Details

Time bar (total: 9.6s)

sample79.0ms

Algorithm
intervals
Results
19.0ms281×body80valid
16.0ms52×body640valid
12.0ms25×body1280valid
4.0ms20×body320valid
2.0ms13×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03217
17117
224117
374717
4219617
5500117

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
37.0b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
142×associate-*l/
102×flip3-- flip--
68×frac-times
66×sqrt-div
64×frac-add
44×pow1
34×associate-*r/
17×pow-prod-down
16×add-exp-log add-cbrt-cube
8×prod-exp cbrt-unprod
6×add-sqr-sqrt
5×add-cube-cbrt *-un-lft-identity
4×pow-sqr pow-prod-up add-log-exp
3×sqrt-prod
2×pow-plus
1×pow2 rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 swap-sqr associate-*r* associate-*l* *-commutative flip-+
Counts
4 → 135
Calls
4 calls:
65.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
94.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series724.0ms

Counts
4 → 12
Calls
4 calls:
284.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
29.0ms
(cos (/ (+ phi1 phi2) 2.0))
25.0ms
(cos (/ (+ phi1 phi2) 2.0))
386.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify58.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013733924
150013756

prune459.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 26.7b

localize22.0ms

Local error

Found 4 expressions with local error:

4.0b
(cos (/ (+ phi1 phi2) 2.0))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
37.0b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite466.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 100
Calls
4 calls:
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
423.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series452.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(cos (/ (+ phi1 phi2) 2.0))
24.0ms
(cos (/ (+ phi1 phi2) 2.0))
24.0ms
(cos (/ (+ phi1 phi2) 2.0))
380.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2.0))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify67.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012784428
150014345

prune562.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 26.7b

localize26.0ms

Local error

Found 4 expressions with local error:

4.0b
(cos (/ (+ phi1 phi2) 2.0))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
37.0b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite589.0ms

Algorithm
rewrite-expression-head
Rules
128×associate-*l/
96×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 100
Calls
4 calls:
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
10.0ms
(cos (/ (+ phi1 phi2) 2.0))
548.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series451.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(cos (/ (+ phi1 phi2) 2.0))
24.0ms
(cos (/ (+ phi1 phi2) 2.0))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
376.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (* (* (cbrt (cbrt (pow (cos (/ (+ phi1 phi2) 2.0)) 3))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))) (cbrt (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify63.0ms

Algorithm
egg-herbie
Counts
112 → 112
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012864578
150014514

prune651.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 26.7b

localize20.0ms

Local error

Found 4 expressions with local error:

4.0b
(cos (/ (+ phi1 phi2) 2.0))
4.0b
(cos (/ (+ phi1 phi2) 2.0))
37.0b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
37.0b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite283.0ms

Algorithm
rewrite-expression-head
Rules
256×associate-*l/
192×flip3-- flip--
132×sqrt-div
128×frac-times frac-add
64×associate-*r/
8×add-sqr-sqrt
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log add-cbrt-cube add-log-exp
2×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 172
Calls
4 calls:
15.0ms
(cos (/ (+ phi1 phi2) 2.0))
19.0ms
(cos (/ (+ phi1 phi2) 2.0))
137.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
93.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series816.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
24.0ms
(cos (/ (+ phi1 phi2) 2.0))
388.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
377.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify80.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012666778
150016662

prune768.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 26.7b

regimes716.0ms

Accuracy

69.9% (4.2b remaining)

Error of 29.3b against oracle of 25.1b and baseline of 38.9b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02734
12734

end0.0ms

sample2.0s

Algorithm
intervals
Results
549.0ms8383×body80valid
380.0ms1313×body640valid
323.0ms759×body1280valid
142.0ms708×body320valid
50.0ms371×body160valid