Details

analyze778.0ms

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

sample225.0ms

Algorithm

intervals

Results

124.0ms	92×	body	1280	valid
48.0ms	55×	body	640	valid
19.0ms	24×	body	320	valid
14.0ms	71×	body	80	valid
6.0ms	14×	body	160	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5018	48

prune10.0ms

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: 0.4b

Counts

2 → 2

localize39.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
1.0b	(-.f64 3 (sqrt.f64 5))
1.9b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-cube-cbrt_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `associate-r_binary64` `associate-r/_binary64` `associate-l*_binary64`
5×	`difference-of-squares_binary64` `sqrt-prod_binary64`
4×	`sub-neg_binary64` `associate-/r/_binary64` `times-frac_binary64`
3×	`flip3-+_binary64` `flip3--_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `diff-cos_binary64` `-commutative_binary64`

Counts

4 → 84

Calls

4 calls:

15.0ms	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
13.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
5.0ms	(-.f64 3 (sqrt.f64 5))
6.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series360.0ms

Counts

4 → 10

Calls

4 calls:

335.0ms	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (-.f64 3 (sqrt.f64 5)) 2) (cos.f64 y)))))
15.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
0.0ms	(-.f64 3 (sqrt.f64 5))
10.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify48.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	4937	2438
1	4937	2438

prune221.0ms

Filtered

71 candidates to 94 candidates (-32.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	84	10	94
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	85	11	96

Merged error: 0.0b

Counts

96 → 11

localize36.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
0.4b	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (/.f64 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
1.9b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
16×	`*-un-lft-identity_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`associate-*r/_binary64`
12×	`associate-r_binary64`
11×	`pow1_binary64`
10×	`add-cube-cbrt_binary64`
8×	`flip3--_binary64` `flip--_binary64`
7×	`associate-l_binary64`
6×	`add-log-exp_binary64`
5×	`sub-neg_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `times-frac_binary64`
4×	`pow-prod-down_binary64` `associate-/r/_binary64` `sqrt-prod_binary64` `frac-times_binary64` `associate-*l/_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`associate-/r*_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `diff-cos_binary64`

Counts

4 → 101

Calls

4 calls:

22.0ms	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
15.0ms	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (/.f64 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))
15.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series387.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
336.0ms	(/.f64 (+.f64 2 (.f64 (.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (.f64 (/.f64 (/.f64 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))
15.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
10.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify82.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4988	3187
1	4988	3187

prune240.0ms

Filtered

83 candidates to 113 candidates (-36.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	108	5	113
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	113	11	124

Merged error: 0.0b

Counts

124 → 11

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))
0.3b	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
1.9b	(-.f64 (cos.f64 x) (cos.f64 y))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
45×	`*-un-lft-identity_binary64`
44×	`associate-l_binary64`
36×	`times-frac_binary64`
24×	`add-cube-cbrt_binary64`
17×	`difference-of-squares_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
15×	`associate-r_binary64`
13×	`pow1_binary64`
10×	`associate-*r/_binary64`
9×	`distribute-lft-out--_binary64`
8×	`flip3--_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `difference-of-sqr-1_binary64` `prod-exp_binary64`
5×	`pow-prod-down_binary64` `sub-neg_binary64`
4×	`unswap-sqr_binary64` `frac-times_binary64`
3×	`associate-l/_binary64` `-commutative_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
1×	`diff-log_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `diff-cos_binary64`

Counts

4 → 130

Calls

4 calls:

14.0ms	(*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))
24.0ms	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
13.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

series58.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))
26.0ms	(.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))
15.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
10.0ms	(-.f64 (cos.f64 x) (cos.f64 y))

simplify88.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4948	2008
1	4948	2008

prune271.0ms

Filtered

96 candidates to 142 candidates (-47.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	140	2	142
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	143	10	153

Merged error: 0.0b

Counts

153 → 10

localize42.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 2 (.f64 (log.f64 (pow.f64 (exp.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (*.f64 (/.f64 (/.f64 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))
0.4b	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
1.9b	(-.f64 (cos.f64 x) (cos.f64 y))
3.2b	(log.f64 (pow.f64 (exp.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64`
12×	`add-exp-log_binary64`
11×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
10×	`log-prod_binary64`
6×	`add-log-exp_binary64` `sub-neg_binary64` `pow1_binary64` `associate-r_binary64` `associate-r/_binary64` `associate-l*_binary64`
5×	`unpow-prod-down_binary64`
4×	`associate-/r/_binary64` `times-frac_binary64` `sqrt-prod_binary64`
3×	`flip3-+_binary64` `rem-log-exp_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `exp-sum_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip--_binary64` `associate-*l/_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `associate-/r_binary64` `diff-log_binary64` `log-pow_binary64` `sqr-pow_binary64` `unpow-prod-up_binary64` `clear-num_binary64` `pow-sub_binary64` `frac-2neg_binary64` `div-inv_binary64` `log-div_binary64` `pow-exp_binary64` `diff-cos_binary64` `-commutative_binary64`

Counts

4 → 92

Calls

4 calls:

15.0ms	(/.f64 (+.f64 2 (.f64 (log.f64 (pow.f64 (exp.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (*.f64 (/.f64 (/.f64 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))
13.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
5.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
6.0ms	(log.f64 (pow.f64 (exp.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))))

series381.0ms

Counts

4 → 12

Calls

4 calls:

305.0ms	(/.f64 (+.f64 2 (.f64 (log.f64 (pow.f64 (exp.f64 (.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16)))) (-.f64 (cos.f64 x) (cos.f64 y)))) (.f64 3 (+.f64 (+.f64 1 (.f64 (/.f64 (-.f64 (sqrt.f64 5) 1) 2) (cos.f64 x))) (*.f64 (/.f64 (/.f64 4 (+.f64 3 (sqrt.f64 5))) 2) (cos.f64 y)))))
15.0ms	(*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))
9.0ms	(-.f64 (cos.f64 x) (cos.f64 y))
52.0ms	(log.f64 (pow.f64 (exp.f64 (*.f64 (sqrt.f64 2) (-.f64 (sin.f64 x) (/.f64 (sin.f64 y) 16)))) (-.f64 (sin.f64 y) (/.f64 (sin.f64 x) 16))))

simplify55.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5010	2941

prune191.0ms

Filtered

79 candidates to 104 candidates (-31.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	104	10	114

Merged error: 0.0b

Counts

114 → 10

regimes130.0ms

Accuracy

0% (0.4b 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 (2.0ms)

Iter	Nodes	Cost
0	113	54
1	113	54

end0.0ms

sample6.9s

Algorithm

intervals

Results

3.6s	2689×	body	1280	valid
1.9s	1862×	body	640	valid
477.0ms	757×	body	320	valid
444.0ms	2338×	body	80	valid
151.0ms	354×	body	160	valid

Details

analyze778.0ms

sample225.0ms

simplify29.0ms

prune10.0ms

localize39.0ms

rewrite41.0ms

series360.0ms

simplify48.0ms

prune221.0ms

localize36.0ms

rewrite60.0ms

series387.0ms

simplify82.0ms

prune240.0ms

localize35.0ms

rewrite63.0ms

series58.0ms

simplify88.0ms

prune271.0ms

localize42.0ms

rewrite42.0ms

series381.0ms

simplify55.0ms

prune191.0ms

regimes130.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample6.9s

Profiling