Details

sample630.0ms

Algorithm

intervals

Results

322.0ms	93×	body	1280	valid
206.0ms	60×	body	640	valid
28.0ms	71×	body	80	valid
26.0ms	21×	body	320	valid
9.0ms	11×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

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

prune68.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize75.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

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 theta) (sin delta))
20.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
3.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
10.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series643.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(* (sin theta) (sin delta))
277.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
16.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
284.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify798.0ms

Counts

70 → 70

Iterations

Iter	Nodes
done	5001
2	1120
1	312
0	144

prune778.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize105.0ms

Local error

Found 4 expressions with local error:

0.2b	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
0.2b	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
0.3b	(/ (- (* (cos delta) (cos delta)) (* (* (pow (sin phi1) 2) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))))) (+ (* (sin phi1) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))) (cos delta)))
0.3b	(- (* (cos delta) (cos delta)) (* (* (pow (sin phi1) 2) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`pow1`
3×	`associate-/r` `associate-/l`
2×	`asin-acos` `flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sqr-cos` `clear-num` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `associate--l+` `flip-+` `div-inv`

Counts

4 → 61

Calls

4 calls:

2.0ms	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
2.0ms	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
67.0ms	(/ (- (* (cos delta) (cos delta)) (* (* (pow (sin phi1) 2) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))))) (+ (* (sin phi1) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))) (cos delta)))
21.0ms	(- (* (cos delta) (cos delta)) (* (* (pow (sin phi1) 2) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))))

series2.3s

Counts

4 → 12

Calls

4 calls:

8.0ms	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
13.0ms	(asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))
1.4s	(/ (- (* (cos delta) (cos delta)) (* (* (pow (sin phi1) 2) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta))))))) (+ (* (sin phi1) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))) (cos delta)))
875.0ms	(- (* (cos delta) (cos delta)) (* (* (pow (sin phi1) 2) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))) (sin (asin (+ (* (* (cos theta) (cos phi1)) (sin delta)) (* (sin phi1) (cos delta)))))))

simplify1.4s

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	2934
1	523
0	188

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize112.0ms

Local error

Found 4 expressions with local error:

0.2b	(asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))
0.3b	(/ (pow (cos delta) 2) (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)))
0.3b	(/ (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (/ (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)) (* (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2))))
0.4b	(- (/ (pow (cos delta) 2) (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta))) (/ (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (/ (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)) (* (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)))))

rewrite292.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
66×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
37×	`add-cube-cbrt`
25×	`add-exp-log`
15×	`add-cbrt-cube`
14×	`unpow-prod-down`
12×	`div-exp`
11×	`associate-/l*`
10×	`associate-/r*` `difference-of-squares`
6×	`cbrt-undiv` `div-inv` `unpow2` `add-log-exp` `sqr-pow`
4×	`pow1`
3×	`asin-acos` `prod-exp` `associate-/r/`
2×	`pow-to-exp` `clear-num` `frac-2neg` `div-sub` `pow-exp` `sin-diff` `distribute-lft-out--`
1×	`sub-neg` `flip3-+` `flip3--` `diff-log` `frac-sub` `cbrt-unprod` `flip-+` `flip--` `associate--r-`

Counts

4 → 136

Calls

4 calls:

3.0ms	(asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))
32.0ms	(/ (pow (cos delta) 2) (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)))
49.0ms	(/ (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (/ (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)) (* (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2))))
198.0ms	(- (/ (pow (cos delta) 2) (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta))) (/ (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (/ (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)) (* (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)))))

series4.0s

Counts

4 → 12

Calls

4 calls:

8.0ms	(asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))
372.0ms	(/ (pow (cos delta) 2) (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)))
682.0ms	(/ (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (/ (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)) (* (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2))))
2.9s	(- (/ (pow (cos delta) 2) (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta))) (/ (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (/ (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)) (* (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)))))

simplify2.0s

Counts

148 → 148

Iterations

Iter	Nodes
done	5001
2	4515
1	881
0	365

prune2.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize148.0ms

Local error

Found 4 expressions with local error:

0.2b	(asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))
0.2b	(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
0.3b	(/ (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (/ (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)) (* (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2))))
0.4b	(- (* (cos delta) (/ (cos delta) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))))) (/ (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (/ (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)) (* (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac`
20×	`add-sqr-sqrt` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
13×	`add-cbrt-cube`
9×	`div-exp`
7×	`associate-/r*`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-inv`
4×	`pow1` `asin-acos`
3×	`prod-exp` `associate-/l*`
2×	`div-sub` `sin-diff`
1×	`pow-to-exp` `clear-num` `sub-neg` `frac-2neg` `flip3--` `diff-log` `pow-exp` `associate-*r/` `associate-/r/` `frac-sub` `cbrt-unprod` `flip--` `associate--r-`

Counts

4 → 81

Calls

4 calls:

3.0ms	(asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))
4.0ms	(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
53.0ms	(/ (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (/ (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)) (* (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2))))
30.0ms	(- (* (cos delta) (/ (cos delta) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))))) (/ (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (/ (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)) (* (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)))))

series3.3s

Counts

4 → 12

Calls

4 calls:

16.0ms	(asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))
15.0ms	(asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))
721.0ms	(/ (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (/ (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)) (* (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2))))
2.6s	(- (* (cos delta) (/ (cos delta) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin delta) (* (cos phi1) (cos theta))) (* (sin phi1) (cos delta))))))))) (/ (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (/ (+ (* (sin phi1) (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta)) (* (sin (asin (+ (* (* (sin delta) (cos phi1)) (cos theta)) (* (sin phi1) (cos delta))))) (pow (sin phi1) 2)))))

simplify1.7s

Counts

93 → 93

Iterations

Iter	Nodes
done	5001
2	3839
1	705
0	275

prune1.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes1.2s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	51
1	51
0	37

end0.0ms

sample22.1s

Algorithm

intervals

Results

12.9s	3157×	body	1280	valid
5.3s	1870×	body	640	valid
1.5s	1966×	body	80	valid
1.2s	695×	body	320	valid
357.0ms	312×	body	160	valid