Details

Time bar (total: 10.8s)

sample88.0ms

Algorithm
intervals
Results
33.0ms277×body80valid
18.0ms49×body640valid
9.0ms19×body1280valid
6.0ms21×body320valid
2.0ms12×body160valid

simplify52.0ms

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: 40.1b

localize16.0ms

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))
36.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite81.0ms

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:
10.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
50.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series551.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
410.0ms
(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
013123624
150023529

prune488.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 26.0b

localize22.0ms

Local error

Found 4 expressions with local error:

3.6b
(cos (/ (+ phi1 phi2) 2.0))
3.6b
(cos (/ (+ phi1 phi2) 2.0))
26.7b
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))
36.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite74.0ms

Algorithm
rewrite-expression-head
Rules
60×associate-*l/
47×flip3-- flip--
42×sqrt-div
40×frac-add
36×frac-times
18×associate-*r/
11×*-un-lft-identity
9×add-exp-log add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt
5×pow1
4×times-frac associate-/r* add-log-exp
3×sqrt-prod
2×cbrt-undiv flip3-+ div-exp associate-/r/ flip-+ associate-/l/ distribute-lft-out
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 prod-exp clear-num cbrt-unprod div-inv associate-/l*
Counts
4 → 96
Calls
4 calls:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
10.0ms
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))
48.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

series694.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
116.0ms
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))
522.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify47.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010572690
150022584

prune484.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 26.0b

localize26.0ms

Local error

Found 4 expressions with local error:

3.6b
(cos (/ (+ phi1 phi2) 2.0))
12.9b
(/ (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (cbrt (+ lambda1 lambda2)) (cbrt (+ lambda1 lambda2)))) (cbrt (+ lambda1 lambda2)))
13.7b
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (cbrt (+ lambda1 lambda2)) (cbrt (+ lambda1 lambda2))))
36.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (cbrt (+ lambda1 lambda2)) (cbrt (+ lambda1 lambda2)))) (cbrt (+ lambda1 lambda2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite154.0ms

Algorithm
rewrite-expression-head
Rules
110×cbrt-div
100×times-frac
78×associate-*l/
74×associate-/r/
72×frac-times
69×*-un-lft-identity
56×cbrt-prod flip3-+ flip-+
47×flip3-- flip--
42×add-sqr-sqrt sqrt-div
41×add-cube-cbrt
40×frac-add
36×associate-*r/
34×add-exp-log
21×add-cbrt-cube
14×distribute-lft-out associate-/l*
13×cbrt-undiv div-exp
10×div-inv
8×prod-exp associate-/r* cbrt-unprod
5×pow1
4×add-log-exp
3×sqrt-prod associate-/l/
2×frac-2neg clear-num
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 227
Calls
4 calls:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
25.0ms
(/ (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (cbrt (+ lambda1 lambda2)) (cbrt (+ lambda1 lambda2)))) (cbrt (+ lambda1 lambda2)))
14.0ms
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (cbrt (+ lambda1 lambda2)) (cbrt (+ lambda1 lambda2))))
93.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (cbrt (+ lambda1 lambda2)) (cbrt (+ lambda1 lambda2)))) (cbrt (+ lambda1 lambda2)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.0s

Counts
4 → 12
Calls
4 calls:
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
141.0ms
(/ (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (cbrt (+ lambda1 lambda2)) (cbrt (+ lambda1 lambda2)))) (cbrt (+ lambda1 lambda2)))
232.0ms
(/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (cbrt (+ lambda1 lambda2)) (cbrt (+ lambda1 lambda2))))
630.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (/ (/ (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0))) (* (cbrt (+ lambda1 lambda2)) (cbrt (+ lambda1 lambda2)))) (cbrt (+ lambda1 lambda2)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify82.0ms

Algorithm
egg-herbie
Counts
239 → 239
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
017376816
150026499

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 26.0b

localize23.0ms

Local error

Found 4 expressions with local error:

3.6b
(cos (/ (+ phi1 phi2) 2.0))
36.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
36.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
36.6b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
384×associate-*l/
288×flip3-- flip--
198×sqrt-div
192×frac-times frac-add
96×associate-*r/
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))
46.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
48.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
49.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series1.2s

Counts
4 → 12
Calls
4 calls:
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
400.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
410.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
405.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify110.0ms

Algorithm
egg-herbie
Counts
256 → 256
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
0126610063
150019903

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 26.0b

regimes502.0ms

Accuracy

73.6% (3.6b remaining)

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

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03938
13938

end0.0ms

sample2.5s

Algorithm
intervals
Results
939.0ms8397×body80valid
488.0ms1350×body640valid
394.0ms784×body1280valid
193.0ms704×body320valid
78.0ms371×body160valid