Details

Time bar (total: 5.8s)

sample66.0ms

Algorithm
intervals
Results
19.0ms255×body80valid
14.0ms45×body640valid
10.0ms23×body1280valid
4.0ms20×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: 2.3b

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)))
2.2b
(cos (/ (+ phi1 phi2) 2.0))

rewrite21.0ms

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)
10.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series902.0ms

Counts
4 → 12
Calls
4 calls:
356.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
431.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
85.0ms
(* (- 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 (29.0ms)

IterNodesCost
0328677
11130579
25001569

prune269.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (hypot (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (- phi1 phi2)) R)
0.2b
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
0.4b
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
2.2b
(cos (/ (+ phi1 phi2) 2.0))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
15×*-un-lft-identity
13×add-cube-cbrt
10×pow1 associate-*r*
9×log-prod
8×add-exp-log associate-*l* log-pow add-cbrt-cube
6×exp-prod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
2×pow-prod-down associate-*l/ prod-exp *-commutative cbrt-unprod unswap-sqr
1×flip3-- rem-log-exp flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 80
Calls
4 calls:
3.0ms
(* (hypot (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (- phi1 phi2)) R)
22.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
11.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series576.0ms

Counts
4 → 12
Calls
4 calls:
439.0ms
(* (hypot (* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0))))) (- phi1 phi2)) R)
86.0ms
(* (- lambda1 lambda2) (log (exp (cos (/ (+ phi1 phi2) 2.0)))))
25.0ms
(log (exp (cos (/ (+ phi1 phi2) 2.0))))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0332829
11132701
25001690

prune339.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 2.2b

localize16.0ms

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)
2.2b
(cos (/ (+ phi1 phi2) 2.0))

rewrite28.0ms

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)))
1.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
1.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series191.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
28.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
47.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
30.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify43.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0273715
11100668
25002655

prune345.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 2.2b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.3b
(log1p (cos (/ (+ phi1 phi2) 2.0)))
0.4b
(log (exp (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))))
2.2b
(cos (/ (+ phi1 phi2) 2.0))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
5×pow1 expm1-log1p-u
4×add-exp-log log-pow add-cbrt-cube log1p-expm1-u add-log-exp
3×log-prod exp-prod
2×expm1-udef
1×log-div log1p-udef expm1-log1p exp-diff log1p-expm1 rem-log-exp
Counts
4 → 49
Calls
4 calls:
0.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
0.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
1.0ms
(log (exp (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series191.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
58.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
52.0ms
(log (exp (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))))
30.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify50.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 4 (45.0ms)

IterNodesCost
0125329
1214289
2470289
31244289
45001281

prune252.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 2.2b

regimes362.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02010
12010

end0.0ms

sample1.9s

Algorithm
intervals
Results
554.0ms8384×body80valid
377.0ms1256×body640valid
366.0ms820×body1280valid
165.0ms748×body320valid
51.0ms357×body160valid