Details

Time bar (total: 6.7s)

sample73.0ms

Algorithm
intervals
Results
17.0ms260×body80valid
14.0ms33×body1280valid
10.0ms36×body640valid
4.0ms19×body320valid
2.0ms14×body160valid

simplify59.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0348
1788
22618
38348
426008
550018
done50018

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 2.7b

localize14.0ms

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)))
3.3b
(cos (/ (+ phi1 phi2) 2.0))

rewrite46.0ms

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))
7.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
24.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
14.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
398.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
486.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
93.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify37.0ms

Counts
75 → 75
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0328677
11130579
25001569
done5001569

prune269.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b
(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.3b
(cos (/ (+ phi1 phi2) 2.0))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
11×pow1 add-sqr-sqrt add-cbrt-cube
9×*-un-lft-identity
7×add-cube-cbrt
6×associate-*r* associate-*l* prod-exp
4×expm1-log1p-u pow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
2×associate-*l/ *-commutative
1×hypot-udef flip3-- 1-exp flip-- distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 64
Calls
4 calls:
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
16.0ms
(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
23.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
395.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
487.0ms
(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
91.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
31.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify40.0ms

Counts
76 → 76
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0370704
11197587
25001577
done5001577

prune270.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.5b

localize22.0ms

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))))
3.3b
(cos (/ (+ phi1 phi2) 2.0))

rewrite82.0ms

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:
11.0ms
(exp (cos (/ (+ phi1 phi2) 2.0)))
39.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
20.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))

series200.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(exp (cos (/ (+ phi1 phi2) 2.0)))
93.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
31.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify66.0ms

Counts
85 → 85
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0225596
1690508
23156502
35001502
done5001502

prune340.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 2.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(log (exp (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.5b
(log (log (exp (exp (cos (/ (+ phi1 phi2) 2.0))))))
0.5b
(exp (exp (cos (/ (+ phi1 phi2) 2.0))))
3.3b
(cos (/ (+ phi1 phi2) 2.0))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
10×log-prod
9×add-sqr-sqrt add-cube-cbrt exp-prod *-un-lft-identity log-pow
7×pow1
5×add-exp-log add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
2×rem-log-exp
1×rem-exp-log
Counts
4 → 57
Calls
4 calls:
7.0ms
(log (exp (exp (cos (/ (+ phi1 phi2) 2.0)))))
7.0ms
(log (log (exp (exp (cos (/ (+ phi1 phi2) 2.0))))))
23.0ms
(exp (exp (cos (/ (+ phi1 phi2) 2.0))))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))

series186.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(log (exp (exp (cos (/ (+ phi1 phi2) 2.0)))))
30.0ms
(log (log (exp (exp (cos (/ (+ phi1 phi2) 2.0))))))
78.0ms
(exp (exp (cos (/ (+ phi1 phi2) 2.0))))
31.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify130.0ms

Counts
69 → 69
Iterations

Useful iterations: 4 (125.0ms)

IterNodesCost
0169451
1369390
2986390
33356388
45001378
done5001378

prune270.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 2.5b

regimes409.0ms

Accuracy

0% (0.2b remaining)

Error of 3.6b against oracle of 3.5b and baseline of 3.6b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0228
1248
2248
done248

end0.0ms

sample2.0s

Algorithm
intervals
Results
556.0ms8377×body80valid
382.0ms1279×body640valid
361.0ms821×body1280valid
150.0ms717×body320valid
47.0ms337×body160valid