Details

Time bar (total: 26.1s)

sample194.0ms

Algorithm
intervals
Results
63.0ms47×body640valid
45.0ms273×body80valid
17.0ms18×body1280valid
10.0ms19×body320valid
5.0ms14×body160valid

simplify1.3s

Counts
1 → 1
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
01732
13416
27616
325916
4105516
done500116

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.9b

localize46.0ms

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)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite89.0ms

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:
1.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
14.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
53.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
20.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.7s

Counts
4 → 12
Calls
4 calls:
661.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
816.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
158.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
44.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.1s

Counts
75 → 75
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01391279
13351271
214311079
done50021069

prune845.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.7b

localize62.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
0.5b
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.5b
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-prod
26×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt associate-*r*
10×unpow-prod-down cube-prod
7×pow1 add-exp-log
6×add-cbrt-cube
5×associate-*l* unswap-sqr
4×expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
3×cube-mult pow-unpow unpow3
2×associate-*l/
1×pow-to-exp flip3-- pow-pow pow1/3 pow-prod-down pow-exp prod-exp *-commutative flip-- rem-cbrt-cube cbrt-unprod distribute-lft-out-- rem-cube-cbrt difference-of-squares
Counts
4 → 97
Calls
4 calls:
64.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
4.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
6.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
20.0ms
(cos (/ (+ phi1 phi2) 2.0))

series342.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
49.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
97.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
45.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify3.0s

Counts
109 → 109
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01311572
13231287
219511143
done50011141

prune1.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.7b

localize67.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (cbrt (pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)))
0.5b
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
0.6b
(pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)
2.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
63×cbrt-prod
39×unpow-prod-down cube-prod
22×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×add-exp-log cube-mult unpow3 sqr-pow
6×pow-unpow add-cbrt-cube
5×pow1 pow-exp
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp
2×pow-pow rem-cube-cbrt
1×pow1/3
Counts
4 → 122
Calls
4 calls:
29.0ms
(cbrt (cbrt (pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)))
7.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
13.0ms
(pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)
24.0ms
(cos (/ (+ phi1 phi2) 2.0))

series358.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(cbrt (cbrt (pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)))
98.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
148.0ms
(pow (pow (cos (/ (+ phi1 phi2) 2.0)) 3) 3)
52.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify3.9s

Counts
134 → 134
Iterations

Useful iterations: 2 (500.0ms)

IterNodesCost
01392358
13801678
218331552
done50001552

prune1.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 2.7b

localize60.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (cos (/ (+ phi1 phi2) 2.0)))
0.2b
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.5b
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
2.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite187.0ms

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-exp-log add-cbrt-cube
5×associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×distribute-rgt-in distribute-lft-in
2×associate-*l/
1×flip3-- rem-log-exp pow-prod-down prod-exp *-commutative flip-- cbrt-unprod rem-exp-log distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 73
Calls
4 calls:
25.0ms
(exp (cos (/ (+ phi1 phi2) 2.0)))
93.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
44.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
22.0ms
(cos (/ (+ phi1 phi2) 2.0))

series365.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(exp (cos (/ (+ phi1 phi2) 2.0)))
169.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
54.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
50.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify980.0ms

Counts
85 → 85
Iterations

Useful iterations: done (976.0ms)

IterNodesCost
01201104
1245993
2879875
done5001870

prune826.0ms

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 2.7b

regimes1.3s

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01922
12222
done2222

end0.0ms

sample7.0s

Algorithm
intervals
Results
2.2s8460×body80valid
1.6s1269×body640valid
1.4s777×body1280valid
497.0ms733×body320valid
186.0ms369×body160valid