Details

sample777.0ms

Algorithm

intervals

Results

406.0ms	91×	body	1280	valid
196.0ms	55×	body	640	valid
82.0ms	68×	body	80	valid
47.0ms	25×	body	320	valid
20.0ms	17×	body	160	valid

simplify62.0ms

Counts

1 → 1

Iterations

Iter	Nodes
4	55
3	55
2	54
1	35
0	22

prune23.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize91.0ms

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))))
0.5b	(- (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:

11.0ms	(* (sin theta) (sin delta))
17.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
4.0ms	(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)))))))

series558.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (sin theta) (sin delta))
212.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
14.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
262.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify4.1s

Counts

74 → 74

Iterations

Iter	Nodes
4	5201
3	1916
2	718
1	315
0	148

prune2.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize137.0ms

Local error

Found 4 expressions with local error:

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

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
20×	`add-cbrt-cube` `add-exp-log`
18×	`add-sqr-sqrt` `pow-prod-down`
10×	`*-un-lft-identity`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `difference-of-squares` `sqr-pow`
6×	`pow-unpow` `unpow-prod-down` `cube-prod` `add-log-exp`
5×	`sin-mult`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `pow-plus` `unpow3`
1×	`cube-div` `pow2` `frac-times` `difference-cubes` `sub-neg` `flip3--` `diff-log` `swap-sqr` `associate-r` `associate-l` `associate-l/` `associate-r/` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 109

Calls

4 calls:

73.0ms	(* (* (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)))))))
5.0ms	(pow (cos delta) 3)
12.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
10.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series2.1s

Counts

4 → 12

Calls

4 calls:

274.0ms	(* (* (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)))))))
44.0ms	(pow (cos delta) 3)
1.4s	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
432.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify2.0s

Counts

121 → 121

Iterations

Iter	Nodes
2	2991
1	672
0	240

prune3.9s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize115.0ms

Local error

Found 4 expressions with local error:

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

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

47×	`pow1`
20×	`add-cbrt-cube` `add-exp-log`
18×	`add-sqr-sqrt` `pow-prod-down`
10×	`*-un-lft-identity`
9×	`prod-exp` `cbrt-unprod`
8×	`add-cube-cbrt` `difference-of-squares` `sqr-pow`
6×	`pow-unpow` `unpow-prod-down` `cube-prod` `add-log-exp`
5×	`sin-mult`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
3×	`pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `pow-plus` `unpow3`
1×	`cube-div` `pow2` `frac-times` `difference-cubes` `sub-neg` `flip3--` `diff-log` `swap-sqr` `associate-r` `associate-l` `associate-l/` `associate-r/` `*-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 109

Calls

4 calls:

54.0ms	(* (* (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)))))))
3.0ms	(pow (cos delta) 3)
13.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
19.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series2.1s

Counts

4 → 12

Calls

4 calls:

273.0ms	(* (* (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)))))))
51.0ms	(pow (cos delta) 3)
1.4s	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3))
349.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify2.4s

Counts

121 → 121

Iterations

Iter	Nodes
2	2991
1	672
0	240

prune3.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize312.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* (cos phi1) (cos theta)) (* (cos phi1) (cos theta)))
0.4b	(- (* (* (cos delta) (cos delta)) (cos delta)) (+ (+ (* (* (cos theta) (* (cos theta) (cos theta))) (* (* (sin phi1) (* (sin phi1) (sin phi1))) (* (* (* (sin delta) (* (sin delta) (sin delta))) (cos phi1)) (* (cos phi1) (cos phi1))))) (+ (* (* (cos phi1) (* (cos theta) (* (sin delta) (* (cos delta) (cos delta))))) (pow (sin phi1) 5)) (* (* (* (sin phi1) (* (sin phi1) (sin phi1))) (* (sin phi1) (* (sin phi1) (sin phi1)))) (* (* (cos delta) (cos delta)) (cos delta))))) (+ (* (* (* 2 (sin delta)) (cos phi1)) (* (cos theta) (* (pow (sin phi1) 5) (* (cos delta) (cos delta))))) (* (* 3 (* (* (sin delta) (* (sin phi1) (sin phi1))) (* (sin delta) (* (sin phi1) (sin phi1))))) (* (* (* (cos phi1) (cos theta)) (* (cos phi1) (cos theta))) (cos delta))))))
0.5b	(pow (sin phi1) 5)
0.5b	(pow (sin phi1) 5)

