Details

sample36.0ms

Algorithm

intervals

Results

8.0ms	40×	body	2560	valid
7.0ms	194×	body	80	valid
5.0ms	28×	body	1280	valid
2.0ms	76×	body	80	nan
1.0ms	10×	body	640	valid
0.0ms	2×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	12	17
1	22	17
2	42	16
3	83	16
4	102	16
5	110	16
done	110	16

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.4b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`add-sqr-sqrt`
8×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`times-frac` `associate-/l*`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out`
3×	`associate-r` `pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `flip--` `associate-/l/`
1×	`neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `div-sub` `associate-l` `prod-diff` `clear-num` `associate-/r` `-commutative` `flip-+` `div-inv`

Counts

4 → 83

Calls

4 calls:

35.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series243.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
19.0ms	(* (* 3.0 a) c)
47.0ms	(- (* b b) (* (* 3.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify638.0ms

Counts

95 → 95

Iterations

Useful iterations: done (635.0ms)

Iter	Nodes	Cost
0	168	1499
1	441	1413
2	1852	1207
done	5000	1206

prune258.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.4b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite41.0ms

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-r` `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-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 94

Calls

4 calls:

25.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
6.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series209.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
19.0ms	(* (* 3.0 a) c)
46.0ms	(- (* b b) (* (* 3.0 a) c))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify639.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (124.0ms)

Iter	Nodes	Cost
0	161	1863
1	383	1562
2	1514	1315
done	5000	1315

prune242.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 5.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
0.4b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
14×	`add-exp-log` `add-cbrt-cube`
12×	`*-un-lft-identity`
10×	`pow1`
8×	`add-cube-cbrt`
6×	`times-frac` `associate-/r*` `add-log-exp`
5×	`sqrt-prod`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `associate-r` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-/r/` `distribute-lft-out--`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 84

Calls

4 calls:

21.0ms	(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
7.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series324.0ms

Counts

4 → 12

Calls

4 calls:

194.0ms	(/ (* 3.0 a) (- (sqrt (- (* b b) (* (* 3.0 a) c))) b))
19.0ms	(* (* 3.0 a) c)
43.0ms	(- (* b b) (* (* 3.0 a) c))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify646.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (128.0ms)

Iter	Nodes	Cost
0	161	1483
1	398	1385
2	1751	1231
done	5000	1231

prune249.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
0.4b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
24.8b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite41.0ms

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-r` `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-l` `*-commutative` `distribute-lft-out--`

Counts

4 → 94

Calls

4 calls:

24.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
7.0ms	(* (* 3.0 a) c)
3.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series211.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (sqrt (- (* b b) (* (* 3.0 a) c))) b)
19.0ms	(* (* 3.0 a) c)
47.0ms	(- (* b b) (* (* 3.0 a) c))
67.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify633.0ms

Counts

106 → 106

Iterations

Useful iterations: 2 (122.0ms)

Iter	Nodes	Cost
0	161	1863
1	383	1562
2	1514	1315
done	5000	1315

prune221.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 5.7b

regimes451.0ms

Accuracy

82.8% (4.9b remaining)

Error of 10.7b against oracle of 5.8b and baseline of 34.3b

bsearch117.0ms

Steps

Iters	Range		Point
8	10920358539895.18	4.2009936632527795e+17	11181767625882.13
11	-1.829086240692416e+154	-2.187052964502477e+134	-8.555281377770497e+140

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	42
1	35	42
done	35	42

end0.0ms

sample1.1s

Algorithm

intervals

Results

234.0ms	1105×	body	2560	valid
215.0ms	5867×	body	80	valid
154.0ms	909×	body	1280	valid
94.0ms	2861×	body	80	nan
57.0ms	422×	body	640	valid
27.0ms	96×	body	5120	valid
21.0ms	214×	body	320	valid
8.0ms	119×	body	160	valid