Details

analyze721.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
50%	50%	0%	5
50%	50%	0%	6
50%	50%	0%	7
50%	50%	0%	8
50%	50%	0%	9
50%	50%	0%	10
50%	50%	0%	11
50%	50%	0%	12
50%	50%	0%	13
50%	49.9%	0%	14

sample39.0ms

Algorithm

intervals

Results

11.0ms	41×	body	1280	valid
9.0ms	49×	body	640	valid
6.0ms	138×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	7×	body	160	valid

simplify669.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (168.0ms)

Iter	Nodes	Cost
0	5718	24

prune3.0ms

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: 0.2b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
18×	`pow1_binary64`
15×	`times-frac_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
8×	`tan-quot_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`associate-/l*_binary64`
3×	`associate-/r*_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `associate-/r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 109

Calls

4 calls:

7.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
8.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series368.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
59.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
48.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
70.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify90.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4921	1997
1	4921	1997

prune139.0ms

Filtered

83 candidates to 121 candidates (-45.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	110	11	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	111	11	122

Merged error: 0.0b

Counts

122 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
0.2b	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
0.2b	(*.f64 (tan.f64 x) (sin.f64 x))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64` `tan-quot_binary64`
3×	`associate-/r_binary64` `swap-sqr_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-plus_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `pow-sqr_binary64` `flip--_binary64` `frac-times_binary64` `pow2_binary64`

Counts

4 → 83

Calls

4 calls:

6.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
6.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
5.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series260.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
84.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
51.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
50.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify95.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4961	1297
1	4961	1297

prune79.0ms

Filtered

62 candidates to 95 candidates (-53.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	95	11	106

Merged error: 0.0b

Counts

106 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
0.2b	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
0.2b	(*.f64 (tan.f64 x) (sin.f64 x))
0.2b	(*.f64 (tan.f64 x) (sin.f64 x))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `tan-quot_binary64` `associate-*l/_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 82

Calls

4 calls:

6.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
6.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
5.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
6.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

series250.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
74.0ms	(/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))
44.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
51.0ms	(*.f64 (tan.f64 x) (sin.f64 x))

simplify94.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4976	1260
1	4976	1260

prune76.0ms

Filtered

68 candidates to 94 candidates (-38.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	94	11	105

Merged error: 0.0b

Counts

105 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x))))
0.2b	(/.f64 (cos.f64 x) (sin.f64 x))
0.2b	(/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac_binary64`
75×	`add-sqr-sqrt_binary64`
63×	`*-un-lft-identity_binary64`
58×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `div-inv_binary64`
5×	`tan-quot_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `associate-/r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `pow-sqr_binary64` `flip--_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 144

Calls

4 calls:

18.0ms	(-.f64 1 (/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x))))
4.0ms	(/.f64 (cos.f64 x) (sin.f64 x))
7.0ms	(/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series243.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(-.f64 1 (/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x))))
34.0ms	(/.f64 (cos.f64 x) (sin.f64 x))
88.0ms	(/.f64 (tan.f64 x) (/.f64 (cos.f64 x) (sin.f64 x)))
44.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify104.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4950	3153
1	4950	3153

prune114.0ms

Filtered

115 candidates to 156 candidates (-35.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	156	11	167

Merged error: 0.0b

Counts

167 → 11

regimes70.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	34
1	47	34

end0.0ms

sample1.0s

Algorithm

intervals

Results

396.0ms	1484×	body	1280	valid
232.0ms	1283×	body	640	valid
175.0ms	4280×	body	80	valid
81.0ms	648×	body	320	valid
27.0ms	305×	body	160	valid

Details

analyze721.0ms

sample39.0ms

simplify669.0ms

prune3.0ms

localize19.0ms

rewrite28.0ms

series368.0ms

simplify90.0ms

prune139.0ms

localize14.0ms

rewrite25.0ms

series260.0ms

simplify95.0ms

prune79.0ms

localize13.0ms

rewrite25.0ms

series250.0ms

simplify94.0ms

prune76.0ms

localize14.0ms

rewrite41.0ms

series243.0ms

simplify104.0ms

prune114.0ms

regimes70.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample1.0s

Profiling