Details

analyze2.2s

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

sample102.0ms

Algorithm

intervals

Results

20.0ms	191×	body	80	valid
17.0ms	18×	body	1280	valid
12.0ms	26×	body	640	valid
10.0ms	98×	body	80	invalid
8.0ms	18×	body	640	invalid
5.0ms	15×	body	320	valid
2.0ms	3×	body	1280	invalid
2.0ms	6×	body	320	invalid
1.0ms	6×	body	160	valid
0.0ms	2×	body	160	invalid

simplify49.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5055	32

prune17.0ms

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: 39.9b

Counts

2 → 2

localize236.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
36.7b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

198×	`flip3--` `flip--`
196×	`frac-times`
138×	`sqrt-div`
136×	`frac-add`
98×	`associate-r/` `associate-l/`
73×	`cos-mult`
12×	`pow1` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `sqrt-prod`
1×	`pow2` `sqr-cos-a` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 192

Calls

4 calls:

4.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
24.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series166.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
148.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify134.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4968	12293
1	4968	12293

prune568.0ms

Filtered

135 candidates to 204 candidates (-51.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	192	12	204
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	194	12	206

Merged error: 23.2b

Counts

206 → 12

localize22.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
36.7b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

96×	`flip3--` `flip--`
80×	`associate-*l/`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`unpow-prod-down` `pow-unpow` `cube-prod` `sqrt-prod`
1×	`cube-mult` `pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `flip3-+` `pow1/2` `unpow3` `pow-exp` `flip-+` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 116

Calls

4 calls:

2.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
19.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))) (* (- phi1 phi2) (- phi1 phi2))))

series164.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
143.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify51.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5853	5997

prune336.0ms

Filtered

87 candidates to 128 candidates (-47.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	124	4	128
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	129	11	140

Merged error: 23.2b

Counts

140 → 11

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
36.7b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

96×	`flip3--` `flip--`
80×	`associate-*l/`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
4×	`add-exp-log` `log-pow` `add-cbrt-cube` `add-log-exp`
3×	`log-prod` `exp-prod` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `rem-log-exp` `flip-+`

Counts

4 → 108

Calls

4 calls:

6.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
18.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

series159.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
144.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify50.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5693	6333

prune336.0ms

Filtered

85 candidates to 120 candidates (-41.2%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	119	12	131

Merged error: 23.2b

Counts

131 → 12

localize30.0ms

Local error

Found 4 expressions with local error:

2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
2.6b	(cos (/ (+ phi1 phi2) 2.0))
36.7b	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

96×	`flip3--` `flip--`
80×	`associate-*l/`
66×	`sqrt-div`
64×	`frac-times` `frac-add`
32×	`associate-*r/`
6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `flip-+`

Counts

4 → 100

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
28.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

series159.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
145.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (log (exp (cos (/ (+ phi1 phi2) 2.0))))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify51.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5661	6503

prune333.0ms

Filtered

80 candidates to 112 candidates (-40.0%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	112	12	124

Merged error: 23.2b

Counts

124 → 12

regimes1.0s

Accuracy

31.9% (11.5b remaining)

Error of 33.6b against oracle of 22.1b and baseline of 39.0b

bsearch81.0ms

Steps

Iters	Range		Point
8	-2.7510576485257e+119	-3.6923955403706485e+116	-1.058854383797295e+117

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	126	44
1	126	44

end0.0ms

sample2.9s

Algorithm

intervals

Results

643.0ms	5876×	body	80	valid
402.0ms	833×	body	640	valid
366.0ms	509×	body	1280	valid
268.0ms	2450×	body	80	invalid
215.0ms	458×	body	640	invalid
191.0ms	267×	body	1280	invalid
182.0ms	499×	body	320	valid
76.0ms	283×	body	160	valid
74.0ms	209×	body	320	invalid
24.0ms	104×	body	160	invalid

Details

analyze2.2s

sample102.0ms

simplify49.0ms

prune17.0ms

localize236.0ms

rewrite58.0ms

series166.0ms

simplify134.0ms

prune568.0ms

localize22.0ms

rewrite40.0ms

series164.0ms

simplify51.0ms

prune336.0ms

localize23.0ms

rewrite43.0ms

series159.0ms

simplify50.0ms

prune336.0ms

localize30.0ms

rewrite51.0ms

series159.0ms

simplify51.0ms

prune333.0ms

regimes1.0s

bsearch81.0ms

simplify2.0ms

end0.0ms

sample2.9s

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