Details

sample464.0ms

Algorithm

intervals

Results

88.0ms	36×	body	2560	valid
49.0ms	189×	body	80	valid
39.0ms	104×	body	80	nan
32.0ms	16×	body	640	valid
11.0ms	25×	body	1280	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	3×	body	160	valid

simplify581.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.6b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite236.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 171

Calls

4 calls:

120.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
122.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
45.0ms	(- (* b_2 b_2) (* a c))
135.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	2149
1	583
0	244

prune846.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.5b

localize28.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.8b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite225.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 194

Calls

4 calls:

13.0ms	(- (* b_2 b_2) (* a c))
111.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
76.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series752.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(- (* b_2 b_2) (* a c))
263.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
326.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
98.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

206 → 206

Iterations

Iter	Nodes
done	5000
2	4614
1	804
0	315

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite167.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`prod-diff`
54×	`add-cube-cbrt`
35×	`sqrt-prod`
23×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
13×	`associate-r` `add-exp-log`
11×	`times-frac` `fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `neg-mul-1` `associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `neg-log` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

110.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
34.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
93.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
43.0ms	(- (* b_2 b_2) (* a c))
88.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.2s

Counts

181 → 181

Iterations

Iter	Nodes
done	5001
2	3576
1	652
0	263

prune881.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
26.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite148.0ms

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-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `log1p-expm1-u` `flip--`
3×	`associate-/r*` `diff-log`
2×	`sub-neg` `sqrt-div` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `neg-log` `div-inv`

Counts

4 → 171

Calls

4 calls:

89.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
33.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
108.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
65.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	2149
1	583
0	244

prune788.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.4b

regimes775.0ms

Accuracy

86.1% (4.0b remaining)

Error of 9.6b against oracle of 5.6b and baseline of 34.4b

bsearch143.0ms

Steps

Iters	Range		Point
6	5.84949006905106e+100	6.027833473435204e+101	5.878879592304488e+101
6	-3.94223749317518e-93	-9.247487777844521e-94	-1.2208633566514056e-93
6	-3.687013704912239e+33	-6.257941608560553e+32	-2.7267558266977494e+33

simplify9.0ms

Iterations

Iter	Nodes
done	41
1	41
0	35

end0.0ms

sample2.9s

Algorithm

intervals

Results

878.0ms	5821×	body	80	valid
731.0ms	1063×	body	2560	valid
366.0ms	950×	body	1280	valid
273.0ms	2885×	body	80	nan
110.0ms	475×	body	640	valid
53.0ms	116×	body	5120	valid
45.0ms	239×	body	320	valid
12.0ms	105×	body	160	valid