Details

sample111.0ms

Algorithm

intervals

Results

28.0ms	210×	body	80	valid
25.0ms	23×	body	2560	valid
18.0ms	25×	body	1280	valid
10.0ms	84×	body	80	nan
4.0ms	8×	body	640	valid
3.0ms	9×	body	320	valid
2.0ms	2×	body	5120	valid
1.0ms	2×	body	160	valid

simplify107.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	95
7	95
6	94
5	92
4	84
3	67
2	43
1	24
0	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.5b

localize36.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
0.8b	(- (* b b) (* (* 4 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 88

Calls

4 calls:

66.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
11.0ms	(- (* b b) (* (* 4 a) c))
50.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series449.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (- (sqrt (- (* b b) (* (* 4 a) c))) b) a)
63.0ms	(- (* b b) (* (* 4 a) c))
126.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
117.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.2s

Counts

100 → 100

Iterations

Iter	Nodes
done	5000
2	1158
1	394
0	161

prune529.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.5b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b))
0.8b	(- (* b b) (* (* 4 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `insert-posit16` `flip--`
3×	`associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

42.0ms	(/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b))
8.0ms	(- (* b b) (* (* 4 a) c))
55.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series962.0ms

Counts

4 → 12

Calls

4 calls:

286.0ms	(/ a (- (sqrt (- (* b b) (* (* 4 a) c))) b))
58.0ms	(- (* b b) (* (* 4 a) c))
132.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
485.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify2.6s

Counts

99 → 99

Iterations

Iter	Nodes
done	5002
3	4251
2	1045
1	352
0	156

prune540.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
0.8b	(- (* b b) (* (* 4 a) c))
1.0b	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
20.8b	(sqrt (- (* b b) (* (* 4 a) c)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
18×	`*-un-lft-identity`
13×	`associate-r` `add-exp-log` `add-cube-cbrt`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `insert-posit16` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

153.0ms	(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
15.0ms	(- (* b b) (* (* 4 a) c))
47.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
13.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

series419.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (- (sqrt (- (* b b) (* (* 4 a) c))) b) (/ 1 a))
73.0ms	(- (* b b) (* (* 4 a) c))
118.0ms	(- (sqrt (- (* b b) (* (* 4 a) c))) b)
87.0ms	(sqrt (- (* b b) (* (* 4 a) c)))

simplify1.4s

Counts

101 → 101

Iterations

Iter	Nodes
done	5003
2	1455
1	458
0	181

prune527.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.5b

localize35.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- (sqrt (+ (* (* a c) -4) (* b b))) b) a)
0.8b	(+ (* (* a c) -4) (* b b))
1.0b	(- (sqrt (+ (* (* a c) -4) (* b b))) b)
20.8b	(sqrt (+ (* (* a c) -4) (* b b)))

rewrite442.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`insert-posit16`
3×	`associate-/r*`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `div-inv`

Counts

4 → 87

Calls

4 calls:

237.0ms	(/ (- (sqrt (+ (* (* a c) -4) (* b b))) b) a)
23.0ms	(+ (* (* a c) -4) (* b b))
145.0ms	(- (sqrt (+ (* (* a c) -4) (* b b))) b)
35.0ms	(sqrt (+ (* (* a c) -4) (* b b)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

168.0ms	(/ (- (sqrt (+ (* (* a c) -4) (* b b))) b) a)
81.0ms	(+ (* (* a c) -4) (* b b))
116.0ms	(- (sqrt (+ (* (* a c) -4) (* b b))) b)
96.0ms	(sqrt (+ (* (* a c) -4) (* b b)))

simplify3.2s

Counts

99 → 99

Iterations

Iter	Nodes
done	5002
3	4236
2	910
1	329
0	137

prune379.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 5.5b

regimes425.0ms

Accuracy

81.2% (5.1b remaining)

Error of 10.8b against oracle of 5.7b and baseline of 33.0b

bsearch428.0ms

Steps

Iters	Range		Point
8	5.451909898538592e-70	5.081728108716245e-67	1.546013236023957e-67
7	6.366271362828677e-80	2.0474353944207673e-78	1.6168702840263923e-79
8	1.9015403840268286e-125	4.787339246176752e-121	1.3353078790738604e-121
7	-9.460060253608456e+39	-2.573022393154551e+38	-9.348931433494438e+39

simplify23.0ms

Iterations

Iter	Nodes
done	47
3	47
2	44
1	41
0	33

end0.0ms

sample4.4s

Algorithm

intervals

Results

971.0ms	1084×	body	2560	valid
952.0ms	5870×	body	80	valid
817.0ms	907×	body	1280	valid
764.0ms	3007×	body	80	nan
298.0ms	447×	body	640	valid
145.0ms	101×	body	5120	valid
114.0ms	232×	body	320	valid
29.0ms	109×	body	160	valid