Details

sample109.0ms

Algorithm

intervals

Results

19.0ms	35×	body	2560	valid
18.0ms	28×	body	1280	valid
17.0ms	188×	body	80	valid
7.0ms	85×	body	80	nan
5.0ms	14×	body	640	valid
4.0ms	5×	body	5120	valid
3.0ms	10×	body	320	valid
1.0ms	4×	body	160	valid

simplify374.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	98
7	98
6	97
5	95
4	87
3	72
2	42
1	24
0	14

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.3b

localize59.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`insert-posit16`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`neg-sub0` `cbrt-undiv` `sum-log` `flip3-+` `flip3--` `sqrt-div` `div-exp` `associate-+l-` `flip-+` `flip--` `associate-/l/`
1×	`+-commutative` `rem-sqrt-square` `clear-num` `associate-/r*` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `cbrt-unprod` `div-inv`

Counts

4 → 74

Calls

4 calls:

135.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
10.0ms	(- (* b b) (* (* 4.0 a) c))
28.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series601.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
93.0ms	(- (* b b) (* (* 4.0 a) c))
159.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
132.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.3s

Counts

86 → 86

Iterations

Iter	Nodes
done	5001
2	1368
1	414
0	158

prune1.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.8b

localize57.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
0.8b	(- (* b b) (* (* 4.0 a) c))
1.6b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite357.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-exp-log`
16×	`*-un-lft-identity`
13×	`add-cbrt-cube`
11×	`add-sqr-sqrt`
10×	`prod-exp` `add-log-exp`
8×	`add-cube-cbrt`
7×	`pow1` `associate-r`
5×	`associate-l`
4×	`div-exp` `cbrt-unprod` `insert-posit16` `distribute-lft-out`
3×	`flip3-+` `times-frac` `sqrt-prod` `flip-+`
2×	`frac-times` `cbrt-undiv` `rec-exp` `sum-log` `distribute-rgt-neg-in` `flip3--` `sqrt-div` `1-exp` `associate-*l/` `flip--`
1×	`neg-sub0` `+-commutative` `rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `associate-+l-` `div-inv` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

264.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
20.0ms	(- (* b b) (* (* 4.0 a) c))
53.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series568.0ms

Counts

4 → 12

Calls

4 calls:

198.0ms	(* (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* 2.0 a)))
81.0ms	(- (* b b) (* (* 4.0 a) c))
149.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
139.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.9s

Counts

96 → 96

Iterations

Iter	Nodes
done	5000
2	1842
1	489
0	185

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.8b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) (* 2.0 a))
0.8b	(- (* b b) (* a (* c 4.0)))
1.6b	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
21.2b	(sqrt (- (* b b) (* a (* c 4.0))))

rewrite288.0ms

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:

152.0ms	(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) (* 2.0 a))
22.0ms	(- (* b b) (* a (* c 4.0)))
78.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
32.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

series565.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(/ (- (sqrt (- (* b b) (* a (* c 4.0)))) b) (* 2.0 a))
78.0ms	(- (* b b) (* a (* c 4.0)))
113.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
171.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

simplify2.9s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
2	1258
1	402
0	158

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 4.8b

localize145.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
1.6b	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
21.2b	(sqrt (- (* b b) (* a (* c 4.0))))
21.2b	(sqrt (- (* b b) (* a (* c 4.0))))

rewrite219.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `insert-posit16` `flip--` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 64

Calls

4 calls:

78.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
96.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
12.0ms	(sqrt (- (* b b) (* a (* c 4.0))))
27.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

series608.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
170.0ms	(- (sqrt (- (* b b) (* a (* c 4.0)))) b)
134.0ms	(sqrt (- (* b b) (* a (* c 4.0))))
151.0ms	(sqrt (- (* b b) (* a (* c 4.0))))

simplify4.6s

Counts

76 → 76

Iterations

Iter	Nodes
done	5001
3	2214
2	598
1	193
0	83

prune1.1s

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 4.8b

regimes1.0s

Accuracy

83.9% (4.7b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 34.7b

bsearch186.0ms

Steps

Iters	Range		Point
6	1.5727591416233446e-143	1.789606490082599e-142	1.744031351412433e-142
8	-1.3198903247987554e+155	-1.1250773400730914e+152	-1.2705286994550075e+152

simplify20.0ms

Iterations

Iter	Nodes
done	31
1	31
0	26

end0.0ms

sample3.6s

Algorithm

intervals

Results

885.0ms	5804×	body	80	valid
830.0ms	932×	body	1280	valid
668.0ms	1083×	body	2560	valid
339.0ms	2988×	body	80	nan
136.0ms	489×	body	640	valid
95.0ms	107×	body	5120	valid
51.0ms	247×	body	320	valid
16.0ms	121×	body	160	valid