Details

Time bar (total: 13.1s)

sample90.0ms

Algorithm
intervals
Results
28.0ms276×body80valid
21.0ms45×body640valid
15.0ms27×body1280valid
5.0ms16×body320valid
2.0ms11×body160valid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03217
17117
224117
374717
4219617
5500117

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.3b

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))))
4.9b
(cos (/ (+ phi1 phi2) 2.0))
4.9b
(cos (/ (+ phi1 phi2) 2.0))
34.4b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite100.0ms

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:
26.0ms
(* (* (- 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))
48.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series541.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (* (- 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))
395.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify58.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
013733925
150013756

prune457.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 24.8b

localize25.0ms

Local error

Found 4 expressions with local error:

4.9b
(cos (/ (+ phi1 phi2) 2.0))
34.4b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
34.4b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
34.4b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite176.0ms

Algorithm
rewrite-expression-head
Rules
384×associate-*l/
288×flip3-- flip--
198×sqrt-div
192×frac-times frac-add
96×associate-*r/
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 244
Calls
4 calls:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
45.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
47.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
48.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.2s

Counts
4 → 12
Calls
4 calls:
25.0ms
(cos (/ (+ phi1 phi2) 2.0))
398.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
398.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
395.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify118.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
0126610063
150019903

prune1.1s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 24.8b

localize29.0ms

Local error

Found 4 expressions with local error:

34.4b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
34.4b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
35.6b
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
35.6b
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
512×associate-*l/
384×flip3-- flip--
256×frac-times frac-add
132×cbrt-div sqrt-div
128×associate-*r/
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 cbrt-prod sqrt-prod
4×add-exp-log flip3-+ add-cbrt-cube flip-+ add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 pow1/3
Counts
4 → 312
Calls
4 calls:
44.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
46.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
28.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
31.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.9s

Counts
4 → 12
Calls
4 calls:
568.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
401.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
459.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
460.0ms
(cbrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify143.0ms

Algorithm
egg-herbie
Counts
324 → 324
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
0143113406
1500113236

prune1.7s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 24.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
0.0b
(* (- phi1 phi2) (- phi1 phi2))
2.0b
(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
34.7b
(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite938.0ms

Algorithm
rewrite-expression-head
Rules
47×flip3-- flip--
36×sqrt-div
32×frac-add
28×associate-*r/
27×add-sqr-sqrt
26×*-un-lft-identity
20×frac-times
14×pow1
12×add-cube-cbrt
11×associate-*r*
10×associate-*l/
9×add-log-exp
8×add-exp-log associate-*l* add-cbrt-cube
7×swap-sqr sqrt-prod
6×distribute-lft-out--
4×difference-of-squares
3×sub-neg unswap-sqr
2×distribute-rgt-in distribute-lft-in flip3-+ diff-log pow-prod-down prod-exp *-commutative cbrt-unprod flip-+
1×pow2 rem-sqrt-square sqrt-pow1 pow-plus pow1/2 associate--l+ sum-log pow-sqr pow-prod-up
Counts
4 → 130
Calls
4 calls:
567.0ms
(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
17.0ms
(* (- phi1 phi2) (- phi1 phi2))
71.0ms
(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
275.0ms
(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

series397.0ms

Counts
4 → 12
Calls
4 calls:
203.0ms
(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
17.0ms
(* (- phi1 phi2) (- phi1 phi2))
29.0ms
(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
148.0ms
(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

simplify112.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
07252598
136752543
250012539

prune451.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 24.5b

regimes823.0ms

Accuracy

73.9% (3.8b remaining)

Error of 28.9b against oracle of 25.1b and baseline of 39.8b

bsearch3.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02734
12734

end0.0ms

sample2.5s

Algorithm
intervals
Results
874.0ms8523×body80valid
516.0ms1251×body640valid
465.0ms829×body1280valid
213.0ms667×body320valid
76.0ms361×body160valid