Details

Time bar (total: 21.6s)

sample113.0ms

Algorithm
intervals
Results
37.0ms49×body640valid
24.0ms258×body80valid
14.0ms25×body1280valid
9.0ms31×body320valid
2.0ms10×body160valid

simplify1.6s

Counts
1 → 1
Iterations
IterNodes
done5001
41037
3259
276
134
017

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 4.4b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
3.6b
(cos (/ (+ phi2 phi1) 2.0))

rewrite64.0ms

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 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 (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
7.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
37.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
17.0ms
(cos (/ (+ phi2 phi1) 2.0))

series1.5s

Counts
4 → 12
Calls
4 calls:
651.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2))
712.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0))) (- phi1 phi2)) R)
129.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2.0)))
41.0ms
(cos (/ (+ phi2 phi1) 2.0))

simplify1.3s

Counts
75 → 75
Iterations
IterNodes
done5001
21577
1359
0142

prune744.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.2b

localize48.0ms

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))
3.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite59.0ms

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-cbrt-cube associate-*r* add-exp-log
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×sub-neg pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 85
Calls
4 calls:
0.0ms
(hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
7.0ms
(* (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
33.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
15.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.8s

Counts
4 → 12
Calls
4 calls:
903.0ms
(hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
668.0ms
(* (hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2)) R)
178.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2))
47.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.3s

Counts
97 → 97
Iterations
IterNodes
done5000
21891
1415
0183

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.2b
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.2b
(* (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2))
0.4b
(log1p (cos (/ (+ phi1 phi2) 2.0)))
3.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
20×*-un-lft-identity
18×prod-diff add-cube-cbrt
11×distribute-rgt-in distribute-lft-in
6×pow1 add-cbrt-cube add-exp-log
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-- pow-prod-down prod-exp log1p-expm1 *-commutative cbrt-unprod flip-- distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Counts
4 → 77
Calls
4 calls:
0.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
28.0ms
(* (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2))
0.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
9.0ms
(cos (/ (+ phi1 phi2) 2.0))

series421.0ms

Counts
4 → 12
Calls
4 calls:
81.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
227.0ms
(* (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))) (- lambda1 lambda2))
82.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
30.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify1.1s

Counts
89 → 89
Iterations
IterNodes
done5000
21061
1302
0151

prune811.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.2b

localize52.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
0.1b
(* (hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
0.2b
(* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2))
3.6b
(cos (* 0.5 (+ phi1 phi2)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
22×*-un-lft-identity
20×add-cube-cbrt
18×prod-diff
12×distribute-rgt-in distribute-lft-in
8×pow1 add-cbrt-cube associate-*r* add-exp-log
6×associate-*l*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×cos-sum sub-neg pow-prod-down prod-exp associate-*r/ *-commutative cbrt-unprod unswap-sqr
1×hypot-udef flip3-- flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 87
Calls
4 calls:
0.0ms
(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
6.0ms
(* (hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
38.0ms
(* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2))
15.0ms
(cos (* 0.5 (+ phi1 phi2)))

series1.8s

Counts
4 → 12
Calls
4 calls:
921.0ms
(hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2))
625.0ms
(* (hypot (* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2)) (- phi1 phi2)) R)
196.0ms
(* (cos (* 0.5 (+ phi1 phi2))) (- lambda1 lambda2))
41.0ms
(cos (* 0.5 (+ phi1 phi2)))

simplify1.1s

Counts
99 → 99
Iterations
IterNodes
done5001
21929
1426
0195

prune817.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes865.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 0.1b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done26
126
020

end0.0ms

sample4.8s

Algorithm
intervals
Results
2.0s8314×body80valid
836.0ms740×body320valid
766.0ms1272×body640valid
609.0ms770×body1280valid
87.0ms346×body160valid