Details

Time bar (total: 6.6s)

sample63.0ms

Algorithm
intervals
Results
17.0ms278×body80valid
12.0ms44×body640valid
12.0ms29×body1280valid
2.0ms11×body320valid
1.0ms10×body160valid

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0348
1788
22618
38348
426008
550018

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.4b

localize17.0ms

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)))
2.6b
(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))

series947.0ms

Counts
4 → 12
Calls
4 calls:
375.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
453.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
90.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0328677
11130579
25001569

prune260.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.3b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
0.4b
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
0.5b
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
2.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite26.0ms

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:
13.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
2.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
2.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series196.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
31.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
49.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
27.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify43.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0273715
11100668
25002655

prune328.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 2.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
0.3b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
2.6b
(cos (/ (+ phi1 phi2) 2.0))
2.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*l*
11×pow1 add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
7×sqrt-prod
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod log1p-expm1-u add-log-exp
2×*-commutative unswap-sqr
Counts
4 → 65
Calls
4 calls:
5.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
6.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
649.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
448.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
30.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0318932
11240780
25002773

prune298.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (hypot (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
0.5b
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
2.6b
(cos (/ (+ phi1 phi2) 2.0))
2.6b
(cos (/ (+ phi1 phi2) 2.0))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×associate-*l*
4×expm1-log1p-u log-pow log1p-expm1-u add-log-exp
3×log-prod exp-prod pow-prod-down prod-exp sqrt-prod cbrt-unprod
1×rem-log-exp associate-*r* *-commutative
Counts
4 → 58
Calls
4 calls:
6.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
6.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series535.0ms

Counts
4 → 12
Calls
4 calls:
452.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
27.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify68.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0273792
1790611
22631581
35002578

prune295.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.3b

regimes327.0ms

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.6b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02310
12310

end0.0ms

sample1.8s

Algorithm
intervals
Results
538.0ms8426×body80valid
359.0ms1275×body640valid
315.0ms790×body1280valid
146.0ms730×body320valid
52.0ms361×body160valid