Details

Time bar (total: 41.7s)

sample229.0ms

Algorithm
intervals
Results
53.0ms21×body160valid
45.0ms56×body640valid
38.0ms253×body80valid
28.0ms24×body1280valid
16.0ms33×body320valid

simplify4.2s

Counts
1 → 1
Iterations
IterNodes
done5000
51728
4730
3231
272
134
017

prune27.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.9b

localize53.0ms

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)
0.2b
(* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2))
4.4b
(cos (/ (+ phi2 phi1) 2.0))

rewrite108.0ms

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-exp-log associate-*r* add-cbrt-cube
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×sub-neg associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 85
Calls
4 calls:
1.0ms
(hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
16.0ms
(* (hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
61.0ms
(* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2))
24.0ms
(cos (/ (+ phi2 phi1) 2.0))

series2.3s

Counts
4 → 12
Calls
4 calls:
1.1s
(hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
895.0ms
(* (hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
260.0ms
(* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2))
59.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify4.8s

Counts
97 → 97
Iterations
IterNodes
done5010
34195
21125
1432
0190

prune1.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 4.7b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
0.1b
(* R (hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)))
0.2b
(* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2))
4.4b
(cos (/ (+ phi2 phi1) 2.0))

rewrite98.0ms

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-exp-log associate-*r* add-cbrt-cube
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×sub-neg associate-*r/ pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 85
Calls
4 calls:
1.0ms
(hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
14.0ms
(* R (hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)))
48.0ms
(* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2))
30.0ms
(cos (/ (+ phi2 phi1) 2.0))

series2.5s

Counts
4 → 12
Calls
4 calls:
1.2s
(hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
993.0ms
(* R (hypot (* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)))
258.0ms
(* (cos (/ (+ phi2 phi1) 2.0)) (- lambda1 lambda2))
50.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify4.2s

Counts
97 → 97
Iterations
IterNodes
done5004
34046
21120
1433
0189

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.7b

localize74.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (expm1 (log1p (cos (/ (+ phi2 phi1) 2.0)))) (- lambda1 lambda2))
0.2b
(expm1 (log1p (cos (/ (+ phi2 phi1) 2.0))))
0.4b
(log1p (cos (/ (+ phi2 phi1) 2.0)))
4.4b
(cos (/ (+ phi2 phi1) 2.0))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
20×*-un-lft-identity
18×add-cube-cbrt prod-diff
11×distribute-rgt-in distribute-lft-in
6×pow1 add-exp-log add-cbrt-cube
5×expm1-log1p-u associate-*r*
4×log1p-expm1-u add-log-exp
3×associate-*l*
2×sub-neg associate-*r/
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 → 77
Calls
4 calls:
49.0ms
(* (expm1 (log1p (cos (/ (+ phi2 phi1) 2.0)))) (- lambda1 lambda2))
0.0ms
(expm1 (log1p (cos (/ (+ phi2 phi1) 2.0))))
1.0ms
(log1p (cos (/ (+ phi2 phi1) 2.0)))
23.0ms
(cos (/ (+ phi2 phi1) 2.0))

series602.0ms

Counts
4 → 12
Calls
4 calls:
332.0ms
(* (expm1 (log1p (cos (/ (+ phi2 phi1) 2.0)))) (- lambda1 lambda2))
103.0ms
(expm1 (log1p (cos (/ (+ phi2 phi1) 2.0))))
106.0ms
(log1p (cos (/ (+ phi2 phi1) 2.0)))
60.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify3.4s

Counts
89 → 89
Iterations
IterNodes
done5000
31964
2666
1297
0151

prune964.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 4.7b

localize82.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (* (cos (/ (+ phi2 phi1) 2.0)) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))
4.4b
(cos (/ (+ phi2 phi1) 2.0))
4.4b
(cos (/ (+ phi2 phi1) 2.0))
4.4b
(cos (/ (+ phi2 phi1) 2.0))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
1×cbrt-prod cbrt-div cube-unmult pow1/3 associate-*r/ cos-mult rem-cbrt-cube
Counts
4 → 40
Calls
4 calls:
29.0ms
(cbrt (* (cos (/ (+ phi2 phi1) 2.0)) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))
34.0ms
(cos (/ (+ phi2 phi1) 2.0))
25.0ms
(cos (/ (+ phi2 phi1) 2.0))
24.0ms
(cos (/ (+ phi2 phi1) 2.0))

series223.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(cbrt (* (cos (/ (+ phi2 phi1) 2.0)) (* (cos (/ (+ phi2 phi1) 2.0)) (cos (/ (+ phi2 phi1) 2.0)))))
60.0ms
(cos (/ (+ phi2 phi1) 2.0))
53.0ms
(cos (/ (+ phi2 phi1) 2.0))
52.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify6.1s

Counts
52 → 52
Iterations
IterNodes
done5001
53615
4955
3389
2154
187
048

prune688.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 4.7b

regimes1.4s

Accuracy

0% (0.2b remaining)

Error of 3.8b against oracle of 3.6b and baseline of 3.8b

bsearch0.0ms

simplify5.0ms

Iterations
IterNodes
done19
119
016

end0.0ms

sample7.2s

Algorithm
intervals
Results
3.1s8281×body80valid
1.4s1342×body640valid
1.3s805×body1280valid
381.0ms697×body320valid
245.0ms336×body160valid