Details

Time bar (total: 13.1s)

sample274.0ms

Algorithm
intervals
Results
193.0ms150×body1280valid
44.0ms60×body640valid
13.0ms23×body320valid
4.0ms13×body160valid
2.0ms10×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: 17.6b

Counts
2 → 1

localize28.0ms

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)
1.3b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
4.1b
(cos (- lambda1 lambda2))

rewrite16.0ms

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)))
3.0ms
(* (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))

series171.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))
45.0ms
(* (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)))))
17.0ms
(cos (- lambda1 lambda2))

simplify105.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0264773
11022655
24705655
35002655

prune305.0ms

Filtered
69 candidates to 49 candidates (71.0%)
Pruning

16 alts after pruning (16 fresh and 0 done)

PrunedKeptTotal
New531669
Fresh000
Picked101
Done000
Total541670

Merged error: 3.6b

Counts
70 → 16

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
0.2b
(* (sin phi1) (sin phi2))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
1.3b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin 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-*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 phi1) (sin phi2))
3.0ms
(* (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))))))

series326.0ms

Counts
4 → 12
Calls
4 calls:
193.0ms
(* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))
47.0ms
(* (sin phi1) (sin phi2))
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))))))

simplify66.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
04861308
121651096
250011095

prune431.0ms

Filtered
84 candidates to 55 candidates (65.5%)
Pruning

19 alts after pruning (19 fresh and 0 done)

PrunedKeptTotal
New721284
Fresh8715
Picked101
Done000
Total8119100

Merged error: 3.5b

Counts
100 → 19

localize31.0ms

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) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))) R)
1.3b
(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

rewrite15.0ms

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:
5.0ms
(* (sin lambda1) (sin lambda2))
4.0ms
(* (sin phi1) (sin phi2))
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))) R)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

series173.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin lambda1) (sin lambda2))
46.0ms
(* (sin phi1) (sin phi2))
68.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2))))))) R)
16.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (cos phi1) (* (cos phi2) (+ (* (sin lambda1) (sin lambda2)) (* (cos lambda1) (cos lambda2)))))))

simplify76.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0260929
1823774
21865774
33003774
45001774

prune400.0ms

Filtered
76 candidates to 51 candidates (67.1%)
Pruning

18 alts after pruning (18 fresh and 0 done)

PrunedKeptTotal
New75176
Fresh11718
Picked101
Done000
Total771895

Merged error: 3.5b

Counts
95 → 18

localize40.0ms

Local error

Found 4 expressions with local error:

0.2b
(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (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)))))))
1.3b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cube-cbrt log-prod *-un-lft-identity
8×pow1
7×exp-sum
6×add-exp-log associate-*l* add-cbrt-cube
4×exp-prod add-log-exp
3×associate-*r*
2×log-pow unswap-sqr
1×acos-asin rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod rem-exp-log
Counts
4 → 57
Calls
4 calls:
2.0ms
(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
5.0ms
(* (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))))))

series152.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))))
70.0ms
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
47.0ms
(log (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))))))

simplify159.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 3 (22.0ms)

IterNodesCost
01741588
13951344
28181299
312161293
428531293
550011293

prune300.0ms

Filtered
69 candidates to 45 candidates (65.2%)
Pruning

21 alts after pruning (21 fresh and 0 done)

PrunedKeptTotal
New62769
Fresh31417
Picked101
Done000
Total662187

Merged error: 3.5b

Counts
87 → 21

regimes1.7s

Accuracy

0% (0.3b remaining)

Error of 3.6b against oracle of 3.2b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03219
13219

end0.0ms

sample8.2s

Algorithm
intervals
Results
5.8s4753×body1280valid
1.6s2151×body640valid
313.0ms680×body320valid
78.0ms250×body160valid
51.0ms14×body2560valid
24.0ms152×body80valid

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