Details

Time bar (total: 39.9s)

sample636.0ms

Algorithm
intervals
Results
476.0ms115×body1280valid
77.0ms48×body640valid
26.0ms22×body320valid
20.0ms63×body80valid
6.0ms8×body160valid

simplify45.0ms

Counts
1 → 1
Iterations

Useful iterations: 1 (8.0ms)

IterNodesCost
02233
13632
26032
37032
done7032

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize56.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

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:
13.0ms
(* (sin theta) (sin delta))
14.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
15.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

series599.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (sin theta) (sin delta))
231.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
8.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
281.0ms
(- (cos delta) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))

simplify2.6s

Counts
84 → 84
Iterations

Useful iterations: done (2.6s)

IterNodesCost
01581747
13221677
27621492
319151479
done50001418

prune792.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize82.0ms

Local error

Found 4 expressions with local error:

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

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
34×cbrt-prod
33×prod-diff
29×add-sqr-sqrt
26×*-un-lft-identity
24×add-cube-cbrt
7×pow1 add-exp-log add-cbrt-cube
6×add-log-exp sqr-pow
5×cube-mult unpow-prod-down unpow3 cube-prod
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow fma-neg difference-of-squares
2×cube-div pow-pow 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 → 109
Calls
4 calls:
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
9.0ms
(pow (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
34.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
10.0ms
(cbrt (pow (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

series940.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
432.0ms
(pow (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
275.0ms
(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)))
220.0ms
(cbrt (pow (* (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))

simplify4.1s

Counts
121 → 121
Iterations

Useful iterations: done (4.1s)

IterNodesCost
02217078
14635790
210834445
347984008
done50004006

prune1.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize99.0ms

Local error

Found 4 expressions with local error:

0.3b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
0.4b
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.5b
(- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×add-cube-cbrt *-un-lft-identity
11×pow1
9×times-frac
8×add-exp-log add-cbrt-cube
6×add-log-exp
5×sin-mult
4×expm1-log1p-u associate-*l/ cos-mult log1p-expm1-u associate-/l/
3×swap-sqr associate-*r* associate-*l* associate-/r* associate-/l*
2×flip3-- frac-sub flip-- sub-div
1×cbrt-undiv pow2 sub-neg asin-acos sqr-cos frac-2neg pow-plus fma-neg diff-log div-sub div-exp prod-diff pow-prod-down prod-exp associate--l+ clear-num pow-sqr *-commutative pow-prod-up cbrt-unprod sqr-sin div-inv unswap-sqr
Counts
4 → 92
Calls
4 calls:
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
45.0ms
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
13.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
43.0ms
(- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))

series2.0s

Counts
4 → 12
Calls
4 calls:
8.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
1.1s
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
257.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))
634.0ms
(- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2)))

simplify1.4s

Counts
104 → 104
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02236043
15495590
217564963
done50014045

prune1.2s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b
(* (sin theta) (sin delta))
0.3b
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
0.3b
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
0.6b
(- (cos delta) (expm1 (log1p (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
17×*-un-lft-identity
15×add-cube-cbrt
9×prod-diff
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
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×sub-neg asin-acos flip3-- diff-log flip-- distribute-lft-out-- expm1-udef associate--r- difference-of-squares
Counts
4 → 81
Calls
4 calls:
12.0ms
(* (sin theta) (sin delta))
12.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
1.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
8.0ms
(- (cos delta) (expm1 (log1p (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

series936.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* (sin theta) (sin delta))
511.0ms
(* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1))
8.0ms
(asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))
364.0ms
(- (cos delta) (expm1 (log1p (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1)))))

simplify2.7s

Counts
93 → 93
Iterations

Useful iterations: done (2.7s)

IterNodesCost
01812957
13612183
28641840
326181635
done50001625

prune727.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes460.0ms

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
02435
13035
done3035

end0.0ms

sample19.0s

Algorithm
intervals
Results
11.3s3100×body1280valid
4.9s1894×body640valid
1.0s2037×body80valid
994.0ms690×body320valid
295.0ms279×body160valid