Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.2%	0.1%	6
21.9%	78%	0.1%	7
23.4%	76.5%	0.1%	8
24.2%	75.7%	0.1%	9
24.6%	75.3%	0.1%	10
24.8%	75.1%	0.1%	11
24.9%	75%	0.1%	12
24.9%	75%	0.1%	13
25%	75%	0.1%	14

sample114.0ms

Algorithm

intervals

Results

55.0ms	122×	body	1280	valid
28.0ms	27×	body	2560	valid
13.0ms	47×	body	640	valid
3.0ms	14×	body	320	valid
2.0ms	40×	body	80	valid
1.0ms	6×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune5.0ms

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: 36.5b

Counts

2 → 1

localize16.0ms

Local error

Found 2 expressions with local error:

1.2b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
2.4b	(tan.f64 (+.f64 x eps))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64` `tan-quot_binary64`
2×	`tan-sum_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `frac-sub_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

2 → 24

Calls

2 calls:

7.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
7.0ms	(tan.f64 (+.f64 x eps))

series46.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
18.0ms	(tan.f64 (+.f64 x eps))

simplify57.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune53.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	22	8	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	23	8	31

Merged error: 16.1b

Counts

31 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (tan.f64 x) (tan.f64 eps))
0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
3.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
22×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
13×	`times-frac_binary64`
9×	`tan-quot_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
5×	`distribute-lft-out_binary64`
4×	`associate-/l*_binary64`
3×	`associate-/l/_binary64` `associate-/r_binary64` `associate-r_binary64` `associate-l*_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `frac-add_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `frac-sub_binary64` `frac-times_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

5.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
9.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
13.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series208.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
59.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
22.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
106.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

simplify53.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5109	1560

prune137.0ms

Filtered

73 candidates to 97 candidates (-32.9%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	84	13	97
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	90	15	105

Merged error: 15.9b

Counts

105 → 15

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))
0.2b	(*.f64 (sin.f64 x) (sin.f64 eps))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
3.1b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
26×	`times-frac_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
7×	`associate-/r*_binary64` `distribute-lft-out_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `distribute-lft-out--_binary64`
5×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `associate-/l*_binary64` `div-exp_binary64`
4×	`associate-/l/_binary64`
3×	`associate-r_binary64` `associate-/r/_binary64` `associate-l_binary64` `tan-quot_binary64`
2×	`flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `sin-mult_binary64` `div-inv_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `cos-mult_binary64` `frac-add_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-sub_binary64` `*-commutative_binary64`

Counts

4 → 108

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))
5.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
8.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
20.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))

series197.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))))
9.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
22.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
105.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) (tan.f64 x))

simplify50.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4991	2589
1	4991	2589

prune110.0ms

Filtered

79 candidates to 120 candidates (-51.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	8	6	14
Picked	1	0	1
Done	0	0	0
Total	127	8	135

Merged error: 13.9b

Counts

135 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 x) (sin.f64 eps))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
3.3b	(+.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) -1)

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`times-frac_binary64`
3×	`associate-r_binary64` `associate-l_binary64` `sin-mult_binary64` `difference-of-sqr--1_binary64` `div-inv_binary64`
2×	`associate-/l/_binary64` `associate-/r_binary64` `distribute-lft-out_binary64` `cos-mult_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `unswap-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 81

Calls

4 calls:

6.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
9.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
9.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
16.0ms	(+.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) -1)

series95.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
22.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
23.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
41.0ms	(+.f64 (/.f64 1 (-.f64 1 (/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps))))) -1)

simplify62.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4971	1224
1	4971	1224

prune79.0ms

Filtered

60 candidates to 93 candidates (-55.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	92	9	101

Merged error: 13.9b

Counts

101 → 9

regimes114.0ms

Accuracy

0% (0.4b remaining)

Error of 12.9b against oracle of 12.5b and baseline of 12.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	60	45
1	60	45

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	3335×	body	1280	valid
571.0ms	647×	body	2560	valid
418.0ms	1863×	body	640	valid
109.0ms	737×	body	320	valid
56.0ms	1074×	body	80	valid
34.0ms	344×	body	160	valid

Details

analyze1.0s

sample114.0ms

simplify12.0ms

prune5.0ms

localize16.0ms

rewrite15.0ms

series46.0ms

simplify57.0ms

prune53.0ms

localize12.0ms

rewrite36.0ms

series208.0ms

simplify53.0ms

prune137.0ms

localize24.0ms

rewrite50.0ms

series197.0ms

simplify50.0ms

prune110.0ms

localize26.0ms

rewrite41.0ms

series95.0ms

simplify62.0ms

prune79.0ms

regimes114.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.7s

Profiling