Details

Time bar (total: 40.6s)

sample159.0ms

Algorithm
intervals
Results
41.0ms255×body80valid
26.0ms37×body640valid
25.0ms25×body1280valid
14.0ms28×body320valid
5.0ms14×body160valid

simplify949.0ms

Counts
1 → 1
Iterations
IterNodes
done5001
41037
3259
276
134
017

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.1b

localize20.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
2.9b
(cos (/ (+ phi2 phi1) 2.0))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity
8×associate-*l*
7×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r*
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
3 → 53
Calls
3 calls:
12.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
37.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
10.0ms
(cos (/ (+ phi2 phi1) 2.0))

series921.0ms

Counts
3 → 9
Calls
3 calls:
752.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
133.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
35.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify662.0ms

Counts
62 → 62
Iterations
IterNodes
done5000
21324
1306
0127

prune535.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.0b

localize39.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2)))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2))))
2.9b
(cos (* 0.5 (+ phi1 phi2)))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×*-un-lft-identity
8×associate-*l*
7×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r*
3×expm1-log1p-u log1p-expm1-u add-log-exp
2×cos-sum pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×distribute-rgt-in distribute-lft-in flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
3 → 55
Calls
3 calls:
10.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2)))) (- phi1 phi2)) R)
46.0ms
(* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2))))
14.0ms
(cos (* 0.5 (+ phi1 phi2)))

series869.0ms

Counts
3 → 9
Calls
3 calls:
720.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2)))) (- phi1 phi2)) R)
111.0ms
(* (- lambda1 lambda2) (cos (* 0.5 (+ phi1 phi2))))
37.0ms
(cos (* 0.5 (+ phi1 phi2)))

simplify839.0ms

Counts
64 → 64
Iterations
IterNodes
done5000
21369
1319
0139

prune518.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b
(- (* (cos (* 0.5 phi2)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* phi1 0.5))))
0.1b
(* (hypot (* (- lambda1 lambda2) (- (* (cos (* 0.5 phi2)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* phi1 0.5))))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (- (* (cos (* 0.5 phi2)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* phi1 0.5)))))
0.2b
(* (sin (* 0.5 phi2)) (sin (* phi1 0.5)))

rewrite343.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×*-un-lft-identity
11×associate-*l*
10×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
9×flip3-- associate-*r* flip-- sin-mult
8×frac-times cos-mult
6×add-log-exp
4×expm1-log1p-u associate-*r/ frac-sub log1p-expm1-u sub-div
3×distribute-rgt-in sub-neg distribute-lft-in prod-diff pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×associate-*l/
1×fma-neg diff-log distribute-lft-out-- difference-of-squares
Counts
4 → 101
Calls
4 calls:
60.0ms
(- (* (cos (* 0.5 phi2)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* phi1 0.5))))
11.0ms
(* (hypot (* (- lambda1 lambda2) (- (* (cos (* 0.5 phi2)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* phi1 0.5))))) (- phi1 phi2)) R)
227.0ms
(* (- lambda1 lambda2) (- (* (cos (* 0.5 phi2)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* phi1 0.5)))))
40.0ms
(* (sin (* 0.5 phi2)) (sin (* phi1 0.5)))

series23.8s

Counts
4 → 12
Calls
4 calls:
144.0ms
(- (* (cos (* 0.5 phi2)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* phi1 0.5))))
23.1s
(* (hypot (* (- lambda1 lambda2) (- (* (cos (* 0.5 phi2)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* phi1 0.5))))) (- phi1 phi2)) R)
405.0ms
(* (- lambda1 lambda2) (- (* (cos (* 0.5 phi2)) (cos (* phi1 0.5))) (* (sin (* 0.5 phi2)) (sin (* phi1 0.5)))))
101.0ms
(* (sin (* 0.5 phi2)) (sin (* phi1 0.5)))

simplify480.0ms

Counts
113 → 113
Iterations
IterNodes
done5000
1907
0311

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* lambda2 (cos (* phi1 0.5))) (cos (* 0.5 phi2)))
0.1b
(* lambda1 (sin (* phi1 0.5)))
0.2b
(* (sin (* 0.5 phi2)) (sin (* phi1 0.5)))
1.9b
(* lambda2 (* (sin (* 0.5 phi2)) (sin (* phi1 0.5))))

rewrite134.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1 add-cbrt-cube add-exp-log
14×add-sqr-sqrt
10×*-un-lft-identity associate-*r* associate-*l* add-cube-cbrt
8×pow-prod-down prod-exp cbrt-unprod
4×expm1-log1p-u *-commutative log1p-expm1-u add-log-exp
2×sin-mult unswap-sqr
1×associate-*r/
Counts
4 → 82
Calls
4 calls:
34.0ms
(* (* lambda2 (cos (* phi1 0.5))) (cos (* 0.5 phi2)))
22.0ms
(* lambda1 (sin (* phi1 0.5)))
28.0ms
(* (sin (* 0.5 phi2)) (sin (* phi1 0.5)))
47.0ms
(* lambda2 (* (sin (* 0.5 phi2)) (sin (* phi1 0.5))))

series385.0ms

Counts
4 → 12
Calls
4 calls:
106.0ms
(* (* lambda2 (cos (* phi1 0.5))) (cos (* 0.5 phi2)))
71.0ms
(* lambda1 (sin (* phi1 0.5)))
105.0ms
(* (sin (* 0.5 phi2)) (sin (* phi1 0.5)))
103.0ms
(* lambda2 (* (sin (* 0.5 phi2)) (sin (* phi1 0.5))))

simplify954.0ms

Counts
94 → 94
Iterations
IterNodes
done5001
21447
1320
0139

prune894.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes1.2s

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done33
133
024

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.4s8331×body80valid
1.3s1253×body640valid
1.2s758×body1280valid
502.0ms722×body320valid
106.0ms397×body160valid