Details

sample264.0ms

Algorithm

intervals

Results

165.0ms	103×	body	1280	valid
58.0ms	68×	body	640	valid
11.0ms	20×	body	320	valid
9.0ms	57×	body	80	valid
3.0ms	8×	body	160	valid

simplify27.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	33
1	35	33
2	54	33
3	57	33
done	57	33

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize31.0ms

Local error

Found 4 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`associate-r` `associate-l`
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 → 48

Calls

4 calls:

1.0ms	(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
4.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series469.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))
156.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
182.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify965.0ms

Counts

60 → 60

Iterations

Useful iterations: 3 (297.0ms)

Iter	Nodes	Cost
0	112	1516
1	229	1446
2	560	1280
3	1931	1278
done	5000	1278

prune360.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize40.0ms

Local error

Found 4 expressions with local error:

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

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`swap-sqr` `associate-r` `associate-l` `sin-mult`
2×	`asin-acos` `associate-*r/` `cos-mult`
1×	`pow2` `sub-neg` `sqr-cos` `flip3--` `pow-plus` `diff-log` `pow-prod-down` `prod-exp` `associate--l+` `pow-sqr` `*-commutative` `pow-prod-up` `frac-sub` `flip--` `cbrt-unprod` `sqr-sin` `sub-div` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
8.0ms	(- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
5.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series657.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
495.0ms	(- (* (cos delta) (cos delta)) (* (pow (sin phi1) 2) (* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
149.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify554.0ms

Counts

70 → 70

Iterations

Useful iterations: 2 (131.0ms)

Iter	Nodes	Cost
0	146	2808
1	358	2451
2	1357	2063
done	5000	2063

prune476.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize60.0ms

Local error

Found 4 expressions with local error:

0.4b	(pow (sin phi1) 3)
0.4b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.4b	(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
0.5b	(pow (sin phi1) 4)

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
13×	`add-log-exp`
11×	`*-un-lft-identity`
9×	`add-cube-cbrt`
7×	`unpow-prod-down`
6×	`pow1` `add-exp-log` `pow-unpow`
5×	`add-cbrt-cube`
4×	`difference-of-squares`
3×	`diff-log` `cube-prod` `sum-log` `sqr-pow`
2×	`pow-to-exp` `pow-pow` `pow-exp`
1×	`cube-mult` `sub-neg` `asin-acos` `flip3--` `unpow3` `flip--` `associate--r+` `distribute-lft-out--` `unpow2` `rem-cube-cbrt`

Counts

4 → 68

Calls

4 calls:

2.0ms	(pow (sin phi1) 3)
1.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
1.4s	(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
2.0ms	(pow (sin phi1) 4)

series621.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(pow (sin phi1) 3)
7.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
549.0ms	(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
31.0ms	(pow (sin phi1) 4)

simplify698.0ms

Counts

80 → 80

Iterations

Useful iterations: 2 (215.0ms)

Iter	Nodes	Cost
0	176	2364
1	425	2234
2	1568	2074
done	5000	2074

prune683.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
0.5b	(pow (sin phi1) 4)
0.7b	(pow (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) 3)
7.2b	(cbrt (pow (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) 3))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
14×	`*-un-lft-identity`
13×	`add-log-exp`
12×	`cbrt-prod` `add-cube-cbrt`
10×	`unpow-prod-down`
6×	`pow1` `add-exp-log` `pow-unpow` `cube-prod`
5×	`add-cbrt-cube`
4×	`difference-of-squares` `sqr-pow`
3×	`diff-log` `sum-log`
2×	`cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp`
1×	`sub-neg` `flip3--` `pow1/3` `flip--` `rem-cbrt-cube` `associate--r+` `distribute-lft-out--` `unpow2` `rem-cube-cbrt`

Counts

4 → 81

Calls

4 calls:

1.4s	(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
1.0ms	(pow (sin phi1) 4)
1.0ms	(pow (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) 3)
1.0ms	(cbrt (pow (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) 3))

series483.0ms

Counts

4 → 12

Calls

4 calls:

409.0ms	(- (pow (cos delta) 2) (+ (* (pow (sin delta) 2) (* (pow (cos phi1) 2) (* (pow (cos theta) 2) (pow (sin phi1) 2)))) (+ (* 2 (* (sin delta) (* (cos phi1) (* (pow (sin phi1) 3) (* (cos delta) (cos theta)))))) (* (pow (sin phi1) 4) (pow (cos delta) 2)))))
34.0ms	(pow (sin phi1) 4)
33.0ms	(pow (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) 3)
8.0ms	(cbrt (pow (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) 3))

simplify635.0ms

Counts

93 → 93

Iterations

Useful iterations: 2 (195.0ms)

Iter	Nodes	Cost
0	177	3314
1	412	3060
2	1461	2767
done	5000	2767

prune721.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

regimes415.0ms

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)

Iter	Nodes	Cost
0	47	90
1	67	90
done	67	90

end0.0ms

sample7.9s

Algorithm

intervals

Results

5.0s	3113×	body	1280	valid
1.7s	1894×	body	640	valid
438.0ms	723×	body	320	valid
308.0ms	1978×	body	80	valid
112.0ms	292×	body	160	valid