Details

Time bar (total: 12.9s)

sample317.0ms

Algorithm
intervals
Results
209.0ms160×body1280valid
57.0ms67×body640valid
6.0ms11×body320valid
3.0ms10×body160valid
2.0ms8×body80valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02612
13412
23612
33612

prune5.0ms

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: 15.2b

Counts
2 → 1

localize43.0ms

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)
1.1b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.8b
(cos (- lambda1 lambda2))

rewrite25.0ms

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:
8.0ms
(* (sin phi1) (sin phi2))
6.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
2.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
7.0ms
(cos (- lambda1 lambda2))

series122.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (sin phi1) (sin phi2))
46.0ms
(* (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)))))
25.0ms
(cos (- lambda1 lambda2))

simplify48.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0200661
1565569
21790569
35001569

prune307.0ms

Filtered
67 candidates to 49 candidates (73.1%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New521567
Fresh000
Picked101
Done000
Total531568

Merged error: 3.7b

Counts
68 → 15

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (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))))))

rewrite16.0ms

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))
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))))))

series176.0ms

Counts
4 → 12
Calls
4 calls:
46.0ms
(* (sin lambda1) (sin lambda2))
43.0ms
(* (sin phi1) (sin phi2))
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))))))

simplify75.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
0260929
1831774
21930774
33056774
45001774

prune391.0ms

Filtered
76 candidates to 51 candidates (67.1%)
Pruning

17 alts after pruning (17 fresh and 0 done)

PrunedKeptTotal
New651176
Fresh8614
Picked101
Done000
Total741791

Merged error: 3.6b

Counts
91 → 17

localize42.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (sin lambda2))
0.6b
(cbrt (sin lambda2))
0.6b
(cbrt (sin lambda2))
1.1b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2)))))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log add-cbrt-cube add-log-exp
3×pow1/3
1×acos-asin
Counts
4 → 41
Calls
4 calls:
2.0ms
(cbrt (sin lambda2))
2.0ms
(cbrt (sin lambda2))
1.0ms
(cbrt (sin lambda2))
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2)))))))

series326.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(cbrt (sin lambda2))
120.0ms
(cbrt (sin lambda2))
96.0ms
(cbrt (sin lambda2))
17.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (* (sin lambda1) (* (cbrt (sin lambda2)) (cbrt (sin lambda2)))) (cbrt (sin lambda2)))))))

simplify107.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 3 (28.0ms)

IterNodesCost
0138507
1324445
2863439
33015436
45001436

prune353.0ms

Filtered
53 candidates to 42 candidates (79.2%)
Pruning

17 alts after pruning (16 fresh and 1 done)

PrunedKeptTotal
New52153
Fresh11516
Picked011
Done000
Total531770

Merged error: 3.6b

Counts
70 → 17

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.3b
(pow (* (sin phi1) (sin phi2)) 3)
1.1b
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
23.8b
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×pow1 add-exp-log add-cbrt-cube
8×cbrt-prod add-cube-cbrt *-un-lft-identity
4×add-log-exp
3×pow-unpow associate-*r* associate-*l* sin-mult
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod rem-cube-cbrt sqr-pow
1×acos-asin pow-to-exp cbrt-div pow1/3 *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 68
Calls
4 calls:
5.0ms
(* (sin phi1) (sin phi2))
5.0ms
(pow (* (sin phi1) (sin phi2)) 3)
2.0ms
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
3.0ms
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

series169.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(* (sin phi1) (sin phi2))
64.0ms
(pow (* (sin phi1) (sin phi2)) 3)
16.0ms
(acos (+ (cbrt (pow (* (sin phi1) (sin phi2)) 3)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
46.0ms
(cbrt (pow (* (sin phi1) (sin phi2)) 3))

simplify44.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0265595
1984538
25002537

prune401.0ms

Filtered
80 candidates to 54 candidates (67.5%)
Pruning

16 alts after pruning (15 fresh and 1 done)

PrunedKeptTotal
New78280
Fresh21315
Picked101
Done011
Total811697

Merged error: 3.6b

Counts
97 → 16

regimes1.4s

Accuracy

0% (0.4b remaining)

Error of 4.0b against oracle of 3.6b and baseline of 4.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03424
13424

end0.0ms

sample8.5s

Algorithm
intervals
Results
6.1s4718×body1280valid
1.6s2145×body640valid
324.0ms681×body320valid
99.0ms298×body160valid
38.0ms13×body2560valid
24.0ms148×body80valid

Profiling

Loading profile data...