Details

sample129.0ms

Algorithm

intervals

Results

14.0ms	191×	body	80	valid
13.0ms	30×	body	2560	valid
12.0ms	28×	body	1280	valid
8.0ms	22×	body	640	valid
6.0ms	80×	body	80	nan
2.0ms	4×	body	5120	valid
2.0ms	5×	body	320	valid
0.0ms	2×	body	160	valid

simplify96.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	10	13
1	19	13
2	33	13
3	46	13
4	49	13
done	49	13

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.6b	(- (* b_2 b_2) (* a c))
22.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite195.0ms

Algorithm

rewrite-expression-head

Rules

79×	`add-sqr-sqrt`
78×	`*-un-lft-identity`
61×	`prod-diff`
58×	`add-cube-cbrt`
38×	`sqrt-prod`
26×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in` `times-frac`
11×	`fma-neg`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`neg-mul-1` `associate-/l*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u`
3×	`diff-log` `associate-/r*`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 171

Calls

4 calls:

110.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
44.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
9.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series377.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
98.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
50.0ms	(- (* b_2 b_2) (* a c))
125.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.5s

Counts

183 → 183

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	242	5993
1	546	4313
2	1414	3549
done	5001	3001

prune513.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (pow b_2 2) (* a c))
2.5b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
8.0b	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
22.1b	(sqrt (- (pow b_2 2) (* a c)))

rewrite340.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
117×	`*-un-lft-identity`
85×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
8×	`fma-neg` `prod-diff`
7×	`flip3--` `flip--`
6×	`unpow-prod-down` `div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num` `unpow2` `sqr-pow`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 208

Calls

4 calls:

20.0ms	(- (pow b_2 2) (* a c))
188.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
98.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
20.0ms	(sqrt (- (pow b_2 2) (* a c)))

series685.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (pow b_2 2) (* a c))
213.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) a)
315.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
108.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify1.9s

Counts

220 → 220

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	332	5836
1	769	5059
2	2431	4856
done	5000	4842

prune1.1s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (pow b_2 2) (* a c))
2.6b	(* (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) (/ 1 a))
8.0b	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
22.1b	(sqrt (- (pow b_2 2) (* a c)))

rewrite391.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
52×	`times-frac`
37×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
18×	`add-cbrt-cube`
14×	`difference-of-squares`
13×	`associate-r`
10×	`sqrt-prod`
9×	`div-exp`
8×	`fma-neg` `prod-diff` `prod-exp`
7×	`pow1` `distribute-lft-out--`
6×	`unpow-prod-down` `associate-/r*` `add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `cbrt-unprod` `log1p-expm1-u`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `1-exp` `associate-/l/` `unpow2` `sqr-pow`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 162

Calls

4 calls:

32.0ms	(- (pow b_2 2) (* a c))
211.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) (/ 1 a))
105.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
30.0ms	(sqrt (- (pow b_2 2) (* a c)))

series653.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (pow b_2 2) (* a c))
220.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2)) (/ 1 a))
283.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (pow b_2 2) (* a c))) b_2))
107.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify3.6s

Counts

174 → 174

Iterations

Useful iterations: done (3.6s)

Iter	Nodes	Cost
0	278	3714
1	721	3155
2	2280	2836
done	5000	2656

prune816.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

localize38.0ms

Local error

Found 4 expressions with local error:

6.2b	(/ (* c a) (* (cbrt a) (cbrt (- (sqrt (- (pow b_2 2) (* a c))) b_2))))
22.1b	(sqrt (- (pow b_2 2) (* a c)))
22.1b	(sqrt (- (pow b_2 2) (* a c)))
22.1b	(sqrt (- (pow b_2 2) (* a c)))

rewrite162.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log`
12×	`add-cbrt-cube`
10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3--` `div-exp` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div` `associate-*r/` `associate-/r/`
1×	`frac-2neg` `times-frac` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

62.0ms	(/ (* c a) (* (cbrt a) (cbrt (- (sqrt (- (pow b_2 2) (* a c))) b_2))))
32.0ms	(sqrt (- (pow b_2 2) (* a c)))
35.0ms	(sqrt (- (pow b_2 2) (* a c)))
28.0ms	(sqrt (- (pow b_2 2) (* a c)))

series1.6s

Counts

4 → 12

Calls

4 calls:

1.3s	(/ (* c a) (* (cbrt a) (cbrt (- (sqrt (- (pow b_2 2) (* a c))) b_2))))
101.0ms	(sqrt (- (pow b_2 2) (* a c)))
87.0ms	(sqrt (- (pow b_2 2) (* a c)))
99.0ms	(sqrt (- (pow b_2 2) (* a c)))

simplify967.0ms

Counts

88 → 88

Iterations

Useful iterations: done (962.0ms)

Iter	Nodes	Cost
0	161	1505
1	423	1347
2	1554	1218
done	5001	1204

prune644.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.0b

regimes382.0ms

Accuracy

87.9% (3.3b remaining)

Error of 8.9b against oracle of 5.7b and baseline of 32.6b

bsearch214.0ms

Steps

Iters	Range	Point
0	2.0836136179885362e+135	2.1675125417143413e+135	2.1255630798514387e+135
10	-5.856593162926158e-110	-5.919731712082881e-125	-4.561190783883462e-123
7	-3.4482088762076956e+69	-1.445974953615168e+68	-3.1028950157805323e+69

Iters

Range

Point

2.0836136179885362e+135

2.1675125417143413e+135

2.1255630798514387e+135

-5.856593162926158e-110

-5.919731712082881e-125

-4.561190783883462e-123

-3.4482088762076956e+69

-1.445974953615168e+68

-3.1028950157805323e+69

simplify9.0ms

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	46	113
1	54	111
done	54	111

end0.0ms

sample3.3s

Algorithm

intervals

Results

955.0ms	5781×	body	80	valid
667.0ms	1103×	body	2560	valid
418.0ms	917×	body	1280	valid
306.0ms	2885×	body	80	nan
193.0ms	431×	body	640	valid
101.0ms	231×	body	320	valid
63.0ms	118×	body	5120	valid
15.0ms	108×	body	160	valid