Details

Time bar (total: 41.4s)

sample680.0ms

Algorithm
intervals
Results
475.0ms109×body1280valid
115.0ms56×body640valid
28.0ms22×body320valid
22.0ms62×body80valid
5.0ms7×body160valid

simplify62.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
02233
13632
26032
37032
done7032

prune59.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize63.0ms

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)))))))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
10×add-cube-cbrt *-un-lft-identity
8×pow1 add-exp-log add-cbrt-cube
6×associate-*r* associate-*l* add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-neg prod-diff
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×sub-neg asin-acos flip3-- diff-log flip--
Counts
4 → 72
Calls
4 calls:
4.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
42.0ms
(* (sin theta) (sin delta))
27.0ms
(* (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)))))))

series665.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
77.0ms
(* (sin theta) (sin delta))
238.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
340.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify3.2s

Counts
84 → 84
Iterations

Useful iterations: done (3.2s)

IterNodesCost
01571824
13211677
27921492
320621479
done50001418

prune811.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize69.0ms

Local error

Found 4 expressions with local error:

0.2b
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.2b
(fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))
0.2b
(* (sin theta) (sin delta))
0.4b
(fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (- (sin phi1)) (cos delta))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 add-exp-log add-cube-cbrt *-un-lft-identity add-cbrt-cube
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×associate-*r* associate-*l*
2×fma-udef
1×asin-acos pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
Counts
4 → 51
Calls
4 calls:
13.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
1.0ms
(fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))
18.0ms
(* (sin theta) (sin delta))
0.0ms
(fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (- (sin phi1)) (cos delta))

series575.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
205.0ms
(fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))
67.0ms
(* (sin theta) (sin delta))
287.0ms
(fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (- (sin phi1)) (cos delta))

simplify3.2s

Counts
63 → 63
Iterations

Useful iterations: 4 (1.1s)

IterNodesCost
0106958
1191950
2429834
31013829
43038828
done5000828

prune642.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin phi1) (cos delta))
0.2b
(asin (+ (* (cos phi1) (* (cos theta) (sin delta))) (* (sin phi1) (cos delta))))
0.2b
(* (sin theta) (sin delta))
0.4b
(fma (sin (asin (+ (* (cos phi1) (* (cos theta) (sin delta))) (* (sin phi1) (cos delta))))) (- (sin phi1)) (cos delta))

rewrite32.0ms

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*
4×expm1-log1p-u log1p-expm1-u add-log-exp
2×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
1×asin-acos sin-cos-mult fma-udef sin-mult
Counts
4 → 62
Calls
4 calls:
12.0ms
(* (sin phi1) (cos delta))
3.0ms
(asin (+ (* (cos phi1) (* (cos theta) (sin delta))) (* (sin phi1) (cos delta))))
15.0ms
(* (sin theta) (sin delta))
0.0ms
(fma (sin (asin (+ (* (cos phi1) (* (cos theta) (sin delta))) (* (sin phi1) (cos delta))))) (- (sin phi1)) (cos delta))

series417.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* (sin phi1) (cos delta))
14.0ms
(asin (+ (* (cos phi1) (* (cos theta) (sin delta))) (* (sin phi1) (cos delta))))
73.0ms
(* (sin theta) (sin delta))
280.0ms
(fma (sin (asin (+ (* (cos phi1) (* (cos theta) (sin delta))) (* (sin phi1) (cos delta))))) (- (sin phi1)) (cos delta))

simplify3.7s

Counts
74 → 74
Iterations

Useful iterations: 4 (2.1s)

IterNodesCost
0138964
1270924
2655814
31423810
43806809
done5000809

prune677.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize101.0ms

Local error

Found 4 expressions with local error:

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

rewrite140.0ms

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
6×pow-unpow
4×difference-cubes expm1-log1p-u log1p-expm1-u distribute-lft-out-- add-log-exp
3×pow-pow swap-sqr associate-*r* associate-*l* pow-exp associate-/r* rem-cube-cbrt
2×cube-mult pow-to-exp unpow3 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 clear-num pow-sqr cos-mult *-commutative pow-prod-up flip-- div-inv sin-mult unswap-sqr
Counts
4 → 151
Calls
4 calls:
23.0ms
(* (cos delta) (cos delta))
94.0ms
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)) (fma (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)) (* (cos delta) (cos delta))))
9.0ms
(pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)
4.0ms
(pow (cos delta) 3)

series2.5s

Counts
4 → 12
Calls
4 calls:
27.0ms
(* (cos delta) (cos delta))
2.0s
(/ (- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)) (fma (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)) (* (cos delta) (cos delta))))
403.0ms
(pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)
58.0ms
(pow (cos delta) 3)

simplify2.4s

Counts
163 → 163
Iterations

Useful iterations: done (2.4s)

IterNodesCost
03419927
18809405
236989036
done50009031

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

regimes430.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
03081
13781
done3781

end0.0ms

sample19.3s

Algorithm
intervals
Results
12.1s3128×body1280valid
4.4s1826×body640valid
992.0ms1996×body80valid
938.0ms745×body320valid
277.0ms305×body160valid