Details

sample104.0ms

Algorithm

intervals

Results

22.0ms	38×	body	2560	valid
19.0ms	190×	body	80	valid
17.0ms	36×	body	1280	valid
7.0ms	79×	body	80	nan
4.0ms	11×	body	640	valid
3.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify115.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	14	17
1	25	17
2	46	16
3	87	16
4	120	16
5	129	16
done	129	16

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize19.0ms

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))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite267.0ms

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:

119.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
18.0ms	(- (* b b) (* (* 4.0 a) c))
103.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

165.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) (* 2.0 a))
58.0ms	(- (* b b) (* (* 4.0 a) c))
91.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
87.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.0s

Counts

118 → 118

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	195	2476
1	521	2183
2	2396	1862
done	5000	1794

prune422.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.6b

localize27.0ms

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))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite184.0ms

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:

81.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
9.0ms	(- (* 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)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

189.0ms	(/ 1 (/ (* 2.0 a) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b)))
55.0ms	(- (* b b) (* (* 4.0 a) c))
108.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
99.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.3s

Counts

164 → 164

Iterations

Useful iterations: done (2.3s)

Iter	Nodes	Cost
0	261	4025
1	674	3498
2	3313	3147
done	5001	3070

prune536.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite372.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
55×	`prod-diff`
50×	`*-un-lft-identity`
46×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`add-exp-log`
20×	`distribute-rgt-in` `distribute-lft-in`
13×	`add-cbrt-cube`
10×	`prod-exp`
8×	`add-log-exp`
7×	`pow1` `fma-neg` `associate-l`
6×	`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--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow-prod-down` `associate-l/` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 154

Calls

4 calls:

19.0ms	(- (* b b) (* (* 4.0 a) c))
242.0ms	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
82.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series495.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* b b) (* (* 4.0 a) c))
202.0ms	(* (/ 1 (* 2.0 a)) (- (sqrt (- (* b b) (* (* 4.0 a) c))) b))
108.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
105.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.2s

Counts

166 → 166

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	248	4732
1	729	4004
2	4154	3129
done	5000	3126

prune489.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.5b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
0.2b	(- (* b b) (* (* 4.0 a) c))
0.8b	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
21.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite250.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

107.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
14.0ms	(- (* b b) (* (* 4.0 a) c))
112.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
12.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series491.0ms

Counts

4 → 12

Calls

4 calls:

157.0ms	(/ (- (sqrt (- (* b b) (* (* 4.0 a) c))) b) a)
73.0ms	(- (* b b) (* (* 4.0 a) c))
141.0ms	(- (sqrt (- (* b b) (* (* 4.0 a) c))) b)
120.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify2.9s

Counts

130 → 130

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	199	2768
1	509	2465
2	2273	2185
done	5004	2115

prune512.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.5b

regimes252.0ms

Accuracy

84.5% (4.3b remaining)

Error of 10.3b against oracle of 6.0b and baseline of 33.8b

bsearch225.0ms

Steps

Iters	Range		Point
9	3.58845601849977e-79	3.3299624871078663e-72	2.071930020515771e-74
9	-7.561250615295736e+156	-1.350243324689865e+150	-4.919628179067154e+153

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	30	46
1	38	44
done	38	44

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	1053×	body	2560	valid
1.0s	5922×	body	80	valid
409.0ms	906×	body	1280	valid
286.0ms	2894×	body	80	nan
134.0ms	458×	body	640	valid
86.0ms	85×	body	5120	valid
49.0ms	220×	body	320	valid
18.0ms	121×	body	160	valid