Details

sample77.0ms

Algorithm

intervals

Results

25.0ms	77×	body	1280	valid
15.0ms	67×	body	640	valid
13.0ms	264×	body	80	valid
7.0ms	44×	body	320	valid
1.0ms	13×	body	160	valid

simplify105.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	12	19
1	26	13
2	52	12
3	75	12
4	102	12
5	122	12
6	139	12
7	143	12
8	145	12
done	145	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.5b	(* (fma a1 a1 (* a2 a2)) (/ (cos th) (sqrt 2.0)))
0.7b	(/ (cos th) (sqrt 2.0))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
38×	`times-frac`
32×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-r` `sqrt-prod`
10×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r*`
5×	`pow1`
3×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `fma-udef`

Counts

3 → 95

Calls

3 calls:

0.0ms	(fma a1 a1 (* a2 a2))
14.0ms	(* (fma a1 a1 (* a2 a2)) (/ (cos th) (sqrt 2.0)))
4.0ms	(/ (cos th) (sqrt 2.0))

series271.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(fma a1 a1 (* a2 a2))
175.0ms	(* (fma a1 a1 (* a2 a2)) (/ (cos th) (sqrt 2.0)))
57.0ms	(/ (cos th) (sqrt 2.0))

simplify631.0ms

Counts

104 → 104

Iterations

Useful iterations: done (628.0ms)

Iter	Nodes	Cost
0	143	1357
1	284	1272
2	1062	1139
done	5001	1125

prune262.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma a1 a1 (* a2 a2))
0.5b	(* (fma a1 a1 (* a2 a2)) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.7b	(/ (cos th) (sqrt (sqrt 2.0)))
0.7b	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

1137×	`sqrt-prod`
1119×	`times-frac`
625×	`add-sqr-sqrt`
578×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-r`
34×	`associate-/l*`
22×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
18×	`associate-/r*`
13×	`unswap-sqr`
7×	`cbrt-undiv` `div-exp`
6×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `clear-num`
1×	`associate-r/` `pow-prod-down` `-commutative` `fma-udef` `associate-/l/`

Counts

4 → 716

Calls

4 calls:

0.0ms	(fma a1 a1 (* a2 a2))
94.0ms	(* (fma a1 a1 (* a2 a2)) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
5.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
21.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(fma a1 a1 (* a2 a2))
178.0ms	(* (fma a1 a1 (* a2 a2)) (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
99.0ms	(/ (cos th) (sqrt (sqrt 2.0)))
72.0ms	(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify1.9s

Counts

728 → 728

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	622	16144
1	1532	13593
2	4480	12555
done	5001	12553

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (fma a1 a1 (* a2 a2)) (cos th))
0.4b	(* (* (fma a1 a1 (* a2 a2)) (cos th)) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
1.0b	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
1.0b	(/ 1 (sqrt (sqrt 2.0)))

rewrite176.0ms

Algorithm

rewrite-expression-head

Rules

1116×	`sqrt-prod`
1098×	`times-frac`
581×	`add-sqr-sqrt`
579×	`add-cube-cbrt` `*-un-lft-identity`
286×	`associate-r`
54×	`add-exp-log`
34×	`add-cbrt-cube` `associate-/l*`
25×	`pow1`
22×	`div-inv`
20×	`sqrt-pow1` `div-exp`
18×	`associate-/r*`
16×	`prod-exp`
14×	`pow-flip`
10×	`cbrt-undiv` `pow1/2` `cbrt-unprod` `pow-div`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-l` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative` `inv-pow`
1×	`associate-*r/` `associate-/l/` `unswap-sqr`

Counts

4 → 742

Calls

4 calls:

3.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
81.0ms	(* (* (fma a1 a1 (* a2 a2)) (cos th)) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
18.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms	(/ 1 (sqrt (sqrt 2.0)))

series277.0ms

Counts

4 → 8

Calls

4 calls:

96.0ms	(* (fma a1 a1 (* a2 a2)) (cos th))
181.0ms	(* (* (fma a1 a1 (* a2 a2)) (cos th)) (/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))))
0.0ms	(/ (/ 1 (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.0ms	(/ 1 (sqrt (sqrt 2.0)))

simplify2.2s

Counts

750 → 750

Iterations

Useful iterations: 2 (1.2s)

Iter	Nodes	Cost
0	628	16103
1	1909	11892
2	4186	10892
done	5000	10892

prune938.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0))))
0.3b	(* (cos th) (fma a1 a1 (* a2 a2)))
0.3b	(* (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (cbrt 1) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
1.0b	(/ (cbrt 1) (sqrt (sqrt 2.0)))

rewrite446.0ms

Algorithm

rewrite-expression-head

Rules

1905×	`sqrt-prod`
1498×	`times-frac`
885×	`add-sqr-sqrt`
749×	`*-un-lft-identity`
737×	`add-cube-cbrt`
703×	`associate-r`
378×	`cbrt-prod`
49×	`add-exp-log`
45×	`add-cbrt-cube`
42×	`unswap-sqr`
21×	`associate-/r*`
19×	`associate-l`
18×	`cbrt-undiv` `div-exp`
16×	`div-inv`
14×	`prod-exp` `cbrt-unprod`
8×	`pow1`
7×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `pow-prod-down` `clear-num` `*-commutative` `fma-udef`
1×	`distribute-rgt-in` `frac-times` `distribute-lft-in` `associate-r/` `associate-l/`

Counts

4 → 935

Calls

4 calls:

7.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0))))
4.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
327.0ms	(* (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (cbrt 1) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
5.0ms	(/ (cbrt 1) (sqrt (sqrt 2.0)))

series843.0ms

Counts

4 → 10

Calls

4 calls:

504.0ms	(/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0))))
109.0ms	(* (cos th) (fma a1 a1 (* a2 a2)))
231.0ms	(* (/ (* (cos th) (fma a1 a1 (* a2 a2))) (sqrt (sqrt (sqrt 2.0)))) (/ (/ (cbrt 1) (sqrt (sqrt 2.0))) (sqrt (sqrt (sqrt 2.0)))))
0.0ms	(/ (cbrt 1) (sqrt (sqrt 2.0)))

simplify2.9s

Counts

945 → 945

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	1105	28096
1	3696	22348
done	5000	20444

prune1.6s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

regimes161.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	19
1	18	19
done	18	19

end0.0ms

sample2.3s

Algorithm

intervals

Results

823.0ms	2511×	body	1280	valid
452.0ms	2041×	body	640	valid
415.0ms	8164×	body	80	valid
158.0ms	1027×	body	320	valid
61.0ms	537×	body	160	valid