Details

Time bar (total: 35.5s)

sample585.0ms

Algorithm
intervals
Results
395.0ms110×body1280valid
105.0ms58×body640valid
27.0ms23×body320valid
18.0ms58×body80valid
4.0ms7×body160valid

simplify25.0ms

Counts
1 → 1
Iterations
IterNodes
done62
362
256
135
022

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b
(atan2 (* (sin delta) (* (cos phi1) (sin theta))) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))))))
0.3b
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))))
0.3b
(asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))
0.7b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta))))))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt add-log-exp
3×associate-*r* associate-*l*
1×asin-acos sub-neg flip3-- diff-log pow-prod-down prod-exp *-commutative cbrt-unprod flip-- sin-mult unswap-sqr
Counts
4 → 46
Calls
4 calls:
0.0ms
(atan2 (* (sin delta) (* (cos phi1) (sin theta))) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))))))
13.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))))
1.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))
6.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta))))))))

series545.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(atan2 (* (sin delta) (* (cos phi1) (sin theta))) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))))))
237.0ms
(* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))))
10.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta)))))
264.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (cos delta) (sin phi1)) (* (cos theta) (* (cos phi1) (sin delta))))))))

simplify813.0ms

Counts
58 → 58
Iterations
IterNodes
done5000
2933
1284
0135

prune714.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize109.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (log (exp (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))))))
0.3b
(asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))
0.7b
(- (cos delta) (* (sin phi1) (sin (log (exp (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1)))))))))
2.8b
(log (exp (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
15×log-prod
14×add-sqr-sqrt
12×*-un-lft-identity sin-sum add-cube-cbrt
7×pow1
6×distribute-rgt-in distribute-lft-in add-cbrt-cube add-exp-log associate--r+ add-log-exp
4×log-pow
3×exp-prod associate-*r* associate-*l*
2×asin-acos
1×log-div sub-neg flip3-- exp-diff diff-log rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-- sin-mult unswap-sqr
Counts
4 → 67
Calls
4 calls:
22.0ms
(* (sin phi1) (sin (log (exp (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))))))
1.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))
15.0ms
(- (cos delta) (* (sin phi1) (sin (log (exp (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1)))))))))
5.0ms
(log (exp (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))))

series584.0ms

Counts
4 → 12
Calls
4 calls:
260.0ms
(* (sin phi1) (sin (log (exp (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))))))
15.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))
293.0ms
(- (cos delta) (* (sin phi1) (sin (log (exp (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1)))))))))
17.0ms
(log (exp (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))))

simplify781.0ms

Counts
79 → 79
Iterations
IterNodes
done5001
21212
1353
0167

prune962.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize123.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))
0.3b
(asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))
0.3b
(asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))
0.5b
(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))) (pow (sin phi1) 2))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
3×asin-acos
1×sqr-cos sub-neg flip3-- diff-log associate--l+ flip--
Counts
4 → 37
Calls
4 calls:
1.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))
2.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))
1.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))
45.0ms
(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))) (pow (sin phi1) 2))))

series864.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))
16.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))
16.0ms
(asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))
817.0ms
(- (* (cos delta) (cos delta)) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))) (* (sin (asin (+ (* (cos delta) (sin phi1)) (* (* (sin delta) (cos theta)) (cos phi1))))) (pow (sin phi1) 2))))

simplify682.0ms

Counts
49 → 49
Iterations
IterNodes
done5001
21251
1265
099

prune742.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize166.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (pow (sin phi1) 2) (+ (* (pow (cos delta) 2) (pow (sin phi1) 2)) (* (* (pow (sin delta) 2) (pow (cos phi1) 2)) (pow (cos theta) 2))))
0.3b
(pow (sin phi1) 3)
0.3b
(pow (sin phi1) 3)
0.6b
(- (pow (cos delta) 2) (* (pow (sin phi1) 2) (+ (* (pow (cos delta) 2) (pow (sin phi1) 2)) (* (* (pow (sin delta) 2) (pow (cos phi1) 2)) (pow (cos theta) 2)))))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
19×add-sqr-sqrt
13×*-un-lft-identity add-cube-cbrt
11×add-exp-log
10×unpow-prod-down
8×add-cbrt-cube associate-*l*
6×pow1 pow-unpow cube-prod add-log-exp
4×unswap-sqr sqr-pow
3×pow-to-exp associate-*r* pow-exp prod-exp
2×distribute-rgt-in cube-mult pow-pow distribute-lft-in unpow3 associate-*r/ associate--r+ unpow2 rem-cube-cbrt
1×sub-neg flip3-+ flip3-- diff-log *-commutative cbrt-unprod flip-+ flip--
Counts
4 → 91
Calls
4 calls:
71.0ms
(* (pow (sin phi1) 2) (+ (* (pow (cos delta) 2) (pow (sin phi1) 2)) (* (* (pow (sin delta) 2) (pow (cos phi1) 2)) (pow (cos theta) 2))))
7.0ms
(pow (sin phi1) 3)
6.0ms
(pow (sin phi1) 3)
25.0ms
(- (pow (cos delta) 2) (* (pow (sin phi1) 2) (+ (* (pow (cos delta) 2) (pow (sin phi1) 2)) (* (* (pow (sin delta) 2) (pow (cos phi1) 2)) (pow (cos theta) 2)))))

series762.0ms

Counts
4 → 12
Calls
4 calls:
313.0ms
(* (pow (sin phi1) 2) (+ (* (pow (cos delta) 2) (pow (sin phi1) 2)) (* (* (pow (sin delta) 2) (pow (cos phi1) 2)) (pow (cos theta) 2))))
56.0ms
(pow (sin phi1) 3)
36.0ms
(pow (sin phi1) 3)
358.0ms
(- (pow (cos delta) 2) (* (pow (sin phi1) 2) (+ (* (pow (cos delta) 2) (pow (sin phi1) 2)) (* (* (pow (sin delta) 2) (pow (cos phi1) 2)) (pow (cos theta) 2)))))

simplify2.3s

Counts
103 → 103
Iterations
IterNodes
done5000
23467
1500
0153

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations
IterNodes
done32
132
024

end0.0ms

sample21.7s

Algorithm
intervals
Results
13.8s3184×body1280valid
4.2s1794×body640valid
1.9s722×body320valid
814.0ms1995×body80valid
283.0ms305×body160valid