Details

Time bar (total: 5.4s)

sample66.0ms

Algorithm
intervals
Results
19.0ms269×body80valid
11.0ms42×body640valid
11.0ms29×body1280valid
5.0ms25×body320valid
1.0ms8×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: 2.6b

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)))
3.5b
(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))

series886.0ms

Counts
4 → 12
Calls
4 calls:
353.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
424.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
83.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
25.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify36.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0328677
11130579
25001569

prune258.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 2.5b

localize17.0ms

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))))
0.4b
(log1p (cos (/ (+ phi1 phi2) 2.0)))
3.5b
(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×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:
7.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
1.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
1.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series248.0ms

Counts
4 → 12
Calls
4 calls:
114.0ms
(* (- lambda1 lambda2) (expm1 (log1p (cos (/ (+ phi1 phi2) 2.0)))))
51.0ms
(expm1 (log1p (cos (/ (+ phi1 phi2) 2.0))))
56.0ms
(log1p (cos (/ (+ phi1 phi2) 2.0)))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0191432
1547363
22476363
35001363

prune261.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.4b

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)
3.5b
(cos (/ (+ phi1 phi2) 2.0))

rewrite22.0ms

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:
10.0ms
(* (- 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))

series190.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (- lambda1 lambda2) (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3)))
26.0ms
(cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))
51.0ms
(pow (cos (/ (+ phi1 phi2) 2.0)) 3)
26.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify43.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
0273715
11100668
25002655

prune338.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(expm1 (log (+ 1 (cos (/ (+ phi1 phi2) 2.0)))))
0.4b
(log (+ 1 (cos (/ (+ phi1 phi2) 2.0))))
0.5b
(+ 1 (cos (/ (+ phi1 phi2) 2.0)))
3.5b
(cos (/ (+ phi1 phi2) 2.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
6×add-sqr-sqrt add-cube-cbrt add-log-exp
5×pow1 add-exp-log log1p-expm1-u
4×expm1-log1p-u log-prod add-cbrt-cube
3×fma-def
2×log-div expm1-log1p log1p-def flip3-+ flip-+ distribute-lft-out
1×+-commutative rem-log-exp sum-log log-pow expm1-udef
Counts
4 → 56
Calls
4 calls:
1.0ms
(expm1 (log (+ 1 (cos (/ (+ phi1 phi2) 2.0)))))
3.0ms
(log (+ 1 (cos (/ (+ phi1 phi2) 2.0))))
7.0ms
(+ 1 (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))

series170.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(expm1 (log (+ 1 (cos (/ (+ phi1 phi2) 2.0)))))
57.0ms
(log (+ 1 (cos (/ (+ phi1 phi2) 2.0))))
30.0ms
(+ 1 (cos (/ (+ phi1 phi2) 2.0)))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))

simplify51.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (14.0ms)

IterNodesCost
0172419
1539344
21602339
35002339

prune262.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 2.4b

regimes366.0ms

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
02010
12010

end0.0ms

sample2.0s

Algorithm
intervals
Results
541.0ms8336×body80valid
359.0ms1269×body640valid
343.0ms738×body320valid
289.0ms728×body1280valid
55.0ms379×body160valid