Details

sample121.0ms

Algorithm

intervals

Results

33.0ms	164×	body	80	valid
24.0ms	43×	body	2560	valid
14.0ms	32×	body	1280	valid
7.0ms	80×	body	80	nan
6.0ms	16×	body	640	valid
5.0ms	8×	body	5120	valid
2.0ms	7×	body	320	valid
1.0ms	6×	body	160	valid

simplify118.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	14	365
1	24	365
2	44	325
3	78	325
4	102	325
5	111	325
done	111	325

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.5b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
0.2b	(* (* 4.0 a) c)
1.5b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite139.0ms

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:

81.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
13.0ms	(* (* 4.0 a) c)
36.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series326.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) 2.0)
21.0ms	(* (* 4.0 a) c)
106.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
83.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

102 → 102

Iterations

Useful iterations: 2 (456.0ms)

Iter	Nodes	Cost
0	174	36258
1	432	33986
2	1950	33546
done	5001	33546

prune654.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 10.3b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt c)
0.6b	(cbrt c)
1.5b	(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
21.2b	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`add-cbrt-cube` `add-exp-log` `sqrt-prod`
2×	`flip3--` `pow1/3` `sqrt-div` `flip--` `difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt c)
1.0ms	(cbrt c)
69.0ms	(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
15.0ms	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

series863.0ms

Counts

4 → 12

Calls

4 calls:

296.0ms	(cbrt c)
282.0ms	(cbrt c)
144.0ms	(- (sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c)))) b)
140.0ms	(sqrt (- (* b b) (* (* (* 4.0 a) (* (cbrt c) (cbrt c))) (cbrt c))))

simplify1.1s

Counts

64 → 64

Iterations

Useful iterations: 2 (274.0ms)

Iter	Nodes	Cost
0	104	22748
1	245	20689
2	1002	14931
done	5000	14931

prune515.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 10.3b

localize56.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (* 1 (sqrt (- (* b b) (* c (* 4.0 a))))) b) 2.0)
0.2b	(* c (* 4.0 a))
1.5b	(- (* 1 (sqrt (- (* b b) (* c (* 4.0 a))))) b)
21.2b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`times-frac`
11×	`add-cbrt-cube` `add-exp-log`
10×	`pow1`
6×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`associate-/l*`
3×	`associate-/r` `flip3--` `associate-l*` `pow-prod-down` `prod-exp` `sqrt-prod` `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-r` `*-commutative` `div-inv`

Counts

4 → 80

Calls

4 calls:

42.0ms	(/ (- (* 1 (sqrt (- (* b b) (* c (* 4.0 a))))) b) 2.0)
21.0ms	(* c (* 4.0 a))
18.0ms	(- (* 1 (sqrt (- (* b b) (* c (* 4.0 a))))) b)
7.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series391.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (- (* 1 (sqrt (- (* b b) (* c (* 4.0 a))))) b) 2.0)
21.0ms	(* c (* 4.0 a))
114.0ms	(- (* 1 (sqrt (- (* b b) (* c (* 4.0 a))))) b)
109.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify1.8s

Counts

92 → 92

Iterations

Useful iterations: 2 (466.0ms)

Iter	Nodes	Cost
0	171	31176
1	433	27103
2	1737	26663
done	5001	26663

prune568.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 10.3b

localize127.0ms

Local error

Found 4 expressions with local error:

1.5b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
10×	`sqrt-prod`
9×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt`
6×	`sqrt-div` `add-log-exp`
4×	`flip3--` `add-cbrt-cube` `add-exp-log` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`difference-of-squares`
1×	`sub-neg` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

47.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
7.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
9.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
117.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
86.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.6s

Counts

72 → 72

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	81	23268
1	199	20547
2	792	20387
3	4453	20227
done	5000	20187

prune548.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 10.3b

regimes426.0ms

Accuracy

87.5% (2.8b remaining)

Error of 14.6b against oracle of 11.8b and baseline of 34.2b

bsearch167.0ms

Steps

Iters	Range		Point
4	1.2765290296533779e-46	2.1214586855945932e-46	1.9152049814236774e-46
10	-1.1071683335692419e+166	-3.0632372757179626e+150	-1.3392371992290793e+154

simplify11.0ms

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	30	910
1	38	869
2	39	869
done	39	869

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.1s	2874×	body	80	nan
554.0ms	5792×	body	80	valid
530.0ms	1094×	body	2560	valid
431.0ms	887×	body	1280	valid
170.0ms	467×	body	640	valid
75.0ms	243×	body	320	valid
55.0ms	108×	body	5120	valid
16.0ms	117×	body	160	valid