Details

Time bar (total: 37.9s)

sample587.0ms

Algorithm
intervals
Results
384.0ms115×body1280valid
110.0ms48×body640valid
29.0ms22×body320valid
28.0ms63×body80valid
6.0ms8×body160valid

simplify534.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02233
13533
25533
35833
done5833

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize77.0ms

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)))))))

rewrite48.0ms

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:
21.0ms
(* (sin theta) (sin delta))
15.0ms
(* (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))))
8.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series638.0ms

Counts
4 → 12
Calls
4 calls:
61.0ms
(* (sin theta) (sin delta))
253.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
18.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
306.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify5.8s

Counts
70 → 70
Iterations

Useful iterations: 3 (760.0ms)

IterNodesCost
01391435
12881368
27091231
317151229
448041229
done50001229

prune631.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize81.0ms

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))

rewrite67.0ms

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))))
30.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
21.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
10.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

series832.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
322.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
299.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
194.0ms
(cbrt (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

simplify2.9s

Counts
77 → 77
Iterations

Useful iterations: done (2.9s)

IterNodesCost
01432286
13112038
27671819
334051814
done50001806

prune727.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize86.0ms

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

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity
10×add-cube-cbrt
6×pow1 add-exp-log unpow-prod-down pow-unpow cube-prod add-cbrt-cube add-log-exp
2×cube-mult pow-to-exp pow-pow unpow3 pow-exp 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 → 70
Calls
4 calls:
8.0ms
(pow (sin phi1) 3)
13.0ms
(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3))))
7.0ms
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)
19.0ms
(cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)))

series932.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(pow (sin phi1) 3)
294.0ms
(- (cos delta) (cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3))))
298.0ms
(pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)
307.0ms
(cbrt (* (pow (sin phi1) 3) (pow (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 3)))

simplify940.0ms

Counts
82 → 82
Iterations

Useful iterations: done (936.0ms)

IterNodesCost
01381874
13241689
29821532
done50001530

prune784.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize38.0ms

Local error

Found 4 expressions with local error:

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

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*l*
7×associate-*r*
6×add-log-exp
5×associate-*r/ pow-prod-down prod-exp cbrt-unprod
3×*-commutative
2×distribute-rgt-in distribute-lft-in cos-mult associate--r+ unswap-sqr
1×sub-neg flip3-- flip3-+ diff-log frac-add sin-cos-mult flip-- flip-+ sin-mult
Counts
4 → 75
Calls
4 calls:
15.0ms
(* (sin theta) (sin delta))
31.0ms
(* (sin delta) (* (cos phi1) (cos theta)))
159.0ms
(* (sin phi1) (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
7.0ms
(- (cos delta) (* (sin phi1) (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))

series719.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(* (sin theta) (sin delta))
155.0ms
(* (sin delta) (* (cos phi1) (cos theta)))
253.0ms
(* (sin phi1) (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
252.0ms
(- (cos delta) (* (sin phi1) (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta)))))

simplify1.3s

Counts
87 → 87
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01701476
14401389
215881260
done50001258

prune671.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes490.0ms

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
02031
12831
done2831

end0.0ms

sample18.7s

Algorithm
intervals
Results
12.0s3100×body1280valid
3.6s1894×body640valid
1.3s690×body320valid
1.1s2037×body80valid
228.0ms279×body160valid