Details

analyze567.0ms

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

sample53.0ms

Algorithm

intervals

Results

16.0ms	57×	body	1280	valid
11.0ms	53×	body	640	valid
6.0ms	123×	body	80	valid
2.0ms	14×	body	320	valid
1.0ms	9×	body	160	valid

simplify926.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (279.0ms)

Iter	Nodes	Cost
0	4852	24
1	4852	24

prune8.0ms

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: 0.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.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))

rewrite44.0ms

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:

24.0ms	(/.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))

series436.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 1 (.f64 (tan.f64 x) (tan.f64 x))))
55.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
49.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
66.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify128.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5330	2263

prune746.0ms

Filtered

79 candidates to 121 candidates (-53.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	108	13	121
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	13	122

Merged error: 0.1b

Counts

122 → 13

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

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:

21.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
8.0ms	(+.f64 (tan.f64 x) 1)
7.0ms	(-.f64 1 (tan.f64 x))
10.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series209.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(*.f64 (+.f64 (tan.f64 x) 1) (-.f64 1 (tan.f64 x)))
29.0ms	(+.f64 (tan.f64 x) 1)
39.0ms	(-.f64 1 (tan.f64 x))
66.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify85.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5116	1310

prune507.0ms

Filtered

69 candidates to 98 candidates (-42.0%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	95	3	98
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	96	15	111

Merged error: 0.0b

Counts

111 → 15

localize26.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
21×	`pow1_binary64` `associate-r_binary64`
20×	`times-frac_binary64`
18×	`add-exp-log_binary64`
15×	`add-cbrt-cube_binary64`
11×	`associate-l_binary64`
8×	`tan-quot_binary64`
6×	`swap-sqr_binary64`
5×	`unswap-sqr_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `associate-r/_binary64` `associate-/l_binary64` `-commutative_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `pow-prod-up_binary64` `cbrt-undiv_binary64` `pow-plus_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `div-inv_binary64` `div-exp_binary64` `pow-sqr_binary64` `flip--_binary64` `flip-+_binary64` `pow2_binary64`
1×	`clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `pow-flip_binary64`

Counts

4 → 131

Calls

4 calls:

8.0ms	(/.f64 1 (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) 1))
21.0ms	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) 1)))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

series534.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/.f64 1 (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) 1))
252.0ms	(.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (/.f64 1 (+.f64 (*.f64 (tan.f64 x) (tan.f64 x)) 1)))
53.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
70.0ms	(*.f64 (tan.f64 x) (tan.f64 x))

simplify95.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4996	2491
1	4996	2491

prune545.0ms

Filtered

86 candidates to 143 candidates (-66.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	12	13
Picked	1	0	1
Done	1	0	1
Total	145	13	158

Merged error: 0.0b

Counts

158 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

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))
0.4b	(log.f64 (exp.f64 (/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 (.f64 (tan.f64 x) (tan.f64 x)) 1))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64` `log-pow_binary64`
21×	`exp-prod_binary64`
19×	`pow1_binary64`
15×	`times-frac_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `tan-quot_binary64`
6×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
3×	`log-prod_binary64`
2×	`pow-prod-down_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` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `div-sub_binary64` `div-inv_binary64` `log-div_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 103

Calls

4 calls:

3.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
12.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
12.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 (.f64 (tan.f64 x) (tan.f64 x)) 1))))

series434.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(-.f64 1 (*.f64 (tan.f64 x) (tan.f64 x)))
77.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
45.0ms	(*.f64 (tan.f64 x) (tan.f64 x))
245.0ms	(log.f64 (exp.f64 (/.f64 (-.f64 1 (.f64 (tan.f64 x) (tan.f64 x))) (+.f64 (.f64 (tan.f64 x) (tan.f64 x)) 1))))

simplify87.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5131	1806

prune391.0ms

Filtered

79 candidates to 115 candidates (-45.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	114	1	115
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	115	13	128

Merged error: 0.0b

Counts

128 → 13

regimes371.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	28
1	29	28

end0.0ms

sample1.2s

Algorithm

intervals

Results

378.0ms	1481×	body	1280	valid
220.0ms	1288×	body	640	valid
169.0ms	4315×	body	80	valid
74.0ms	597×	body	320	valid
27.0ms	319×	body	160	valid

Details

analyze567.0ms

sample53.0ms

simplify926.0ms

prune8.0ms

localize13.0ms

rewrite44.0ms

series436.0ms

simplify128.0ms

prune746.0ms

localize30.0ms

rewrite52.0ms

series209.0ms

simplify85.0ms

prune507.0ms

localize26.0ms

rewrite44.0ms

series534.0ms

simplify95.0ms

prune545.0ms

localize19.0ms

rewrite36.0ms

series434.0ms

simplify87.0ms

prune391.0ms

regimes371.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.2s

Profiling