Details

sample70.0ms

Algorithm

intervals

Results

16.0ms	186×	body	80	valid
14.0ms	29×	body	2560	valid
10.0ms	24×	body	1280	valid
7.0ms	88×	body	80	nan
6.0ms	17×	body	640	valid
2.0ms	10×	body	320	valid
2.0ms	3×	body	5120	valid

simplify105.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	93
7	93
6	92
5	90
4	82
3	66
2	40
1	21
0	12

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
1.0b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
1.6b	(- (* b b) (* (* 3 a) c))
24.4b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

105.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
32.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
11.0ms	(- (* b b) (* (* 3 a) c))
13.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
132.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
82.0ms	(- (* b b) (* (* 3 a) c))
76.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.6s

Counts

88 → 88

Iterations

Iter	Nodes
3	4801
2	1250
1	395
0	157

prune1.0s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.4b

localize39.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3 a))
1.0b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
1.6b	(- (* b b) (* (* 3 a) c))
24.4b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

18.0ms	(/ 1 (* 3 a))
44.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
11.0ms	(- (* b b) (* (* 3 a) c))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ 1 (* 3 a))
113.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
56.0ms	(- (* b b) (* (* 3 a) c))
97.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.5s

Counts

86 → 86

Iterations

Iter	Nodes
3	3421
2	939
1	325
0	140

prune982.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
1.0b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
1.6b	(- (* b b) (* (* 3 a) c))
24.4b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

20.0ms	(* (* 3 a) c)
50.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
8.0ms	(- (* b b) (* (* 3 a) c))
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* 3 a) c)
119.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
80.0ms	(- (* b b) (* (* 3 a) c))
85.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.0s

Counts

76 → 76

Iterations

Iter	Nodes
3	3413
2	953
1	297
0	123

prune882.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 5.4b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3 (* a c))
1.0b	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
1.6b	(- (* b b) (* 3 (* a c)))
24.4b	(sqrt (- (* b b) (* 3 (* a c))))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`pow1`
9×	`add-cbrt-cube` `add-exp-log`
8×	`*-un-lft-identity` `add-log-exp`
6×	`add-cube-cbrt`
4×	`sqrt-prod` `insert-posit16`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `difference-of-squares`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r` `*-commutative` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

26.0ms	(* 3 (* a c))
36.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
16.0ms	(- (* b b) (* 3 (* a c)))
21.0ms	(sqrt (- (* b b) (* 3 (* a c))))

series323.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* 3 (* a c))
116.0ms	(- (sqrt (- (* b b) (* 3 (* a c)))) b)
62.0ms	(- (* b b) (* 3 (* a c)))
123.0ms	(sqrt (- (* b b) (* 3 (* a c))))

simplify1.3s

Counts

76 → 76

Iterations

Iter	Nodes
3	2559
2	778
1	281
0	120

prune902.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 5.4b

regimes654.0ms

Accuracy

84.1% (4.5b remaining)

Error of 10.4b against oracle of 5.9b and baseline of 34.1b

bsearch205.0ms

Steps

Iters	Range		Point
9	2.5177836961106285e-119	1.1213560046341023e-113	2.223474256889498e-114
9	-7.719337631483544e+158	-3.157324857634874e+150	-1.5144039826007546e+152

simplify9.0ms

Iterations

Iter	Nodes
2	32
1	32
0	27

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	1091×	body	2560	valid
929.0ms	5837×	body	80	valid
568.0ms	912×	body	1280	valid
393.0ms	2906×	body	80	nan
280.0ms	460×	body	640	valid
103.0ms	126×	body	5120	valid
79.0ms	227×	body	320	valid
23.0ms	98×	body	160	valid