Details

sample95.0ms

Algorithm

intervals

Results

16.0ms	35×	body	2560	valid
15.0ms	190×	body	80	valid
11.0ms	29×	body	1280	valid
7.0ms	92×	body	80	nan
5.0ms	16×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	3×	body	160	valid

simplify128.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	82	16
4	104	16
5	112	16
done	112	16

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.5b	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
1.1b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
22.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

11.0ms	(- (* b b) (* (* 3.0 a) c))
120.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
59.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* b b) (* (* 3.0 a) c))
163.0ms	(/ (- (sqrt (- (* b b) (* (* 3.0 a) c))) b) (* 3.0 a))
116.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
89.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify1.5s

Counts

118 → 118

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	195	2476
1	475	2171
2	1417	1877
done	5000	1791

prune372.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 3.0 (* a c)))
0.5b	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
1.1b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
22.0b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite285.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
21×	`add-cube-cbrt`
19×	`prod-diff`
18×	`sqrt-prod`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
6×	`times-frac` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-/l/`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 106

Calls

4 calls:

10.0ms	(- (* b b) (* 3.0 (* a c)))
152.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
98.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
21.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (* b b) (* 3.0 (* a c)))
157.0ms	(/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) (* 3.0 a))
116.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
107.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify1.3s

Counts

118 → 118

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	194	2476
1	477	2171
2	1407	1863
done	5001	1791

prune386.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 3.0 (* a c))
0.2b	(- (* b b) (* 3.0 (* a c)))
1.1b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
22.0b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
19×	`prod-diff`
16×	`sqrt-prod`
10×	`pow1`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`fma-neg`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `associate-l` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
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 → 94

Calls

4 calls:

24.0ms	(* 3.0 (* a c))
10.0ms	(- (* b b) (* 3.0 (* a c)))
80.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
18.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series301.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(* 3.0 (* a c))
69.0ms	(- (* b b) (* 3.0 (* a c)))
107.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
101.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify2.9s

Counts

106 → 106

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	158	1860
1	362	1561
2	1016	1332
3	3975	1245
done	5000	1245

prune341.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 3.0 (* a c)))
0.3b	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) a))
1.1b	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
22.0b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
36×	`add-cube-cbrt`
34×	`times-frac`
26×	`add-exp-log`
22×	`associate-r`
19×	`prod-diff` `sqrt-prod`
16×	`add-cbrt-cube`
13×	`associate-l`
8×	`div-exp` `prod-exp` `add-log-exp` `difference-of-squares`
7×	`pow1` `fma-neg`
6×	`unswap-sqr`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp` `div-inv`
1×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 141

Calls

4 calls:

20.0ms	(- (* b b) (* 3.0 (* a c)))
162.0ms	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) a))
89.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
12.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series437.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(- (* b b) (* 3.0 (* a c)))
133.0ms	(* (/ 1 3.0) (/ (- (sqrt (- (* b b) (* 3.0 (* a c)))) b) a))
129.0ms	(- (sqrt (- (* b b) (* 3.0 (* a c)))) b)
115.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify1.6s

Counts

153 → 153

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	260	3336
1	665	2916
2	2012	2489
done	5000	2418

prune495.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.6b

regimes423.0ms

Accuracy

84.2% (4.6b remaining)

Error of 10.0b against oracle of 5.4b and baseline of 34.2b

bsearch236.0ms

Steps

Iters	Range		Point
11	1.5906747666251227e-34	6.100620313640196e-08	1.611450844781215e-34
9	-6.354265220965125e+156	-1.769171722317776e+149	-1.074189026339084e+154

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	40
1	33	40
done	33	40

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.2s	5881×	body	80	valid
883.0ms	849×	body	1280	valid
563.0ms	1076×	body	2560	valid
215.0ms	467×	body	640	valid
202.0ms	2915×	body	80	nan
62.0ms	106×	body	5120	valid
45.0ms	214×	body	320	valid
17.0ms	121×	body	160	valid