Details

Time bar (total: 7.5s)

sample73.0ms

Algorithm
intervals
Results
17.0ms276×body80valid
16.0ms33×body1280valid
12.0ms44×body640valid
4.0ms19×body320valid
1.0ms11×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: 40.7b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
2.4b
(cos (/ (+ phi1 phi2) 2.0))
2.4b
(cos (/ (+ phi1 phi2) 2.0))
37.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite207.0ms

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:
71.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
102.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series516.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
28.0ms
(cos (/ (+ phi1 phi2) 2.0))
376.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify59.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013733924
150013756

prune441.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 26.6b

localize21.0ms

Local error

Found 4 expressions with local error:

2.4b
(cos (/ (+ phi1 phi2) 2.0))
2.4b
(cos (/ (+ phi1 phi2) 2.0))
37.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
37.5b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite439.0ms

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:
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
11.0ms
(cos (/ (+ phi1 phi2) 2.0))
104.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
292.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series780.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(cos (/ (+ phi1 phi2) 2.0))
22.0ms
(cos (/ (+ phi1 phi2) 2.0))
364.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))
370.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify82.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
012666780
150016664

prune746.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 26.6b

localize4.0ms

Local error

Found 1 expressions with local error:

0.0b
(* R (- phi2 phi1))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt
5×*-un-lft-identity associate-*r*
3×pow1 add-exp-log add-cube-cbrt associate-*l* add-cbrt-cube
2×distribute-rgt-in sub-neg distribute-lft-in associate-*r/
1×flip3-- pow-prod-down prod-exp *-commutative flip-- cbrt-unprod distribute-lft-out-- add-log-exp difference-of-squares unswap-sqr
Counts
1 → 26
Calls
1 calls:
23.0ms
(* R (- phi2 phi1))

series30.0ms

Counts
1 → 3
Calls
1 calls:
30.0ms
(* R (- phi2 phi1))

simplify44.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
011298
146288
2188388
3500288

prune60.0ms

Pruning

14 alts after pruning (11 fresh and 3 done)

Merged error: 26.5b

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt (- phi2 phi1)) (cbrt (- phi2 phi1)))
0.6b
(cbrt (- phi2 phi1))
0.6b
(cbrt (- phi2 phi1))
0.6b
(cbrt (- phi2 phi1))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
43×cbrt-prod
37×add-sqr-sqrt
35×*-un-lft-identity
18×cbrt-div
15×add-cube-cbrt
11×pow1
10×swap-sqr
9×flip3-- pow1/3 flip-- distribute-lft-out--
8×associate-*r* associate-*l*
7×difference-of-squares
6×add-exp-log
4×frac-times add-cbrt-cube add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 101
Calls
4 calls:
38.0ms
(* (cbrt (- phi2 phi1)) (cbrt (- phi2 phi1)))
4.0ms
(cbrt (- phi2 phi1))
6.0ms
(cbrt (- phi2 phi1))
4.0ms
(cbrt (- phi2 phi1))

series493.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(* (cbrt (- phi2 phi1)) (cbrt (- phi2 phi1)))
129.0ms
(cbrt (- phi2 phi1))
125.0ms
(cbrt (- phi2 phi1))
130.0ms
(cbrt (- phi2 phi1))

simplify149.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 3 (141.0ms)

IterNodesCost
0260760
1908723
24494670
35001660

prune265.0ms

Pruning

20 alts after pruning (17 fresh and 3 done)

Merged error: 26.3b

regimes934.0ms

Accuracy

71.3% (3.9b remaining)

Error of 29.1b against oracle of 25.2b and baseline of 38.8b

bsearch3.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02734
12734

end0.0ms

sample2.0s

Algorithm
intervals
Results
530.0ms8376×body80valid
381.0ms1335×body640valid
338.0ms839×body1280valid
139.0ms698×body320valid
47.0ms355×body160valid