Details

sample101.0ms

Algorithm

intervals

Results

25.0ms	271×	body	80	valid
20.0ms	46×	body	640	valid
14.0ms	22×	body	1280	valid
9.0ms	27×	body	320	valid
2.0ms	9×	body	160	valid

simplify79.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	5002	32

prune16.0ms

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: 38.5b

Counts

2 → 2

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.7b	(cos (/ (+ phi1 phi2) 2.0))
2.7b	(cos (/ (+ phi1 phi2) 2.0))
35.9b	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

142×	`associate-*l/`
102×	`flip3--` `flip--`
68×	`frac-times`
66×	`sqrt-div`
64×	`frac-add`
44×	`pow1`
34×	`associate-*r/`
17×	`pow-prod-down`
16×	`add-exp-log` `add-cbrt-cube`
8×	`prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`pow-sqr` `pow-prod-up` `add-log-exp`
3×	`sqrt-prod`
2×	`pow-plus`
1×	`pow2` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip-+`

Counts

4 → 135

Calls

4 calls:

13.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
4.0ms	(cos (/ (+ phi1 phi2) 2.0))
17.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series179.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
137.0ms	(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify47.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	5122	6821

prune237.0ms

Filtered

78 candidates to 147 candidates (-88.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	143	4	147
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	143	6	149

Merged error: 23.9b

Counts

149 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
2.7b	(cos (/ (+ phi1 phi2) 2.0))
2.7b	(cos (/ (+ phi1 phi2) 2.0))
35.9b	(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` `rem-sqrt-square` `sqr-cos` `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))))

series158.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
5.0ms	(cos (/ (+ phi1 phi2) 2.0))
140.0ms	(sqrt (+ (* (- lambda1 lambda2) (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify101.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5045	11939

prune465.0ms

Filtered

137 candidates to 204 candidates (-48.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	199	5	204
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	201	9	210

Merged error: 21.0b

Counts

210 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- phi1 phi2) (- phi1 phi2))
1.0b	(+ (* lambda1 lambda1) (- (* lambda2 lambda2) (* (* lambda1 lambda2) 2)))
2.8b	(- (* lambda2 lambda2) (* (* lambda1 lambda2) 2))
35.9b	(sqrt (+ (+ (* lambda1 lambda1) (- (* lambda2 lambda2) (* (* lambda1 lambda2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
19×	`flip3--` `flip--`
18×	`sqrt-div`
16×	`frac-add`
12×	`pow1` `frac-times`
11×	`add-log-exp`
10×	`flip3-+` `flip-+`
9×	`add-cube-cbrt`
7×	`swap-sqr`
6×	`add-exp-log` `associate-r/` `associate-l/` `add-cbrt-cube` `distribute-lft-out--`
5×	`associate-r` `associate-l`
4×	`sub-neg` `difference-of-squares`
3×	`sqrt-prod`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `diff-log` `sum-log`
1×	`+-commutative` `pow2` `associate-+r-` `rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2` `pow-prod-down` `prod-exp` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `unswap-sqr`

Counts

4 → 103

Calls

4 calls:

9.0ms	(* (- phi1 phi2) (- phi1 phi2))
6.0ms	(+ (* lambda1 lambda1) (- (* lambda2 lambda2) (* (* lambda1 lambda2) 2)))
3.0ms	(- (* lambda2 lambda2) (* (* lambda1 lambda2) 2))
12.0ms	(sqrt (+ (+ (* lambda1 lambda1) (- (* lambda2 lambda2) (* (* lambda1 lambda2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* (- phi1 phi2) (- phi1 phi2))
6.0ms	(+ (* lambda1 lambda1) (- (* lambda2 lambda2) (* (* lambda1 lambda2) 2)))
6.0ms	(- (* lambda2 lambda2) (* (* lambda1 lambda2) 2))
47.0ms	(sqrt (+ (+ (* lambda1 lambda1) (- (* lambda2 lambda2) (* (* lambda1 lambda2) 2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify38.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4989	2572
1	4989	2572

prune192.0ms

Filtered

73 candidates to 115 candidates (-57.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	113	11	124

Merged error: 20.7b

Counts

124 → 11

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b	(* R (- phi2 phi1))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
5×	`-un-lft-identity` `associate-r*`
3×	`pow1` `add-exp-log` `add-cube-cbrt` `associate-l` `add-cbrt-cube`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-*r/`
1×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `unswap-sqr`

Counts

1 → 26

Calls

1 calls:

6.0ms

(* R (- phi2 phi1))

series7.0ms

Counts

1 → 3

Calls

1 calls:

7.0ms

(* R (- phi2 phi1))

simplify35.0ms

Algorithm

egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5005	186

prune27.0ms

Filtered

17 candidates to 29 candidates (-70.6%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	23	6	29
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	23	17	40

Merged error: 20.6b

Counts

40 → 17

regimes1.6s

Accuracy

58.7% (6.9b remaining)

Error of 28.6b against oracle of 21.7b and baseline of 38.5b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	108
1	33	108

end0.0ms

sample3.0s

Algorithm

intervals

Results

801.0ms	8341×	body	80	valid
595.0ms	1316×	body	640	valid
520.0ms	774×	body	1280	valid
265.0ms	801×	body	320	valid
82.0ms	352×	body	160	valid

Details

sample101.0ms

simplify79.0ms

prune16.0ms

localize16.0ms

rewrite52.0ms

series179.0ms

simplify47.0ms

prune237.0ms

localize17.0ms

rewrite58.0ms

series158.0ms

simplify101.0ms

prune465.0ms

localize15.0ms

rewrite34.0ms

series66.0ms

simplify38.0ms

prune192.0ms

localize4.0ms

rewrite7.0ms

series7.0ms

simplify35.0ms

prune27.0ms

regimes1.6s

bsearch2.0ms

simplify1.0ms

end0.0ms

sample3.0s

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