Details

Time bar (total: 1.5m)

sample61.0ms

Algorithm
intervals
Results
16.0ms255×body80valid
11.0ms40×body640valid
9.0ms22×body1280valid
5.0ms26×body320valid
2.0ms14×body160valid

simplify51.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03217
17117
224117
374717
4219617
5500117

prune3.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.7b
(cos (/ (+ phi1 phi2) 2.0))
4.7b
(cos (/ (+ phi1 phi2) 2.0))
37.4b
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite105.0ms

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:
32.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
6.0ms
(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))))

series547.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
395.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify65.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013733925
150013756

prune464.0ms

Filtered
147 candidates to 77 candidates (52.4%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 25.4b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.7b
(cos (/ (+ phi1 phi2) 2.0))
4.7b
(cos (/ (+ phi1 phi2) 2.0))
37.4b
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
97×flip3-- flip--
82×associate-*r/ associate-*l/
66×sqrt-div
64×frac-times frac-add
10×pow1
9×add-exp-log add-cbrt-cube
7×add-sqr-sqrt
6×add-cube-cbrt *-un-lft-identity
4×add-log-exp
3×associate-*l* pow-prod-down prod-exp sqrt-prod cbrt-unprod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 associate-*r* *-commutative flip-+
Counts
4 → 113
Calls
4 calls:
14.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
6.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
72.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series633.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
428.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify61.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
013213716
150013613

prune511.0ms

Filtered
125 candidates to 86 candidates (68.8%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.4b

localize27.0ms

Local error

Found 4 expressions with local error:

4.7b
(cos (/ (+ phi1 phi2) 2.0))
4.7b
(cos (/ (+ phi1 phi2) 2.0))
27.8b
(/ (* (cos (/ (+ phi1 phi2) 2.0)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (+ lambda1 lambda2))
37.4b
(sqrt (+ (* (- lambda1 lambda2) (/ (* (cos (/ (+ phi1 phi2) 2.0)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
47×flip3-- flip--
42×sqrt-div
40×frac-add
36×frac-times
28×associate-*l/
20×associate-*r/
13×add-exp-log add-cbrt-cube
11×*-un-lft-identity
8×add-sqr-sqrt
7×add-cube-cbrt
5×pow1
4×times-frac associate-/r* add-log-exp
3×cbrt-undiv div-exp prod-exp sqrt-prod cbrt-unprod
2×flip3-+ associate-/r/ flip-+ associate-/l/ distribute-lft-out
1×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num div-inv associate-/l*
Counts
4 → 98
Calls
4 calls:
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
7.0ms
(cos (/ (+ phi1 phi2) 2.0))
19.0ms
(/ (* (cos (/ (+ phi1 phi2) 2.0)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (+ lambda1 lambda2))
61.0ms
(sqrt (+ (* (- lambda1 lambda2) (/ (* (cos (/ (+ phi1 phi2) 2.0)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

series803.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(cos (/ (+ phi1 phi2) 2.0))
26.0ms
(cos (/ (+ phi1 phi2) 2.0))
230.0ms
(/ (* (cos (/ (+ phi1 phi2) 2.0)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (+ lambda1 lambda2))
516.0ms
(sqrt (+ (* (- lambda1 lambda2) (/ (* (cos (/ (+ phi1 phi2) 2.0)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify49.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
010952873
150012734

prune495.0ms

Filtered
110 candidates to 80 candidates (72.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 25.4b

localize22.0ms

Local error

Found 4 expressions with local error:

28.5b
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
28.5b
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
28.5b
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
37.4b
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite3.0s

Algorithm
rewrite-expression-head
Rules
29930×associate-*l/
20428×frac-times
16050×flip3-- flip--
15576×cbrt-div
5990×associate-*r/
5826×sqrt-div
5824×frac-add
6×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube add-log-exp
3×cbrt-prod pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 flip3-+ pow1/2 flip-+
Counts
4 → 5890
Calls
4 calls:
24.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
24.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
37.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
560.0ms
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

series1.1s

Counts
4 → 12
Calls
4 calls:
241.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
246.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
248.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
404.0ms
(sqrt (+ (* (* (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))) (* (- phi1 phi2) (- phi1 phi2))))

simplify5.5s

Algorithm
egg-herbie
Counts
5902 → 5902
Iterations

Useful iterations: 0 (259.0ms)

IterNodesCost
022397604260

prune1.2m

Filtered
5902 candidates to 5897 candidates (99.9%)
Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 25.4b

regimes520.0ms

Accuracy

74.8% (3.5b remaining)

Error of 28.6b against oracle of 25.1b and baseline of 39.2b

bsearch3.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03334
13334

end0.0ms

sample1.8s

Algorithm
intervals
Results
550.0ms8358×body80valid
357.0ms1224×body640valid
335.0ms805×body1280valid
157.0ms755×body320valid
54.0ms392×body160valid