Details

sample77.0ms

Algorithm

intervals

Results

15.0ms	43×	body	2560	valid
11.0ms	80×	body	80	nan
9.0ms	165×	body	80	valid
9.0ms	32×	body	1280	valid
3.0ms	16×	body	640	valid
3.0ms	8×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	5×	body	160	valid

simplify63.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	104
5	104
4	96
3	76
2	41
1	21
0	12

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (* 3.0 a) c)
0.7b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
1.5b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite234.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
14×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
10×	`pow1`
8×	`add-cube-cbrt`
6×	`times-frac` `sqrt-prod` `associate-/l*` `add-log-exp` `difference-of-squares`
4×	`prod-exp` `cbrt-unprod`
3×	`flip3--` `associate-r` `pow-prod-down` `flip--` `distribute-lft-out--`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `clear-num` `associate-/r` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-l` `-commutative` `div-inv`

Counts

4 → 78

Calls

4 calls:

27.0ms	(* (* 3.0 a) c)
128.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
61.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
13.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series458.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* 3.0 a) c)
161.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
147.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
128.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.4s

Counts

90 → 90

Iterations

Iter	Nodes
done	5000
2	2394
1	432
0	164

prune576.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.6b

localize6.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify0.0ms

Counts

0 → 0

Iterations

Iter	Nodes
done	0
0	0

prune78.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 3.6b

localize31.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
0.5b	(* (* 3.0 a) c)
1.5b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
18×	`times-frac`
17×	`add-cube-cbrt`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow1` `difference-of-squares`
8×	`sqrt-prod`
6×	`associate-/l*` `add-log-exp`
5×	`distribute-lft-out--`
3×	`associate-/r` `flip3--` `associate-r*` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
2×	`sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `associate-l` `*-commutative` `div-inv`

Counts

4 → 90

Calls

4 calls:

123.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
27.0ms	(* (* 3.0 a) c)
62.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series379.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) 3.0)
34.0ms	(* (* 3.0 a) c)
128.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
91.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.4s

Counts

102 → 102

Iterations

Iter	Nodes
done	5001
2	1938
1	427
0	172

prune570.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (/ 1 (* 3.0 a)))
0.5b	(* (* 3.0 a) c)
1.5b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
21.2b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite237.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

171.0ms	(* (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (/ 1 (* 3.0 a)))
16.0ms	(* (* 3.0 a) c)
40.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
8.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (/ 1 (* 3.0 a)))
25.0ms	(* (* 3.0 a) c)
103.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
105.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify2.4s

Counts

99 → 99

Iterations

Iter	Nodes
done	5002
2	3176
1	511
0	190

prune459.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.6b

regimes664.0ms

Accuracy

87.6% (4.2b remaining)

Error of 9.6b against oracle of 5.4b and baseline of 39.5b

bsearch74.0ms

Steps

Iters	Range		Point
2	3.964947473899983e-62	4.720485511979589e-62	4.626043257219638e-62
7	-5.856362438573669e+138	-1.280729871585891e+137	-1.376057351631615e+138

simplify8.0ms

Iterations

Iter	Nodes
done	33
1	33
0	27

end0.0ms

sample3.1s

Algorithm

intervals

Results

692.0ms	2874×	body	80	nan
586.0ms	1095×	body	2560	valid
471.0ms	5793×	body	80	valid
357.0ms	887×	body	1280	valid
154.0ms	468×	body	640	valid
127.0ms	243×	body	320	valid
92.0ms	107×	body	5120	valid
15.0ms	115×	body	160	valid