Details

analyze490.0ms

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

sample34.0ms

Algorithm

intervals

Results

11.0ms	44×	body	1280	valid
6.0ms	37×	body	640	valid
6.0ms	157×	body	80	valid
2.0ms	11×	body	320	valid
1.0ms	7×	body	160	valid

simplify314.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (175.0ms)

Iter	Nodes	Cost
0	4853	24
1	4853	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

localize9.0ms

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))

rewrite235.0ms

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`
4×	`insert-posit16`
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 → 113

Calls

4 calls:

9.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
4.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
12.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
205.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series890.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
204.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
196.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
196.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	833	9
1	833	9
0	833	9
1	833	9
0	1	3
1	1	3
0	833	9
1	833	9
0	833	9
1	833	9
0	1	3
1	1	3
0	878	9
1	878	9
0	878	9
1	878	9
0	1	3
1	1	3
0	1358	9
1	1358	9
0	1358	9
1	1358	9
0	1	3
1	1	3

simplify119.0ms

Counts

125 → 125

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	5491	2099

prune130.0ms

Filtered

82 candidates to 125 candidates (-52.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	116	9	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	9	126

Merged error: 0.0b

Counts

126 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite34.0ms

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` `insert-posit16` `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 → 90

Calls

4 calls:

5.0ms	(-.f64 1 (tan.f64 x))
15.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
5.0ms	(+.f64 (tan.f64 x) 1)
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series2.1s

Counts

4 → 12

Calls

4 calls:

219.0ms	(-.f64 1 (tan.f64 x))
860.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
870.0ms	(+.f64 (tan.f64 x) 1)
189.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	833	9
1	833	9
0	833	9
1	833	9
0	1	3
1	1	3
0	28027	9
0	28027	9
0	1	3
1	1	3
0	19139	9
1	19139	9
0	19139	9
1	19139	9
0	1	3
1	1	3
0	2348	9
1	2348	9
0	2348	9
1	2348	9
0	1	3
1	1	3

simplify118.0ms

Counts

102 → 102

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5511	1069

prune97.0ms

Filtered

72 candidates to 102 candidates (-41.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	99	3	102
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	102	9	111

Merged error: 0.0b

Counts

111 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
0.2b	(+.f64 (tan.f64 x) 1)
0.2b	(exp.f64 (+.f64 (tan.f64 x) 1))
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`
11×	`add-cube-cbrt_binary64`
9×	`add-log-exp_binary64`
8×	`exp-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`log-pow_binary64`
4×	`log-prod_binary64` `insert-posit16` `tan-quot_binary64`
3×	`swap-sqr_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`rem-exp-log_binary64` `exp-sum_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 75

Calls

4 calls:

6.0ms	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
5.0ms	(+.f64 (tan.f64 x) 1)
7.0ms	(exp.f64 (+.f64 (tan.f64 x) 1))
7.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series2.9s

Counts

4 → 12

Calls

4 calls:

967.0ms	(log.f64 (exp.f64 (+.f64 (tan.f64 x) 1)))
846.0ms	(+.f64 (tan.f64 x) 1)
870.0ms	(exp.f64 (+.f64 (tan.f64 x) 1))
196.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	833	9
1	833	9
0	833	9
1	833	9
0	1	3
1	1	3
0	28051	9
0	28051	9
0	1	3
1	1	3
0	28027	9
0	28027	9
0	1	3
1	1	3
0	28200	9
0	28200	9
0	1	3
1	1	3

simplify130.0ms

Counts

87 → 87

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	5393	639

prune80.0ms

Filtered

59 candidates to 87 candidates (-47.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	87	9	96

Merged error: 0.0b

Counts

96 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(log.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))
0.2b	(pow.f64 (tan.f64 x) 2)
0.2b	(*.f64 (tan.f64 x) (tan.f64 x))
0.4b	(exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
24×	`exp-prod_binary64`
16×	`difference-of-squares_binary64`
13×	`pow1_binary64` `add-cube-cbrt_binary64` `log-pow_binary64`
7×	`add-log-exp_binary64` `add-exp-log_binary64` `unpow-prod-down_binary64`
6×	`add-cbrt-cube_binary64`
5×	`unpow2_binary64` `sqr-pow_binary64`
4×	`log-prod_binary64` `insert-posit16` `tan-quot_binary64`
3×	`pow-unpow_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`sub-neg_binary64` `rem-exp-log_binary64` `exp-diff_binary64` `exp-sum_binary64` `distribute-lft-out--_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `rem-log-exp_binary64` `associate-r/_binary64` `pow-pow_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `pow-sqr_binary64` `log-div_binary64` `frac-times_binary64` `pow-exp_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 99

Calls

4 calls:

9.0ms	(log.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))
4.0ms	(pow.f64 (tan.f64 x) 2)
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
9.0ms	(exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))

series817.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(log.f64 (exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2))))
196.0ms	(pow.f64 (tan.f64 x) 2)
187.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
203.0ms	(exp.f64 (-.f64 1 (pow.f64 (tan.f64 x) 2)))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	899	9
1	899	9
0	899	9
1	899	9
0	1	3
1	1	3
0	833	9
1	833	9
0	833	9
1	833	9
0	1	3
1	1	3
0	836	9
1	836	9
0	836	9
1	836	9
0	1	3
1	1	3
0	1040	9
1	1040	9
0	1040	9
1	1040	9
0	1	3
1	1	3

simplify151.0ms

Counts

111 → 111

Iterations

Useful iterations: 0 (124.0ms)

Iter	Nodes	Cost
0	4962	887
1	4962	887

prune89.0ms

Filtered

78 candidates to 111 candidates (-42.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	111	9	120

Merged error: 0.0b

Counts

120 → 9

regimes83.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	26	31
1	26	31

end0.0ms

sample966.0ms

Algorithm

intervals

Results

379.0ms	1508×	body	1280	valid
196.0ms	1182×	body	640	valid
163.0ms	4334×	body	80	valid
79.0ms	658×	body	320	valid
26.0ms	318×	body	160	valid

Details

analyze490.0ms

sample34.0ms

simplify314.0ms

prune3.0ms

localize9.0ms

rewrite235.0ms

series890.0ms

simplify119.0ms

prune130.0ms

localize9.0ms

rewrite34.0ms

series2.1s

simplify118.0ms

prune97.0ms

localize14.0ms

rewrite27.0ms

series2.9s

simplify130.0ms

prune80.0ms

localize13.0ms

rewrite32.0ms

series817.0ms

simplify151.0ms

prune89.0ms

regimes83.0ms

bsearch0.0ms

simplify6.0ms

end0.0ms

sample966.0ms

Profiling