Details

analyze2.1s

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
4.7%	95.1%	0.2%	12
5.9%	93.2%	0.8%	13
8.5%	90.2%	1.3%	14

sample94.0ms

Algorithm

intervals

Results

21.0ms	171×	body	80	valid
15.0ms	34×	body	640	valid
10.0ms	15×	body	1280	valid
7.0ms	73×	body	80	invalid
6.0ms	20×	body	320	valid
5.0ms	8×	body	1280	invalid
5.0ms	11×	body	640	invalid
4.0ms	16×	body	160	valid
2.0ms	6×	body	320	invalid
0.0ms	1×	body	160	invalid

simplify123.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (120.0ms)

Iter	Nodes	Cost
0	5041	32

prune4.0ms

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: 43.4b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
40.0b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/_binary64`
102×	`flip3--_binary64` `flip--_binary64`
68×	`frac-times_binary64`
66×	`sqrt-div_binary64`
64×	`frac-add_binary64`
44×	`pow1_binary64`
34×	`associate-*r/_binary64`
17×	`pow-prod-down_binary64`
16×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`add-log-exp_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
3×	`sqrt-prod_binary64`
2×	`pow-plus_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

14.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
8.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
19.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

series242.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (*.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
187.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2))) (.f64 (-.f64 lambda1 lambda2) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

simplify49.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	5175	6839

prune176.0ms

Filtered

76 candidates to 147 candidates (-93.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	139	8	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	140	8	148

Merged error: 30.6b

Counts

148 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
3.3b	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
40.0b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--_binary64` `flip--_binary64`
196×	`frac-times_binary64`
138×	`sqrt-div_binary64`
136×	`frac-add_binary64`
130×	`associate-*l/_binary64`
74×	`associate-*r/_binary64`
73×	`cos-mult_binary64`
12×	`pow1_binary64` `add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `sqrt-prod_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `sqrt-pow1_binary64` `sqr-cos-a_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `pow-sqr_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 192

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
26.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

series206.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(*.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))
5.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
6.0ms	(cos.f64 (/.f64 (+.f64 phi1 phi2) 2))
184.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (.f64 (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)) (cos.f64 (/.f64 (+.f64 phi1 phi2) 2)))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

simplify93.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4997	11646
1	4997	11646

prune214.0ms

Filtered

107 candidates to 204 candidates (-90.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	204	8	212

Merged error: 30.5b

Counts

212 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (+.f64 phi1 phi2)) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
0.5b	(+.f64 1/2 (*.f64 (cos.f64 (+.f64 phi1 phi2)) 1/2))
3.5b	(cos.f64 (+.f64 phi1 phi2))
40.0b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (+.f64 phi1 phi2)) 1/2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

656×	`frac-times_binary64`
600×	`flip3--_binary64` `flip--_binary64`
442×	`associate-*r/_binary64`
420×	`sqrt-div_binary64`
416×	`frac-add_binary64`
328×	`associate-*l/_binary64`
147×	`flip3-+_binary64` `flip-+_binary64`
13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-l_binary64`
2×	`unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `distribute-rgt-out_binary64` `distribute-rgt1-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `cos-sum_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 476

Calls

4 calls:

42.0ms	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (+.f64 phi1 phi2)) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
4.0ms	(+.f64 1/2 (*.f64 (cos.f64 (+.f64 phi1 phi2)) 1/2))
5.0ms	(cos.f64 (+.f64 phi1 phi2))
31.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (+.f64 phi1 phi2)) 1/2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

series1.4s

Counts

4 → 12

Calls

4 calls:

783.0ms	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (+.f64 phi1 phi2)) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
8.0ms	(+.f64 1/2 (*.f64 (cos.f64 (+.f64 phi1 phi2)) 1/2))
4.0ms	(cos.f64 (+.f64 phi1 phi2))
630.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (cos.f64 (+.f64 phi1 phi2)) 1/2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

simplify226.0ms

Algorithm

egg-herbie

Counts

488 → 488

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5307	36813

prune791.0ms

Filtered

264 candidates to 488 candidates (-84.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	478	10	488
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	481	15	496

Merged error: 28.1b

Counts

496 → 15

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.5b	(+.f64 1/2 (.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))) 1/2))
40.0b	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))) 1/2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

656×	`frac-times_binary64`
600×	`flip3--_binary64` `flip--_binary64`
442×	`associate-*r/_binary64`
420×	`sqrt-div_binary64`
416×	`frac-add_binary64`
328×	`associate-*l/_binary64`
147×	`flip3-+_binary64` `flip-+_binary64`
17×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`pow1_binary64` `associate-r_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`sqrt-prod_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
3×	`unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `distribute-rgt-out_binary64` `distribute-rgt1-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `sin-mult_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 487

Calls

4 calls:

43.0ms	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
6.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(+.f64 1/2 (.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))) 1/2))
31.0ms	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))) 1/2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

series5.0s

Counts

4 → 12

Calls

4 calls:

2.5s	(.f64 R (sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))) 1/2))) (*.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2)))))
10.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
25.0ms	(+.f64 1/2 (.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 phi1) (sin.f64 phi2))) 1/2))
2.4s	(sqrt.f64 (+.f64 (.f64 (.f64 (-.f64 lambda1 lambda2) (-.f64 lambda1 lambda2)) (+.f64 1/2 (.f64 (-.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 phi1) (sin.f64 phi2))) 1/2))) (.f64 (-.f64 phi1 phi2) (-.f64 phi1 phi2))))

simplify246.0ms

Algorithm

egg-herbie

Counts

499 → 499

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5003	46260

prune844.0ms

Filtered

269 candidates to 499 candidates (-85.5%)

Pruning

18 alts after pruning (17 fresh and 1 done)

	Pruned	Kept	Total
New	495	4	499
Fresh	1	13	14
Picked	0	1	1
Done	0	0	0
Total	496	18	514

Merged error: 28.1b

Counts

514 → 18

regimes1.3s

Accuracy

68.8% (4.6b remaining)

Error of 28.4b against oracle of 23.8b and baseline of 38.7b

bsearch3.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	96	71
1	96	71

end0.0ms

sample3.0s

Algorithm

intervals

Results

611.0ms	868×	body	640	valid
588.0ms	5873×	body	80	valid
333.0ms	483×	body	1280	valid
223.0ms	2293×	body	80	invalid
201.0ms	300×	body	1280	invalid
197.0ms	438×	body	640	invalid
178.0ms	524×	body	320	valid
82.0ms	248×	body	320	invalid
65.0ms	252×	body	160	valid
22.0ms	106×	body	160	invalid

Details

analyze2.1s

sample94.0ms

simplify123.0ms

prune4.0ms

localize16.0ms

rewrite58.0ms

series242.0ms

simplify49.0ms

prune176.0ms

localize17.0ms

rewrite65.0ms

series206.0ms

simplify93.0ms

prune214.0ms

localize17.0ms

rewrite154.0ms

series1.4s

simplify226.0ms

prune791.0ms

localize25.0ms

rewrite163.0ms

series5.0s

simplify246.0ms

prune844.0ms

regimes1.3s

bsearch3.0ms

simplify2.0ms

end0.0ms

sample3.0s

Profiling