rewrite24.8s

Algorithm

rewrite-expression-head

Rules

25942×	`associate-*r/`
11858×	`associate-*l/`
11835×	`cos-mult`
8464×	`frac-add`
6680×	`sin-mult`
6206×	`frac-times`
2331×	`frac-sub`
410×	`flip3-+` `flip-+`
45×	`pow1`
33×	`add-log-exp`
18×	`add-exp-log`
17×	`pow-prod-down`
16×	`add-cbrt-cube`
15×	`sum-log`
8×	`add-sqr-sqrt` `*-un-lft-identity` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
7×	`diff-log`
6×	`pow-unpow` `unpow-prod-down`
4×	`pow-sqr` `pow-prod-up` `insert-posit16`
2×	`pow-to-exp` `pow-pow` `pow-plus` `pow-exp` `sqr-pow`
1×	`pow2` `sub-neg` `flip3--` `swap-sqr` `associate-r` `associate-l` `*-commutative` `flip--` `associate--r+`

Counts

4 → 2425

Calls

4 calls:

51.0ms	(* (* (cos phi1) (cos theta)) (* (cos phi1) (cos theta)))
23.6s	(- (* (* (cos delta) (cos delta)) (cos delta)) (+ (+ (* (* (cos theta) (* (cos theta) (cos theta))) (* (* (sin phi1) (* (sin phi1) (sin phi1))) (* (* (* (sin delta) (* (sin delta) (sin delta))) (cos phi1)) (* (cos phi1) (cos phi1))))) (+ (* (* (cos phi1) (* (cos theta) (* (sin delta) (* (cos delta) (cos delta))))) (pow (sin phi1) 5)) (* (* (* (sin phi1) (* (sin phi1) (sin phi1))) (* (sin phi1) (* (sin phi1) (sin phi1)))) (* (* (cos delta) (cos delta)) (cos delta))))) (+ (* (* (* 2 (sin delta)) (cos phi1)) (* (cos theta) (* (pow (sin phi1) 5) (* (cos delta) (cos delta))))) (* (* 3 (* (* (sin delta) (* (sin phi1) (sin phi1))) (* (sin delta) (* (sin phi1) (sin phi1))))) (* (* (* (cos phi1) (cos theta)) (* (cos phi1) (cos theta))) (cos delta))))))
4.0ms	(pow (sin phi1) 5)
3.0ms	(pow (sin phi1) 5)

series1.4s

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (* (cos phi1) (cos theta)) (* (cos phi1) (cos theta)))
1.2s	(- (* (* (cos delta) (cos delta)) (cos delta)) (+ (+ (* (* (cos theta) (* (cos theta) (cos theta))) (* (* (sin phi1) (* (sin phi1) (sin phi1))) (* (* (* (sin delta) (* (sin delta) (sin delta))) (cos phi1)) (* (cos phi1) (cos phi1))))) (+ (* (* (cos phi1) (* (cos theta) (* (sin delta) (* (cos delta) (cos delta))))) (pow (sin phi1) 5)) (* (* (* (sin phi1) (* (sin phi1) (sin phi1))) (* (sin phi1) (* (sin phi1) (sin phi1)))) (* (* (cos delta) (cos delta)) (cos delta))))) (+ (* (* (* 2 (sin delta)) (cos phi1)) (* (cos theta) (* (pow (sin phi1) 5) (* (cos delta) (cos delta))))) (* (* 3 (* (* (sin delta) (* (sin phi1) (sin phi1))) (* (sin delta) (* (sin phi1) (sin phi1))))) (* (* (* (cos phi1) (cos theta)) (* (cos phi1) (cos theta))) (cos delta))))))
64.0ms	(pow (sin phi1) 5)
53.0ms	(pow (sin phi1) 5)

simplify3.6m

Counts

2437 → 2437

Iterations

Iter	Nodes
1	32232
0	9472

prune2.7m

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes1.1s

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify29.0ms

Iterations

Iter	Nodes
2	106
1	106
0	68

end0.0ms

sample17.1s

Algorithm

intervals

Results

10.4s	3114×	body	1280	valid
4.1s	1892×	body	640	valid
1.0s	688×	body	320	valid
790.0ms	2005×	body	80	valid
486.0ms	301×	body	160	valid