Details

sample85.0ms

Algorithm

intervals

Results

48.0ms	274×	body	80	valid
9.0ms	84×	body	80	nan

simplify160.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	158
7	158
6	157
5	150
4	138
3	110
2	62
1	36
0	20

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 22.0b

localize150.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(- (* b b) (* (* 4.0 a) c))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u` `flip--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

12.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series373.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* b b) (* (* 4.0 a) c))
70.0ms	(- (* b b) (* (* 4.0 a) c))
89.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
151.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
3	2176
2	551
1	177
0	71

prune829.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.9b

localize171.0ms

Local error

Found 4 expressions with local error:

8.4b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`*-un-lft-identity` `add-cube-cbrt`
10×	`fma-neg` `prod-diff`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-div`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`neg-mul-1` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 88

Calls

4 calls:

16.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
79.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
93.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
124.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
3	2880
2	822
1	281
0	115

prune924.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.4b

localize166.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
2.6b	(/ (* 2.0 c) (fma b -2 (/ (* a 2.0) (/ b c))))
5.3b	(/ (* a 2.0) (/ b c))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

34×	`times-frac`
22×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
16×	`associate-/r*`
8×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`clear-num` `frac-2neg` `flip3--` `sqrt-div` `flip--` `associate-/l*`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/r/`

Counts

4 → 104

Calls

4 calls:

6.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(/ (* 2.0 c) (fma b -2 (/ (* a 2.0) (/ b c))))
12.0ms	(/ (* a 2.0) (/ b c))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series528.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* b b) (* (* 4.0 a) c))
307.0ms	(/ (* 2.0 c) (fma b -2 (/ (* a 2.0) (/ b c))))
48.0ms	(/ (* a 2.0) (/ b c))
109.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

116 → 116

Iterations

Iter	Nodes
done	5009
2	2166
1	595
0	224

prune1.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.4b

localize193.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* (* 4.0 a) c))
2.6b	(/ (* 2.0 c) (fma b -2 (* a (/ 2.0 (/ b c)))))
5.8b	(* a (/ 2.0 (/ b c)))
24.6b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
53×	`add-sqr-sqrt`
44×	`associate-r`
43×	`*-un-lft-identity` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
3×	`associate-/r` `associate-l*` `sqrt-prod` `unswap-sqr`
2×	`flip3--` `sqrt-div` `flip--`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `pow-prod-down` `associate-r/` `associate-/r/` `-commutative` `associate-/l*`

Counts

4 → 124

Calls

4 calls:

7.0ms	(- (* b b) (* (* 4.0 a) c))
10.0ms	(/ (* 2.0 c) (fma b -2 (* a (/ 2.0 (/ b c)))))
41.0ms	(* a (/ 2.0 (/ b c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (* b b) (* (* 4.0 a) c))
281.0ms	(/ (* 2.0 c) (fma b -2 (* a (/ 2.0 (/ b c)))))
36.0ms	(* a (/ 2.0 (/ b c)))
99.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

136 → 136

Iterations

Iter	Nodes
done	5000
2	2815
1	749
0	269

prune1.2s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 4.8b

regimes687.0ms

Accuracy

94.5% (0.9b remaining)

Error of 7.1b against oracle of 6.2b and baseline of 22.9b

bsearch205.0ms

Steps

Iters	Range		Point
5	2.6243927093659187e+107	5.901159163981397e+107	3.3738862806344735e+107
8	-2.748004767191833e+152	-7.260401024913698e+147	-2.221067196710922e+149

simplify22.0ms

Iterations

Iter	Nodes
done	53
1	53
0	45

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.7s	8687×	body	80	valid
291.0ms	2881×	body	80	nan