Details

analyze6.0ms

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

sample217.0ms

Algorithm

intervals

Results

179.0ms	130×	body	2048	valid
18.0ms	60×	body	1024	valid
4.0ms	33×	body	512	valid
4.0ms	256×	pre	128	true
2.0ms	4×	body	4096	valid
2.0ms	23×	body	256	valid
0.0ms	6×	body	128	valid

simplify11.0ms

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: 60.2b

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)))

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`
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:

4.0ms	(/.f64 1 (tan.f64 x))
16.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

series254.0ms

Counts

2 → 6

Calls

2 calls:

92.0ms	(/.f64 1 (tan.f64 x))
162.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (tan.f64 x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5138	998

prune50.0ms

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x 1/3) (+.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)

rewrite32.0ms

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 x 1/3) (+.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)

series197.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(+.f64 (.f64 x 1/3) (+.f64 (.f64 1/45 (pow.f64 x 3)) (*.f64 2/945 (pow.f64 x 5))))
71.0ms	(*.f64 2/945 (pow.f64 x 5))
45.0ms	(*.f64 1/45 (pow.f64 x 3))
23.0ms	(*.f64 x 1/3)

simplify63.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5023	1182

prune90.0ms

Filtered

63 candidates to 99 candidates (-57.1%)

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: 0.1b

Counts

100 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series616.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
142.0ms	(cbrt.f64 x)
153.0ms	(cbrt.f64 x)
145.0ms	(cbrt.f64 x)

simplify60.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4935	588
1	4935	588

prune104.0ms

Filtered

65 candidates to 85 candidates (-30.8%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	79	14	93

Merged error: 0.1b

Counts

93 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
0.6b	(cbrt.f64 (*.f64 x 1/3))
0.6b	(cbrt.f64 (*.f64 x 1/3))
0.6b	(cbrt.f64 (*.f64 x 1/3))

rewrite18.0ms

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))

series787.0ms

Counts

4 → 12

Calls

4 calls:

240.0ms	(.f64 (cbrt.f64 (.f64 x 1/3)) (cbrt.f64 (*.f64 x 1/3)))
186.0ms	(cbrt.f64 (*.f64 x 1/3))
171.0ms	(cbrt.f64 (*.f64 x 1/3))
190.0ms	(cbrt.f64 (*.f64 x 1/3))

simplify66.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5095	556

prune78.0ms

Filtered

48 candidates to 70 candidates (-45.8%)

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	0	11	11
Picked	0	1	1
Done	0	2	2
Total	66	18	84

Merged error: 0.0b

Counts

84 → 18

regimes48.0ms

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

sample6.7s

Algorithm

intervals

Results

5.5s	4035×	body	2048	valid
665.0ms	1998×	body	1024	valid
137.0ms	1046×	body	512	valid
128.0ms	8000×	pre	128	true
124.0ms	208×	body	4096	valid
39.0ms	477×	body	256	valid
10.0ms	236×	body	128	valid

Details

analyze6.0ms

sample217.0ms

simplify11.0ms

prune1.0ms

localize5.0ms

rewrite24.0ms

series254.0ms

simplify66.0ms

prune50.0ms

localize11.0ms

rewrite32.0ms

series197.0ms

simplify63.0ms

prune90.0ms

localize14.0ms

rewrite16.0ms

series616.0ms

simplify60.0ms

prune104.0ms

localize15.0ms

rewrite18.0ms

series787.0ms

simplify66.0ms

prune78.0ms

regimes48.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample6.7s

Profiling