Details

Time bar (total: 11.4s)

sample288.0ms

Algorithm
intervals
Results
193.0ms154×body1280valid
48.0ms66×body640valid
15.0ms31×body320valid
6.0ms4×body160valid
0.0ms2×body80valid

simplify2.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03319
13319

prune11.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 16.2b

Counts
2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
0.7b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.0b
(cos (- lambda1 lambda2))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
6×associate-*r* associate-*l*
4×add-log-exp
2×cos-sum pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin cos-diff sub-neg sin-mult
Counts
4 → 55
Calls
4 calls:
5.0ms
(* (sin phi1) (sin phi2))
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))

series56.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (sin phi1) (sin phi2))
32.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
9.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms
(cos (- lambda1 lambda2))

simplify40.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
04934887
14934887

prune179.0ms

Filtered
49 candidates to 67 candidates (-36.7%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New531467
Fresh000
Picked101
Done000
Total541468

Merged error: 4.0b

Counts
68 → 14

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.7b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
9×associate-*r* associate-*l*
4×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×sin-mult
1×acos-asin
Counts
4 → 64
Calls
4 calls:
6.0ms
(* (sin lambda1) (sin lambda2))
5.0ms
(* (sin phi1) (sin phi2))
4.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series84.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (sin lambda1) (sin lambda2))
10.0ms
(* (sin phi1) (sin phi2))
49.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
14.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify38.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
049271173
149271173

prune186.0ms

Filtered
54 candidates to 76 candidates (-40.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New651176
Fresh11213
Picked101
Done000
Total771390

Merged error: 3.9b

Counts
90 → 13

localize34.0ms

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

rewrite14.0ms

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:
6.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
3.0ms
(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)))))))))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))

series110.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))) R)
30.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
14.0ms
(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)))))))

simplify61.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
050461928

prune159.0ms

Filtered
41 candidates to 70 candidates (-70.7%)
Pruning

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New66470
Fresh3912
Picked101
Done000
Total701383

Merged error: 3.9b

Counts
83 → 13

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(exp (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
0.4b
(log (exp (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))))
0.5b
(asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
0.6b
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
13×*-un-lft-identity
12×exp-prod
9×add-log-exp
7×add-cube-cbrt log-pow
6×log-prod exp-sum difference-of-squares
5×pow1
4×add-exp-log asin-acos add-cbrt-cube
3×sub-neg times-frac distribute-lft-out-- associate--r-
2×exp-diff diff-log rem-exp-log
1×log-div flip3-- rem-log-exp flip--
Counts
4 → 65
Calls
4 calls:
8.0ms
(exp (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
8.0ms
(log (exp (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))))
2.0ms
(asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
8.0ms
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

series118.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(exp (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))))
28.0ms
(log (exp (- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))))
14.0ms
(asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
26.0ms
(- (/ PI 2) (asin (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))

simplify81.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
048812375
148812375

prune108.0ms

Filtered
56 candidates to 77 candidates (-37.5%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New71677
Fresh3912
Picked101
Done000
Total751590

Merged error: 3.7b

Counts
90 → 15

regimes820.0ms

Accuracy

0% (0.6b remaining)

Error of 3.9b against oracle of 3.2b and baseline of 3.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03833
13833

end0.0ms

sample8.8s

Algorithm
intervals
Results
6.2s4851×body1280valid
1.5s2059×body640valid
344.0ms676×body320valid
87.0ms261×body160valid
37.0ms11×body2560valid
25.0ms147×body80valid

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