Details

Time bar (total: 25.6s)

sample139.0ms

Algorithm
intervals
Results
60.0ms273×body80valid
17.0ms36×body640valid
17.0ms25×body1280valid
8.0ms18×body320valid
3.0ms14×body160valid

simplify798.0ms

Counts
1 → 1

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.5b
(cos (/ (+ phi1 phi2) 2.0))
4.5b
(cos (/ (+ phi1 phi2) 2.0))
37.7b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite321.0ms

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:
106.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
12.0ms
(cos (/ (+ phi1 phi2) 2.0))
163.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series749.0ms

Counts
4 → 12
Calls
4 calls:
116.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
36.0ms
(cos (/ (+ phi1 phi2) 2.0))
38.0ms
(cos (/ (+ phi1 phi2) 2.0))
559.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify575.0ms

Counts
147 → 147

prune678.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 26.8b

localize71.0ms

Local error

Found 4 expressions with local error:

4.5b
(cos (/ (+ phi1 phi2) 2.0))
4.5b
(cos (/ (+ phi1 phi2) 2.0))
37.7b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
37.7b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite393.0ms

Algorithm
rewrite-expression-head
Rules
256×associate-*l/
192×flip3-- flip--
132×sqrt-div
128×frac-times frac-add
64×associate-*r/
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 172
Calls
4 calls:
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
14.0ms
(cos (/ (+ phi1 phi2) 2.0))
141.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
188.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.4s

Counts
4 → 12
Calls
4 calls:
34.0ms
(cos (/ (+ phi1 phi2) 2.0))
52.0ms
(cos (/ (+ phi1 phi2) 2.0))
658.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
646.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify756.0ms

Counts
184 → 184

prune1.3s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 26.8b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- phi1 phi2) (- phi1 phi2))
0.0b
(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
2.2b
(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
37.7b
(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite2.4s

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:
66.0ms
(* (- phi1 phi2) (- phi1 phi2))
1.4s
(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
176.0ms
(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
772.0ms
(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

series708.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (- phi1 phi2) (- phi1 phi2))
371.0ms
(* R (sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2)))))
54.0ms
(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
256.0ms
(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

simplify2.1s

Counts
142 → 142

prune729.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 26.4b

localize37.0ms

Local error

Found 4 expressions with local error:

2.2b
(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
2.2b
(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
37.7b
(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))
37.7b
(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite2.0s

Algorithm
rewrite-expression-head
Rules
42×flip3-- flip--
36×sqrt-div
32×frac-add
16×frac-times
14×add-log-exp
8×add-sqr-sqrt associate-*r/ associate-*l/
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log diff-log add-cbrt-cube
2×sub-neg rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate--l+ sum-log flip-+
Counts
4 → 90
Calls
4 calls:
211.0ms
(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
193.0ms
(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
779.0ms
(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))
781.0ms
(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

series613.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
36.0ms
(- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1)))
284.0ms
(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))
250.0ms
(sqrt (+ (- (+ (pow lambda1 2) (pow lambda2 2)) (* 2 (* lambda2 lambda1))) (* (- phi1 phi2) (- phi1 phi2))))

simplify1.5s

Counts
102 → 102

prune774.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 26.4b

regimes1.2s

Accuracy

70.2% (4.2b remaining)

Error of 29.3b against oracle of 25.1b and baseline of 39.2b

bsearch6.0ms

simplify1.1s

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.6s8341×body80valid
1.2s763×body1280valid
939.0ms1307×body640valid
450.0ms689×body320valid
94.0ms379×body160valid