Details

analyze17.3s

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

sample129.0ms

Algorithm

intervals

Results

76.0ms	137×	body	1280	valid
18.0ms	256×	pre	80	true
13.0ms	55×	body	640	valid
3.0ms	16×	body	320	valid
2.0ms	38×	body	80	valid
1.0ms	10×	body	160	valid

simplify424.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	185	9
1	185	9

prune4.0ms

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: 11.8b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
0.2b	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
2.9b	(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:

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

series118.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(+.f64 x (-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a)))
43.0ms	(-.f64 (tan.f64 (+.f64 y z)) (tan.f64 a))
29.0ms	(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

prune53.0ms

Filtered

39 candidates to 49 candidates (-25.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	43	6	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	6	50

Merged error: 0.1b

Counts

50 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
11×	`add-log-exp_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`tan-quot_binary64`
6×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/l/_binary64` `associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `associate-+r-_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `frac-add_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 88

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
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)))
16.0ms	(-.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))

series366.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))))
147.0ms	(+.f64 x (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)))
132.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
23.0ms	(*.f64 (tan.f64 y) (tan.f64 z))

simplify55.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5084	1882

prune86.0ms

Filtered

75 candidates to 100 candidates (-33.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	93	7	100
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	97	9	106

Merged error: 0.1b

Counts

106 → 9

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) x)
0.2b	(-.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))
2.3b	(exp.f64 (+.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) x))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
17×	`add-log-exp_binary64`
14×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`tan-quot_binary64` `exp-prod_binary64`
4×	`distribute-lft-out_binary64` `sum-log_binary64`
3×	`diff-log_binary64` `associate-r_binary64` `associate-l_binary64` `rem-exp-log_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `associate-+l-_binary64` `difference-of-squares_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `associate-+l+_binary64` `exp-diff_binary64` `unswap-sqr_binary64` `exp-sum_binary64` `prod-exp_binary64` `times-frac_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 69

Calls

4 calls:

17.0ms	(+.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) x)
13.0ms	(-.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))
18.0ms	(exp.f64 (+.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) x))

series567.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(+.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) x)
132.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
23.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
181.0ms	(exp.f64 (+.f64 (-.f64 (/.f64 (+.f64 (tan.f64 y) (tan.f64 z)) (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a)) x))

simplify46.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5267	1464

prune73.0ms

Filtered

59 candidates to 81 candidates (-37.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	80	1	81
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	80	10	90

Merged error: 0.0b

Counts

90 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

123×	`times-frac_binary64`
104×	`*-un-lft-identity_binary64`
83×	`add-sqr-sqrt_binary64`
67×	`add-cube-cbrt_binary64`
23×	`associate-/r*_binary64`
19×	`add-exp-log_binary64`
16×	`distribute-lft-out_binary64` `associate-/r/_binary64`
15×	`tan-quot_binary64`
13×	`add-cbrt-cube_binary64`
8×	`div-exp_binary64`
7×	`pow1_binary64` `div-inv_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64`
5×	`flip3-+_binary64` `frac-add_binary64` `difference-of-squares_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `div-sub_binary64` `inv-pow_binary64` `prod-exp_binary64` `pow-flip_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 177

Calls

4 calls:

31.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (+.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
6.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
12.0ms	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (+.f64 (tan.f64 y) (tan.f64 z))))
9.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (+.f64 (tan.f64 y) (tan.f64 z)))

series315.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(-.f64 (/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (+.f64 (tan.f64 y) (tan.f64 z)))) (tan.f64 a))
23.0ms	(*.f64 (tan.f64 y) (tan.f64 z))
61.0ms	(/.f64 1 (/.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (+.f64 (tan.f64 y) (tan.f64 z))))
67.0ms	(/.f64 (-.f64 1 (*.f64 (tan.f64 y) (tan.f64 z))) (+.f64 (tan.f64 y) (tan.f64 z)))

simplify60.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4995	3966
1	4995	3966

prune86.0ms

Filtered

120 candidates to 189 candidates (-57.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	189	10	199

Merged error: 0.0b

Counts

199 → 10

regimes588.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	53	20
1	53	20

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.7s	3842×	body	1280	valid
543.0ms	8000×	pre	80	true
493.0ms	1969×	body	640	valid
111.0ms	665×	body	320	valid
65.0ms	1238×	body	80	valid
37.0ms	286×	body	160	valid

Details

analyze17.3s

sample129.0ms

simplify424.0ms

prune4.0ms

localize12.0ms

rewrite22.0ms

series118.0ms

simplify64.0ms

prune53.0ms

localize15.0ms

rewrite48.0ms

series366.0ms

simplify55.0ms

prune86.0ms

localize18.0ms

rewrite55.0ms

series567.0ms

simplify46.0ms

prune73.0ms

localize15.0ms

rewrite65.0ms

series315.0ms

simplify60.0ms

prune86.0ms

regimes588.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample3.3s

Profiling