Details

sample125.0ms

Algorithm

intervals

Results

32.0ms	34×	body	2560	valid
28.0ms	198×	body	80	valid
21.0ms	29×	body	1280	valid
12.0ms	91×	body	80	nan
4.0ms	8×	body	640	valid
3.0ms	7×	body	320	valid
2.0ms	2×	body	5120	valid
2.0ms	6×	body	160	valid

simplify134.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
1.2b	(- (* b b) (* (* 3 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
27.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite149.0ms

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:

76.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
15.0ms	(- (* b b) (* (* 3 a) c))
46.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
10.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series483.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) (* 3 a))
60.0ms	(- (* b b) (* (* 3 a) c))
125.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
132.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify3.7s

Counts

88 → 88

Iterations

Iter	Nodes
3	4847
2	1252
1	394
0	157

prune883.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3 a) c)
1.2b	(- (* b b) (* (* 3 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
27.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite65.0ms

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:

14.0ms	(* (* 3 a) c)
7.0ms	(- (* b b) (* (* 3 a) c))
36.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series284.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* 3 a) c)
64.0ms	(- (* b b) (* (* 3 a) c))
91.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
94.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.8s

Counts

76 → 76

Iterations

Iter	Nodes
3	3323
2	951
1	295
0	123

prune509.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.7b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1 (* 3 a))
1.2b	(- (* b b) (* (* 3 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
27.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite59.0ms

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:

9.0ms	(/ 1 (* 3 a))
8.0ms	(- (* b b) (* (* 3 a) c))
34.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series267.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1 (* 3 a))
58.0ms	(- (* b b) (* (* 3 a) c))
98.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
84.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify1.8s

Counts

86 → 86

Iterations

Iter	Nodes
3	3422
2	959
1	325
0	140

prune521.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.7b

localize23.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
1.2b	(- (* b b) (* (* 3 a) c))
1.4b	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
27.8b	(sqrt (- (* b b) (* (* 3 a) c)))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

58.0ms	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
8.0ms	(- (* b b) (* (* 3 a) c))
34.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* 1/3 (/ (- (sqrt (- (* b b) (* (* 3 a) c))) b) a))
64.0ms	(- (* b b) (* (* 3 a) c))
89.0ms	(- (sqrt (- (* b b) (* (* 3 a) c))) b)
111.0ms	(sqrt (- (* b b) (* (* 3 a) c)))

simplify2.5s

Counts

99 → 99

Iterations

Iter	Nodes
3	4688
2	1353
1	444
0	179

prune800.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 7.7b

regimes519.0ms

Accuracy

83.2% (4.7b remaining)

Error of 10.3b against oracle of 5.7b and baseline of 33.5b

bsearch206.0ms

Steps

Iters	Range		Point
8	2.764110880089542e-64	2.3245141193625934e-60	1.9824764136407443e-61
8	-4.0875164467587936e+40	-1.4884796866541563e+36	-4.024746736984847e+40

simplify10.0ms

Iterations

Iter	Nodes
2	32
1	32
0	27

end0.0ms

sample4.3s

Algorithm

intervals

Results

1.1s	1057×	body	2560	valid
939.0ms	908×	body	1280	valid
906.0ms	5887×	body	80	valid
508.0ms	2991×	body	80	nan
247.0ms	444×	body	640	valid
141.0ms	109×	body	5120	valid
106.0ms	233×	body	320	valid
28.0ms	110×	body	160	valid