Details

analyze764.0ms

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

sample86.0ms

Algorithm

intervals

Results

43.0ms	111×	body	1280	valid
16.0ms	19×	body	2560	valid
13.0ms	61×	body	640	valid
2.0ms	17×	body	320	valid
2.0ms	17×	body	160	valid
1.0ms	31×	body	80	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune2.0ms

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: 37.5b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

1.5b	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
4.8b	(tan.f64 (+.f64 x eps))

rewrite11.0ms

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))
4.0ms	(tan.f64 (+.f64 x eps))

series49.0ms

Counts

2 → 6

Calls

2 calls:

31.0ms	(-.f64 (tan.f64 (+.f64 x eps)) (tan.f64 x))
18.0ms	(tan.f64 (+.f64 x eps))

simplify53.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4924	332
1	4924	332

prune50.0ms

Filtered

25 candidates to 30 candidates (-20.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	23	7	30
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	24	7	31

Merged error: 14.3b

Counts

31 → 7

localize11.0ms

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))
2.5b	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite33.0ms

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))))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
12.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series236.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+.f64 (tan.f64 x) (tan.f64 eps))
67.0ms	(/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps))))
26.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
119.0ms	(-.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

simplify50.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5109	1560

prune130.0ms

Filtered

73 candidates to 97 candidates (-32.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	87	10	97
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	92	12	104

Merged error: 14.2b

Counts

104 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.2b	(*.f64 (tan.f64 x) (tan.f64 eps))
0.3b	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
2.5b	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1_binary64`
45×	`tan-quot_binary64`
21×	`frac-times_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`pow-prod-down_binary64`
15×	`associate-*r/_binary64`
14×	`associate-*l/_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64`
5×	`frac-sub_binary64`
4×	`pow-prod-up_binary64` `pow-sqr_binary64`
3×	`*-commutative_binary64`
2×	`flip3-+_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `flip-+_binary64` `associate--l+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `swap-sqr_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64` `pow2_binary64`

Counts

4 → 109

Calls

4 calls:

6.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
5.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
11.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
13.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

series565.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
25.0ms	(*.f64 (tan.f64 x) (tan.f64 eps))
39.0ms	(.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (*.f64 (tan.f64 x) (tan.f64 eps)))
473.0ms	(-.f64 (.f64 (/.f64 (+.f64 (tan.f64 x) (tan.f64 eps)) (-.f64 1 (.f64 (.f64 (tan.f64 x) (tan.f64 eps)) (.f64 (tan.f64 x) (tan.f64 eps))))) (+.f64 1 (*.f64 (tan.f64 x) (tan.f64 eps)))) (tan.f64 x))

simplify33.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	4984	1908
1	4984	1908

prune140.0ms

Filtered

74 candidates to 121 candidates (-63.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	114	7	121
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	118	15	133

Merged error: 14.1b

Counts

133 → 15

localize34.0ms

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)))))
0.3b	(*.f64 (sin.f64 x) (sin.f64 eps))
0.3b	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
2.5b	(-.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))

rewrite47.0ms

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:

12.0ms	(/.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)))
19.0ms	(-.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))

series222.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/.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)))))
10.0ms	(*.f64 (sin.f64 x) (sin.f64 eps))
25.0ms	(/.f64 (.f64 (sin.f64 x) (sin.f64 eps)) (.f64 (cos.f64 x) (cos.f64 eps)))
120.0ms	(-.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))

simplify47.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4991	2589
1	4991	2589

prune88.0ms

Filtered

79 candidates to 120 candidates (-51.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	4	10	14
Picked	1	0	1
Done	0	0	0
Total	123	12	135

Merged error: 12.3b

Counts

135 → 12

regimes135.0ms

Accuracy

0% (0.3b remaining)

Error of 12.6b against oracle of 12.3b and baseline of 12.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	57	43
1	57	43

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	3331×	body	1280	valid
525.0ms	603×	body	2560	valid
393.0ms	1758×	body	640	valid
123.0ms	816×	body	320	valid
54.0ms	1145×	body	80	valid
33.0ms	347×	body	160	valid

Details

analyze764.0ms

sample86.0ms

simplify7.0ms

prune2.0ms

localize8.0ms

rewrite11.0ms

series49.0ms

simplify53.0ms

prune50.0ms

localize11.0ms

rewrite33.0ms

series236.0ms

simplify50.0ms

prune130.0ms

localize14.0ms

rewrite38.0ms

series565.0ms

simplify33.0ms

prune140.0ms

localize34.0ms

rewrite47.0ms

series222.0ms

simplify47.0ms

prune88.0ms

regimes135.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling