Details

Time bar (total: 13.0s)

sample59.0ms

Algorithm
intervals
Results
18.0ms291×body80valid
11.0ms39×body640valid
7.0ms18×body1280valid
4.0ms21×body320valid
1.0ms8×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03217
17117
224117
374717
4219617
5500117

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 39.0b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
35.7b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
276×*-un-lft-identity
142×associate-*l/
113×associate-*l*
102×flip3-- flip--
92×swap-sqr
75×distribute-lft-out--
68×frac-times
66×sqrt-div
64×frac-add
51×sqrt-prod
48×distribute-lft-out
46×add-sqr-sqrt
44×pow1
34×associate-*r/
26×associate-*r*
17×add-cube-cbrt pow-prod-down
16×add-exp-log add-cbrt-cube
12×unswap-sqr
8×prod-exp cbrt-unprod
5×*-commutative
4×pow-sqr pow-prod-up add-log-exp difference-of-squares
2×pow-plus
1×pow2 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 232
Calls
4 calls:
26.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))
95.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series552.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
403.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify85.0ms

Algorithm
egg-herbie
Counts
244 → 244
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
015515319
150015234

prune469.0ms

Filtered
244 candidates to 103 candidates (42.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2377244
Fresh000
Picked011
Done000
Total2378245

Merged error: 27.5b

Counts
245 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

4.0b
(cos (* 0.5 (+ phi2 phi1)))
4.0b
(cos (* 0.5 (+ phi2 phi1)))
4.0b
(cos (* 0.5 (+ phi2 phi1)))
35.7b
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite162.0ms

Algorithm
rewrite-expression-head
Rules
136×*-un-lft-identity
61×associate-*l*
57×distribute-lft-out
41×distribute-lft-out--
36×sqrt-prod
20×flip3-- flip--
18×sqrt-div
16×frac-add
12×cos-sum
8×frac-times
6×+-commutative distribute-rgt-in add-sqr-sqrt distribute-lft-in
5×pow1 add-cube-cbrt
4×add-exp-log associate-*r/ associate-*l/ add-cbrt-cube add-log-exp
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 97
Calls
4 calls:
9.0ms
(cos (* 0.5 (+ phi2 phi1)))
7.0ms
(cos (* 0.5 (+ phi2 phi1)))
7.0ms
(cos (* 0.5 (+ phi2 phi1)))
133.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series587.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(cos (* 0.5 (+ phi2 phi1)))
27.0ms
(cos (* 0.5 (+ phi2 phi1)))
28.0ms
(cos (* 0.5 (+ phi2 phi1)))
502.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify97.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 1 (13.0ms)

IterNodesCost
05384018
126293980
250013980

prune341.0ms

Filtered
109 candidates to 53 candidates (48.6%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1036109
Fresh246
Picked101
Done101
Total10710117

Merged error: 21.5b

Counts
117 → 10

localize41.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
4.0b
(cos (* 0.5 (+ phi2 phi1)))
4.0b
(cos (* 0.5 (+ phi2 phi1)))
35.7b
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite312.0ms

Algorithm
rewrite-expression-head
Rules
164×*-un-lft-identity
74×associate-*l*
65×distribute-lft-out
51×distribute-lft-out--
36×sqrt-prod
33×add-sqr-sqrt
21×flip3-- flip--
18×sqrt-div
16×frac-add
15×unswap-sqr
9×add-log-exp
8×frac-times cos-sum
7×difference-of-squares
5×pow1 +-commutative add-cube-cbrt
4×add-exp-log distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/ add-cbrt-cube
2×diff-log associate--l+
1×sub-neg unpow-prod-down rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 sum-log flip-+ unpow2 sqr-pow
Counts
4 → 118
Calls
4 calls:
130.0ms
(- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
7.0ms
(cos (* 0.5 (+ phi2 phi1)))
7.0ms
(cos (* 0.5 (+ phi2 phi1)))
161.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.4s

Counts
4 → 12
Calls
4 calls:
422.0ms
(- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
27.0ms
(cos (* 0.5 (+ phi2 phi1)))
33.0ms
(cos (* 0.5 (+ phi2 phi1)))
956.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (cos (* 0.5 (+ phi2 phi1))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify140.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
07916476
135926429
250026429

prune760.0ms

Filtered
130 candidates to 61 candidates (46.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1291130
Fresh189
Picked101
Done000
Total1319140

Merged error: 21.5b

Counts
140 → 9

localize60.0ms

Local error

Found 4 expressions with local error:

0.3b
(pow (cos (* 0.5 (+ phi2 phi1))) 2)
2.0b
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
4.0b
(cos (* 0.5 (+ phi2 phi1)))
35.7b
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite371.0ms

Algorithm
rewrite-expression-head
Rules
166×*-un-lft-identity
74×associate-*l*
65×distribute-lft-out
51×distribute-lft-out--
36×sqrt-prod
35×add-sqr-sqrt
21×flip3-- flip--
18×sqrt-div
16×frac-add
15×unswap-sqr
9×add-log-exp
8×frac-times
7×add-cube-cbrt difference-of-squares
6×pow1
5×add-exp-log
4×unpow-prod-down cos-sum associate-*r/ associate-*l/ add-cbrt-cube
3×+-commutative pow-unpow
2×distribute-rgt-in distribute-lft-in diff-log associate--l+ unpow2 sqr-pow
1×pow-to-exp sub-neg rem-sqrt-square pow-pow sqrt-pow1 flip3-+ pow1/2 pow-exp sum-log flip-+
Counts
4 → 125
Calls
4 calls:
3.0ms
(pow (cos (* 0.5 (+ phi2 phi1))) 2)
161.0ms
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
7.0ms
(cos (* 0.5 (+ phi2 phi1)))
193.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

series4.0s

Counts
4 → 12
Calls
4 calls:
41.0ms
(pow (cos (* 0.5 (+ phi2 phi1))) 2)
774.0ms
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
28.0ms
(cos (* 0.5 (+ phi2 phi1)))
3.1s
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* 0.5 phi2)) (cos (* 0.5 phi1))) (* (sin (* 0.5 phi2)) (sin (* 0.5 phi1)))) 2)) (* (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify177.0ms

Algorithm
egg-herbie
Counts
137 → 137
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
010118223
149517904
250017904

prune761.0ms

Filtered
137 candidates to 66 candidates (48.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1370137
Fresh088
Picked011
Done000
Total1379146

Merged error: 21.5b

Counts
146 → 9

regimes596.0ms

Accuracy

51.5% (9.2b remaining)

Error of 28.3b against oracle of 19.1b and baseline of 38.0b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07460
17860
27860

end0.0ms

sample1.8s

Algorithm
intervals
Results
534.0ms8282×body80valid
354.0ms1271×body640valid
321.0ms805×body1280valid
147.0ms730×body320valid
53.0ms390×body160valid