Details

sample588.0ms

Algorithm

intervals

Results

317.0ms	115×	body	1280	valid
185.0ms	48×	body	640	valid
24.0ms	63×	body	80	valid
22.0ms	22×	body	320	valid
5.0ms	8×	body	160	valid

simplify68.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	22	33
1	36	32
2	60	32
3	70	32
done	70	32

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize53.0ms

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

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-neg` `prod-diff`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `sin-mult` `unswap-sqr`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--`

Counts

4 → 72

Calls

4 calls:

28.0ms	(* (sin theta) (sin delta))
43.0ms	(* (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))))
9.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* (sin theta) (sin delta))
251.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
9.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
267.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify2.8s

Counts

84 → 84

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	157	1824
1	321	1677
2	794	1492
3	2040	1479
done	5000	1418

prune828.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize77.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.4b	(pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)
0.6b	(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)))
17.9b	(cbrt (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

34×	`cbrt-prod`
33×	`prod-diff`
29×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
24×	`add-cube-cbrt`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-log-exp` `sqr-pow`
5×	`cube-mult` `unpow-prod-down` `unpow3` `cube-prod`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `fma-neg` `difference-of-squares`
2×	`cube-div` `pow-pow` `pow-exp` `sin-mult` `rem-cube-cbrt`
1×	`pow-to-exp` `sub-neg` `asin-acos` `cbrt-div` `flip3--` `pow1/3` `diff-log` `pow-prod-down` `prod-exp` `flip--` `rem-cbrt-cube` `cbrt-unprod` `distribute-lft-out--`

Counts

4 → 109

Calls

4 calls:

1.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
19.0ms	(pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)
20.0ms	(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)))
5.0ms	(cbrt (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3))

series944.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
371.0ms	(pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)
313.0ms	(- (cos delta) (cbrt (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)))
252.0ms	(cbrt (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3))

simplify4.2s

Counts

121 → 121

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	217	7078
1	455	5790
2	1078	4417
3	4828	4008
done	5000	4008

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.1b

localize70.0ms

Local error

Found 4 expressions with local error:

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

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

96×	`prod-diff`
57×	`add-sqr-sqrt`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
45×	`unpow-prod-down` `cube-prod`
29×	`sqr-pow`
23×	`cube-mult` `unpow3`
12×	`fma-neg`
8×	`pow1` `add-exp-log` `add-cbrt-cube` `difference-of-squares`
6×	`pow-unpow` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`pow-to-exp`
1×	`difference-cubes` `cube-div` `sub-neg` `asin-acos` `flip3--` `diff-log` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod` `sin-mult` `distribute-lft-out--`

Counts

4 → 192

Calls

4 calls:

1.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
4.0ms	(pow (cos delta) 3)
28.0ms	(pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)
60.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3))

series1.1s

Counts

4 → 12

Calls

4 calls:

14.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
50.0ms	(pow (cos delta) 3)
350.0ms	(pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3)
709.0ms	(- (pow (cos delta) 3) (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 3))

simplify2.5s

Counts

204 → 204

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	283	15777
1	693	9051
2	2523	6779
done	5001	4761

prune1.3s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize66.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.3b	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.3b	(/ (- (* (cos delta) (cos delta)) (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 2)) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)))
0.5b	(- (* (cos delta) (cos delta)) (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 2))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
18×	`times-frac`
16×	`add-cube-cbrt` `*-un-lft-identity`
15×	`difference-of-squares`
6×	`add-exp-log` `prod-diff` `add-cbrt-cube` `associate-/l*` `unpow2` `add-log-exp` `sqr-pow`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u`
3×	`associate-/r*`
2×	`asin-acos` `flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `unpow-prod-down` `sqr-cos` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `associate--l+` `clear-num` `div-inv`

Counts

4 → 89

Calls

4 calls:

1.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
1.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
73.0ms	(/ (- (* (cos delta) (cos delta)) (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 2)) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)))
33.0ms	(- (* (cos delta) (cos delta)) (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 2))

series1.8s

Counts

4 → 12

Calls

4 calls:

16.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
16.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
1.1s	(/ (- (* (cos delta) (cos delta)) (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 2)) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)))
617.0ms	(- (* (cos delta) (cos delta)) (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 2))

simplify2.0s

Counts

101 → 101

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	222	5526
1	542	5011
2	1828	4534
done	5000	4375

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

regimes497.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	35
1	30	35
done	30	35

end0.0ms

sample18.8s

Algorithm

intervals

Results

12.2s	3100×	body	1280	valid
3.9s	1894×	body	640	valid
1.1s	690×	body	320	valid
766.0ms	2037×	body	80	valid
194.0ms	279×	body	160	valid