Details

sample292.0ms

Algorithm

intervals

Results

168.0ms	97×	body	1280	valid
63.0ms	64×	body	640	valid
18.0ms	67×	body	80	valid
13.0ms	20×	body	320	valid
4.0ms	8×	body	160	valid

simplify20.0ms

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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.1b

Counts

2 → 1

localize29.0ms

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)))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

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

series111.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(* (sin theta) (sin delta))
42.0ms	(* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))
8.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
50.0ms	(- (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))))

simplify654.0ms

Counts

70 → 70

Iterations

Useful iterations: 3 (233.0ms)

Iter	Nodes	Cost
0	132	1435
1	278	1368
2	721	1231
3	2011	1229
done	5000	1229

prune172.0ms

Filtered

50 candidates to 70 candidates (-40.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	62	8	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	8	71

Merged error: 0.0b

Counts

71 → 8

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(pow (cos delta) 3)
0.5b	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`pow-unpow`
4×	`unpow-prod-down` `cube-prod` `add-log-exp`
3×	`pow-pow` `pow-exp` `rem-cube-cbrt`
2×	`cube-mult` `pow-to-exp` `asin-acos` `unpow3` `sqr-pow`
1×	`cube-div` `pow-prod-down` `prod-exp` `cbrt-unprod` `sin-mult`

Counts

4 → 62

Calls

4 calls:

2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(pow (cos delta) 3)
8.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

series90.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms	(pow (cos delta) 3)
70.0ms	(pow (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))))) 3)

simplify1.6s

Counts

74 → 74

Iterations

Useful iterations: 3 (347.0ms)

Iter	Nodes	Cost
0	109	1265
1	260	1181
2	838	1037
3	4351	1031
done	5000	1031

prune191.0ms

Filtered

48 candidates to 74 candidates (-54.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	73	9	82

Merged error: 0.0b

Counts

82 → 9

localize47.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
0.3b	(pow (sin phi1) 3)
0.3b	(pow (cos delta) 3)
0.6b	(pow (+ (* (sin phi1) (cos delta)) (* (cos theta) (* (sin delta) (cos phi1)))) 3)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down` `pow-unpow` `cube-prod`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
4×	`add-log-exp`
3×	`cube-div` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `pow-exp` `rem-cube-cbrt` `sqr-pow`
2×	`sin-cos-mult`
1×	`asin-acos` `flip3-+` `associate-*r/` `frac-add` `flip-+`

Counts

4 → 80

Calls

4 calls:

2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
3.0ms	(pow (sin phi1) 3)
3.0ms	(pow (cos delta) 3)
12.0ms	(pow (+ (* (sin phi1) (cos delta)) (* (cos theta) (* (sin delta) (cos phi1)))) 3)

series72.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
6.0ms	(pow (sin phi1) 3)
5.0ms	(pow (cos delta) 3)
55.0ms	(pow (+ (* (sin phi1) (cos delta)) (* (cos theta) (* (sin delta) (cos phi1)))) 3)

simplify541.0ms

Counts

92 → 92

Iterations

Useful iterations: 2 (128.0ms)

Iter	Nodes	Cost
0	157	1352
1	431	1209
2	1731	1073
done	5000	1073

prune218.0ms

Filtered

57 candidates to 92 candidates (-61.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	92	9	101

Merged error: 0.0b

Counts

101 → 9

localize42.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

2.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
12.0ms	(/ (- (* (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)))))))) (+ (cos delta) (* (sin phi1) (sin (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))))))))
7.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

series587.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))
353.0ms	(/ (- (* (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)))))))) (+ (cos delta) (* (sin phi1) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))))
185.0ms	(- (* (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))))))))
43.0ms	(* (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))))

simplify600.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (188.0ms)

Iter	Nodes	Cost
0	221	6085
1	572	5628
2	2204	4900
done	5001	4900

prune204.0ms

Filtered

73 candidates to 96 candidates (-31.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	95	10	105

Merged error: 0.0b

Counts

105 → 10

regimes624.0ms

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	35	86
1	48	86
done	48	86

end0.0ms

sample9.1s

Algorithm

intervals

Results

5.6s	3227×	body	1280	valid
1.8s	1783×	body	640	valid
544.0ms	765×	body	320	valid
408.0ms	1955×	body	80	valid
121.0ms	270×	body	160	valid

Details

sample292.0ms

simplify20.0ms

prune7.0ms

localize29.0ms

rewrite21.0ms

series111.0ms

simplify654.0ms

prune172.0ms

localize41.0ms

rewrite16.0ms

series90.0ms

simplify1.6s

prune191.0ms

localize47.0ms

rewrite22.0ms

series72.0ms

simplify541.0ms

prune218.0ms

localize42.0ms

rewrite31.0ms

series587.0ms

simplify600.0ms

prune204.0ms

regimes624.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample9.1s

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