Details

sample267.0ms

Algorithm

intervals

Results

161.0ms	97×	body	1280	valid
60.0ms	67×	body	640	valid
12.0ms	22×	body	320	valid
9.0ms	55×	body	80	valid
6.0ms	15×	body	160	valid

simplify29.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	22	33
1	36	32
2	59	32
3	67	32
done	67	32

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

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)))))))

rewrite14.0ms

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:

4.0ms	(* (sin theta) (sin delta))
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))))
3.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (sin theta) (sin delta))
151.0ms	(* (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))))
175.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify1.7s

Counts

84 → 84

Iterations

Useful iterations: 3 (494.0ms)

Iter	Nodes	Cost
0	157	1824
1	318	1677
2	795	1492
3	2260	1479
done	5000	1479

prune517.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (sin phi1) (sin (log (exp (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))))
0.5b	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))))
3.8b	(log (exp (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`log-prod`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sin-sum`
7×	`pow1`
6×	`add-exp-log` `distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube` `associate--r+` `add-log-exp`
4×	`expm1-log1p-u` `log-pow` `log1p-expm1-u`
3×	`exp-prod` `fma-neg` `associate-r` `associate-l` `prod-diff`
2×	`asin-acos`
1×	`sub-neg` `log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sin-mult` `unswap-sqr`

Counts

4 → 81

Calls

4 calls:

8.0ms	(* (sin phi1) (sin (log (exp (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
0.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
4.0ms	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))))
2.0ms	(log (exp (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))

series335.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(* (sin phi1) (sin (log (exp (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))))
6.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
171.0ms	(- (cos delta) (* (sin phi1) (sin (log (exp (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))))))
6.0ms	(log (exp (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))))

simplify2.0s

Counts

93 → 93

Iterations

Useful iterations: 3 (808.0ms)

Iter	Nodes	Cost
0	177	2878
1	343	2632
2	845	2324
3	2494	2226
done	5000	2226

prune592.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

4.0ms	(* (sin theta) (sin delta))
0.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.0ms	(fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (cos delta))

series230.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin theta) (sin delta))
6.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
6.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
172.0ms	(fma (- (sin phi1)) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (cos delta))

simplify1.4s

Counts

63 → 63

Iterations

Useful iterations: 3 (146.0ms)

Iter	Nodes	Cost
0	92	988
1	173	983
2	377	867
3	760	859
4	1709	859
done	5000	859

prune436.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

0.3b	(acos (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))))
0.5b	(fma (- (sin phi1)) (sin (- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta))
4.1b	(- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
45×	`add-cube-cbrt`
39×	`prod-diff`
37×	`times-frac`
13×	`fma-neg`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `div-inv`
2×	`acos-asin` `difference-of-squares`
1×	`sub-neg` `asin-acos` `flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--` `associate--r-`

Counts

4 → 100

Calls

4 calls:

0.0ms	(acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
0.0ms	(fma (- (sin phi1)) (sin (- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta))
14.0ms	(- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))

series230.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
6.0ms	(asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))
181.0ms	(fma (- (sin phi1)) (sin (- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (cos delta))
36.0ms	(- (/ PI 2) (acos (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))

simplify1.1s

Counts

112 → 112

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	163	5817
1	299	3869
2	667	3062
3	2082	2326
done	5000	2317

prune627.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

regimes383.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	54
1	37	54
done	37	54

end0.0ms

sample8.3s

Algorithm

intervals

Results

5.2s	3165×	body	1280	valid
1.9s	1848×	body	640	valid
403.0ms	663×	body	320	valid
319.0ms	2008×	body	80	valid
132.0ms	316×	body	160	valid