Details

sample510.0ms

Algorithm

intervals

Results

260.0ms	92×	body	1280	valid
173.0ms	69×	body	640	valid
20.0ms	68×	body	80	valid
15.0ms	16×	body	320	valid
7.0ms	11×	body	160	valid

simplify51.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	62
3	62
2	56
1	35
0	22

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize84.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
0.2b	(* (sin theta) (sin delta))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.5b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite36.0ms

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`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 58

Calls

4 calls:

10.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
10.0ms	(* (sin theta) (sin delta))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
13.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series549.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
74.0ms	(* (sin theta) (sin delta))
14.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
235.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.7s

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
2	1127
1	312
0	144

prune898.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize216.0ms

Local error

Found 4 expressions with local error:

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

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1`
18×	`add-cbrt-cube` `add-exp-log`
17×	`pow-prod-down`
16×	`sin-mult`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
10×	`cos-mult`
8×	`prod-exp` `cbrt-unprod`
7×	`associate-/l/`
6×	`frac-sub` `add-log-exp`
5×	`associate-l/` `associate-r/` `difference-of-squares`
4×	`pow-sqr` `pow-prod-up` `associate-/l*` `sub-div`
3×	`frac-times` `associate-/r*`
2×	`pow-plus` `flip3--` `associate-/r/` `flip--`
1×	`pow2` `cbrt-undiv` `asin-acos` `sqr-cos` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `swap-sqr` `div-exp` `associate-r` `associate-l` `associate--l+` `*-commutative` `flip-+` `div-inv`

Counts

4 → 105

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
70.0ms	(/ (- (* (cos delta) (cos delta)) (* (* (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)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
71.0ms	(* (* (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)))))))
57.0ms	(- (* (cos delta) (cos delta)) (* (* (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))))))))

series2.6s

Counts

4 → 12

Calls

4 calls:

12.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.4s	(/ (- (* (cos delta) (cos delta)) (* (* (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)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
270.0ms	(* (* (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)))))))
865.0ms	(- (* (cos delta) (cos delta)) (* (* (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))))))))

simplify3.2s

Counts

117 → 117

Iterations

Iter	Nodes
done	5002
2	4106
1	747
0	260

prune1.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize367.0ms

Local error

Found 4 expressions with local error:

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

rewrite2.6m

Algorithm

rewrite-expression-head

Rules

157×	`pow1`
83×	`pow-prod-down`
54×	`add-cbrt-cube` `add-exp-log`
51×	`associate-*r/`
48×	`associate-*l/`
39×	`sin-mult`
35×	`prod-exp` `cbrt-unprod`
24×	`frac-add`
17×	`cos-mult` `frac-sub`
13×	`add-sqr-sqrt` `pow-sqr` `pow-prod-up` `add-log-exp`
12×	`*-un-lft-identity` `add-cube-cbrt`
9×	`frac-times` `times-frac`
6×	`sin-cos-mult`
5×	`flip3-+` `pow-plus` `flip-+`
3×	`associate-/r` `sum-log` `diff-log` `associate-/l`
2×	`pow2` `flip3--` `swap-sqr` `associate-r` `associate-l` `associate-/r/` `*-commutative` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sqr-cos` `clear-num` `sub-neg` `frac-2neg` `div-sub` `div-exp` `associate--l+` `div-inv` `associate--r+` `difference-of-squares`

Counts

4 → 163

Calls

4 calls:

31.0ms	(* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1)))
2.4m	(/ (- (- (* (cos delta) (cos delta)) (+ (+ (* (* (cos theta) (* (sin delta) (* (* (cos delta) (sin phi1)) (* (sin phi1) (sin phi1))))) (cos phi1)) (* (cos theta) (* (* (* (sin delta) (cos phi1)) (cos delta)) (* (sin phi1) (* (sin phi1) (sin phi1)))))) (* (* (* (sin phi1) (sin phi1)) (cos delta)) (* (* (sin phi1) (sin phi1)) (cos delta))))) (* (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))) (* (* (cos phi1) (sin delta)) (* (cos phi1) (sin delta))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
169.0ms	(* (* (* (sin phi1) (sin phi1)) (cos delta)) (* (* (sin phi1) (sin phi1)) (cos delta)))
12.2s	(- (* (cos delta) (cos delta)) (+ (+ (* (* (cos theta) (* (sin delta) (* (* (cos delta) (sin phi1)) (* (sin phi1) (sin phi1))))) (cos phi1)) (* (cos theta) (* (* (* (sin delta) (cos phi1)) (cos delta)) (* (sin phi1) (* (sin phi1) (sin phi1)))))) (* (* (* (sin phi1) (sin phi1)) (cos delta)) (* (* (sin phi1) (sin phi1)) (cos delta)))))

