Details

analyze531.0ms

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

sample36.0ms

Algorithm

intervals

Results

11.0ms	39×	body	1280	valid
8.0ms	40×	body	640	valid
6.0ms	149×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	11×	body	160	valid

simplify573.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	5726	15

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: 0.3b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

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

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

series92.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
51.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
9.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
22.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify57.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4967	1280
1	4967	1280

prune122.0ms

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

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

6.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
6.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
10.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series80.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(-.f64 1 (/.f64 (*.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x)))
10.0ms	(*.f64 (tan.f64 x) (sin.f64 x))
44.0ms	(/.f64 (-.f64 1 (/.f64 (.f64 (tan.f64 x) (sin.f64 x)) (cos.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
9.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify61.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4927	1823
1	4927	1823

prune71.0ms

Filtered

78 candidates to 117 candidates (-50.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	117	11	128

Merged error: 0.0b

Counts

128 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 1 (tan.f64 x))
0.1b	(/.f64 (-.f64 1 (tan.f64 x)) (+.f64 1 (pow.f64 (tan.f64 x) 2)))
0.2b	(*.f64 (+.f64 1 (tan.f64 x)) (/.f64 (-.f64 1 (tan.f64 x)) (+.f64 1 (pow.f64 (tan.f64 x) 2))))
0.2b	(pow.f64 (tan.f64 x) 2)

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

87×	`*-un-lft-identity_binary64`
62×	`add-sqr-sqrt_binary64`
49×	`times-frac_binary64`
30×	`associate-r_binary64` `add-cube-cbrt_binary64`
18×	`difference-of-squares_binary64`
15×	`distribute-lft-out_binary64`
12×	`add-exp-log_binary64`
11×	`add-cbrt-cube_binary64`
9×	`distribute-lft-out--_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-/l*_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`associate-/r_binary64` `associate-/r/_binary64` `associate-l*_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `flip3--_binary64` `unpow2_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

3.0ms	(+.f64 1 (tan.f64 x))
10.0ms	(/.f64 (-.f64 1 (tan.f64 x)) (+.f64 1 (pow.f64 (tan.f64 x) 2)))
19.0ms	(*.f64 (+.f64 1 (tan.f64 x)) (/.f64 (-.f64 1 (tan.f64 x)) (+.f64 1 (pow.f64 (tan.f64 x) 2))))
3.0ms	(pow.f64 (tan.f64 x) 2)

series89.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 1 (tan.f64 x))
31.0ms	(/.f64 (-.f64 1 (tan.f64 x)) (+.f64 1 (pow.f64 (tan.f64 x) 2)))
42.0ms	(*.f64 (+.f64 1 (tan.f64 x)) (/.f64 (-.f64 1 (tan.f64 x)) (+.f64 1 (pow.f64 (tan.f64 x) 2))))
9.0ms	(pow.f64 (tan.f64 x) 2)

simplify66.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4961	2115
1	4961	2115

prune114.0ms

Filtered

100 candidates to 147 candidates (-47.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	3	6	9
Picked	1	0	1
Done	0	1	1
Total	148	10	158

Merged error: 0b

Counts

158 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(pow.f64 (tan.f64 x) 2)
0.3b	(-.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 2))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

53×	`add-sqr-sqrt_binary64`
48×	`*-un-lft-identity_binary64`
36×	`times-frac_binary64`
15×	`difference-of-squares_binary64`
12×	`add-cube-cbrt_binary64` `unpow-prod-down_binary64`
9×	`pow-unpow_binary64`
8×	`distribute-lft-out--_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-log-exp_binary64` `distribute-rgt-out--_binary64` `unpow2_binary64` `sqr-pow_binary64` `div-inv_binary64`
5×	`distribute-lft-out_binary64`
4×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
3×	`pow-to-exp_binary64` `pow-pow_binary64` `pow-exp_binary64`
2×	`flip3-+_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`

Counts

4 → 96

Calls

4 calls:

3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)
3.0ms	(pow.f64 (tan.f64 x) 2)
41.0ms	(-.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 2))))

series90.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(pow.f64 (tan.f64 x) 2)
9.0ms	(pow.f64 (tan.f64 x) 2)
9.0ms	(pow.f64 (tan.f64 x) 2)
62.0ms	(-.f64 (/.f64 1 (+.f64 1 (pow.f64 (tan.f64 x) 2))) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 1 (pow.f64 (tan.f64 x) 2))))

simplify57.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4914	1498
1	4914	1498

prune68.0ms

Filtered

66 candidates to 108 candidates (-63.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	108	10	118

Merged error: 0b

Counts

118 → 10

regimes98.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	18
1	46	18

end0.0ms

sample1.1s

Algorithm

intervals

Results

401.0ms	1488×	body	1280	valid
237.0ms	1309×	body	640	valid
170.0ms	4260×	body	80	valid
81.0ms	637×	body	320	valid
27.0ms	306×	body	160	valid

Details

analyze531.0ms

sample36.0ms

simplify573.0ms

prune3.0ms

localize9.0ms

rewrite28.0ms

series92.0ms

simplify57.0ms

prune122.0ms

localize13.0ms

rewrite32.0ms

series80.0ms

simplify61.0ms

prune71.0ms

localize10.0ms

rewrite43.0ms

series89.0ms

simplify66.0ms

prune114.0ms

localize9.0ms

rewrite54.0ms

series90.0ms

simplify57.0ms

prune68.0ms

regimes98.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling