Details

Time bar (total: 41.7s)

sample691.0ms

Algorithm
intervals
Results
415.0ms89×body1280valid
164.0ms67×body640valid
38.0ms21×body320valid
30.0ms63×body80valid
19.0ms16×body160valid

simplify60.0ms

Counts
1 → 1
Iterations
IterNodes
done55
355
254
135
022

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize66.0ms

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

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt
8×pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r* associate-*l* add-log-exp
4×insert-posit16
2×pow-prod-down prod-exp *-commutative cbrt-unprod sin-mult unswap-sqr
1×asin-acos sub-neg flip3-- diff-log flip--
Counts
4 → 62
Calls
4 calls:
19.0ms
(* (sin theta) (sin delta))
18.0ms
(* (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))))
6.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series560.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(* (sin theta) (sin delta))
221.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
13.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
258.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.2s

Counts
74 → 74
Iterations
IterNodes
done2000
32000
2734
1317
0148

prune787.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize112.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm
rewrite-expression-head
Rules
54×pow1
22×add-cbrt-cube add-exp-log
19×pow-prod-down
14×add-sqr-sqrt
12×*-un-lft-identity add-cube-cbrt
10×prod-exp cbrt-unprod
6×pow-unpow
5×pow-sqr pow-prod-up sin-mult
4×unpow-prod-down cube-prod swap-sqr associate-*r* associate-*l* insert-posit16 add-log-exp
3×pow-pow pow-plus pow-exp rem-cube-cbrt
2×pow2 cube-mult pow-to-exp unpow3 *-commutative sqr-pow
1×cube-div frac-times sqr-cos associate-*l/ associate-*r/ cos-mult unswap-sqr
Counts
4 → 114
Calls
4 calls:
9.0ms
(* (cos delta) (cos delta))
60.0ms
(* (* (sin phi1) (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)))))))
19.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
6.0ms
(pow (cos delta) 3)

series677.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* (cos delta) (cos delta))
252.0ms
(* (* (sin phi1) (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)))))))
358.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
43.0ms
(pow (cos delta) 3)

simplify1.5s

Counts
126 → 126
Iterations
IterNodes
done2003
32003
21695
1535
0180

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize112.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos theta) (cos phi1)) (sin delta))))))
0.3b
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos theta) (cos phi1)) (sin delta))))
0.4b
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos theta) (cos phi1)) (sin delta)))))))
0.7b
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos theta) (cos phi1)) (sin delta)))))))))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
8×*-un-lft-identity add-cube-cbrt
7×pow1
6×add-cbrt-cube add-exp-log add-log-exp
5×log-prod
4×log-pow insert-posit16
3×exp-prod associate-*r* associate-*l*
2×sub-neg exp-sum
1×log-div asin-acos flip3-- exp-diff diff-log rem-log-exp pow-prod-down prod-exp *-commutative cbrt-unprod flip-- sin-mult unswap-sqr
Counts
4 → 61
Calls
4 calls:
12.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos theta) (cos phi1)) (sin delta))))))
2.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos theta) (cos phi1)) (sin delta))))
6.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos theta) (cos phi1)) (sin delta)))))))
10.0ms
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos theta) (cos phi1)) (sin delta)))))))))

series816.0ms

Counts
4 → 12
Calls
4 calls:
248.0ms
(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos theta) (cos phi1)) (sin delta))))))
7.0ms
(asin (+ (* (sin phi1) (cos delta)) (* (* (cos theta) (cos phi1)) (sin delta))))
284.0ms
(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos theta) (cos phi1)) (sin delta)))))))
276.0ms
(log (exp (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos theta) (cos phi1)) (sin delta)))))))))

simplify1.8s

Counts
73 → 73
Iterations
IterNodes
done2004
42004
31907
2721
1295
0142

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize137.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×pow-unpow
4×unpow-prod-down cube-prod insert-posit16 add-log-exp
3×pow-pow pow-exp rem-cube-cbrt
2×cbrt-prod cube-mult pow-to-exp cbrt-div pow1/3 unpow3 cos-mult sqr-pow
1×cube-div pow-prod-down prod-exp cbrt-unprod sin-mult
Counts
4 → 70
Calls
4 calls:
4.0ms
(cbrt (* (cos delta) (cos delta)))
4.0ms
(cbrt (* (cos delta) (cos delta)))
10.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
3.0ms
(pow (cos delta) 3)

series943.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(cbrt (* (cos delta) (cos delta)))
238.0ms
(cbrt (* (cos delta) (cos delta)))
403.0ms
(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)
44.0ms
(pow (cos delta) 3)

simplify1.2s

Counts
82 → 82
Iterations
IterNodes
done2022
32022
21027
1352
0130

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

regimes770.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify7.0ms

Iterations
IterNodes
done32
132
024

end0.0ms

sample26.4s

Algorithm
intervals
Results
16.4s3096×body1280valid
5.8s1840×body640valid
1.8s690×body320valid
1.6s2047×body80valid
409.0ms327×body160valid