8%	50.3%	3
37.3%	12.4%	50.3%	4
43.5%	6.2%	50.3%	5
46.6%	3.1%	50.3%	6
48.1%	1.6%	50.3%	7
48.9%	0.8%	50.3%	8
49.3%	0.4%	50.3%	9
49.5%	0.2%	50.3%	10
49.6%	0.1%	50.3%	11
49.6%	0%	50.3%	12
49.7%	0%	50.3%	13
49.7%	0%	50.3%	14

sample216.0ms

Algorithm

intervals

Results

151.0ms	108×	body	2560	valid
44.0ms	83×	body	1280	valid
7.0ms	34×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	17×	body	320	valid
1.0ms	12×	body	160	valid
0.0ms	2×	body	80	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	8
1	71	8

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: 59.5b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (tan.f64 x))
2.9b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
27×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
9×	`difference-of-squares_binary64`
7×	`distribute-lft-out--_binary64`
6×	`add-exp-log_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`div-exp_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `tan-quot_binary64`

Counts

2 → 60

Calls

2 calls:

7.0ms	(/.f64 1 (tan.f64 x))
14.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series29.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(/.f64 1 (tan.f64 x))
18.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4848	639
1	4848	639

prune63.0ms

Filtered

40 candidates to 66 candidates (-65.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	1	67

Merged error: 0.3b

Counts

67 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 1/45 (pow.f64 x 3)) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 x 1/3)))
0.1b	(*.f64 1/45 (pow.f64 x 3))
0.1b	(*.f64 2/945 (pow.f64 x 5))
0.3b	(*.f64 x 1/3)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
22×	`associate-r_binary64`
16×	`add-exp-log_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `associate-l_binary64`
8×	`unswap-sqr_binary64` `unpow-prod-down_binary64`
7×	`prod-exp_binary64`
6×	`pow1_binary64`
4×	`sqr-pow_binary64` `cube-prod_binary64`
3×	`cbrt-unprod_binary64` `sum-log_binary64` `*-commutative_binary64`
2×	`pow-to-exp_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-+r+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 87

Calls

4 calls:

9.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 x 1/3)))
8.0ms	(*.f64 1/45 (pow.f64 x 3))
5.0ms	(*.f64 2/945 (pow.f64 x 5))
4.0ms	(*.f64 x 1/3)

series18.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 x 1/3)))
4.0ms	(*.f64 1/45 (pow.f64 x 3))
5.0ms	(*.f64 2/945 (pow.f64 x 5))
2.0ms	(*.f64 x 1/3)

simplify52.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5108	791

prune109.0ms

Filtered

64 candidates to 99 candidates (-54.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	92	7	99
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	92	8	100

Merged error: 0.2b

Counts

100 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/45 (pow.f64 x 3))
0.1b	(*.f64 2/945 (pow.f64 x 5))
0.4b	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
0.4b	(*.f64 x (sqrt.f64 1/3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
31×	`associate-r_binary64`
21×	`add-exp-log_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
15×	`add-cbrt-cube_binary64`
11×	`pow1_binary64`
10×	`associate-l_binary64` `prod-exp_binary64`
9×	`unswap-sqr_binary64`
8×	`unpow-prod-down_binary64`
7×	`sqrt-prod_binary64`
6×	`cbrt-unprod_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `sqr-pow_binary64` `cube-prod_binary64` `*-commutative_binary64`
2×	`pow-to-exp_binary64` `pow-exp_binary64`
1×	`unpow3_binary64` `cube-mult_binary64`

Counts

4 → 99

Calls

4 calls:

7.0ms	(*.f64 1/45 (pow.f64 x 3))
6.0ms	(*.f64 2/945 (pow.f64 x 5))
7.0ms	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
5.0ms	(*.f64 x (sqrt.f64 1/3))

series24.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(*.f64 1/45 (pow.f64 x 3))
5.0ms	(*.f64 2/945 (pow.f64 x 5))
10.0ms	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))
5.0ms	(*.f64 x (sqrt.f64 1/3))

simplify38.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5155	631

prune122.0ms

Filtered

62 candidates to 111 candidates (-79.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	107	12	119

Merged error: 0.1b

Counts

119 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/45 (pow.f64 x 3))
0.1b	(*.f64 2/945 (pow.f64 x 5))
0.2b	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
0.4b	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

38×	`associate-r_binary64`
37×	`add-sqr-sqrt_binary64`
29×	`add-exp-log_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`unpow-prod-down_binary64` `prod-exp_binary64`
15×	`add-cbrt-cube_binary64`
13×	`sqrt-prod_binary64`
11×	`unswap-sqr_binary64`
10×	`associate-l_binary64`
6×	`pow1_binary64` `cbrt-unprod_binary64` `sqr-pow_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `cube-prod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`pow-prod-down_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 110

Calls

4 calls:

6.0ms	(*.f64 1/45 (pow.f64 x 3))
6.0ms	(*.f64 2/945 (pow.f64 x 5))
9.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
7.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

series32.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(*.f64 1/45 (pow.f64 x 3))
5.0ms	(*.f64 2/945 (pow.f64 x 5))
8.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
15.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

simplify65.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4869	792
1	4869	792

prune121.0ms

Filtered

70 candidates to 122 candidates (-74.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	5	5	10
Picked	1	0	1
Done	0	1	1
Total	125	9	134

Merged error: 0.0b

Counts

134 → 9

regimes46.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	15
1	18	15

end0.0ms

sample7.0s

Algorithm

intervals

Results

5.0s	3163×	body	2560	valid
1.3s	2542×	body	1280	valid
231.0ms	1245×	body	640	valid
135.0ms	8000×	pre	80	true
76.0ms	672×	body	320	valid
27.0ms	334×	body	160	valid
2.0ms	44×	body	80	valid

Details

analyze5.0ms

sample216.0ms

simplify7.0ms

prune2.0ms

localize5.0ms

rewrite24.0ms

series29.0ms

simplify62.0ms

prune63.0ms

localize9.0ms

rewrite29.0ms

series18.0ms

simplify52.0ms

prune109.0ms

localize12.0ms

rewrite27.0ms

series24.0ms

simplify38.0ms

prune122.0ms

localize16.0ms

rewrite33.0ms

series32.0ms

simplify65.0ms

prune121.0ms

regimes46.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample7.0s

Profiling