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

sample231.0ms

Algorithm

intervals

Results

160.0ms	102×	body	2560	valid
49.0ms	82×	body	1280	valid
7.0ms	38×	body	640	valid
4.0ms	256×	pre	80	true
2.0ms	18×	body	320	valid
1.0ms	14×	body	160	valid
0.0ms	2×	body	80	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	220	8
1	220	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: 59.9b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1.0 (tan.f64 x))
3.4b	(-.f64 (/.f64 1.0 x) (/.f64 1.0 (tan.f64 x)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
20×	`*-un-lft-identity_binary64`
19×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`distribute-lft-out--_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64` `div-inv_binary64`
2×	`pow1_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `flip--_binary64` `frac-sub_binary64` `tan-quot_binary64`

Counts

2 → 49

Calls

2 calls:

7.0ms	(/.f64 1.0 (tan.f64 x))
14.0ms	(-.f64 (/.f64 1.0 x) (/.f64 1.0 (tan.f64 x)))

series51.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(/.f64 1.0 (tan.f64 x))
36.0ms	(-.f64 (/.f64 1.0 x) (/.f64 1.0 (tan.f64 x)))

simplify42.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4931	557
1	4931	557

prune71.0ms

Filtered

45 candidates to 55 candidates (-22.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	1	56

Merged error: 0.3b

Counts

56 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333))
0.0b	(+.f64 (.f64 0.022222222222222227 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))
0.1b	(*.f64 0.0021164021164021135 (pow.f64 x 5))
0.1b	(*.f64 0.022222222222222227 (pow.f64 x 3))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

5.0ms	(+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333))
9.0ms	(+.f64 (.f64 0.022222222222222227 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))
6.0ms	(*.f64 0.0021164021164021135 (pow.f64 x 5))
7.0ms	(*.f64 0.022222222222222227 (pow.f64 x 3))

series51.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333))
7.0ms	(+.f64 (.f64 0.022222222222222227 (pow.f64 x 3)) (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (*.f64 x 0.3333333333333333)))
7.0ms	(*.f64 0.0021164021164021135 (pow.f64 x 5))
6.0ms	(*.f64 0.022222222222222227 (pow.f64 x 3))

simplify67.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4959	877
1	4959	877

prune96.0ms

Filtered

60 candidates to 92 candidates (-53.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	88	4	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	88	5	93

Merged error: 0.2b

Counts

93 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333))) (cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))
0.7b	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
0.7b	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
0.7b	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`flip3-+_binary64` `pow1/3_binary64` `flip-+_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` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 87

Calls

4 calls:

14.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333))) (cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))
5.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
5.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
5.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333))) (cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (*.f64 x 0.3333333333333333))))
72.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
75.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
74.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))

simplify66.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4957	2218
1	4957	2218

prune254.0ms

Filtered

80 candidates to 99 candidates (-23.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	91	13	104

Merged error: 0.1b

Counts

104 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
0.7b	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
0.7b	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
0.7b	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`cbrt-div_binary64` `*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `pow1_binary64` `pow1/3_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`

Counts

4 → 52

Calls

4 calls:

5.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
5.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
5.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
7.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))

series287.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
72.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
72.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))
72.0ms	(cbrt.f64 (+.f64 (.f64 0.0021164021164021135 (pow.f64 x 5)) (.f64 x 0.3333333333333333)))

simplify41.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5155	1372

prune232.0ms

Filtered

60 candidates to 64 candidates (-6.7%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	1	9	10
Picked	0	1	1
Done	0	2	2
Total	62	15	77

Merged error: 0.1b

Counts

77 → 15

regimes85.0ms

Accuracy

0% (0.1b remaining)

Error of 0.3b against oracle of 0.2b 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

sample7.1s

Algorithm

intervals

Results

5.2s	3225×	body	2560	valid
1.3s	2504×	body	1280	valid
235.0ms	1265×	body	640	valid
132.0ms	8000×	pre	80	true
76.0ms	643×	body	320	valid
26.0ms	316×	body	160	valid
2.0ms	47×	body	80	valid

Details

analyze5.0ms

sample231.0ms

simplify13.0ms

prune2.0ms

localize5.0ms

rewrite24.0ms

series51.0ms

simplify42.0ms

prune71.0ms

localize9.0ms

rewrite29.0ms

series51.0ms

simplify67.0ms

prune96.0ms

localize14.0ms

rewrite34.0ms

series302.0ms

simplify66.0ms

prune254.0ms

localize18.0ms

rewrite23.0ms

series287.0ms

simplify41.0ms

prune232.0ms

regimes85.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample7.1s

Profiling