Details

analyze795.0ms

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
50%	50%	0.1%	4
74.9%	25%	0.1%	5
74.9%	25%	0.1%	6
74.9%	25%	0.1%	7
74.9%	25%	0.1%	8
74.9%	25%	0.1%	9
74.9%	25%	0.1%	10
74.9%	25%	0.1%	11
74.9%	25%	0.1%	12
74.9%	25%	0.1%	13
74.9%	25%	0.1%	14

sample179.0ms

Algorithm

intervals

Results

120.0ms	123×	body	1024	valid
28.0ms	39×	body	512	valid
15.0ms	80×	body	128	valid
6.0ms	14×	body	256	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4924	77
1	4924	77

prune9.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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 → 2

localize33.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
0.7b	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
1.0b	(-.f64 3 (sqrt.f64 5))
1.7b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-l_binary64`
8×	`add-log-exp_binary64` `sub-neg_binary64` `add-cube-cbrt_binary64`
7×	`associate-r_binary64`
6×	`associate-*r/_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `sqrt-prod_binary64`
4×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`diff-log_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`times-frac_binary64` `diff-cos_binary64`

Counts

4 → 81

Calls

4 calls:

13.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
10.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
5.0ms	(-.f64 3 (sqrt.f64 5))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series269.0ms

Counts

4 → 10

Calls

4 calls:

121.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
72.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
0.0ms	(-.f64 3 (sqrt.f64 5))
76.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify73.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5130	1546

prune216.0ms

Filtered

62 candidates to 91 candidates (-46.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	9	91
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Merged error: 0.1b

Counts

93 → 10

localize43.0ms

Local error

Found 4 expressions with local error:

0.6b	(+.f64 (cos.f64 x) (cos.f64 y))
0.7b	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
1.0b	(-.f64 3 (sqrt.f64 5))
1.5b	(-.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 y) 3))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
18×	`difference-of-squares_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
10×	`add-log-exp_binary64`
9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`sqr-pow_binary64`
6×	`sub-neg_binary64` `distribute-lft-out--_binary64`
5×	`add-cube-cbrt_binary64`
4×	`associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `flip--_binary64`
2×	`diff-log_binary64`
1×	`sum-cos_binary64` `difference-cubes_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `associate-r_binary64` `+-commutative_binary64` `sqrt-prod_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 84

Calls

4 calls:

5.0ms	(+.f64 (cos.f64 x) (cos.f64 y))
12.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
5.0ms	(-.f64 3 (sqrt.f64 5))
14.0ms	(-.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 y) 3))

series280.0ms

Counts

4 → 10

Calls

4 calls:

62.0ms	(+.f64 (cos.f64 x) (cos.f64 y))
76.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
0.0ms	(-.f64 3 (sqrt.f64 5))
142.0ms	(-.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 y) 3))

simplify89.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4902	1830
1	4902	1830

prune231.0ms

Filtered

61 candidates to 94 candidates (-54.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	93	11	104

Merged error: 0.1b

Counts

104 → 11

localize44.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
0.6b	(+.f64 (cos.f64 x) (cos.f64 y))
0.7b	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
1.5b	(-.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 y) 3))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
18×	`difference-of-squares_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-l_binary64`
8×	`add-log-exp_binary64` `add-cube-cbrt_binary64` `sqr-pow_binary64`
7×	`sub-neg_binary64` `associate-r_binary64`
6×	`associate-*r/_binary64` `distribute-lft-out--_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`unswap-sqr_binary64` `*-commutative_binary64`
1×	`sum-cos_binary64` `difference-cubes_binary64` `flip3-+_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `times-frac_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 99

Calls

4 calls:

12.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
5.0ms	(+.f64 (cos.f64 x) (cos.f64 y))
11.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
15.0ms	(-.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 y) 3))

series412.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
55.0ms	(+.f64 (cos.f64 x) (cos.f64 y))
78.0ms	(.f64 3/2 (.f64 (cos.f64 x) (-.f64 (sqrt.f64 5) 1)))
161.0ms	(-.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 y) 3))

simplify94.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4919	2200
1	4919	2200

prune324.0ms

Filtered

71 candidates to 111 candidates (-56.3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	108	14	122

Merged error: 0.1b

Counts

122 → 14

localize52.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.f64 (.f64 3/2 (.f64 (cos.f64 x) (+.f64 -1 (.f64 5 (sqrt.f64 5))))) (+.f64 (.f64 (sqrt.f64 5) (sqrt.f64 5)) (+.f64 (.f64 1 1) (.f64 (sqrt.f64 5) 1))))
0.6b	(+.f64 (cos.f64 x) (cos.f64 y))
1.0b	(*.f64 (sqrt.f64 5) (sqrt.f64 5))
1.5b	(-.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 y) 3))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
19×	`pow1_binary64`
18×	`sqrt-prod_binary64`
16×	`difference-of-squares_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`add-cube-cbrt_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
8×	`add-log-exp_binary64` `pow1/2_binary64` `swap-sqr_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
5×	`pow-prod-up_binary64` `distribute-lft-out--_binary64`
4×	`cbrt-unprod_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-/r*_binary64` `cbrt-undiv_binary64` `times-frac_binary64` `div-exp_binary64` `pow-sqr_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `associate-/r/_binary64`
1×	`sum-cos_binary64` `difference-cubes_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip--_binary64` `pow2_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 122

Calls

4 calls:

19.0ms	(/.f64 (.f64 3/2 (.f64 (cos.f64 x) (+.f64 -1 (.f64 5 (sqrt.f64 5))))) (+.f64 (.f64 (sqrt.f64 5) (sqrt.f64 5)) (+.f64 (.f64 1 1) (.f64 (sqrt.f64 5) 1))))
5.0ms	(+.f64 (cos.f64 x) (cos.f64 y))
10.0ms	(*.f64 (sqrt.f64 5) (sqrt.f64 5))
13.0ms	(-.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 y) 3))

series548.0ms

Counts

4 → 10

Calls

4 calls:

316.0ms	(/.f64 (.f64 3/2 (.f64 (cos.f64 x) (+.f64 -1 (.f64 5 (sqrt.f64 5))))) (+.f64 (.f64 (sqrt.f64 5) (sqrt.f64 5)) (+.f64 (.f64 1 1) (.f64 (sqrt.f64 5) 1))))
58.0ms	(+.f64 (cos.f64 x) (cos.f64 y))
0.0ms	(*.f64 (sqrt.f64 5) (sqrt.f64 5))
174.0ms	(-.f64 (pow.f64 (cos.f64 x) 3) (pow.f64 (cos.f64 y) 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5994	2368

prune389.0ms

Filtered

79 candidates to 132 candidates (-67.1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	132	0	132
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	132	14	146

Merged error: 0.1b

Counts

146 → 14

regimes231.0ms

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	107	132
1	107	132

end0.0ms

sample5.5s

Algorithm

intervals

Results

3.6s	3499×	body	1024	valid
891.0ms	1380×	body	512	valid
500.0ms	2520×	body	128	valid
241.0ms	590×	body	256	valid
22.0ms	11×	body	2048	valid

Details

analyze795.0ms

sample179.0ms

simplify50.0ms

prune9.0ms

localize33.0ms

rewrite48.0ms

series269.0ms

simplify73.0ms

prune216.0ms

localize43.0ms

rewrite53.0ms

series280.0ms

simplify89.0ms

prune231.0ms

localize44.0ms

rewrite64.0ms

series412.0ms

simplify94.0ms

prune324.0ms

localize52.0ms

rewrite77.0ms

series548.0ms

simplify58.0ms

prune389.0ms

regimes231.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample5.5s

Profiling