Details

Time bar (total: 11.3s)

sample269.0ms

Algorithm
intervals
Results
180.0ms148×body1280valid
50.0ms73×body640valid
10.0ms22×body320valid
3.0ms1×body2560valid
2.0ms8×body160valid
1.0ms4×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02612
13412
23612
33612

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 16.4b

Counts
2 → 1

localize28.0ms

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)
0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
3.2b
(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))

series46.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (sin phi1) (sin phi2))
25.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2))))) R)
7.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
5.0ms
(cos (- lambda1 lambda2))

simplify44.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0200661
1565569
21790569
35001569

prune170.0ms

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: 3.2b

Counts
68 → 14

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (sin phi2))
0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (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:
4.0ms
(* (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))))))

series74.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin phi1) (sin phi2))
11.0ms
(* (sin lambda1) (sin lambda2))
41.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
12.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify73.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (6.0ms)

IterNodesCost
0260929
1831774
21930774
33056774
45001774

prune184.0ms

Filtered
51 candidates to 76 candidates (-49.0%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New641276
Fresh10313
Picked101
Done000
Total751590

Merged error: 3.1b

Counts
90 → 15

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin lambda1) (sin lambda2))
0.2b
(* (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)))))))
0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
9×pow1 associate-*l*
8×add-exp-log add-cbrt-cube
7×log-prod
6×associate-*r*
4×exp-sum add-log-exp
3×unswap-sqr
2×pow-prod-down prod-exp *-commutative cbrt-unprod
1×acos-asin rem-log-exp log-pow sin-mult
Counts
4 → 61
Calls
4 calls:
5.0ms
(* (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))))))

series94.0ms

Counts
4 → 12
Calls
4 calls:
11.0ms
(* (sin lambda1) (sin lambda2))
41.0ms
(* (exp (log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))) R)
30.0ms
(log (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))))
12.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

simplify66.0ms

Algorithm
egg-herbie
Counts
73 → 73
Iterations

Useful iterations: 3 (31.0ms)

IterNodesCost
02291302
16201089
214391074
324051072
450011072

prune169.0ms

Filtered
52 candidates to 73 candidates (-40.4%)
Pruning

14 alts after pruning (13 fresh and 1 done)

PrunedKeptTotal
New70373
Fresh41014
Picked011
Done000
Total741488

Merged error: 3.1b

Counts
88 → 14

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
0.3b
(pow (* (sin lambda1) (sin lambda2)) 3)
0.8b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
27.6b
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite13.0ms

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*
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-prod-down pow-exp prod-exp cbrt-unprod sin-mult rem-cube-cbrt sqr-pow
1×acos-asin pow-to-exp cbrt-div pow1/3 *-commutative rem-cbrt-cube unswap-sqr
Counts
4 → 67
Calls
4 calls:
3.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
5.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
1.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
3.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

series81.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
16.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
12.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
9.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify176.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
02851038
11031891
24820890
35001890

prune118.0ms

Filtered
52 candidates to 79 candidates (-51.9%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New78179
Fresh01212
Picked011
Done011
Total781593

Merged error: 3.1b

Counts
93 → 15

regimes1.2s

Accuracy

0% (0.3b 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
03219
13219

end0.0ms

sample8.4s

Algorithm
intervals
Results
5.9s4773×body1280valid
1.5s2118×body640valid
321.0ms687×body320valid
85.0ms268×body160valid
46.0ms14×body2560valid
24.0ms141×body80valid

Profiling

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