Details

sample71.0ms

Algorithm

intervals

Results

15.0ms	36×	body	2560	valid
13.0ms	190×	body	80	valid
9.0ms	28×	body	1280	valid
6.0ms	92×	body	80	nan
4.0ms	16×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	3×	body	160	valid
0.0ms	1×	body	5120	valid

simplify92.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (7.0ms)

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

localize13.0ms

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)))

rewrite230.0ms

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:

113.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
21.0ms	(- (* b b) (* (* 4.0 a) c))
74.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

166.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
69.0ms	(- (* b b) (* (* 4.0 a) c))
115.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
114.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.5s

Counts

118 → 118

Iterations

Useful iterations: done (1.5s)

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

localize18.0ms

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)))

rewrite227.0ms

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:

66.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
12.0ms	(- (* b b) (* (* 4.0 a) c))
113.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series521.0ms

Counts

4 → 12

Calls

4 calls:

205.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
77.0ms	(- (* b b) (* (* 4.0 a) c))
119.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
119.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.3s

Counts

164 → 164

Iterations

Useful iterations: done (1.3s)

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

prune585.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.6b

localize30.0ms

Local error

Found 4 expressions with local error:

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

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

11.0ms	(- (* b b) (* (* 4.0 a) c))
190.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
57.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
33.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(- (* b b) (* (* 4.0 a) c))
177.0ms	(* (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (/ 1 (* 2.0 a)))
131.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
106.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify1.4s

Counts

127 → 127

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	221	2739
1	536	2324
2	1687	1964
done	5001	1892

prune877.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 4.6b

localize30.0ms

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)))

rewrite143.0ms

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:

52.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
64.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
11.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
156.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
111.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
142.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify3.0s

Counts

128 → 128

Iterations

Useful iterations: done (3.0s)

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

prune543.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 4.6b

regimes288.0ms

Accuracy

84.2% (4.6b remaining)

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

bsearch261.0ms

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

sample3.3s

Algorithm

intervals

Results

712.0ms	2915×	body	80	nan
666.0ms	1076×	body	2560	valid
614.0ms	5882×	body	80	valid
540.0ms	848×	body	1280	valid
141.0ms	468×	body	640	valid
99.0ms	212×	body	320	valid
63.0ms	107×	body	5120	valid
19.0ms	122×	body	160	valid