Details

Time bar (total: 26.5s)

sample161.0ms

Algorithm
intervals
Results
51.0ms46×body640valid
39.0ms269×body80valid
19.0ms24×body1280valid
12.0ms26×body320valid
3.0ms11×body160valid

simplify4.4s

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
01732
13416
27616
325716
482616
5235516
done500016

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize18.0ms

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))

rewrite67.0ms

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))
11.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
42.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
12.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
548.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
814.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
139.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
34.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify2.5s

Counts
75 → 75
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01391279
13271271
29601077
331941060
done50001059

prune419.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
0.1b
(* (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b
(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
2.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite72.0ms

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 (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
9.0ms
(* (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
38.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
18.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.9s

Counts
4 → 12
Calls
4 calls:
901.0ms
(hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
771.0ms
(* (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
169.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
33.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify3.0s

Counts
97 → 97
Iterations

Useful iterations: done (3.0s)

IterNodesCost
01842005
13691831
29741583
332521484
done50001301

prune424.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.0b

localize40.0ms

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))

rewrite81.0ms

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:
44.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
3.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
5.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
24.0ms
(cos (/ (+ phi1 phi2) 2.0))

series327.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
47.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
93.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
32.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.2s

Counts
109 → 109
Iterations

Useful iterations: done (1.2s)

IterNodesCost
01311572
12671275
28621143
done50001138

prune555.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.0b

localize54.0ms

Local error

Found 4 expressions with local error:

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

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
20×cbrt-prod log-pow
16×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
15×exp-prod
14×unpow-prod-down cube-prod
10×pow1
5×add-exp-log add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-unpow log-prod
2×cube-mult unpow3 sqr-pow
1×pow-to-exp pow-pow pow1/3 rem-log-exp pow-exp rem-cbrt-cube rem-cube-cbrt
Counts
4 → 90
Calls
4 calls:
10.0ms
(cbrt (pow (log (exp (cos (/ (+ phi1 phi2) 2.0)))) 3))
31.0ms
(pow (log (exp (cos (/ (+ phi1 phi2) 2.0)))) 3)
52.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
24.0ms
(cos (/ (+ phi1 phi2) 2.0))

series223.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(cbrt (pow (log (exp (cos (/ (+ phi1 phi2) 2.0)))) 3))
77.0ms
(pow (log (exp (cos (/ (+ phi1 phi2) 2.0)))) 3)
42.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
47.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify2.6s

Counts
102 → 102
Iterations

Useful iterations: done (2.5s)

IterNodesCost
01131527
12081063
2438959
32232943
done5001939

prune512.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.0b

regimes540.0ms

Accuracy

0% (0.1b remaining)

Error of 3.6b against oracle of 3.4b and baseline of 3.6b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01416
11716
done1716

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.5s8426×body80valid
955.0ms1319×body640valid
803.0ms778×body1280valid
372.0ms713×body320valid
230.0ms355×body160valid