Details

Time bar (total: 29.4s)

sample200.0ms

Algorithm
intervals
Results
63.0ms282×body80valid
43.0ms26×body1280valid
43.0ms41×body640valid
22.0ms32×body320valid
4.0ms9×body160valid

simplify4.0s

Counts
1 → 1
Iterations
IterNodes
65440
51878
4761
3231
272
134
017

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.3b

localize53.0ms

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)))
2.0b
(cos (/ (+ phi2 phi1) 2))

rewrite35.0ms

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))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
19.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
8.0ms
(cos (/ (+ phi2 phi1) 2))

series1.4s

Counts
4 → 12
Calls
4 calls:
557.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2))
710.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2))) (- phi1 phi2)) R)
110.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi2 phi1) 2)))
28.0ms
(cos (/ (+ phi2 phi1) 2))

simplify1.7s

Counts
79 → 79
Iterations
IterNodes
33897
21082
1359
0144

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.2b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))
0.1b
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
2.0b
(cos (* (+ phi1 phi2) 1/2))

rewrite54.0ms

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 (* (+ phi1 phi2) 1/2))) (- phi1 phi2))
6.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
34.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
12.0ms
(cos (* (+ phi1 phi2) 1/2))

series1.4s

Counts
4 → 12
Calls
4 calls:
555.0ms
(hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2))
682.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)
154.0ms
(* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2)))
26.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify1.5s

Counts
79 → 79
Iterations
IterNodes
33918
21100
1363
0144

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))))
0.3b
(log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))
0.5b
(expm1 (cos (* (+ phi1 phi2) 1/2)))
2.0b
(cos (* (+ phi1 phi2) 1/2))

rewrite58.0ms

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:
25.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))))
0.0ms
(log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))
1.0ms
(expm1 (cos (* (+ phi1 phi2) 1/2)))
31.0ms
(cos (* (+ phi1 phi2) 1/2))

series411.0ms

Counts
4 → 12
Calls
4 calls:
183.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (* (+ phi1 phi2) 1/2)))))
96.0ms
(log1p (expm1 (cos (* (+ phi1 phi2) 1/2))))
104.0ms
(expm1 (cos (* (+ phi1 phi2) 1/2)))
28.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify3.4s

Counts
71 → 71
Iterations
IterNodes
45140
31447
2512
1217
0102

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.2b

localize51.0ms

Local error

Found 4 expressions with local error:

0.5b
(expm1 (* (* (cbrt (cos (* (+ phi1 phi2) 1/2))) (cbrt (cos (* (+ phi1 phi2) 1/2)))) (cbrt (cos (* (+ phi1 phi2) 1/2)))))
2.0b
(cos (* (+ phi1 phi2) 1/2))
2.0b
(cos (* (+ phi1 phi2) 1/2))
2.0b
(cos (* (+ phi1 phi2) 1/2))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
5×log1p-expm1-u
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
1×expm1-log1p expm1-udef
Counts
4 → 42
Calls
4 calls:
0.0ms
(expm1 (* (* (cbrt (cos (* (+ phi1 phi2) 1/2))) (cbrt (cos (* (+ phi1 phi2) 1/2)))) (cbrt (cos (* (+ phi1 phi2) 1/2)))))
11.0ms
(cos (* (+ phi1 phi2) 1/2))
10.0ms
(cos (* (+ phi1 phi2) 1/2))
18.0ms
(cos (* (+ phi1 phi2) 1/2))

series162.0ms

Counts
4 → 12
Calls
4 calls:
80.0ms
(expm1 (* (* (cbrt (cos (* (+ phi1 phi2) 1/2))) (cbrt (cos (* (+ phi1 phi2) 1/2)))) (cbrt (cos (* (+ phi1 phi2) 1/2)))))
25.0ms
(cos (* (+ phi1 phi2) 1/2))
34.0ms
(cos (* (+ phi1 phi2) 1/2))
23.0ms
(cos (* (+ phi1 phi2) 1/2))

simplify1.9s

Counts
54 → 54
Iterations
IterNodes
52574
41072
3439
2204
1104
051

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.2b

regimes795.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations
IterNodes
218
118
014

end0.0ms

sample7.1s

Algorithm
intervals
Results
2.6s8349×body80valid
2.0s1259×body640valid
1.2s783×body1280valid
671.0ms762×body320valid
251.0ms396×body160valid