Details

Time bar (total: 11.5s)

sample260.0ms

Algorithm
intervals
Results
184.0ms158×body1280valid
47.0ms66×body640valid
8.0ms20×body320valid
2.0ms8×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: 16.9b

localize24.0ms

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)
0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.3b
(cos (- lambda1 lambda2))

rewrite14.0ms

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:
4.0ms
(* (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))

series121.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (sin phi1) (sin phi2))
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))

simplify46.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0200661
1565569
21790569
35001569

prune276.0ms

Filtered
67 candidates to 49 candidates (73.1%)
Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.6b

localize32.0ms

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)
0.8b
(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×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 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))))))

series174.0ms

Counts
4 → 12
Calls
4 calls:
43.0ms
(* (sin phi1) (sin phi2))
46.0ms
(* (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))))))

simplify74.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0260929
1831774
21930774
33056774
45001774

prune397.0ms

Filtered
76 candidates to 51 candidates (67.1%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.3b
(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
0.8b
(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
3.2b
(log (exp (* (sin phi1) (sin phi2))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
9×pow1 add-cube-cbrt *-un-lft-identity
8×add-exp-log add-cbrt-cube
6×associate-*r* associate-*l*
5×add-log-exp
3×log-prod log-pow
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×acos-asin exp-prod exp-to-pow rem-log-exp sin-mult
Counts
4 → 59
Calls
4 calls:
5.0ms
(* (sin lambda1) (sin lambda2))
3.0ms
(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
2.0ms
(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
2.0ms
(log (exp (* (sin phi1) (sin phi2))))

series180.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin lambda1) (sin lambda2))
70.0ms
(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
17.0ms
(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
47.0ms
(log (exp (* (sin phi1) (sin phi2))))

simplify68.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0219996
1674837
21567837
32617837
45002837

prune423.0ms

Filtered
71 candidates to 49 candidates (69.0%)
Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 4.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
0.8b
(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
2.3b
(log (exp (* (sin lambda1) (sin lambda2))))
3.2b
(log (exp (* (sin phi1) (sin phi2))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×pow1 add-cube-cbrt *-un-lft-identity
6×add-exp-log log-prod log-pow add-cbrt-cube add-log-exp
3×associate-*r* associate-*l*
2×exp-prod exp-to-pow rem-log-exp
1×acos-asin pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 54
Calls
4 calls:
3.0ms
(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
2.0ms
(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
2.0ms
(log (exp (* (sin lambda1) (sin lambda2))))
2.0ms
(log (exp (* (sin phi1) (sin phi2))))

series177.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(* (acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))) R)
17.0ms
(acos (+ (log (exp (* (sin phi1) (sin phi2)))) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
44.0ms
(log (exp (* (sin lambda1) (sin lambda2))))
47.0ms
(log (exp (* (sin phi1) (sin phi2))))

simplify110.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 5 (103.0ms)

IterNodesCost
01771063
1501900
21081900
31755900
44355900
55002892

prune338.0ms

Filtered
66 candidates to 47 candidates (71.2%)
Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 4.5b

regimes740.0ms

Accuracy

0% (0.3b remaining)

Error of 3.8b against oracle of 3.4b and baseline of 3.8b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03421
13421

end0.0ms

sample7.9s

Algorithm
intervals
Results
5.7s4743×body1280valid
1.5s2143×body640valid
293.0ms679×body320valid
81.0ms281×body160valid
41.0ms11×body2560valid
24.0ms143×body80valid