Details

Time bar (total: 31.6s)

sample102.0ms

Algorithm
intervals
Results
26.0ms37×body1280valid
25.0ms285×body80valid
15.0ms41×body640valid
6.0ms23×body320valid
2.0ms10×body160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
01732
13416
27616
325916
4105516
done500116

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.3b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
0.1b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
4.1b
(cos (/ (+ phi1 phi2) 2.0))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×*-un-lft-identity
8×pow1 add-exp-log add-cube-cbrt associate-*l* add-cbrt-cube
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 (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
12.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
49.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
18.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
455.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
660.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
142.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
43.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify713.0ms

Counts
75 → 75
Iterations

Useful iterations: done (711.0ms)

IterNodesCost
01391279
13351271
214311079
done50021069

prune419.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.1b

localize39.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
0.2b
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.4b
(log1p (cos (/ (+ phi1 phi2) 2.0)))
4.1b
(cos (/ (+ phi1 phi2) 2.0))

rewrite69.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
5×expm1-log1p-u associate-*l*
4×log1p-expm1-u add-log-exp
3×associate-*r*
2×associate-*l/
1×log1p-udef expm1-log1p flip3-- log1p-expm1 pow-prod-down prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Counts
4 → 55
Calls
4 calls:
43.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
1.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
1.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))

series349.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
72.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
80.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
42.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify4.2s

Counts
67 → 67
Iterations

Useful iterations: done (4.2s)

IterNodesCost
098808
1202718
2637624
34541619
done5000616

prune425.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.1b

localize54.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.3b
(- (exp (log1p (cos (/ (+ phi1 phi2) 2.0)))) 1)
0.4b
(log1p (cos (/ (+ phi1 phi2) 2.0)))
4.1b
(cos (/ (+ phi1 phi2) 2.0))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
15×*-un-lft-identity
12×add-cube-cbrt
9×prod-diff
7×add-log-exp
5×expm1-log1p-u
4×pow1 add-exp-log add-cbrt-cube log1p-expm1-u
3×exp-prod fma-neg
2×log1p-udef rem-exp-log difference-of-squares
1×sub-neg expm1-def flip3-- diff-log difference-of-sqr-1 log1p-expm1 flip-- distribute-lft-out--
Counts
4 → 65
Calls
4 calls:
2.0ms
(exp (log1p (cos (/ (+ phi1 phi2) 2.0))))
14.0ms
(- (exp (log1p (cos (/ (+ phi1 phi2) 2.0)))) 1)
1.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
21.0ms
(cos (/ (+ phi1 phi2) 2.0))

series287.0ms

Counts
4 → 12
Calls
4 calls:
65.0ms
(exp (log1p (cos (/ (+ phi1 phi2) 2.0))))
100.0ms
(- (exp (log1p (cos (/ (+ phi1 phi2) 2.0)))) 1)
89.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
34.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify12.2s

Counts
77 → 77
Iterations

Useful iterations: 3 (1.4s)

IterNodesCost
01081081
1234842
2653725
34223668
done5000668

prune544.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.1b

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b
(log1p (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))
4.1b
(cos (/ (+ phi1 phi2) 2.0))
4.1b
(cos (/ (+ phi1 phi2) 2.0))
4.1b
(cos (/ (+ phi1 phi2) 2.0))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
5×expm1-log1p-u
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
1×log1p-udef log1p-expm1
Counts
4 → 38
Calls
4 calls:
0.0ms
(log1p (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))
17.0ms
(cos (/ (+ phi1 phi2) 2.0))
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
31.0ms
(cos (/ (+ phi1 phi2) 2.0))

series231.0ms

Counts
4 → 12
Calls
4 calls:
100.0ms
(log1p (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))
47.0ms
(cos (/ (+ phi1 phi2) 2.0))
53.0ms
(cos (/ (+ phi1 phi2) 2.0))
30.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify2.7s

Counts
50 → 50
Iterations

Useful iterations: 4 (457.0ms)

IterNodesCost
049684
188678
2184436
3535399
42123395
done5001395

prune350.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.1b

regimes521.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01618
11918
done1918

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.4s8353×body80valid
959.0ms1273×body640valid
759.0ms818×body1280valid
329.0ms674×body320valid
97.0ms363×body160valid