Details

Time bar (total: 40.8s)

sample548.0ms

Algorithm
intervals
Results
259.0ms101×body1280valid
119.0ms51×body640valid
71.0ms63×body80valid
48.0ms32×body320valid
6.0ms9×body160valid

simplify43.0ms

Counts
1 → 1
Iterations
IterNodes
done55
355
254
135
022

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize88.0ms

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)))))))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l* add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×asin-acos sub-neg flip3-- diff-log flip--
Counts
4 → 58
Calls
4 calls:
19.0ms
(* (sin theta) (sin delta))
18.0ms
(* (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))))
5.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series608.0ms

Counts
4 → 12
Calls
4 calls:
88.0ms
(* (sin theta) (sin delta))
227.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
284.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.7s

Counts
70 → 70
Iterations
IterNodes
done5000
32191
2722
1312
0144

prune850.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize195.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
4×add-log-exp
3×asin-acos associate-*r* associate-*l*
1×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
Counts
4 → 43
Calls
4 calls:
18.0ms
(* (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))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))

series275.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
15.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
15.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
15.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))

simplify3.1s

Counts
55 → 55
Iterations
IterNodes
done5000
41807
3839
2367
1148
076

prune947.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize225.0ms

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

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×pow-unpow
4×unpow-prod-down cube-prod add-log-exp
3×pow-pow pow-exp rem-cube-cbrt
2×cube-mult pow-to-exp asin-acos unpow3 sqr-pow
1×cube-div pow-prod-down prod-exp cbrt-unprod sin-mult
Counts
4 → 62
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
5.0ms
(pow (cos delta) 3)
16.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series435.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
9.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
48.0ms
(pow (cos delta) 3)
370.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify3.3s

Counts
74 → 74
Iterations
IterNodes
done5003
33325
2933
1321
0120

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize305.0ms

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

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×pow1
11×*-un-lft-identity add-cube-cbrt
7×add-cbrt-cube add-exp-log
6×flip3-+ flip-+
4×frac-times add-log-exp
3×pow-unpow unpow-prod-down cube-prod swap-sqr associate-*r* associate-*l*
2×asin-acos associate-*l/ associate-*r/
1×pow2 distribute-rgt-in cube-mult pow-to-exp pow-pow distribute-lft-in pow-plus unpow3 pow-prod-down pow-exp prod-exp pow-sqr *-commutative pow-prod-up cbrt-unprod rem-cube-cbrt unswap-sqr sqr-pow
Counts
4 → 74
Calls
4 calls:
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(pow (cos delta) 3)
46.0ms
(* (+ (* (cos delta) (sin phi1)) (* (* (cos theta) (cos phi1)) (sin delta))) (+ (* (cos delta) (sin phi1)) (* (* (cos theta) (cos phi1)) (sin delta))))

series270.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
10.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
30.0ms
(pow (cos delta) 3)
215.0ms
(* (+ (* (cos delta) (sin phi1)) (* (* (cos theta) (cos phi1)) (sin delta))) (+ (* (cos delta) (sin phi1)) (* (* (cos theta) (cos phi1)) (sin delta))))

simplify2.6s

Counts
86 → 86
Iterations
IterNodes
done5007
21672
1436
0135

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes897.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify32.0ms

Iterations
IterNodes
done61
161
042

end0.0ms

sample20.9s

Algorithm
intervals
Results
13.3s3199×body1280valid
4.7s1808×body640valid
1.1s745×body320valid
951.0ms1934×body80valid
300.0ms314×body160valid