Details

Time bar (total: 20.9s)

sample159.0ms

Algorithm
intervals
Results
56.0ms253×body80valid
29.0ms28×body1280valid
26.0ms33×body640valid
18.0ms30×body320valid
5.0ms13×body160valid

simplify1.2s

Counts
1 → 1
Iterations
IterNodes
done2013
62013
51878
4761
3231
272
134
017

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.6b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
3.7b
(cos (/ (+ phi2 phi1) 2))

rewrite52.0ms

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:
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
12.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
28.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
10.0ms
(cos (/ (+ phi2 phi1) 2))

series1.3s

Counts
4 → 12
Calls
4 calls:
524.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
612.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
125.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
34.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.1s

Counts
79 → 79
Iterations
IterNodes
done2005
32005
21076
1360
0144

prune752.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.4b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
0.2b
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
0.5b
(expm1 (cos (/ (+ phi2 phi1) 2)))
3.7b
(cos (/ (+ phi2 phi1) 2))

rewrite51.0ms

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×associate-*l* log1p-expm1-u
4×expm1-log1p-u insert-posit16 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:
34.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
0.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
1.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
15.0ms
(cos (/ (+ phi2 phi1) 2))

series425.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi2 phi1) 2)))))
90.0ms
(log1p (expm1 (cos (/ (+ phi2 phi1) 2))))
92.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
50.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.6s

Counts
71 → 71
Iterations
IterNodes
done2000
42000
31782
2532
1221
0103

prune731.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 2.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
3.7b
(cos (/ (+ phi2 phi1) 2))
3.7b
(cos (/ (+ phi2 phi1) 2))
3.7b
(cos (/ (+ phi2 phi1) 2))

rewrite72.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×cbrt-prod cbrt-div pow1/3 pow3 associate-*l/ cos-mult rem-cbrt-cube
Counts
4 → 44
Calls
4 calls:
22.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
21.0ms
(cos (/ (+ phi2 phi1) 2))
14.0ms
(cos (/ (+ phi2 phi1) 2))
14.0ms
(cos (/ (+ phi2 phi1) 2))

series123.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(cbrt (* (* (cos (/ (+ phi2 phi1) 2)) (cos (/ (+ phi2 phi1) 2))) (cos (/ (+ phi2 phi1) 2))))
33.0ms
(cos (/ (+ phi2 phi1) 2))
23.0ms
(cos (/ (+ phi2 phi1) 2))
34.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.1s

Counts
56 → 56
Iterations
IterNodes
done2005
52005
4739
3283
2130
180
049

prune577.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 2.4b

localize87.0ms

Local error

Found 4 expressions with local error:

0.2b
(expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))
0.2b
(log1p (log1p (expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))))
0.5b
(expm1 (cos (/ (+ phi2 phi1) 2)))
3.7b
(cos (/ (+ phi2 phi1) 2))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
6×log1p-expm1-u
5×expm1-log1p-u
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
2×expm1-log1p expm1-udef
1×log1p-udef log1p-expm1
Counts
4 → 46
Calls
4 calls:
1.0ms
(expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))
1.0ms
(log1p (log1p (expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))))
1.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
17.0ms
(cos (/ (+ phi2 phi1) 2))

series687.0ms

Counts
4 → 12
Calls
4 calls:
200.0ms
(expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))
117.0ms
(log1p (log1p (expm1 (expm1 (cos (/ (+ phi2 phi1) 2))))))
334.0ms
(expm1 (cos (/ (+ phi2 phi1) 2)))
35.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.4s

Counts
58 → 58
Iterations
IterNodes
done2000
42000
3896
2350
1174
084

prune551.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 2.4b

regimes1.2s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done21
121
017

end0.0ms

sample7.6s

Algorithm
intervals
Results
2.5s8470×body80valid
2.1s751×body1280valid
1.6s1272×body640valid
706.0ms710×body320valid
212.0ms332×body160valid