Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample107.0ms

Algorithm

intervals

Results

50.0ms	112×	body	1280	valid
23.0ms	24×	body	2560	valid
15.0ms	55×	body	640	valid
8.0ms	39×	body	80	valid
4.0ms	20×	body	320	valid
1.0ms	6×	body	160	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	73	11
1	73	11

prune1.0ms

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: 35.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.7b	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
3.2b	(sin.f64 (+.f64 x eps))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
2×	`pow1_binary64` `add-cube-cbrt_binary64` `sin-sum_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `diff-sin_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

2 → 23

Calls

2 calls:

7.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
5.0ms	(sin.f64 (+.f64 x eps))

series46.0ms

Counts

2 → 6

Calls

2 calls:

30.0ms	(-.f64 (sin.f64 (+.f64 x eps)) (sin.f64 x))
15.0ms	(sin.f64 (+.f64 x eps))

simplify100.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5213	426

prune27.0ms

Filtered

23 candidates to 29 candidates (-26.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	26	3	29
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	27	3	30

Merged error: 0.7b

Counts

30 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (+.f64 x eps))
0.2b	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
0.4b	(/.f64 (+.f64 x (+.f64 x eps)) 2)
3.8b	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

6.0ms	(+.f64 x (+.f64 x eps))
6.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
9.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
8.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

series104.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+.f64 x (+.f64 x eps))
43.0ms	(*.f64 (sin.f64 (/.f64 eps 2)) (cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2)))
26.0ms	(/.f64 (+.f64 x (+.f64 x eps)) 2)
20.0ms	(cos.f64 (/.f64 (+.f64 x (+.f64 x eps)) 2))

simplify88.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	6323	1333

prune91.0ms

Filtered

63 candidates to 90 candidates (-42.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	81	9	90
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	81	12	93

Merged error: 0.4b

Counts

93 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (.f64 eps 1/2))) 3)))
0.5b	(cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3))
0.5b	(pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3)
3.8b	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

28×	`cbrt-prod_binary64`
24×	`add-sqr-sqrt_binary64`
15×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
10×	`unpow-prod-down_binary64` `cube-prod_binary64`
7×	`pow1_binary64` `add-exp-log_binary64`
6×	`add-cbrt-cube_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-unpow_binary64` `associate-l_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `cos-sum_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 86

Calls

4 calls:

10.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (.f64 eps 1/2))) 3)))
3.0ms	(cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3))
4.0ms	(pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3)
5.0ms	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

series142.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (.f64 eps 1/2))) 3)))
20.0ms	(cbrt.f64 (pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3))
63.0ms	(pow.f64 (cos.f64 (+.f64 x (*.f64 eps 1/2))) 3)
19.0ms	(cos.f64 (+.f64 x (*.f64 eps 1/2)))

simplify121.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4847	1676
1	4847	1676

prune82.0ms

Filtered

51 candidates to 98 candidates (-92.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	94	4	98
Fresh	6	4	10
Picked	1	0	1
Done	0	1	1
Total	101	9	110

Merged error: 0.1b

Counts

110 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))
0.3b	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps 1/2)))) 3)))
0.5b	(cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))) 3))
0.5b	(pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))) 3)

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64` `cbrt-prod_binary64`
18×	`associate-r_binary64`
17×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`cube-div_binary64`
10×	`unpow-prod-down_binary64` `cube-prod_binary64`
9×	`pow1_binary64` `add-exp-log_binary64`
8×	`cbrt-div_binary64` `add-cbrt-cube_binary64`
7×	`sin-mult_binary64`
6×	`cos-mult_binary64` `associate-l_binary64` `unswap-sqr_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64` `sqr-pow_binary64`
3×	`pow-unpow_binary64` `flip3--_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64` `unpow3_binary64` `cube-mult_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `rem-cbrt-cube_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`

Counts

4 → 109

Calls

4 calls:

6.0ms	(.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))
16.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps 1/2)))) 3)))
9.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))) 3))
9.0ms	(pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))) 3)

series392.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))
115.0ms	(.f64 (sin.f64 (/.f64 eps 2)) (cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (*.f64 eps 1/2)))) 3)))
80.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))) 3))
155.0ms	(pow.f64 (-.f64 (.f64 (cos.f64 x) (cos.f64 (.f64 eps 1/2))) (.f64 (sin.f64 x) (sin.f64 (.f64 eps 1/2)))) 3)

simplify100.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4993	3871
1	4993	3871

prune166.0ms

Filtered

77 candidates to 121 candidates (-57.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	109	12	121
Fresh	6	1	7
Picked	1	0	1
Done	1	0	1
Total	117	13	130

Merged error: 0.0b

Counts

130 → 13

regimes82.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	61	87
1	61	87

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.5s	3204×	body	1280	valid
676.0ms	679×	body	2560	valid
526.0ms	1881×	body	640	valid
149.0ms	783×	body	320	valid
71.0ms	1115×	body	80	valid
43.0ms	338×	body	160	valid

Details

analyze2.0ms

sample107.0ms

simplify15.0ms

prune1.0ms

localize8.0ms

rewrite12.0ms

series46.0ms

simplify100.0ms

prune27.0ms

localize13.0ms

rewrite32.0ms

series104.0ms

simplify88.0ms

prune91.0ms

localize14.0ms

rewrite24.0ms

series142.0ms

simplify121.0ms

prune82.0ms

localize22.0ms

rewrite44.0ms

series392.0ms

simplify100.0ms

prune166.0ms

regimes82.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample3.1s

Profiling