Details

Time bar (total: 1.5m)

sample59.0ms

Algorithm
intervals
Results
15.0ms255×body80valid
10.0ms40×body640valid
9.0ms22×body1280valid
5.0ms26×body320valid
2.0ms14×body160valid

simplify50.0ms

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: 40.3b

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))))
4.7b
(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))))

rewrite50.0ms

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:
12.0ms
(* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
4.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
17.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

series548.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(* (* (- lambda1 lambda2) (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))
403.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))) (* (- phi1 phi2) (- phi1 phi2))))

simplify64.0ms

Algorithm
egg-herbie
Counts
147 → 147
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013733924
150013756

prune465.0ms

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))))

rewrite48.0ms

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:
8.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
8.0ms
(cos (/ (+ phi1 phi2) 2.0))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
17.0ms
(sqrt (+ (* (- lambda1 lambda2) (* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))) (* (- phi1 phi2) (- phi1 phi2))))

series818.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(* (cos (/ (+ phi1 phi2) 2.0)) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))))
27.0ms
(cos (/ (+ phi1 phi2) 2.0))
231.0ms
(cos (/ (+ phi1 phi2) 2.0))
404.0ms
(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
125 → 125
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013213716
150013613

prune522.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 25.4b

localize23.0ms

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))))

rewrite43.0ms

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))
5.0ms
(cos (/ (+ phi1 phi2) 2.0))
12.0ms
(/ (* (cos (/ (+ phi1 phi2) 2.0)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (+ lambda1 lambda2))
16.0ms
(sqrt (+ (* (- lambda1 lambda2) (/ (* (cos (/ (+ phi1 phi2) 2.0)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

series791.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(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))
509.0ms
(sqrt (+ (* (- lambda1 lambda2) (/ (* (cos (/ (+ phi1 phi2) 2.0)) (* (- (* lambda1 lambda1) (* lambda2 lambda2)) (cos (/ (+ phi1 phi2) 2.0)))) (+ lambda1 lambda2))) (* (- phi1 phi2) (- phi1 phi2))))

simplify55.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
010952873
150012734

prune474.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 25.4b

localize26.0ms

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))))

rewrite2.8s

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:
11.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
11.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
11.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
439.0ms
(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:
242.0ms
(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)))))
245.0ms
(cbrt (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0)))))
400.0ms
(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))))

simplify5.2s

Algorithm
egg-herbie
Counts
5902 → 5902
Iterations

Useful iterations: 0 (279.0ms)

IterNodesCost
022397604261

prune1.2m

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 25.4b

regimes434.0ms

Accuracy

-2.3% (14.4b remaining)

Error of 39.5b against oracle of 25.1b and baseline of 39.2b

bsearch680.0ms

Steps
ItersRangePoint
9
3.39606856293254e+147
2.865773570753347e+153
2.833616540079866e+153
10
1.8725839793603813e+68
1.2115491779261686e+79
1.891486701681941e+68
10
1.7133719513284803e+17
3.9902760699745926e+34
2.05230024370401e+31
8
3.0942019883315414e-162
3.7770015556411144e-158
3.627341585498709e-162
6
3.6874515700475633e-292
3.466594008541499e-291
1.1505150553105537e-291
8
-1.4117657420451131e-33
-4.08727170856852e-36
-1.3990149607820454e-33
8
-1827977.1926269082
-325.1897811235787
-343.89931459918483
7
-5.606151216793589e+47
-4.503215573940787e+45
-5.5068609279832755e+47
7
-9.745800339551167e+209
-9.846449359448498e+207
-2.621984700814708e+208

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0110115
1120115
2134115
3143115
4143115

end0.0ms

sample1.7s

Algorithm
intervals
Results
523.0ms8358×body80valid
325.0ms1224×body640valid
307.0ms805×body1280valid
149.0ms755×body320valid
51.0ms392×body160valid