Details

Time bar (total: 39.9s)

sample720.0ms

Algorithm
intervals
Results
535.0ms115×body1280valid
89.0ms48×body640valid
27.0ms22×body320valid
22.0ms63×body80valid
6.0ms8×body160valid

simplify51.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02233
13533
25533
35833
done5833

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize71.0ms

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))))
0.6b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite65.0ms

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:
25.0ms
(* (sin theta) (sin delta))
29.0ms
(* (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))))
7.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series644.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(* (sin theta) (sin delta))
250.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
9.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
308.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify6.0s

Counts
70 → 70
Iterations

Useful iterations: 3 (645.0ms)

IterNodesCost
01391435
12881368
27091231
317151229
448041229
done50001229

prune602.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
0.6b
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
17.9b
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×cbrt-prod
8×*-un-lft-identity
7×pow1 add-exp-log add-cbrt-cube
6×add-cube-cbrt add-log-exp
3×pow-unpow difference-of-squares sqr-pow
2×cube-div cube-mult unpow-prod-down pow-pow unpow3 cube-prod pow-exp sin-mult rem-cube-cbrt
1×pow-to-exp sub-neg asin-acos cbrt-div flip3-- pow1/3 diff-log pow-prod-down prod-exp flip-- rem-cbrt-cube cbrt-unprod distribute-lft-out--
Counts
4 → 65
Calls
4 calls:
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
11.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
11.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
5.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

series1.3s

Counts
4 → 12
Calls
4 calls:
8.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
392.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
312.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
602.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

simplify2.8s

Counts
77 → 77
Iterations

Useful iterations: done (2.8s)

IterNodesCost
01432286
13112038
27671819
334051814
done50001806

prune716.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.4b
(pow (sin phi1) 3)
0.6b
(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3))))
0.6b
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
17.9b
(cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))

rewrite156.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
6×pow1 add-exp-log cube-div unpow-prod-down pow-unpow cube-prod add-cbrt-cube add-log-exp
5×associate-*r/
3×cbrt-div
2×cube-mult pow-to-exp pow-pow flip3-+ unpow3 frac-add pow-exp cos-mult sin-cos-mult flip-+ rem-cube-cbrt sqr-pow
1×cbrt-prod sub-neg flip3-- pow1/3 diff-log pow-prod-down flip-- rem-cbrt-cube distribute-lft-out-- difference-of-squares
Counts
4 → 76
Calls
4 calls:
5.0ms
(pow (sin phi1) 3)
10.0ms
(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3))))
54.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
82.0ms
(cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))

series824.0ms

Counts
4 → 12
Calls
4 calls:
55.0ms
(pow (sin phi1) 3)
282.0ms
(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3))))
258.0ms
(pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)
228.0ms
(cbrt (* (pow (sin phi1) 3) (pow (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))) 3)))

simplify1.4s

Counts
88 → 88
Iterations

Useful iterations: 2 (353.0ms)

IterNodesCost
01732053
14661847
216951702
done50001702

prune787.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (* (sin theta) (sin delta)) (cos phi1))
0.2b
(* (sin theta) (sin delta))
0.3b
(* (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (cos theta) (sin delta)))) (sin phi1))
0.6b
(- (cos delta) (* (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (cos theta) (sin delta)))) (sin phi1)))

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*r*
7×associate-*l*
6×add-log-exp
5×pow-prod-down prod-exp cbrt-unprod
3×associate-*l/ *-commutative
2×sin-mult unswap-sqr
1×sub-neg flip3-- flip3-+ diff-log flip-- flip-+
Counts
4 → 70
Calls
4 calls:
35.0ms
(* (* (sin theta) (sin delta)) (cos phi1))
13.0ms
(* (sin theta) (sin delta))
81.0ms
(* (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (cos theta) (sin delta)))) (sin phi1))
7.0ms
(- (cos delta) (* (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (cos theta) (sin delta)))) (sin phi1)))

series696.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* (* (sin theta) (sin delta)) (cos phi1))
70.0ms
(* (sin theta) (sin delta))
230.0ms
(* (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (cos theta) (sin delta)))) (sin phi1))
291.0ms
(- (cos delta) (* (+ (* (sin phi1) (cos delta)) (* (cos phi1) (* (cos theta) (sin delta)))) (sin phi1)))

simplify1.6s

Counts
82 → 82
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01521386
13751319
213791172
done50001170

prune450.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes461.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02031
12831
done2831

end0.0ms

sample20.2s

Algorithm
intervals
Results
12.4s3100×body1280valid
4.9s1894×body640valid
1.1s690×body320valid
876.0ms2037×body80valid
197.0ms279×body160valid