Details

analyze690.0ms

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

12.0ms	60×	body	1024	valid
8.0ms	35×	body	512	valid
7.0ms	148×	body	128	valid
1.0ms	13×	body	256	valid

simplify307.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (140.0ms)

Iter	Nodes	Cost
0	5717	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: 0.3b

Counts

2 → 1

localize16.0ms

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))))
0.2b	(-.f64 1 (*.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))

rewrite34.0ms

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))
7.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series641.0ms

Counts

4 → 12

Calls

4 calls:

364.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
88.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
95.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
92.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify78.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4921	1997
1	4921	1997

prune151.0ms

Filtered

83 candidates to 121 candidates (-45.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	112	9	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	9	122

Merged error: 0.0b

Counts

122 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 1 (tan.f64 x))
0.2b	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
0.2b	(+.f64 (tan.f64 x) 1)
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`pow1_binary64`
10×	`add-cube-cbrt_binary64`
9×	`associate-r_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-l_binary64`
5×	`frac-times_binary64`
4×	`flip3-+_binary64` `flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64` `tan-quot_binary64`
3×	`sub-neg_binary64` `swap-sqr_binary64` `associate-r/_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `pow-sqr_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64`

Counts

4 → 86

Calls

4 calls:

4.0ms	(-.f64 1 (tan.f64 x))
11.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
4.0ms	(+.f64 (tan.f64 x) 1)
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series322.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(-.f64 1 (tan.f64 x))
131.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
53.0ms	(+.f64 (tan.f64 x) 1)
82.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify85.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4949	1198
1	4949	1198

prune91.0ms

Filtered

71 candidates to 98 candidates (-38.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Merged error: 0.0b

Counts

107 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (+.f64 (tan.f64 x) 1) (log.f64 (exp.f64 (-.f64 1 (tan.f64 x)))))
0.2b	(+.f64 (tan.f64 x) 1)
0.2b	(exp.f64 (-.f64 1 (tan.f64 x)))
0.3b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
14×	`pow1_binary64` `add-cube-cbrt_binary64`
13×	`associate-r_binary64`
12×	`exp-prod_binary64`
9×	`add-log-exp_binary64`
8×	`log-prod_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`log-pow_binary64` `associate-l_binary64`
4×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `tan-quot_binary64`
3×	`sub-neg_binary64` `swap-sqr_binary64` `exp-sum_binary64` `associate-*l/_binary64`
2×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`diff-log_binary64` `pow-prod-up_binary64` `associate-*r/_binary64` `pow-plus_binary64` `exp-diff_binary64` `pow-sqr_binary64` `+-commutative_binary64` `frac-times_binary64` `pow2_binary64` `sum-log_binary64`

Counts

4 → 93

Calls

4 calls:

14.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (log.f64 (exp.f64 (-.f64 1 (tan.f64 x)))))
4.0ms	(+.f64 (tan.f64 x) 1)
5.0ms	(exp.f64 (-.f64 1 (tan.f64 x)))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series512.0ms

Counts

4 → 12

Calls

4 calls:

308.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (log.f64 (exp.f64 (-.f64 1 (tan.f64 x)))))
41.0ms	(+.f64 (tan.f64 x) 1)
89.0ms	(exp.f64 (-.f64 1 (tan.f64 x)))
73.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify84.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4932	1299
1	4932	1299

prune103.0ms

Filtered

73 candidates to 105 candidates (-43.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	104	10	114

Merged error: 0.0b

Counts

114 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 x) 2)
0.2b	(pow.f64 (sin.f64 x) 2)
0.2b	(pow.f64 (cos.f64 x) 2)
0.2b	(pow.f64 (cos.f64 x) 2)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64` `pow-unpow_binary64` `add-cube-cbrt_binary64` `unpow-prod-down_binary64` `add-sqr-sqrt_binary64`
8×	`pow1_binary64` `add-exp-log_binary64`
4×	`pow-to-exp_binary64` `add-log-exp_binary64` `unpow2_binary64` `pow-pow_binary64` `sqr-pow_binary64` `add-cbrt-cube_binary64` `pow-exp_binary64`

Counts

4 → 72

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 x) 2)
3.0ms	(pow.f64 (sin.f64 x) 2)
2.0ms	(pow.f64 (cos.f64 x) 2)
3.0ms	(pow.f64 (cos.f64 x) 2)

series103.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow.f64 (sin.f64 x) 2)
29.0ms	(pow.f64 (sin.f64 x) 2)
22.0ms	(pow.f64 (cos.f64 x) 2)
28.0ms	(pow.f64 (cos.f64 x) 2)

simplify68.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4910	660
1	4910	660

prune67.0ms

Filtered

48 candidates to 84 candidates (-75.0%)

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

regimes76.0ms

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	30	36
1	30	36

end0.0ms

sample899.0ms

Algorithm

intervals

Results

422.0ms	2069×	body	1024	valid
170.0ms	4399×	body	128	valid
130.0ms	997×	body	512	valid
46.0ms	531×	body	256	valid
1.0ms	4×	body	2048	valid

Details

analyze690.0ms

sample37.0ms

simplify307.0ms

prune3.0ms

localize16.0ms

rewrite34.0ms

series641.0ms

simplify78.0ms

prune151.0ms

localize10.0ms

rewrite33.0ms

series322.0ms

simplify85.0ms

prune91.0ms

localize17.0ms

rewrite38.0ms

series512.0ms

simplify84.0ms

prune103.0ms

localize13.0ms

rewrite17.0ms

series103.0ms

simplify68.0ms

prune67.0ms

regimes76.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample899.0ms

Profiling