Details

Time bar (total: 15.2s)

analyze2.8s

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
7.8%92%0.2%9
7.8%92%0.2%10
10.1%89.7%0.2%11
10.1%89.7%0.2%12
13.9%85.9%0.2%13
13.9%85.9%0.2%14

sample350.0ms

Algorithm
intervals
Results
253.0ms157×body1280valid
64.0ms63×body640valid
9.0ms15×body320valid
3.0ms15×body80valid
2.0ms6×body160valid

simplify13.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (12.0ms)

IterNodesCost
039024
139024

prune24.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 15.0b

Counts
2 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
0.2b
(* (sin phi1) (cos (- lambda1 lambda2)))
3.0b
(cos (- lambda1 lambda2))
3.1b
(sin (- lambda1 lambda2))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×cos-diff add-cube-cbrt *-un-lft-identity
6×associate-*l*
5×distribute-rgt-in distribute-lft-in
4×associate-*r* pow-prod-down prod-exp cbrt-unprod add-log-exp
2×sub-neg *-commutative sin-cos-mult
1×cos-sum sin-sum associate-*r/ sin-diff unswap-sqr
Counts
4 → 62
Calls
4 calls:
6.0ms
(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
5.0ms
(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms
(cos (- lambda1 lambda2))
4.0ms
(sin (- lambda1 lambda2))

series51.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
13.0ms
(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms
(cos (- lambda1 lambda2))
5.0ms
(sin (- lambda1 lambda2))

simplify56.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
04865693
14865693

prune214.0ms

Filtered
54 candidates to 74 candidates (-37.0%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New641074
Fresh101
Picked101
Done000
Total661076

Merged error: 6.8b

Counts
76 → 10

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
0.2b
(* (sin phi1) (cos (- lambda1 lambda2)))
3.0b
(cos (- lambda1 lambda2))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*l*
7×cos-diff associate-*r*
5×distribute-rgt-in distribute-lft-in pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×*-commutative
2×sin-cos-mult unswap-sqr
1×sub-neg cos-sum associate-*r/
Counts
4 → 71
Calls
4 calls:
4.0ms
(* (cos phi1) (sin phi2))
6.0ms
(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
5.0ms
(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms
(cos (- lambda1 lambda2))

series53.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (cos phi1) (sin phi2))
26.0ms
(* (cos phi2) (* (sin phi1) (cos (- lambda1 lambda2))))
13.0ms
(* (sin phi1) (cos (- lambda1 lambda2)))
4.0ms
(cos (- lambda1 lambda2))

simplify69.0ms

Algorithm
egg-herbie
Counts
83 → 83
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
04889755
14889755

prune194.0ms

Filtered
59 candidates to 83 candidates (-40.7%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New78583
Fresh369
Picked101
Done000
Total821193

Merged error: 0.1b

Counts
93 → 11

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (cos phi1) (sin phi2))
0.2b
(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
0.2b
(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×pow1 add-exp-log add-cbrt-cube
12×associate-*l*
11×add-cube-cbrt *-un-lft-identity
10×associate-*r*
9×associate-*r/
6×pow-prod-down prod-exp cbrt-unprod
5×distribute-rgt-in distribute-lft-in
4×*-commutative add-log-exp
3×sin-mult unswap-sqr
2×flip3-+ frac-add cos-mult flip-+
Counts
4 → 85
Calls
4 calls:
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(* (cos phi1) (sin phi2))
10.0ms
(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
10.0ms
(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

series96.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (sin lambda1) (sin lambda2))
9.0ms
(* (cos phi1) (sin phi2))
46.0ms
(* (cos phi2) (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
31.0ms
(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))

simplify52.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
052831210

prune214.0ms

Filtered
66 candidates to 97 candidates (-47.0%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New92597
Fresh3710
Picked101
Done000
Total9612108

Merged error: 0.1b

Counts
108 → 12

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (cos phi2) (cbrt (pow (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)))
0.2b
(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.5b
(pow (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
21.2b
(cbrt (pow (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-prod add-sqr-sqrt
15×associate-*r/
14×associate-*r*
11×pow1 add-exp-log add-cube-cbrt *-un-lft-identity
10×add-cbrt-cube
9×cube-div
6×cbrt-div associate-*l*
4×flip3-+ frac-add cos-mult flip-+ sin-mult add-log-exp unswap-sqr sqr-pow
3×cube-mult unpow-prod-down pow-unpow unpow3 cube-prod pow-prod-down prod-exp cbrt-unprod
2×pow-pow pow-exp *-commutative rem-cube-cbrt
1×distribute-rgt-in pow-to-exp distribute-lft-in pow1/3 rem-cbrt-cube
Counts
4 → 99
Calls
4 calls:
10.0ms
(* (cos phi2) (cbrt (pow (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)))
9.0ms
(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
9.0ms
(pow (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
7.0ms
(cbrt (pow (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))

series167.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (cos phi2) (cbrt (pow (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)))
29.0ms
(* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
61.0ms
(pow (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3)
29.0ms
(cbrt (pow (* (sin phi1) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))) 3))

simplify48.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
054002019

prune172.0ms

Filtered
79 candidates to 111 candidates (-40.5%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1110111
Fresh01111
Picked011
Done000
Total11112123

Merged error: 0.1b

Counts
123 → 12

regimes769.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
016141
116141

end0.0ms

sample9.7s

Algorithm
intervals
Results
7.1s4628×body1280valid
1.7s1930×body640valid
325.0ms565×body320valid
117.0ms664×body80valid
78.0ms213×body160valid

Profiling

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