Details

Time bar (total: 12.0s)

sample280.0ms

Algorithm
intervals
Results
201.0ms161×body1280valid
41.0ms61×body640valid
10.0ms3×body2560valid
8.0ms17×body320valid
4.0ms12×body160valid
0.0ms2×body80valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02612
13412
23612
33612

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 18.0b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.3b
(cos (- lambda1 lambda2))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
11×pow1 add-exp-log add-cbrt-cube
9×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×associate-*r*
4×associate-*l* pow-prod-down prod-exp cbrt-unprod add-log-exp
3×cos-diff
2×cos-sum *-commutative
1×distribute-rgt-in acos-asin sub-neg distribute-lft-in associate-*l/ cos-mult unswap-sqr
Counts
4 → 57
Calls
4 calls:
6.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
4.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.0ms
(cos (- lambda1 lambda2))

series189.0ms

Counts
4 → 12
Calls
4 calls:
115.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
43.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
14.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
17.0ms
(cos (- lambda1 lambda2))

simplify104.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0264773
11022656
24705656
35002656

prune286.0ms

Filtered
69 candidates to 49 candidates (71.0%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New551469
Fresh000
Picked101
Done000
Total561470

Merged error: 4.1b

Counts
70 → 14

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.3b
(* (sin lambda1) (sin lambda2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×associate-*l*
6×cos-mult
5×pow-prod-down prod-exp cbrt-unprod
4×add-log-exp
3×frac-times associate-*r/ *-commutative sin-mult
2×flip3-+ frac-add flip-+ unswap-sqr
1×distribute-rgt-in acos-asin distribute-lft-in associate-*l/
Counts
4 → 72
Calls
4 calls:
10.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
5.0ms
(* (sin lambda1) (sin lambda2))
6.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series317.0ms

Counts
4 → 12
Calls
4 calls:
188.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
43.0ms
(* (sin lambda1) (sin lambda2))
69.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
17.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify68.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04731301
121441097
250021096

prune393.0ms

Filtered
84 candidates to 55 candidates (65.5%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New691584
Fresh12113
Picked101
Done000
Total821698

Merged error: 4.0b

Counts
98 → 16

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.7b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×exp-prod
8×pow1 log-pow
7×associate-*l*
6×add-exp-log add-cbrt-cube
5×add-log-exp
3×acos-asin log-prod associate-*r*
2×exp-diff
1×log-div rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log unswap-sqr
Counts
4 → 58
Calls
4 calls:
9.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
2.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
3.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series175.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
75.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
16.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
16.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify120.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 4 (41.0ms)

IterNodesCost
01791561
14011313
28971309
312551309
435121305
550011305

prune379.0ms

Filtered
70 candidates to 46 candidates (65.7%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New63770
Fresh6915
Picked101
Done000
Total701686

Merged error: 3.9b

Counts
86 → 16

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin lambda1) (sin lambda2))
0.3b
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
0.7b
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.2b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 associate-*l*
8×add-exp-log add-cbrt-cube
7×log-prod
6×associate-*r*
4×exp-sum add-log-exp
3×unswap-sqr
2×pow-prod-down prod-exp *-commutative cbrt-unprod
1×acos-asin rem-log-exp log-pow sin-mult
Counts
4 → 61
Calls
4 calls:
5.0ms
(* (sin lambda1) (sin lambda2))
6.0ms
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
1.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series184.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (sin lambda1) (sin lambda2))
71.0ms
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
53.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
17.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify71.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (34.0ms)

IterNodesCost
02291302
16201089
214391074
324051072
450011072

prune320.0ms

Filtered
73 candidates to 51 candidates (69.9%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New72173
Fresh11415
Picked101
Done000
Total741589

Merged error: 3.9b

Counts
89 → 15

regimes556.0ms

Accuracy

0% (0.4b remaining)

Error of 4.0b against oracle of 3.5b and baseline of 4.0b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03519
13719
23719

end0.0ms

sample8.3s

Algorithm
intervals
Results
6.0s4783×body1280valid
1.5s2111×body640valid
352.0ms707×body320valid
98.0ms276×body160valid
21.0ms6×body2560valid
19.0ms120×body80valid

Profiling

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