Details

Time bar (total: 20.8s)

sample148.0ms

Algorithm
intervals
Results
40.0ms46×body640valid
35.0ms254×body80valid
22.0ms26×body1280valid
12.0ms28×body320valid
2.0ms8×body160valid

simplify1.5s

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

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
0.1b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
1.6b
(cos (/ (+ phi2 phi1) 2.0))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
6×associate-*r*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 63
Calls
4 calls:
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
11.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
23.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
12.0ms
(cos (/ (+ phi2 phi1) 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
567.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
727.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
172.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
51.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify1.2s

Counts
75 → 75
Iterations
IterNodes
done5001
21577
1359
0142

prune749.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
0.1b
(* (hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.1b
(* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2))
1.6b
(cos (/ (+ phi2 phi1) 2.0))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
11×distribute-rgt-in distribute-lft-in
8×pow1 add-cbrt-cube associate-*r* add-exp-log
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×sub-neg pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 85
Calls
4 calls:
0.0ms
(hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
6.0ms
(* (hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
24.0ms
(* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2))
8.0ms
(cos (/ (+ phi2 phi1) 2.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
912.0ms
(hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
725.0ms
(* (hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
200.0ms
(* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2))
29.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify1.4s

Counts
97 → 97
Iterations
IterNodes
done5001
22086
1443
0193

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (cos (/ (+ phi2 phi1) 2.0)))
0.1b
(* (log (exp (cos (/ (+ phi2 phi1) 2.0)))) (- lambda1 lambda2))
0.4b
(log (exp (cos (/ (+ phi2 phi1) 2.0))))
1.6b
(cos (/ (+ phi2 phi1) 2.0))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×*-un-lft-identity
22×add-cube-cbrt
18×prod-diff
11×distribute-rgt-in distribute-lft-in
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-cbrt-cube add-exp-log
5×associate-*r* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×log-prod
2×sub-neg associate-*r/
1×flip3-- rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-- distribute-lft-out-- difference-of-squares unswap-sqr rem-exp-log
Counts
4 → 89
Calls
4 calls:
9.0ms
(exp (cos (/ (+ phi2 phi1) 2.0)))
42.0ms
(* (log (exp (cos (/ (+ phi2 phi1) 2.0)))) (- lambda1 lambda2))
22.0ms
(log (exp (cos (/ (+ phi2 phi1) 2.0))))
9.0ms
(cos (/ (+ phi2 phi1) 2.0))

series309.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(exp (cos (/ (+ phi2 phi1) 2.0)))
161.0ms
(* (log (exp (cos (/ (+ phi2 phi1) 2.0)))) (- lambda1 lambda2))
42.0ms
(log (exp (cos (/ (+ phi2 phi1) 2.0))))
38.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify1.4s

Counts
101 → 101
Iterations
IterNodes
done5000
21128
1326
0164

prune998.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.2b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b
(log1p (exp (cos (/ (+ phi2 phi1) 2.0))))
0.3b
(expm1 (log1p (exp (cos (/ (+ phi2 phi1) 2.0)))))
0.4b
(log (expm1 (log1p (exp (cos (/ (+ phi2 phi1) 2.0))))))
1.6b
(cos (/ (+ phi2 phi1) 2.0))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-exp-log add-cube-cbrt
4×add-cbrt-cube log1p-expm1-u add-log-exp
3×log-prod
1×log1p-udef expm1-log1p rem-log-exp log1p-expm1 log-pow expm1-udef
Counts
4 → 45
Calls
4 calls:
1.0ms
(log1p (exp (cos (/ (+ phi2 phi1) 2.0))))
0.0ms
(expm1 (log1p (exp (cos (/ (+ phi2 phi1) 2.0)))))
2.0ms
(log (expm1 (log1p (exp (cos (/ (+ phi2 phi1) 2.0))))))
18.0ms
(cos (/ (+ phi2 phi1) 2.0))

series591.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(log1p (exp (cos (/ (+ phi2 phi1) 2.0))))
209.0ms
(expm1 (log1p (exp (cos (/ (+ phi2 phi1) 2.0)))))
197.0ms
(log (expm1 (log1p (exp (cos (/ (+ phi2 phi1) 2.0))))))
34.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify1.0s

Counts
57 → 57
Iterations
IterNodes
done5000
31467
2460
1177
089

prune474.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.2b

regimes1.2s

Accuracy

0% (0.2b remaining)

Error of 3.9b against oracle of 3.8b and baseline of 3.9b

bsearch0.0ms

simplify2.0ms

Iterations
IterNodes
done19
119
016

end0.0ms

sample5.1s

Algorithm
intervals
Results
1.5s8430×body80valid
1.2s1221×body640valid
734.0ms785×body1280valid
589.0ms350×body160valid
453.0ms740×body320valid