series1.7s

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1)))
1.1s	(/ (- (- (* (cos delta) (cos delta)) (+ (+ (* (* (cos theta) (* (sin delta) (* (* (cos delta) (sin phi1)) (* (sin phi1) (sin phi1))))) (cos phi1)) (* (cos theta) (* (* (* (sin delta) (cos phi1)) (cos delta)) (* (sin phi1) (* (sin phi1) (sin phi1)))))) (* (* (* (sin phi1) (sin phi1)) (cos delta)) (* (* (sin phi1) (sin phi1)) (cos delta))))) (* (* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1))) (* (* (cos phi1) (sin delta)) (* (cos phi1) (sin delta))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
63.0ms	(* (* (* (sin phi1) (sin phi1)) (cos delta)) (* (* (sin phi1) (sin phi1)) (cos delta)))
496.0ms	(- (* (cos delta) (cos delta)) (+ (+ (* (* (cos theta) (* (sin delta) (* (* (cos delta) (sin phi1)) (* (sin phi1) (sin phi1))))) (cos phi1)) (* (cos theta) (* (* (* (sin delta) (cos phi1)) (cos delta)) (* (sin phi1) (* (sin phi1) (sin phi1)))))) (* (* (* (sin phi1) (sin phi1)) (cos delta)) (* (* (sin phi1) (sin phi1)) (cos delta)))))

simplify4.0s

Counts

175 → 175

Iterations

Iter	Nodes
done	5001
1	1591
0	451

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize241.0ms

Local error

Found 4 expressions with local error:

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

rewrite26.8s

Algorithm

rewrite-expression-head

Rules

157×	`pow1`
101×	`associate-*r/`
91×	`associate-*l/`
83×	`pow-prod-down`
74×	`sin-mult`
54×	`add-cbrt-cube` `add-exp-log`
48×	`frac-add`
35×	`prod-exp` `cbrt-unprod`
34×	`cos-mult` `frac-sub`
19×	`associate-/l/`
18×	`add-sqr-sqrt`
17×	`frac-times`
13×	`*-un-lft-identity` `pow-sqr` `pow-prod-up` `add-cube-cbrt` `add-log-exp`
12×	`times-frac` `sin-cos-mult`
9×	`flip3-+` `flip-+`
5×	`pow-plus` `difference-of-squares`
4×	`associate-/l*`
3×	`associate-/r*` `sum-log` `diff-log`
2×	`pow2` `flip3--` `swap-sqr` `associate-r` `associate-l` `associate-/r/` `*-commutative` `flip--`
1×	`cbrt-undiv` `sqr-cos` `clear-num` `sub-neg` `frac-2neg` `div-sub` `div-exp` `associate--l+` `div-inv` `associate--r+`

Counts

4 → 184

Calls

4 calls:

31.0ms	(* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1)))
18.3s	(/ (- (* (cos delta) (cos delta)) (+ (+ (* (* (cos theta) (* (sin delta) (* (* (cos delta) (sin phi1)) (* (sin phi1) (sin phi1))))) (cos phi1)) (* (cos theta) (* (* (* (sin delta) (cos phi1)) (cos delta)) (* (sin phi1) (* (sin phi1) (sin phi1)))))) (* (* (* (sin phi1) (sin phi1)) (cos delta)) (* (* (sin phi1) (sin phi1)) (cos delta))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
111.0ms	(* (* (* (sin phi1) (sin phi1)) (cos delta)) (* (* (sin phi1) (sin phi1)) (cos delta)))
8.3s	(- (* (cos delta) (cos delta)) (+ (+ (* (* (cos theta) (* (sin delta) (* (* (cos delta) (sin phi1)) (* (sin phi1) (sin phi1))))) (cos phi1)) (* (cos theta) (* (* (* (sin delta) (cos phi1)) (cos delta)) (* (sin phi1) (* (sin phi1) (sin phi1)))))) (* (* (* (sin phi1) (sin phi1)) (cos delta)) (* (* (sin phi1) (sin phi1)) (cos delta)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* (cos theta) (sin phi1)) (* (cos theta) (sin phi1)))
858.0ms	(/ (- (* (cos delta) (cos delta)) (+ (+ (* (* (cos theta) (* (sin delta) (* (* (cos delta) (sin phi1)) (* (sin phi1) (sin phi1))))) (cos phi1)) (* (cos theta) (* (* (* (sin delta) (cos phi1)) (cos delta)) (* (sin phi1) (* (sin phi1) (sin phi1)))))) (* (* (* (sin phi1) (sin phi1)) (cos delta)) (* (* (sin phi1) (sin phi1)) (cos delta))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
65.0ms	(* (* (* (sin phi1) (sin phi1)) (cos delta)) (* (* (sin phi1) (sin phi1)) (cos delta)))
502.0ms	(- (* (cos delta) (cos delta)) (+ (+ (* (* (cos theta) (* (sin delta) (* (* (cos delta) (sin phi1)) (* (sin phi1) (sin phi1))))) (cos phi1)) (* (cos theta) (* (* (* (sin delta) (cos phi1)) (cos delta)) (* (sin phi1) (* (sin phi1) (sin phi1)))))) (* (* (* (sin phi1) (sin phi1)) (cos delta)) (* (* (sin phi1) (sin phi1)) (cos delta)))))

simplify4.3s

Counts

196 → 196

Iterations

Iter	Nodes
done	5001
1	1569
0	447

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

regimes641.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify22.0ms

Iterations

Iter	Nodes
done	75
3	75
2	73
1	69
0	48

end0.0ms

sample13.4s

Algorithm

intervals

Results

8.2s	3149×	body	1280	valid
3.0s	1864×	body	640	valid
716.0ms	1995×	body	80	valid
702.0ms	683×	body	320	valid
218.0ms	309×	body	160	valid