Details

Time bar (total: 12.2s)

sample254.0ms

Algorithm
intervals
Results
175.0ms150×body1280valid
46.0ms72×body640valid
9.0ms21×body320valid
4.0ms1×body2560valid
2.0ms9×body160valid
1.0ms4×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

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.9b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
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)))))
2.6b
(cos (- lambda1 lambda2))

rewrite20.0ms

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:
10.0ms
(* (sin phi1) (sin phi2))
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))

series118.0ms

Counts
4 → 12
Calls
4 calls:
48.0ms
(* (sin phi1) (sin phi2))
43.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
10.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
18.0ms
(cos (- lambda1 lambda2))

simplify43.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0200661
1565569
21790569
35001569

prune344.0ms

Filtered
67 candidates to 49 candidates (73.1%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (sin lambda1) (sin (- lambda2)))
0.3b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))) R)
1.1b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite19.0ms

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 sin-neg distribute-rgt-neg-out
Counts
4 → 65
Calls
4 calls:
7.0ms
(* (sin phi1) (sin phi2))
5.0ms
(* (sin lambda1) (sin (- lambda2)))
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)))))))

series237.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(* (sin phi1) (sin phi2))
75.0ms
(* (sin lambda1) (sin (- lambda2)))
70.0ms
(* (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)))))))

simplify86.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
02811000
1916859
22499835
35001835

prune496.0ms

Filtered
77 candidates to 55 candidates (71.4%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 4.1b

localize39.0ms

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))))))))
0.9b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))
1.1b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite17.0ms

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)))))))))
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

series149.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* (log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))) R)
47.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
17.0ms
(log (exp (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)))))))

simplify132.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 4 (53.0ms)

IterNodesCost
01911646
14181435
210671383
317851383
444921379
550021379

prune510.0ms

Filtered
70 candidates to 46 candidates (65.7%)
Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 4.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.4b
(exp (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))))
0.6b
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
0.9b
(log (exp (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))))
1.1b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
12×log-prod exp-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
8×log-pow
6×pow1 exp-sum
5×add-exp-log add-log-exp
4×add-cbrt-cube
2×rem-log-exp
1×acos-asin rem-exp-log
Counts
4 → 52
Calls
4 calls:
3.0ms
(exp (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))))
2.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
3.0ms
(log (exp (exp (log (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)))))))

series138.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(exp (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))))
50.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2))))))))
17.0ms
(log (exp (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))))))
23.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin (- lambda2)))))))

simplify84.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 6 (74.0ms)

IterNodesCost
01531538
12801348
25771236
310311228
416921228
528471192
650021184

prune354.0ms

Filtered
64 candidates to 42 candidates (65.6%)
Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.0b

regimes1.0s

Accuracy

0% (0.4b remaining)

Error of 3.8b against oracle of 3.5b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03320
13320

end0.0ms

sample8.0s

Algorithm
intervals
Results
5.8s4767×body1280valid
1.4s2120×body640valid
300.0ms682×body320valid
82.0ms287×body160valid
38.0ms11×body2560valid
26.0ms136×body80valid