Details

Time bar (total: 49.3s)

sample177.0ms

Algorithm
intervals
Results
64.0ms289×body80valid
34.0ms49×body640valid
26.0ms30×body1280valid
8.0ms17×body320valid
4.0ms14×body160valid

simplify5.0s

Counts
1 → 1
Iterations
IterNodes
done5003
51878
4761
3231
272
134
017

prune31.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize116.0ms

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)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
3.0b
(cos (/ (+ phi2 phi1) 2.0))

rewrite155.0ms

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 insert-posit16 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 → 67
Calls
4 calls:
1.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
23.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
83.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
46.0ms
(cos (/ (+ phi2 phi1) 2.0))

series2.7s

Counts
4 → 12
Calls
4 calls:
981.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
1.4s
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
217.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
63.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify6.7s

Counts
79 → 79
Iterations
IterNodes
done5000
34278
21073
1363
0146

prune1.6s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.7b

localize150.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (cos (/ (+ phi2 phi1) 2.0)))
0.2b
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2.0)))))
0.5b
(log (exp (cos (/ (+ phi2 phi1) 2.0))))
3.0b
(cos (/ (+ phi2 phi1) 2.0))

rewrite267.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
14×*-un-lft-identity
12×add-cube-cbrt
9×log-prod exp-prod
8×pow1 log-pow
7×associate-*r*
6×add-cbrt-cube add-exp-log
5×associate-*l* add-log-exp
4×expm1-log1p-u insert-posit16 log1p-expm1-u
3×distribute-rgt-in distribute-lft-in
2×associate-*l/
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 → 77
Calls
4 calls:
25.0ms
(exp (cos (/ (+ phi2 phi1) 2.0)))
121.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2.0)))))
63.0ms
(log (exp (cos (/ (+ phi2 phi1) 2.0))))
52.0ms
(cos (/ (+ phi2 phi1) 2.0))

series404.0ms

Counts
4 → 12
Calls
4 calls:
85.0ms
(exp (cos (/ (+ phi2 phi1) 2.0)))
210.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi2 phi1) 2.0)))))
41.0ms
(log (exp (cos (/ (+ phi2 phi1) 2.0))))
68.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify5.1s

Counts
89 → 89
Iterations
IterNodes
done5004
32030
2613
1249
0123

prune1.8s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.7b

localize155.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
0.2b
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.3b
(log1p (cos (/ (+ phi1 phi2) 2.0)))
3.0b
(cos (/ (+ phi1 phi2) 2.0))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity
6×pow1 add-cbrt-cube add-exp-log add-cube-cbrt
5×expm1-log1p-u associate-*l*
4×insert-posit16 log1p-expm1-u add-log-exp
3×associate-*r*
2×associate-*l/
1×log1p-udef expm1-log1p flip3-- pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod flip-- distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Counts
4 → 59
Calls
4 calls:
62.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
1.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
4.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
37.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
325.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
135.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
526.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
46.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify4.2s

Counts
71 → 71
Iterations
IterNodes
done5002
31593
2484
1207
0101

prune1.5s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 2.7b

localize225.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (cos (/ (+ phi2 phi1) 2.0)))
3.0b
(cos (/ (+ phi2 phi1) 2.0))
3.0b
(cos (/ (+ phi2 phi1) 2.0))
3.0b
(cos (/ (+ phi2 phi1) 2.0))

rewrite149.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-prod
1×pow1/3
Counts
4 → 44
Calls
4 calls:
6.0ms
(cbrt (cos (/ (+ phi2 phi1) 2.0)))
48.0ms
(cos (/ (+ phi2 phi1) 2.0))
48.0ms
(cos (/ (+ phi2 phi1) 2.0))
45.0ms
(cos (/ (+ phi2 phi1) 2.0))

series476.0ms

Counts
4 → 12
Calls
4 calls:
307.0ms
(cbrt (cos (/ (+ phi2 phi1) 2.0)))
46.0ms
(cos (/ (+ phi2 phi1) 2.0))
57.0ms
(cos (/ (+ phi2 phi1) 2.0))
66.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify6.6s

Counts
56 → 56
Iterations
IterNodes
done5000
62294
51195
4698
3321
2157
191
050

prune1.2s

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 2.7b

regimes3.2s

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.5b and baseline of 3.7b

bsearch0.0ms

simplify14.0ms

Iterations
IterNodes
done19
119
016

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.1s8371×body80valid
1.5s1368×body640valid
1.0s773×body1280valid
434.0ms731×body320valid
172.0ms387×body160valid