Details

Time bar (total: 8.5s)

sample63.0ms

Algorithm
intervals
Results
17.0ms271×body80valid
12.0ms25×body1280valid
11.0ms39×body640valid
4.0ms19×body320valid
2.0ms14×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03217
17117
224117
374717
4219617
5500117

prune3.0ms

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: 42.3b

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))))
2.5b
(cos (/ (+ phi1 phi2) 2.0))
2.5b
(cos (/ (+ phi1 phi2) 2.0))
39.2b
(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
34×associate-*r/
5×*-commutative
2×swap-sqr associate-*r* associate-*l*
1×pow2 flip3-+ pow1/2 flip-+
Counts
4 → 83
Calls
4 calls:
14.0ms
(* (* (- 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))
20.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series562.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
30.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
410.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify54.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012763364
150013324

prune327.0ms

Filtered
95 candidates to 49 candidates (51.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New89695
Fresh000
Picked011
Done000
Total89796

Merged error: 27.4b

Counts
96 → 7

localize27.0ms

Local error

Found 4 expressions with local error:

2.5b
(cos (* 0.5 (+ phi2 phi1)))
2.5b
(cos (* 0.5 (+ phi2 phi1)))
2.5b
(cos (* 0.5 (+ phi2 phi1)))
39.2b
(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))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
20×flip3-- flip--
18×sqrt-div
16×frac-add
12×cos-sum
8×frac-times
6×+-commutative distribute-rgt-in distribute-lft-in
4×associate-*r/ associate-*l/
1×flip3-+ pow1/2 flip-+
Counts
4 → 31
Calls
4 calls:
4.0ms
(cos (* 0.5 (+ phi2 phi1)))
4.0ms
(cos (* 0.5 (+ phi2 phi1)))
6.0ms
(cos (* 0.5 (+ phi2 phi1)))
24.0ms
(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))))

series595.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(cos (* 0.5 (+ phi2 phi1)))
29.0ms
(cos (* 0.5 (+ phi2 phi1)))
26.0ms
(cos (* 0.5 (+ phi2 phi1)))
511.0ms
(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))))

simplify84.0ms

Algorithm
egg-herbie
Counts
43 → 43
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
05112638
125742638
250012638

prune196.0ms

Filtered
43 candidates to 22 candidates (51.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New39443
Fresh145
Picked101
Done011
Total41950

Merged error: 21.5b

Counts
50 → 9

localize45.0ms

Local error

Found 4 expressions with local error:

2.0b
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
2.5b
(cos (* 0.5 (+ phi2 phi1)))
2.5b
(cos (* 0.5 (+ phi2 phi1)))
39.2b
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 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))))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
21×flip3-- flip--
18×sqrt-div
16×frac-add
8×frac-times cos-sum
5×+-commutative
4×distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/
2×associate--l+
1×sub-neg flip3-+ pow1/2 flip-+
Counts
4 → 33
Calls
4 calls:
20.0ms
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
4.0ms
(cos (* 0.5 (+ phi2 phi1)))
4.0ms
(cos (* 0.5 (+ phi2 phi1)))
25.0ms
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 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))))

series3.0s

Counts
4 → 12
Calls
4 calls:
550.0ms
(- (+ (* (pow lambda2 2) (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))))
27.0ms
(cos (* 0.5 (+ phi2 phi1)))
28.0ms
(cos (* 0.5 (+ phi2 phi1)))
2.4s
(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 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))))

simplify112.0ms

Algorithm
egg-herbie
Counts
45 → 45
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07253898
135673836
250013836

prune526.0ms

Filtered
45 candidates to 27 candidates (60.0%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New44145
Fresh077
Picked011
Done011
Total441054

Merged error: 21.5b

Counts
54 → 10

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b
(* R (- phi2 phi1))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- *-commutative flip--
Counts
1 → 7
Calls
1 calls:
3.0ms
(* R (- phi2 phi1))

series35.0ms

Counts
1 → 3
Calls
1 calls:
35.0ms
(* R (- phi2 phi1))

simplify72.0ms

Algorithm
egg-herbie
Counts
10 → 10
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
04126
18926
221226
355626
4200626
5500126

prune11.0ms

Filtered
10 candidates to 4 candidates (40.0%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New10010
Fresh077
Picked011
Done022
Total101020

Merged error: 21.5b

Counts
20 → 10

regimes790.0ms

Accuracy

54% (8.6b remaining)

Error of 28.9b against oracle of 20.3b and baseline of 39.0b

bsearch4.0ms

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07371
17571
27571

end0.0ms

sample1.8s

Algorithm
intervals
Results
546.0ms8407×body80valid
372.0ms1308×body640valid
315.0ms781×body1280valid
147.0ms735×body320valid
51.0ms332×body160valid