Details

Time bar (total: 7.7s)

sample69.0ms

Algorithm
intervals
Results
16.0ms264×body80valid
13.0ms24×body1280valid
11.0ms39×body640valid
5.0ms21×body320valid
2.0ms16×body160valid

simplify56.0ms

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: 3.9b

localize13.0ms

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)))
2.8b
(cos (/ (+ phi1 phi2) 2.0))

rewrite46.0ms

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))
7.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
26.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
404.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
494.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
95.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify35.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0328677
11130579
25001569

prune267.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
0.1b
(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
2.8b
(cos (/ (+ phi1 phi2) 2.0))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log
11×pow1 add-sqr-sqrt add-cbrt-cube
9×*-un-lft-identity
7×add-cube-cbrt
6×associate-*r* associate-*l* prod-exp
4×expm1-log1p-u pow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
2×associate-*l/ *-commutative
1×hypot-udef flip3-- 1-exp flip-- distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 64
Calls
4 calls:
0.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
20.0ms
(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
23.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
397.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
698.0ms
(* (* 1 (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
96.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0370704
11197587
25001577

prune273.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
0.2b
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.3b
(log1p (cos (/ (+ phi1 phi2) 2.0)))
2.8b
(cos (/ (+ phi1 phi2) 2.0))

rewrite36.0ms

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×expm1-log1p-u associate-*l*
4×log1p-expm1-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:
24.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
0.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))

series267.0ms

Counts
4 → 12
Calls
4 calls:
123.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
55.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
61.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify55.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0191432
1547363
22476363
35001363

prune267.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
0.4b
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
2.8b
(cos (/ (+ phi1 phi2) 2.0))
2.8b
(cos (/ (+ phi1 phi2) 2.0))

rewrite60.0ms

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:
10.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
25.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) (* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
13.0ms
(cos (/ (+ phi1 phi2) 2.0))

series1.3s

Counts
4 → 12
Calls
4 calls:
717.0ms
(* (sqrt (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))) R)
492.0ms
(* (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))

simplify45.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0318932
11240780
25002773

prune267.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 3.6b

regimes341.0ms

Accuracy

0% (0.2b remaining)

Error of 3.7b against oracle of 3.5b and baseline of 3.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0228
1248
2248

end0.0ms

sample2.0s

Algorithm
intervals
Results
534.0ms8514×body80valid
365.0ms1285×body640valid
330.0ms806×body1280valid
146.0ms726×body320valid
50.0ms361×body160valid