Details

Time bar (total: 33.6s)

sample10.5s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 2.270508%

Results
196.0ms149×body1280valid
64.0ms77×body640valid
8.0ms16×body320valid
4.0ms11×body160valid
1.0ms3×body80valid

simplify6.0ms

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: 16.8b

Counts
2 → 1

localize30.0ms

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)
0.9b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (cos (- lambda1 lambda2)))))
2.9b
(cos (- lambda1 lambda2))

rewrite15.0ms

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:
5.0ms
(* (sin phi1) (sin phi2))
4.0ms
(* (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))

series50.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (sin phi1) (sin phi2))
26.0ms
(* (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)))))
5.0ms
(cos (- lambda1 lambda2))

simplify45.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
0200661
1565569
21790569
35001569

prune150.0ms

Filtered
49 candidates to 67 candidates (-36.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New571067
Fresh000
Picked101
Done000
Total581068

Merged error: 4.1b

Counts
68 → 10

localize32.0ms

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)
1.0b
(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))))))

series79.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (sin phi1) (sin phi2))
10.0ms
(* (sin lambda1) (sin lambda2))
44.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))) R)
16.0ms
(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 (6.0ms)

IterNodesCost
0260929
1831774
21930774
33056774
45001774

prune183.0ms

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

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New651176
Fresh639
Picked101
Done000
Total721486

Merged error: 4.0b

Counts
86 → 14

localize38.0ms

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)
1.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
25.7b
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite14.0ms

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))

series87.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))) R)
17.0ms
(pow (* (sin lambda1) (sin lambda2)) 3)
13.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
10.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify191.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
02851038
11031891
24820890
35001890

prune231.0ms

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

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New76379
Fresh4913
Picked101
Done000
Total811293

Merged error: 4.0b

Counts
93 → 12

localize41.0ms

Local error

Found 4 expressions with local error:

0.4b
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))))
0.7b
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))))
1.0b
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
25.7b
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
8×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×exp-prod
5×pow1 add-log-exp
4×add-exp-log log-pow add-cbrt-cube
3×acos-asin log-prod
2×exp-diff
1×cube-div cube-mult unpow-prod-down log-div cbrt-div pow1/3 unpow3 cube-prod rem-log-exp rem-cbrt-cube rem-exp-log sin-mult sqr-pow
Counts
4 → 54
Calls
4 calls:
2.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))))
2.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (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))

series68.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3)))))))
13.0ms
(log (exp (acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))))
13.0ms
(acos (+ (* (sin phi1) (sin phi2)) (* (* (cos phi1) (cos phi2)) (+ (* (cos lambda1) (cos lambda2)) (cbrt (pow (* (sin lambda1) (sin lambda2)) 3))))))
10.0ms
(cbrt (pow (* (sin lambda1) (sin lambda2)) 3))

simplify59.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
01951202
14581048
28891048
316981048
450021048

prune133.0ms

Filtered
46 candidates to 66 candidates (-43.5%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New60666
Fresh2911
Picked101
Done000
Total631578

Merged error: 3.9b

Counts
78 → 15

regimes1.8s

Accuracy

0% (0.3b remaining)

Error of 3.6b against oracle of 3.3b and baseline of 3.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03219
13219

end0.0ms

sample19.8s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 2.270508%

Results
6.5s4803×body1280valid
1.8s2087×body640valid
380.0ms691×body320valid
100.0ms275×body160valid
36.0ms10×body2560valid
24.0ms134×body80valid
4.0ms2×body1280invalid
0.0ms1×body320invalid

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