Details

Time bar (total: 17.5s)

sample284.0ms

Algorithm
intervals
Results
169.0ms97×body1280valid
60.0ms64×body640valid
14.0ms20×body320valid
13.0ms67×body80valid
3.0msbody160valid

simplify25.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02233
13533
25433
35733
done5733

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.1b

Counts
2 → 1

localize30.0ms

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))))
0.5b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
associate-*r* associate-*l* add-log-exp
pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
sub-neg asin-acos flip3-- diff-log flip--
Counts
4 → 58
Calls
4 calls:
5.0ms
(* (sin theta) (sin delta))
6.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
2.0ms
(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)))))))

series103.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (sin theta) (sin delta))
37.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
50.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.1s

Counts
70 → 70
Iterations

Useful iterations: 3 (450.0ms)

IterNodesCost
01321435
12721368
26961231
318841229
done50001229

prune176.0ms

Filtered
51 candidates to 70 candidates (-37.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New62870
Fresh000
Picked101
Done000
Total63871

Merged error: 0.0b

Counts
71 → 8

localize44.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(pow (cos delta) 3)
0.5b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
pow1 add-exp-log add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-cbrt-cube
pow-unpow
unpow-prod-down cube-prod add-log-exp
pow-pow pow-exp rem-cube-cbrt
cube-mult pow-to-exp asin-acos unpow3 sqr-pow
cube-div pow-prod-down prod-exp cbrt-unprod sin-mult
Counts
4 → 62
Calls
4 calls:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(pow (cos delta) 3)
6.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series87.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
8.0ms
(pow (cos delta) 3)
67.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify2.2s

Counts
74 → 74
Iterations

Useful iterations: 3 (618.0ms)

IterNodesCost
01091265
12491181
27611037
341401035
done50011035

prune191.0ms

Filtered
47 candidates to 74 candidates (-57.4%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New72274
Fresh077
Picked101
Done000
Total73982

Merged error: 0.0b

Counts
82 → 9

localize51.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(pow (sin phi1) 3)
0.3b
(pow (cos delta) 3)
0.6b
(pow (+ (* (sin phi1) (cos delta)) (* (cos theta) (* (sin delta) (cos phi1)))) 3)

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
unpow-prod-down pow-unpow cube-prod
pow1 add-exp-log add-cbrt-cube
add-log-exp
cube-div cube-mult pow-to-exp pow-pow unpow3 pow-exp rem-cube-cbrt sqr-pow
sin-cos-mult
asin-acos flip3-+ associate-*r/ frac-add flip-+
Counts
4 → 80
Calls
4 calls:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(pow (sin phi1) 3)
3.0ms
(pow (cos delta) 3)
10.0ms
(pow (+ (* (sin phi1) (cos delta)) (* (cos theta) (* (sin delta) (cos phi1)))) 3)

series71.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms
(pow (sin phi1) 3)
5.0ms
(pow (cos delta) 3)
55.0ms
(pow (+ (* (sin phi1) (cos delta)) (* (cos theta) (* (sin delta) (cos phi1)))) 3)

simplify849.0ms

Counts
92 → 92
Iterations

Useful iterations: 2 (169.0ms)

IterNodesCost
01571352
14121207
215801075
done50001075

prune218.0ms

Filtered
56 candidates to 92 candidates (-64.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New92092
Fresh088
Picked011
Done000
Total929101

Merged error: 0.0b

Counts
101 → 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)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (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)))
0.3b
(- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (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
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
11×pow1
times-frac
add-exp-log add-cbrt-cube
add-log-exp
sin-mult
associate-*r/ cos-mult associate-/l/
swap-sqr associate-*r* associate-*l* associate-/r* associate-/l*
flip3-- associate-/r/ frac-sub flip-- sub-div
cbrt-undiv pow2 sub-neg asin-acos sqr-cos 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-+ sqr-sin div-inv unswap-sqr
Counts
4 → 84
Calls
4 calls:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
14.0ms
(/ (- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (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)))
8.0ms
(- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
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))))))

series558.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
329.0ms
(/ (- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (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)))
178.0ms
(- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
44.0ms
(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify799.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (245.0ms)

IterNodesCost
02216085
15705623
219884986
done50014986

prune207.0ms

Filtered
74 candidates to 96 candidates (-29.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New94296
Fresh077
Picked101
Done011
Total9510105

Merged error: 0.0b

Counts
105 → 10

regimes619.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03586
14686
done4686

end0.0ms

sample8.7s

Algorithm
intervals
Results
5.3s3227×body1280valid
1.8s1783×body640valid
512.0ms765×body320valid
393.0ms1955×body80valid
125.0ms270×body160valid

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