Details

analyze520.0ms

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

sample37.0ms

Algorithm

intervals

Results

11.0ms	40×	body	1280	valid
8.0ms	46×	body	640	valid
6.0ms	141×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	10×	body	160	valid

simplify552.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	5284	15

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: 0.3b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x)))
0.2b	(/.f64 (-.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`pow1_binary64`
12×	`times-frac_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`tan-quot_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`difference-of-squares_binary64`
4×	`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 → 104

Calls

4 calls:

3.0ms	(-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x)))
7.0ms	(/.f64 (-.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
7.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series93.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 1.0 (*.f64 (tan.f64 x) (tan.f64 x)))
49.0ms	(/.f64 (-.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1.0 (.f64 (tan.f64 x) (tan.f64 x))))
10.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
23.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify56.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4951	1205
1	4951	1205

prune164.0ms

Filtered

82 candidates to 116 candidates (-41.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	103	13	116
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	13	117

Merged error: 0.1b

Counts

117 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (tan.f64 x) (sqrt.f64 1.0))
0.2b	(-.f64 (sqrt.f64 1.0) (tan.f64 x))
0.2b	(*.f64 (+.f64 (tan.f64 x) (sqrt.f64 1.0)) (/.f64 (-.f64 (sqrt.f64 1.0) (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0)))
0.3b	(pow.f64 (tan.f64 x) 2)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
30×	`associate-r_binary64`
25×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64`
10×	`add-exp-log_binary64` `difference-of-squares_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `distribute-lft-out_binary64`
7×	`pow1_binary64`
5×	`distribute-lft-out--_binary64` `sqrt-prod_binary64`
4×	`flip3-+_binary64` `associate-l_binary64` `flip-+_binary64`
3×	`pow-unpow_binary64` `unpow-prod-down_binary64`
2×	`cbrt-unprod_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `unpow2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `pow-pow_binary64` `sqr-pow_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

5.0ms	(+.f64 (tan.f64 x) (sqrt.f64 1.0))
5.0ms	(-.f64 (sqrt.f64 1.0) (tan.f64 x))
22.0ms	(*.f64 (+.f64 (tan.f64 x) (sqrt.f64 1.0)) (/.f64 (-.f64 (sqrt.f64 1.0) (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0)))
3.0ms	(pow.f64 (tan.f64 x) 2)

series83.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+.f64 (tan.f64 x) (sqrt.f64 1.0))
8.0ms	(-.f64 (sqrt.f64 1.0) (tan.f64 x))
56.0ms	(*.f64 (+.f64 (tan.f64 x) (sqrt.f64 1.0)) (/.f64 (-.f64 (sqrt.f64 1.0) (tan.f64 x)) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0)))
11.0ms	(pow.f64 (tan.f64 x) 2)

simplify48.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5183	1401

prune133.0ms

Filtered

73 candidates to 110 candidates (-50.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	4	8	12
Picked	0	1	1
Done	0	0	0
Total	111	12	123

Merged error: 0.0b

Counts

123 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (tan.f64 x) (tan.f64 x))
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(cbrt.f64 (pow.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) 3))
0.4b	(pow.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) 3)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
23×	`unpow-prod-down_binary64`
22×	`cbrt-prod_binary64`
16×	`add-cube-cbrt_binary64` `difference-of-squares_binary64` `cube-prod_binary64`
13×	`pow1_binary64`
8×	`add-exp-log_binary64`
7×	`sqr-pow_binary64` `add-cbrt-cube_binary64`
6×	`pow-unpow_binary64`
5×	`unpow2_binary64`
4×	`add-log-exp_binary64` `cube-div_binary64` `distribute-lft-out--_binary64` `tan-quot_binary64`
3×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`cbrt-div_binary64` `pow-to-exp_binary64` `flip3--_binary64` `pow-pow_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-prod-down_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow1/3_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `pow-sqr_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 114

Calls

4 calls:

5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
3.0ms	(pow.f64 (tan.f64 x) 2)
7.0ms	(cbrt.f64 (pow.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) 3))
7.0ms	(pow.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) 3)

series62.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
10.0ms	(pow.f64 (tan.f64 x) 2)
11.0ms	(cbrt.f64 (pow.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) 3))
30.0ms	(pow.f64 (-.f64 1.0 (pow.f64 (tan.f64 x) 2)) 3)

simplify66.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4989	1086
1	4989	1086

prune100.0ms

Filtered

64 candidates to 126 candidates (-96.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	124	2	126
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	127	11	138

Merged error: 0.0b

Counts

138 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(pow.f64 (tan.f64 x) 2)
0.3b	(-.f64 (/.f64 1.0 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

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)
42.0ms	(-.f64 (/.f64 1.0 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0)))

series114.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(pow.f64 (tan.f64 x) 2)
10.0ms	(pow.f64 (tan.f64 x) 2)
11.0ms	(pow.f64 (tan.f64 x) 2)
81.0ms	(-.f64 (/.f64 1.0 (+.f64 (pow.f64 (tan.f64 x) 2) 1.0)) (/.f64 (pow.f64 (tan.f64 x) 2) (+.f64 (pow.f64 (tan.f64 x) 2) 1.0)))

simplify34.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5194	1408

prune98.0ms

Filtered

66 candidates to 99 candidates (-50.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	97	13	110

Merged error: 0.0b

Counts

110 → 13

regimes111.0ms

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	24	18
1	24	18

end0.0ms

sample1.0s

Algorithm

intervals

Results

400.0ms	1512×	body	1280	valid
215.0ms	1251×	body	640	valid
171.0ms	4357×	body	80	valid
71.0ms	581×	body	320	valid
26.0ms	299×	body	160	valid

Details

analyze520.0ms

sample37.0ms

simplify552.0ms

prune4.0ms

localize9.0ms

rewrite27.0ms

series93.0ms

simplify56.0ms

prune164.0ms

localize11.0ms

rewrite38.0ms

series83.0ms

simplify48.0ms

prune133.0ms

localize12.0ms

rewrite26.0ms

series62.0ms

simplify66.0ms

prune100.0ms

localize9.0ms

rewrite54.0ms

series114.0ms

simplify34.0ms

prune98.0ms

regimes111.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling