Details

sample640.0ms

Algorithm

intervals

Results

438.0ms	107×	body	1280	valid
115.0ms	55×	body	640	valid
25.0ms	70×	body	80	valid
23.0ms	19×	body	320	valid
4.0ms	5×	body	160	valid

simplify30.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize111.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (cos phi1) (sin delta)) (cos theta))
0.3b	(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))))))
0.6b	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`associate-r` `add-log-exp`
4×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`*-commutative`
1×	`asin-acos` `sub-neg` `flip3--` `diff-log` `flip--` `sin-mult` `unswap-sqr`

Counts

4 → 57

Calls

4 calls:

23.0ms	(* (* (cos phi1) (sin delta)) (cos theta))
3.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
21.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
11.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series591.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* (* (cos phi1) (sin delta)) (cos theta))
16.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
220.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
247.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify3.4s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	3644
2	936
1	329
0	141

prune828.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize221.0ms

Local error

Found 4 expressions with local error:

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

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

30×	`flip3--` `flip--`
28×	`frac-times`
26×	`cbrt-div`
14×	`associate-*l/`
10×	`add-log-exp`
8×	`associate-*r/`
4×	`add-sqr-sqrt` `pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
3×	`sub-neg` `diff-log`
1×	`cbrt-prod` `pow1/3` `pow3` `rem-cbrt-cube`

Counts

4 → 72

Calls

4 calls:

71.0ms	(cbrt (* (* (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
6.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
5.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
7.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

297.0ms	(cbrt (* (* (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
265.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
260.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
285.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify3.7s

Counts

84 → 84

Iterations

Iter	Nodes
done	5000
2	1224
1	346
0	153

prune1.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize236.0ms

Local error

Found 4 expressions with local error:

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

rewrite278.0ms

Algorithm

rewrite-expression-head

Rules

30×	`flip3--` `flip--`
28×	`frac-times`
26×	`cbrt-div`
14×	`associate-*l/`
13×	`add-log-exp`
8×	`associate-*r/`
6×	`add-sqr-sqrt` `*-un-lft-identity`
4×	`pow1` `add-cbrt-cube` `diff-log` `add-exp-log` `add-cube-cbrt`
3×	`sub-neg`
1×	`cbrt-prod` `sum-log` `pow1/3` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 75

Calls

4 calls:

194.0ms	(cbrt (* (* (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (- (cos delta) (+ (* (* (cos delta) (sin phi1)) (sin phi1)) (* (* (sin phi1) (sin delta)) (* (cos theta) (cos phi1)))))) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
55.0ms	(- (cos delta) (+ (* (* (cos delta) (sin phi1)) (sin phi1)) (* (* (sin phi1) (sin delta)) (* (cos theta) (cos phi1)))))
11.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
11.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

series2.0s

Counts

4 → 12

Calls

4 calls:

1.2s	(cbrt (* (* (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))) (- (cos delta) (+ (* (* (cos delta) (sin phi1)) (sin phi1)) (* (* (sin phi1) (sin delta)) (* (cos theta) (cos phi1)))))) (- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))))
260.0ms	(- (cos delta) (+ (* (* (cos delta) (sin phi1)) (sin phi1)) (* (* (sin phi1) (sin delta)) (* (cos theta) (cos phi1)))))
281.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))
325.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify4.1s

Counts

87 → 87

Iterations

Iter	Nodes
done	5003
2	2663
1	572
0	227

prune1.5s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize102.0ms

Local error

Found 4 expressions with local error:

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

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-cbrt-cube` `add-exp-log`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-log-exp`
7×	`associate-r` `add-cube-cbrt`
5×	`associate-l`
3×	`*-commutative` `sin-mult`
2×	`diff-log` `cos-mult`
1×	`frac-times` `sum-log` `sub-neg` `flip3--` `associate-l/` `associate-r/` `flip--` `associate--r+` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 78

Calls

4 calls:

10.0ms	(* (sin phi1) (sin delta))
65.0ms	(* (* (sin phi1) (sin delta)) (* (cos theta) (cos phi1)))
44.0ms	(* (* (cos delta) (sin phi1)) (sin phi1))
59.0ms	(- (cos delta) (+ (* (* (cos delta) (sin phi1)) (sin phi1)) (* (* (sin phi1) (sin delta)) (* (cos theta) (cos phi1)))))

series617.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(* (sin phi1) (sin delta))
161.0ms	(* (* (sin phi1) (sin delta)) (* (cos theta) (cos phi1)))
92.0ms	(* (* (cos delta) (sin phi1)) (sin phi1))
305.0ms	(- (cos delta) (+ (* (* (cos delta) (sin phi1)) (sin phi1)) (* (* (sin phi1) (sin delta)) (* (cos theta) (cos phi1)))))

simplify1.7s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	1501
1	450
0	165

prune868.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

regimes868.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	46
1	46
0	32

end0.0ms

sample21.5s

Algorithm

intervals

Results

12.7s	3177×	body	1280	valid
5.0s	1820×	body	640	valid
1.4s	726×	body	320	valid
1.1s	1951×	body	80	valid
746.0ms	326×	body	160	valid