Details

sample109.0ms

Algorithm

intervals

Results

33.0ms	36×	body	2560	valid
18.0ms	190×	body	80	valid
12.0ms	28×	body	1280	valid
8.0ms	92×	body	80	nan
6.0ms	16×	body	640	valid
3.0ms	7×	body	320	valid
1.0ms	1×	body	5120	valid
1.0ms	3×	body	160	valid

simplify152.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	86	16
4	108	16
5	116	16
done	116	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite238.0ms

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:

153.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
59.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
13.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series487.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
52.0ms	(- (* b b) (* (* 4.0 a) c))
117.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
132.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.6s

Counts

118 → 118

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	195	2476
1	480	2169
2	1441	1861
done	5000	1789

prune501.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
0.2b	(- (* b b) (* (* 4.0 a) c))
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

61×	`add-sqr-sqrt`
60×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
25×	`add-exp-log`
20×	`sqrt-prod`
19×	`prod-diff`
13×	`add-cbrt-cube`
12×	`div-exp` `associate-/r*`
10×	`difference-of-squares`
9×	`associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `div-inv` `distribute-lft-out--`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`rec-exp` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 152

Calls

4 calls:

96.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
13.0ms	(- (* b b) (* (* 4.0 a) c))
65.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series553.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
69.0ms	(- (* b b) (* (* 4.0 a) c))
138.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
134.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

164 → 164

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	261	4025
1	587	3484
2	1656	3082
done	5001	2938

prune531.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (pow b 2) (* 4.0 (* a c)))
0.2b	(* (/ 1 (* a 2.0)) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
1.1b	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
22.0b	(sqrt (- (pow b 2) (* 4.0 (* a c))))

rewrite511.0ms

Algorithm

rewrite-expression-head

Rules

62×	`prod-diff`
61×	`add-sqr-sqrt`
54×	`*-un-lft-identity`
50×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log`
20×	`distribute-rgt-in` `distribute-lft-in`
14×	`fma-neg`
13×	`add-cbrt-cube`
10×	`prod-exp`
8×	`add-log-exp`
7×	`pow1` `associate-l`
6×	`unpow-prod-down` `associate-r`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `sub-neg` `div-exp` `cbrt-unprod` `log1p-expm1-u` `difference-of-squares`
3×	`times-frac`
2×	`cbrt-undiv` `frac-times` `rec-exp` `sqrt-div` `diff-log` `1-exp` `associate-*r/` `distribute-lft-out--` `unpow2` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 168

Calls

4 calls:

27.0ms	(- (pow b 2) (* 4.0 (* a c)))
277.0ms	(* (/ 1 (* a 2.0)) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
168.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
23.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

series509.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (pow b 2) (* 4.0 (* a c)))
211.0ms	(* (/ 1 (* a 2.0)) (- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b))
133.0ms	(- (sqrt (- (pow b 2) (* 4.0 (* a c)))) b)
102.0ms	(sqrt (- (pow b 2) (* 4.0 (* a c))))

simplify1.8s

Counts

180 → 180

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	261	4960
1	643	4123
2	1980	3296
done	5000	3090

prune572.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.6b

localize16.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
1.1b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

85.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
79.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series472.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
129.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
118.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts

128 → 128

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	113	2856
1	268	2310
2	718	1948
3	2711	1774
done	5001	1674

prune512.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.6b

regimes270.0ms

Accuracy

84.2% (4.6b remaining)

Error of 9.9b against oracle of 5.3b and baseline of 34.2b

bsearch219.0ms

Steps

Iters	Range		Point
11	1.5906747666251227e-34	6.100620313640196e-08	1.611450844781215e-34
9	-6.354265220965125e+156	-1.769171722317776e+149	-1.5501620157466267e+150

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	40
1	35	40
done	35	40

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.1s	5882×	body	80	valid
668.0ms	1076×	body	2560	valid
429.0ms	848×	body	1280	valid
396.0ms	2915×	body	80	nan
138.0ms	468×	body	640	valid
66.0ms	107×	body	5120	valid
50.0ms	212×	body	320	valid
18.0ms	122×	body	160	valid