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

sample251.0ms

Algorithm

intervals

Results

208.0ms	125×	body	2048	valid
23.0ms	70×	body	1024	valid
4.0ms	33×	body	512	valid
4.0ms	256×	pre	128	true
4.0ms	7×	body	4096	valid
1.0ms	13×	body	256	valid
0.0ms	8×	body	128	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	72	12
1	72	12

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: 60.3b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (tan.f64 x))
3.6b	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

rewrite28.0ms

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`
5×	`add-exp-log_binary64` `div-inv_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `div-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64` `tan-quot_binary64`

Counts

2 → 59

Calls

2 calls:

7.0ms	(/.f64 1 (tan.f64 x))
16.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series236.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(/.f64 1 (tan.f64 x))
144.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

simplify64.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5138	998

prune47.0ms

Filtered

40 candidates to 65 candidates (-62.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	1	66

Merged error: 0.3b

Counts

66 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

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×	`associate-l_binary64`
8×	`unswap-sqr_binary64` `unpow-prod-down_binary64`
7×	`prod-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
4×	`sqr-pow_binary64` `cube-prod_binary64`
3×	`cbrt-unprod_binary64` `*-commutative_binary64`
2×	`pow-to-exp_binary64` `pow-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 85

Calls

4 calls:

6.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5)))
6.0ms	(*.f64 2/945 (pow.f64 x 5))
7.0ms	(*.f64 1/45 (pow.f64 x 3))
4.0ms	(*.f64 x 1/3)

series305.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(+.f64 (.f64 1/45 (pow.f64 x 3)) (.f64 2/945 (pow.f64 x 5)))
72.0ms	(*.f64 2/945 (pow.f64 x 5))
43.0ms	(*.f64 1/45 (pow.f64 x 3))
23.0ms	(*.f64 x 1/3)

simplify115.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	4914	1005
1	4914	1005

prune87.0ms

Filtered

62 candidates to 97 candidates (-56.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	91	6	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	7	98

Merged error: 0.1b

Counts

98 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
0.5b	(cbrt.f64 (*.f64 x 1/3))
0.5b	(cbrt.f64 (*.f64 x 1/3))
0.5b	(cbrt.f64 (*.f64 x 1/3))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`pow1/3_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`cbrt-prod_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
2.0ms	(cbrt.f64 (*.f64 x 1/3))
2.0ms	(cbrt.f64 (*.f64 x 1/3))
2.0ms	(cbrt.f64 (*.f64 x 1/3))

series760.0ms

Counts

4 → 12

Calls

4 calls:

213.0ms	(.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
186.0ms	(cbrt.f64 (*.f64 x 1/3))
168.0ms	(cbrt.f64 (*.f64 x 1/3))
193.0ms	(cbrt.f64 (*.f64 x 1/3))

simplify65.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5095	556

prune96.0ms

Filtered

48 candidates to 70 candidates (-45.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	63	7	70
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	63	14	77

Merged error: 0.1b

Counts

77 → 14

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 x 1/3)) (*.f64 (cbrt.f64 x) (cbrt.f64 1/3)))
0.5b	(cbrt.f64 (*.f64 x 1/3))
0.5b	(cbrt.f64 (*.f64 x 1/3))
0.7b	(cbrt.f64 x)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1/3_binary64`
9×	`pow1_binary64` `add-exp-log_binary64`
7×	`pow-prod-down_binary64` `cbrt-prod_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
5×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64`
3×	`cbrt-unprod_binary64` `prod-exp_binary64`
1×	`swap-sqr_binary64` `associate-r_binary64` `pow-prod-up_binary64` `pow-sqr_binary64` `*-commutative_binary64`

Counts

4 → 52

Calls

4 calls:

7.0ms	(.f64 (cbrt.f64 (.f64 x 1/3)) (*.f64 (cbrt.f64 x) (cbrt.f64 1/3)))
2.0ms	(cbrt.f64 (*.f64 x 1/3))
2.0ms	(cbrt.f64 (*.f64 x 1/3))
1.0ms	(cbrt.f64 x)

series730.0ms

Counts

4 → 12

Calls

4 calls:

237.0ms	(.f64 (cbrt.f64 (.f64 x 1/3)) (*.f64 (cbrt.f64 x) (cbrt.f64 1/3)))
169.0ms	(cbrt.f64 (*.f64 x 1/3))
177.0ms	(cbrt.f64 (*.f64 x 1/3))
148.0ms	(cbrt.f64 x)

simplify84.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4899	570
1	4899	570

prune81.0ms

Filtered

48 candidates to 64 candidates (-33.3%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	62	2	64
Fresh	1	10	11
Picked	0	1	1
Done	0	2	2
Total	63	15	78

Merged error: 0.1b

Counts

78 → 15

regimes41.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	22
1	19	22

end0.0ms

sample6.8s

Algorithm

intervals

Results

5.5s	4043×	body	2048	valid
653.0ms	1952×	body	1024	valid
138.0ms	1020×	body	512	valid
129.0ms	225×	body	4096	valid
124.0ms	8000×	pre	128	true
43.0ms	502×	body	256	valid
11.0ms	258×	body	128	valid

Details

analyze5.0ms

sample251.0ms

simplify10.0ms

prune1.0ms

localize5.0ms

rewrite28.0ms

series236.0ms

simplify64.0ms

prune47.0ms

localize10.0ms

rewrite28.0ms

series305.0ms

simplify115.0ms

prune87.0ms

localize14.0ms

rewrite17.0ms

series760.0ms

simplify65.0ms

prune96.0ms

localize17.0ms

rewrite17.0ms

series730.0ms

simplify84.0ms

prune81.0ms

regimes41.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.8s

Profiling