Details

analyze17.2s

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

sample130.0ms

Algorithm

intervals

Results

65.0ms	126×	body	1280	valid
18.0ms	256×	pre	80	true
15.0ms	62×	body	640	valid
4.0ms	23×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	4×	body	160	valid

simplify563.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	186	14
1	186	14

prune10.0ms

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: 13.6b

Counts

2 → 1

localize17.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

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))

series430.0ms

Counts

3 → 9

Calls

3 calls:

152.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
187.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
90.0ms	(tan.f64 (+.f64 y z))

simplify84.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5105	890

prune280.0ms

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

localize22.0ms

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))
0.1b	(+.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))

rewrite40.0ms

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))
14.0ms	(+.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))

series1.4s

Counts

4 → 12

Calls

4 calls:

106.0ms	(+.f64 (tan.f64 y) (tan.f64 z))
577.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
579.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
111.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify83.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5290	2076

prune426.0ms

Filtered

64 candidates to 77 candidates (-20.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	68	9	77
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	75	10	85

Merged error: 0.0b

Counts

85 → 10

localize41.0ms

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 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 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))
0.2b	(*.f64 (tan.f64 y) (sin.f64 z))

rewrite52.0ms

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))
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 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))
5.0ms	(*.f64 (tan.f64 y) (sin.f64 z))

series1.3s

Counts

4 → 12

Calls

4 calls:

580.0ms	(-.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))
567.0ms	(+.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)))
106.0ms	(/.f64 (*.f64 (tan.f64 y) (sin.f64 z)) (cos.f64 z))
74.0ms	(*.f64 (tan.f64 y) (sin.f64 z))

simplify75.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5038	2412

prune423.0ms

Filtered

66 candidates to 84 candidates (-27.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	84	10	94

Merged error: 0.0b

Counts

94 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite57.0ms

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` `associate-*r/_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-exp_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:

23.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (sin.f64 y) (tan.f64 z)) (cos.f64 y)))) (tan.f64 a))
19.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (sin.f64 y) (tan.f64 z)) (cos.f64 y)))) (tan.f64 a)))
7.0ms	(/.f64 (*.f64 (sin.f64 y) (tan.f64 z)) (cos.f64 y))
5.0ms	(*.f64 (sin.f64 y) (tan.f64 z))

series1.4s

Counts

4 → 12

Calls

4 calls:

580.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (sin.f64 y) (tan.f64 z)) (cos.f64 y)))) (tan.f64 a))
573.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (/.f64 (*.f64 (sin.f64 y) (tan.f64 z)) (cos.f64 y)))) (tan.f64 a)))
122.0ms	(/.f64 (*.f64 (sin.f64 y) (tan.f64 z)) (cos.f64 y))
81.0ms	(*.f64 (sin.f64 y) (tan.f64 z))

simplify69.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5108	2412

prune339.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	84	10	94

Merged error: 0.0b

Counts

94 → 10

regimes1.3s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	34
1	62	34

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	3908×	body	1280	valid
550.0ms	8000×	pre	80	true
498.0ms	1954×	body	640	valid
129.0ms	718×	body	320	valid
66.0ms	1160×	body	80	valid
31.0ms	260×	body	160	valid

Details

analyze17.2s

sample130.0ms

simplify563.0ms

prune10.0ms

localize17.0ms

rewrite22.0ms

series430.0ms

simplify84.0ms

prune280.0ms

localize22.0ms

rewrite40.0ms

series1.4s

simplify83.0ms

prune426.0ms

localize41.0ms

rewrite52.0ms

series1.3s

simplify75.0ms

prune423.0ms

localize28.0ms

rewrite57.0ms

series1.4s

simplify69.0ms

prune339.0ms

regimes1.3s

bsearch0.0ms

simplify3.0ms

end0.0ms

sample3.3s

Profiling