Details

Time bar (total: 17.4s)

sample280.0ms

Algorithm
intervals
Results
175.0ms103×body1280valid
61.0ms68×body640valid
12.0ms20×body320valid
9.0ms57×body80valid
3.0ms8×body160valid

simplify21.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
02233
13632
25932
36832
done6832

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.3b
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
0.4b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity
6×pow1 add-exp-log add-cbrt-cube add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×fma-neg associate-*r* associate-*l* prod-diff
2×asin-acos
1×sub-neg flip3-- sin-asin diff-log pow-prod-down prod-exp sin-diff *-commutative flip-- cbrt-unprod sin-mult unswap-sqr
Counts
4 → 62
Calls
4 calls:
1.0ms
(sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
4.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
0.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

series451.0ms

Counts
4 → 12
Calls
4 calls:
125.0ms
(sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
148.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
6.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
173.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

simplify1.4s

Counts
74 → 74
Iterations

Useful iterations: 3 (283.0ms)

IterNodesCost
01321836
12691761
26981550
325791535
done50001535

prune456.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.1b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b
(sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.4b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.7b
(fma (- (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1) (cos delta))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
4×pow1 add-exp-log add-sqr-sqrt expm1-log1p-u add-cube-cbrt *-un-lft-identity add-cbrt-cube log1p-expm1-u add-log-exp
3×asin-acos
1×sin-asin sin-diff fma-udef
Counts
4 → 41
Calls
4 calls:
1.0ms
(sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
0.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.0ms
(fma (- (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1) (cos delta))

series304.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))
6.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
170.0ms
(fma (- (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (sin phi1) (cos delta))

simplify800.0ms

Counts
53 → 53
Iterations

Useful iterations: 3 (78.0ms)

IterNodesCost
0771077
11321067
2252921
3557915
41681915
done5000915

prune448.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
7×pow1 add-exp-log add-cbrt-cube
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×asin-acos pow-unpow
2×pow-pow pow-exp rem-cube-cbrt
1×cube-div cube-mult pow-to-exp unpow-prod-down unpow3 cube-prod pow-prod-down prod-exp cbrt-unprod sin-mult sqr-pow
Counts
4 → 55
Calls
4 calls:
0.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(pow (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) 3)

series244.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
226.0ms
(pow (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) 3)

simplify1.8s

Counts
67 → 67
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
0851367
11931321
26671166
335721166
done50011166

prune584.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b
(pow (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) 3)
0.5b
(acos (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0b
(- (/ PI 2) (acos (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
48×*-un-lft-identity
46×add-cube-cbrt
39×prod-diff
37×times-frac
13×fma-neg
7×pow1 add-exp-log add-cbrt-cube
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u div-inv
3×pow-unpow
2×acos-asin pow-pow pow-exp rem-cube-cbrt difference-of-squares
1×cube-div cube-mult pow-to-exp sub-neg unpow-prod-down asin-acos flip3-- diff-log unpow3 cube-prod pow-prod-down prod-exp flip-- cbrt-unprod sin-mult distribute-lft-out-- associate--r- sqr-pow
Counts
4 → 115
Calls
4 calls:
0.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms
(pow (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) 3)
0.0ms
(acos (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
14.0ms
(- (/ PI 2) (acos (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))

series276.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
230.0ms
(pow (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)) 3)
6.0ms
(acos (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
34.0ms
(- (/ PI 2) (acos (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))

simplify571.0ms

Counts
127 → 127
Iterations

Useful iterations: done (566.0ms)

IterNodesCost
02016053
14344060
213713232
done50003228

prune908.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes520.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
043128
151128
done51128

end0.0ms

sample8.1s

Algorithm
intervals
Results
5.1s3113×body1280valid
1.8s1894×body640valid
452.0ms723×body320valid
347.0ms1978×body80valid
117.0ms292×body160valid