Details

analyze604.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
49.9%	49.9%	0.2%	3
49.9%	49.9%	0.2%	4
49.9%	49.9%	0.2%	5
49.9%	49.9%	0.2%	6
74.9%	25%	0.2%	7
74.9%	25%	0.2%	8
74.9%	25%	0.2%	9
74.9%	25%	0.2%	10
87.3%	12.5%	0.2%	11
87.3%	12.5%	0.2%	12
87.3%	12.5%	0.2%	13
87.3%	12.5%	0.2%	14

sample78.0ms

Algorithm

intervals

Results

39.0ms	216×	body	128	valid
17.0ms	19×	body	1024	valid
8.0ms	13×	body	512	valid
3.0ms	8×	body	256	valid

simplify45.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5324	39

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 1.8b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (sin.f64 ky) 2)
0.4b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
3.5b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.4b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64`
30×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
21×	`times-frac_binary64`
19×	`add-exp-log_binary64`
15×	`sqrt-prod_binary64`
13×	`unpow-prod-down_binary64`
12×	`associate-l_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `prod-exp_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `pow-exp_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `unpow2_binary64` `sqr-pow_binary64` `associate-/l*_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `div-inv_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

4 → 113

Calls

4 calls:

3.0ms	(pow.f64 (sin.f64 ky) 2)
7.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
17.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series2.1s

Counts

4 → 12

Calls

4 calls:

25.0ms	(pow.f64 (sin.f64 ky) 2)
1.1s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
302.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
659.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4968	4123
1	4968	4123

prune179.0ms

Filtered

83 candidates to 125 candidates (-50.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	122	4	126

Merged error: 0b

Counts

126 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
3.5b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.4b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
13.0b	(cbrt.f64 (pow.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 3))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64`
57×	`times-frac_binary64`
55×	`*-un-lft-identity_binary64`
54×	`cbrt-prod_binary64`
51×	`add-cube-cbrt_binary64`
34×	`unpow-prod-down_binary64`
33×	`sqrt-prod_binary64`
24×	`cube-prod_binary64`
18×	`add-exp-log_binary64`
12×	`associate-l_binary64`
8×	`add-cbrt-cube_binary64` `sqrt-div_binary64`
6×	`associate-/r*_binary64` `associate-/r/_binary64` `prod-exp_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `associate-r_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `div-inv_binary64`
3×	`sqr-pow_binary64` `associate-/l*_binary64` `div-exp_binary64` `pow-exp_binary64`
2×	`distribute-lft-out_binary64` `unpow2_binary64` `associate-*r/_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `pow1/2_binary64` `rem-cbrt-cube_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `cube-div_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 159

Calls

4 calls:

7.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
18.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
11.0ms	(cbrt.f64 (pow.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 3))

series3.1s

Counts

4 → 12

Calls

4 calls:

1.1s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
286.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
660.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))
1.1s	(cbrt.f64 (pow.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))) 3))

simplify96.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5144	7418

prune219.0ms

Filtered

95 candidates to 171 candidates (-80.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	171	0	171
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	171	4	175

Merged error: 0b

Counts

175 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
0.9b	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
3.5b	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
9.4b	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
39×	`times-frac_binary64`
38×	`add-cube-cbrt_binary64`
25×	`log-pow_binary64`
24×	`sqrt-prod_binary64` `exp-prod_binary64`
18×	`add-exp-log_binary64`
12×	`associate-l_binary64`
10×	`unpow-prod-down_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `prod-exp_binary64` `sqrt-div_binary64`
5×	`associate-r_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `flip-+_binary64`
3×	`log-prod_binary64` `associate-/l*_binary64` `div-inv_binary64` `div-exp_binary64` `pow-exp_binary64`
2×	`distribute-lft-out_binary64` `unpow2_binary64` `associate-*r/_binary64` `sqr-pow_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

4 → 131

Calls

4 calls:

7.0ms	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
10.0ms	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
17.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
4.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

series2.8s

Counts

4 → 12

Calls

4 calls:

1.1s	(/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))
743.0ms	(log.f64 (exp.f64 (/.f64 1/2 (sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2))))))))
310.0ms	(.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))
657.0ms	(sqrt.f64 (+.f64 1 (.f64 (pow.f64 (/.f64 (.f64 2 l) Om) 2) (+.f64 (pow.f64 (sin.f64 kx) 2) (pow.f64 (sin.f64 ky) 2)))))

simplify84.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5022	5279

prune241.0ms

Filtered

98 candidates to 143 candidates (-45.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	143	4	147

Merged error: 0b

Counts

147 → 4

localize2.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify6.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune0.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	2	2
Total	4	4

Merged error: 0b

Counts

4 → 4

regimes240.0ms

Accuracy

75.9% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.9b

bsearch53.0ms

Steps

Iters	Range		Point
7	3.680983735193328e+291	6.780323583757471e+292	6.582775082776307e+292

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	62
1	36	62

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	6322×	body	128	valid
706.0ms	793×	body	1024	valid
340.0ms	574×	body	512	valid
125.0ms	311×	body	256	valid

Details

analyze604.0ms

sample78.0ms

simplify45.0ms

prune5.0ms

localize24.0ms

rewrite44.0ms

series2.1s

simplify58.0ms

prune179.0ms

localize25.0ms

rewrite64.0ms

series3.1s

simplify96.0ms

prune219.0ms

localize23.0ms

rewrite60.0ms

series2.8s

simplify84.0ms

prune241.0ms

localize2.0ms

rewrite0.0ms

series0.0ms

simplify6.0ms

prune0.0ms

regimes240.0ms

bsearch53.0ms

simplify2.0ms

end0.0ms

sample2.5s

Profiling