Details

analyze16.8s

Algorithm

Search

True	Other	False	Iter
0%	0.2%	99.8%	0
0%	0.2%	99.8%	1
0%	0.2%	99.8%	2
0%	0.2%	99.8%	3
0%	0.2%	99.8%	4
0%	0.2%	99.8%	5
0%	0.2%	99.8%	6
0%	0.2%	99.8%	7
0%	0.2%	99.8%	8
0%	0.2%	99.8%	9
0%	0.2%	99.8%	10
0%	0.2%	99.8%	11
0%	0.2%	99.8%	12
0%	0.2%	99.8%	13
0%	0.2%	99.8%	14

sample119.0ms

Algorithm

intervals

Results

50.0ms	109×	body	1280	valid
28.0ms	72×	body	640	valid
18.0ms	256×	pre	80	true
4.0ms	24×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	10×	body	160	valid

simplify405.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	185	9
1	185	9

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: 11.6b

Counts

2 → 1

localize23.0ms

Local error

Found 3 expressions with local error:

0.1b	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
0.2b	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
3.5b	(tan.f64 (+.f64 y z))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`tan-quot_binary64`
3×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`tan-sum_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `distribute-lft-out--_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `flip3--_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `associate-+r+_binary64`

Counts

3 → 40

Calls

3 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
6.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
6.0ms	(tan.f64 (+.f64 y z))

series123.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
53.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
30.0ms	(tan.f64 (+.f64 y z))

simplify64.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4910	561
1	4910	561

prune81.0ms

Filtered

39 candidates to 49 candidates (-25.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	41	8	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	8	50

Merged error: 0.1b

Counts

50 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 y) (tan.f64 z))
0.1b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
0.2b	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
0.2b	(*.f64 (tan.f64 y) (tan.f64 z))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64`
13×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`tan-quot_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`distribute-lft-out_binary64` `associate-r_binary64` `associate-l_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-+r-_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `times-frac_binary64` `flip--_binary64` `associate-+r+_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 65

Calls

4 calls:

5.0ms	(+.f64 (tan.f64 y) (tan.f64 z))
13.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
13.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

series385.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+.f64 (tan.f64 y) (tan.f64 z))
148.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
183.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
28.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify35.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4951	1271
1	4951	1271

prune116.0ms

Filtered

58 candidates to 77 candidates (-32.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	70	7	77
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 0.0b

Counts

85 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z)))) (tan.f64 a))
0.1b	(/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))
0.2b	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z)))) (tan.f64 a)))
0.2b	(*.f64 (tan.f64 y) (sin.f64 z))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
11×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64`
4×	`times-frac_binary64`
3×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `tan-quot_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/l/_binary64` `associate-+r-_binary64` `flip3--_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `associate-+r+_binary64` `frac-sub_binary64` `-commutative_binary64`

Counts

4 → 72

Calls

4 calls:

19.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z)))) (tan.f64 a))
8.0ms	(/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))
19.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z)))) (tan.f64 a)))
6.0ms	(*.f64 (tan.f64 y) (sin.f64 z))

series353.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z)))) (tan.f64 a))
28.0ms	(/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))
158.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z)))) (tan.f64 a)))
18.0ms	(*.f64 (tan.f64 y) (sin.f64 z))

simplify52.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4938	1475
1	4938	1475

prune105.0ms

Filtered

63 candidates to 84 candidates (-33.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	85	9	94

Merged error: 0.0b

Counts

94 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.f64 x (/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a))))
0.2b	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))
0.2b	(*.f64 (tan.f64 y) (tan.f64 z))
0.2b	(*.f64 (tan.f64 y) (tan.f64 z))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

16×	`associate-*l/_binary64`
14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64` `tan-quot_binary64`
10×	`add-cube-cbrt_binary64`
8×	`associate-/l/_binary64` `pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64` `frac-sub_binary64`
5×	`flip3--_binary64` `flip--_binary64`
3×	`flip3-+_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64` `times-frac_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `frac-add_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-sub_binary64` `div-exp_binary64` `frac-times_binary64` `-commutative_binary64`
1×	`associate-/r*_binary64` `associate-+r-_binary64` `distribute-lft-out_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 87

Calls

4 calls:

13.0ms	(+.f64 x (/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a))))
16.0ms	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

series564.0ms

Counts

4 → 12

Calls

4 calls:

330.0ms	(+.f64 x (/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a))))
182.0ms	(/.f64 (-.f64 (.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (cos.f64 a)) (.f64 (-.f64 1 (.f64 (tan.f64 y) (tan.f64 z))) (sin.f64 a))) (.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (cos.f64 a)))
26.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
26.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify48.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5926	1926

prune92.0ms

Filtered

77 candidates to 99 candidates (-28.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	99	9	108

Merged error: 0.0b

Counts

108 → 9

regimes961.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify8.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	301	32
1	301	32

end0.0ms

sample3.2s

Algorithm

intervals

Results

1.7s	3839×	body	1280	valid
539.0ms	8000×	pre	80	true
493.0ms	2020×	body	640	valid
115.0ms	695×	body	320	valid
64.0ms	1173×	body	80	valid
31.0ms	273×	body	160	valid

Details

analyze16.8s

sample119.0ms

simplify405.0ms

prune5.0ms

localize23.0ms

rewrite21.0ms

series123.0ms

simplify64.0ms

prune81.0ms

localize15.0ms

rewrite38.0ms

series385.0ms

simplify35.0ms

prune116.0ms

localize20.0ms

rewrite54.0ms

series353.0ms

simplify52.0ms

prune105.0ms

localize20.0ms

rewrite42.0ms

series564.0ms

simplify48.0ms

prune92.0ms

regimes961.0ms

bsearch0.0ms

simplify8.0ms

end0.0ms

sample3.2s

Profiling