Details

Time bar (total: 6.6s)

sample91.0ms

Algorithm
intervals
Results
31.0ms276×body80valid
19.0ms45×body640valid
15.0ms27×body1280valid
5.0ms16×body320valid
2.0ms11×body160valid

simplify59.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0348
1788
22618
38348
426008
550018

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.5b

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)))
4.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite22.0ms

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))
3.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
11.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))

series957.0ms

Counts
4 → 12
Calls
4 calls:
377.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
462.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
87.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
31.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify37.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0328677
11130579
25001569

prune278.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 4.3b

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)
4.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite29.0ms

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:
17.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
2.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
1.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
6.0ms
(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)))
27.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
49.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
31.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify47.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0273715
11100668
25002655

prune350.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- 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)))
4.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite18.0ms

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:
10.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
0.0ms
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
0.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))

series270.0ms

Counts
4 → 12
Calls
4 calls:
121.0ms
(* (- lambda1 lambda2) (log1p (expm1 (cos (/ (+ phi1 phi2) 2.0)))))
57.0ms
(log1p (expm1 (cos (/ (+ phi1 phi2) 2.0))))
64.0ms
(expm1 (cos (/ (+ phi1 phi2) 2.0)))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify60.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0206431
1601364
22665364
35001364

prune270.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 4.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
0.5b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))))
4.9b
(cos (/ (+ phi1 phi2) 2.0))
4.9b
(cos (/ (+ phi1 phi2) 2.0))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
21×pow1
18×sqrt-prod
16×*-un-lft-identity
14×add-cube-cbrt
11×associate-*l*
9×associate-*r*
8×add-exp-log sqrt-pow1 pow1/2 swap-sqr add-cbrt-cube
5×pow-prod-up unswap-sqr
4×expm1-log1p-u pow-prod-down log1p-expm1-u add-log-exp
3×pow-sqr
2×associate-*l/ prod-exp *-commutative cbrt-unprod
1×pow2 flip3-- pow-plus sqrt-unprod rem-square-sqrt flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 93
Calls
4 calls:
13.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
7.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))

series519.0ms

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

simplify45.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
02731000
11020845
25001787

prune323.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 4.3b

regimes344.0ms

Accuracy

0% (0.2b remaining)

Error of 3.8b against oracle of 3.6b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01910
11910

end0.0ms

sample2.5s

Algorithm
intervals
Results
876.0ms8523×body80valid
521.0ms1251×body640valid
471.0ms829×body1280valid
205.0ms667×body320valid
77.0ms361×body160valid