Details

Time bar (total: 5.6s)

sample60.0ms

Algorithm
intervals
Results
17.0ms267×body80valid
11.0ms26×body1280valid
9.0ms33×body640valid
4.0ms18×body320valid
2.0ms13×body160valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0348
1788
22618
38348
426008
550018

prune10.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.1b

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)
0.1b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite17.0ms

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))
3.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
7.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series934.0ms

Counts
4 → 12
Calls
4 calls:
371.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
447.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
88.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify39.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0328677
11130579
25001569

prune284.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
0.2b
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.5b
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
3.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
5×associate-*l* log1p-expm1-u
4×expm1-log1p-u add-log-exp
3×associate-*r*
2×associate-*l/
1×log1p-udef expm1-log1p flip3-- log1p-expm1 pow-prod-down prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- expm1-udef difference-of-squares unswap-sqr
Counts
4 → 55
Calls
4 calls:
6.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
1.0ms
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
1.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series266.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
53.0ms
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
64.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify59.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0206431
1601364
22665364
35001364

prune271.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(log1p (log1p (expm1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))))
0.2b
(expm1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.5b
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
3.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
6×log1p-expm1-u
5×expm1-log1p-u
4×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube add-log-exp
2×expm1-log1p expm1-udef
1×log1p-udef log1p-expm1
Counts
4 → 42
Calls
4 calls:
1.0ms
(log1p (log1p (expm1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))))
1.0ms
(expm1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
1.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series301.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(log1p (log1p (expm1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))))
123.0ms
(expm1 (expm1 (cos (/ (+ phi1 phi2) 2.0))))
63.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify190.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 4 (186.0ms)

IterNodesCost
0162304
1393270
21253266
34717264
45001259

prune259.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 3.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b
(exp (cos (/ (+ phi1 phi2) 2.0)))
0.1b
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.4b
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
3.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite30.0ms

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:
5.0ms
(exp (cos (/ (+ phi1 phi2) 2.0)))
12.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
6.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series189.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(exp (cos (/ (+ phi1 phi2) 2.0)))
88.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
26.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
30.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify71.0ms

Algorithm
egg-herbie
Counts
85 → 85
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0224596
1703507
23169501
35002501

prune295.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 3.0b

regimes401.0ms

Accuracy

0% (0.2b remaining)

Error of 3.5b against oracle of 3.3b and baseline of 3.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02112
12112

end0.0ms

sample1.8s

Algorithm
intervals
Results
546.0ms8294×body80valid
376.0ms1333×body640valid
308.0ms761×body1280valid
137.0ms673×body320valid
49.0ms358×body160valid