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

sample245.0ms

Algorithm

intervals

Results

180.0ms	97×	body	2560	valid
43.0ms	81×	body	1280	valid
6.0ms	35×	body	640	valid
4.0ms	256×	pre	80	true
3.0ms	28×	body	320	valid
1.0ms	15×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	73	12
1	73	12

prune5.0ms

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: 59.7b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (tan.f64 x))
4.0b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite21.0ms

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:

4.0ms	(/.f64 1 (tan.f64 x))
15.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series141.0ms

Counts

2 → 6

Calls

2 calls:

52.0ms	(/.f64 1 (tan.f64 x))
89.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

simplify81.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5048	1005

prune47.0ms

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

localize10.0ms

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)

rewrite26.0ms

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)))
6.0ms	(*.f64 1/45 (pow.f64 x 3))
5.0ms	(*.f64 2/945 (pow.f64 x 5))
4.0ms	(*.f64 x 1/3)

series99.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (+.f64 (.f64 2/945 (pow.f64 x 5)) (*.f64 x 1/3)))
23.0ms	(*.f64 1/45 (pow.f64 x 3))
32.0ms	(*.f64 2/945 (pow.f64 x 5))
13.0ms	(*.f64 x 1/3)

simplify81.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5060	1176

prune93.0ms

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

localize14.0ms

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 x (sqrt.f64 1/3))
0.4b	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))

rewrite26.0ms

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:

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

series121.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(*.f64 1/45 (pow.f64 x 3))
31.0ms	(*.f64 2/945 (pow.f64 x 5))
23.0ms	(*.f64 x (sqrt.f64 1/3))
40.0ms	(.f64 (.f64 x (sqrt.f64 1/3)) (sqrt.f64 1/3))

simplify65.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5126	952

prune107.0ms

Filtered

62 candidates to 111 candidates (-79.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	107	4	111
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	109	10	119

Merged error: 0.1b

Counts

119 → 10

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))

rewrite31.0ms

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))
5.0ms	(*.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))

series179.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(*.f64 1/45 (pow.f64 x 3))
32.0ms	(*.f64 2/945 (pow.f64 x 5))
42.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 1/3) 3/2)) (sqrt.f64 (sqrt.f64 1/3)))
81.0ms	(*.f64 x (pow.f64 (sqrt.f64 1/3) 3/2))

simplify96.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4886	1210
1	4886	1210

prune120.0ms

Filtered

70 candidates to 122 candidates (-74.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	125	7	132

Merged error: 0.0b

Counts

132 → 7

regimes21.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	22
1	19	22

end0.0ms

sample7.3s

Algorithm

intervals

Results

5.3s	3208×	body	2560	valid
1.3s	2535×	body	1280	valid
238.0ms	1252×	body	640	valid
129.0ms	8000×	pre	80	true
79.0ms	651×	body	320	valid
26.0ms	308×	body	160	valid
2.0ms	46×	body	80	valid

Details

analyze5.0ms

sample245.0ms

simplify15.0ms

prune5.0ms

localize5.0ms

rewrite21.0ms

series141.0ms

simplify81.0ms

prune47.0ms

localize10.0ms

rewrite26.0ms

series99.0ms

simplify81.0ms

prune93.0ms

localize14.0ms

rewrite26.0ms

series121.0ms

simplify65.0ms

prune107.0ms

localize16.0ms

rewrite31.0ms

series179.0ms

simplify96.0ms

prune120.0ms

regimes21.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample7.3s

Profiling