Details

Time bar (total: 10.4s)

sample67.0ms

Algorithm
intervals
Results
17.0ms267×body80valid
12.0ms42×body640valid
11.0ms25×body1280valid
6.0ms29×body320valid
1.0ms10×body160valid

simplify52.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03217
17117
224117
374717
4219617
5500117

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.6b
(cos (/ (+ phi1 phi2) 2.0))
3.6b
(cos (/ (+ phi1 phi2) 2.0))
36.7b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
130×associate-*l/
97×flip3-- flip--
66×sqrt-div
64×frac-times frac-add
32×associate-*r/
12×add-sqr-sqrt
9×*-un-lft-identity
7×pow1 add-cube-cbrt
6×add-exp-log add-cbrt-cube
5×associate-*l*
4×add-log-exp
3×associate-*r* sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 115
Calls
4 calls:
13.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
46.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series556.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
407.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify56.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
013123623
150023528

prune466.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 26.0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.6b
(cos (* 0.5 (+ phi2 phi1)))
3.6b
(cos (/ (+ phi1 phi2) 2.0))
36.7b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite83.0ms

Algorithm
rewrite-expression-head
Rules
97×flip3-- flip--
82×associate-*l/
80×associate-*r/
66×sqrt-div
64×frac-times frac-add
12×add-sqr-sqrt
9×*-un-lft-identity
7×pow1 add-cube-cbrt
6×add-exp-log add-cbrt-cube
5×associate-*l*
4×add-log-exp
3×associate-*r* sqrt-prod
2×cos-sum
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 flip3-+ pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out-- difference-of-squares unswap-sqr
Counts
4 → 117
Calls
4 calls:
10.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
3.0ms
(cos (* 0.5 (+ phi2 phi1)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
51.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

series750.0ms

Counts
4 → 12
Calls
4 calls:
87.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
30.0ms
(cos (* 0.5 (+ phi2 phi1)))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
606.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify58.0ms

Algorithm
egg-herbie
Counts
129 → 129
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013533644
150033549

prune598.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.0b

localize20.0ms

Local error

Found 4 expressions with local error:

3.6b
(cos (/ (+ phi1 phi2) 2.0))
3.6b
(cos (/ (+ phi1 phi2) 2.0))
36.7b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
36.7b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite123.0ms

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:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
47.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
47.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series862.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(cos (/ (+ phi1 phi2) 2.0))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
402.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
403.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify81.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012666778
150016662

prune774.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 26.0b

localize29.0ms

Local error

Found 4 expressions with local error:

3.6b
(cos (/ (+ phi1 phi2) 2.0))
36.7b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
36.7b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
36.7b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite193.0ms

Algorithm
rewrite-expression-head
Rules
288×flip3-- flip--
240×associate-*r/ associate-*l/
198×sqrt-div
192×frac-times frac-add
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 244
Calls
4 calls:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
50.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
53.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
53.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

series1.2s

Counts
4 → 12
Calls
4 calls:
32.0ms
(cos (/ (+ phi1 phi2) 2.0))
405.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
405.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))
408.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (cos (* 0.5 (+ phi2 phi1))) (- lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify114.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
0126410063
150019903

prune1.8s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 26.0b

regimes446.0ms

Accuracy

73.2% (3.7b remaining)

Error of 29.2b against oracle of 25.6b and baseline of 39.2b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03734
13934
23934

end0.0ms

sample1.9s

Algorithm
intervals
Results
567.0ms8420×body80valid
384.0ms1301×body640valid
328.0ms788×body1280valid
160.0ms762×body320valid
54.0ms370×body160valid