Details

Time bar (total: 15.3s)

sample283.0ms

Algorithm
intervals
Results
176.0ms105×body1280valid
54.0ms55×body640valid
19.0ms72×body80valid
9.0ms15×body320valid
4.0ms9×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03522
15622
25922
35922

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: 0.1b

Counts
2 → 1

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite16.0ms

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* add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×sub-neg asin-acos flip3-- diff-log flip--
Counts
4 → 58
Calls
4 calls:
5.0ms
(* (sin theta) (sin delta))
5.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series393.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (sin theta) (sin delta))
153.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
184.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify93.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0289930
1894837
23513835
35002835

prune383.0ms

Filtered
70 candidates to 51 candidates (72.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New61970
Fresh000
Picked101
Done000
Total62971

Merged error: 0.0b

Counts
71 → 9

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(* (cos delta) (cos delta))
0.3b
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
0.3b
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity
12×times-frac sin-mult
11×pow1 cos-mult
8×add-exp-log add-cbrt-cube
7×associate-/l/
6×frac-sub add-log-exp
5×difference-of-squares
4×associate-*r/ associate-*l/ associate-/l* sub-div
3×swap-sqr associate-*r* associate-*l* associate-/r*
2×frac-times sqr-cos flip3-- associate-/r/ flip--
1×cbrt-undiv pow2 sub-neg asin-acos frac-2neg flip3-+ pow-plus diff-log div-sub div-exp pow-prod-down prod-exp associate--l+ clear-num pow-sqr *-commutative pow-prod-up cbrt-unprod flip-+ div-inv unswap-sqr
Counts
4 → 95
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
4.0ms
(* (cos delta) (cos delta))
8.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
12.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series1.3s

Counts
4 → 12
Calls
4 calls:
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
17.0ms
(* (cos delta) (cos delta))
491.0ms
(- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
795.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify116.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (85.0ms)

IterNodesCost
05853789
130423449
250013421

prune733.0ms

Filtered
107 candidates to 86 candidates (80.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1025107
Fresh448
Picked101
Done000
Total1079116

Merged error: 0.0b

Counts
116 → 9

localize65.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 4)
0.5b
(pow (cos delta) 4)
0.7b
(pow (cos delta) 6)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1
15×add-sqr-sqrt
13×add-cube-cbrt *-un-lft-identity
11×add-exp-log
9×pow-unpow
7×unpow-prod-down
6×add-cbrt-cube
4×pow-pow pow-exp add-log-exp
3×pow-to-exp swap-sqr associate-*r* associate-*l* sqr-pow
2×pow-prod-down prod-exp
1×pow2 pow-plus pow-sqr *-commutative pow-prod-up cbrt-unprod sqr-sin sin-mult unswap-sqr
Counts
4 → 78
Calls
4 calls:
6.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
5.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 4)
2.0ms
(pow (cos delta) 4)
3.0ms
(pow (cos delta) 6)

series495.0ms

Counts
4 → 12
Calls
4 calls:
144.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
277.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 4)
33.0ms
(pow (cos delta) 4)
41.0ms
(pow (cos delta) 6)

simplify54.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
03291131
11258906
25001832

prune707.0ms

Filtered
90 candidates to 56 candidates (62.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New89190
Fresh088
Picked101
Done000
Total90999

Merged error: 0.0b

Counts
99 → 9

localize62.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.4b
(pow (* (cos delta) (cos delta)) 3)
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 4)
0.5b
(pow (cos delta) 4)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
23×pow1
14×add-sqr-sqrt
13×add-exp-log
12×add-cube-cbrt *-un-lft-identity
9×pow-unpow pow-pow add-cbrt-cube
5×unpow-prod-down pow-exp
4×add-log-exp
3×pow-to-exp swap-sqr associate-*r* associate-*l* pow-prod-down prod-exp sqr-pow
2×pow2 pow-plus pow-sqr pow-prod-up cbrt-unprod rem-cube-cbrt
1×cube-div cube-mult unpow3 cube-prod cos-mult *-commutative sqr-sin sin-mult unswap-sqr
Counts
4 → 88
Calls
4 calls:
7.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
5.0ms
(pow (* (cos delta) (cos delta)) 3)
6.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 4)
3.0ms
(pow (cos delta) 4)

series500.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
41.0ms
(pow (* (cos delta) (cos delta)) 3)
277.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 4)
34.0ms
(pow (cos delta) 4)

simplify57.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
03661154
11491918
25001858

prune680.0ms

Filtered
100 candidates to 63 candidates (63.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1000100
Fresh088
Picked011
Done000
Total1009109

Merged error: 0.0b

Counts
109 → 9

regimes457.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
055104
155104

end0.0ms

sample8.7s

Algorithm
intervals
Results
5.3s3058×body1280valid
1.9s1848×body640valid
671.0ms694×body320valid
399.0ms2092×body80valid
140.0ms308×body160valid

Profiling

Loading profile data...