Details

Time bar (total: 54.3s)

sample579.0ms

Algorithm
intervals
Results
350.0ms109×body1280valid
94.0ms56×body640valid
69.0ms22×body320valid
19.0ms62×body80valid
5.0ms7×body160valid

simplify513.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02233
13533
25533
35833
done5833

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite49.0ms

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:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
12.0ms
(* (sin theta) (sin delta))
14.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
17.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series647.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
84.0ms
(* (sin theta) (sin delta))
232.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
314.0ms
(- (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 (667.0ms)

IterNodesCost
01391435
12881368
27111231
316961229
448071229
done50011229

prune671.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

0.2b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin phi1) (sin (* 1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
0.3b
(- (cos delta) (* (sin phi1) (sin (* 1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

rewrite54.0ms

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:
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
12.0ms
(* (sin theta) (sin delta))
22.0ms
(* (sin phi1) (sin (* 1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
15.0ms
(- (cos delta) (* (sin phi1) (sin (* 1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

series541.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
57.0ms
(* (sin theta) (sin delta))
224.0ms
(* (sin phi1) (sin (* 1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
251.0ms
(- (cos delta) (* (sin phi1) (sin (* 1 (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))

simplify6.0s

Counts
70 → 70
Iterations

Useful iterations: 3 (724.0ms)

IterNodesCost
01401525
12901368
27261231
317291229
448311229
done50011229

prune742.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize106.0ms

Local error

Found 4 expressions with local error:

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

rewrite164.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
39×times-frac
38×*-un-lft-identity
32×difference-of-squares
30×add-cube-cbrt
26×sqr-pow
15×pow1
13×associate-/l*
12×add-exp-log unpow-prod-down cube-prod add-cbrt-cube
7×associate-/r/
6×pow-unpow cos-mult
5×frac-add
4×difference-cubes sin-mult distribute-lft-out-- add-log-exp
3×pow-pow flip3-+ swap-sqr associate-*r* associate-*l* pow-exp associate-/r* flip-+ rem-cube-cbrt
2×cube-mult frac-times pow-to-exp unpow3 associate-*r/ pow-prod-down prod-exp cbrt-unprod associate-/l/
1×cbrt-undiv cube-div pow2 sqr-cos flip3-- frac-2neg pow-plus div-sub div-exp associate-*l/ clear-num pow-sqr *-commutative pow-prod-up flip-- div-inv unswap-sqr
Counts
4 → 150
Calls
4 calls:
21.0ms
(* (cos delta) (cos delta))
117.0ms
(/ (- (pow (cos delta) 3) (pow (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) 3)) (+ (* (cos delta) (cos delta)) (* (* (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))))) (sin phi1)) (cos delta)))))
10.0ms
(pow (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) 3)
4.0ms
(pow (cos delta) 3)

series3.1s

Counts
4 → 12
Calls
4 calls:
18.0ms
(* (cos delta) (cos delta))
2.7s
(/ (- (pow (cos delta) 3) (pow (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) 3)) (+ (* (cos delta) (cos delta)) (* (* (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))))) (sin phi1)) (cos delta)))))
349.0ms
(pow (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) 3)
51.0ms
(pow (cos delta) 3)

simplify3.0s

Counts
162 → 162
Iterations

Useful iterations: done (3.0s)

IterNodesCost
037711231
1102410698
2464210216
done500110215

prune1.5s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize145.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
0.3b
(/ (+ (pow (cos delta) 2) (* (+ (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) (cos delta)) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (- (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))
0.3b
(* (* (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))))) (sin phi1)))
0.4b
(/ (+ (* (cos delta) (cos delta)) (+ (* (* (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))))) (sin phi1))) (* (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))) (/ (+ (pow (cos delta) 2) (* (+ (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) (cos delta)) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (- (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

rewrite689.0ms

Algorithm
rewrite-expression-head
Rules
90×times-frac
56×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
43×pow1
23×add-exp-log add-cbrt-cube
18×associate-/r*
17×pow-prod-down
11×associate-/r/ sin-mult
9×associate-/l/
8×frac-add prod-exp cbrt-unprod
6×flip3-- flip-- div-inv associate-/l* add-log-exp
5×associate-*r/ cos-mult
4×cbrt-undiv div-exp pow-sqr pow-prod-up
3×flip3-+ flip-+
2×frac-times frac-2neg pow-plus associate-*l/ clear-num
1×pow2 sub-neg diff-log swap-sqr associate-*r* associate-*l* *-commutative
Counts
4 → 165
Calls
4 calls:
7.0ms
(- (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
103.0ms
(/ (+ (pow (cos delta) 2) (* (+ (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) (cos delta)) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (- (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))
52.0ms
(* (* (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))))) (sin phi1)))
518.0ms
(/ (+ (* (cos delta) (cos delta)) (+ (* (* (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))))) (sin phi1))) (* (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))) (/ (+ (pow (cos delta) 2) (* (+ (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) (cos delta)) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (- (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

series3.4s

Counts
4 → 12
Calls
4 calls:
245.0ms
(- (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))
1.3s
(/ (+ (pow (cos delta) 2) (* (+ (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) (cos delta)) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (- (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))
270.0ms
(* (* (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))))) (sin phi1)))
1.6s
(/ (+ (* (cos delta) (cos delta)) (+ (* (* (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))))) (sin phi1))) (* (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))))) (/ (+ (pow (cos delta) 2) (* (+ (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) (cos delta)) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (- (cos delta) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

simplify3.1s

Counts
177 → 177
Iterations

Useful iterations: done (3.1s)

IterNodesCost
034924709
192121044
2351919702
done500016126

prune2.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes448.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify10.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
035150
148150
done48150

end0.0ms

sample20.8s

Algorithm
intervals
Results
12.4s3128×body1280valid
4.8s1826×body640valid
1.5s1996×body80valid
1.1s745×body320valid
290.0ms305×body160valid