Details

sample162.0ms

Algorithm

intervals

Results

59.0ms	174×	body	80	valid
12.0ms	30×	body	2560	valid
8.0ms	28×	body	1280	valid
7.0ms	97×	body	80	nan
5.0ms	23×	body	640	valid
3.0ms	6×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	8×	body	160	valid

simplify59.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	283
1	19	283
2	33	283
3	46	283
4	49	283
done	49	283

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize65.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
2.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite203.0ms

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:

112.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
13.0ms	(- (* b_2 b_2) (* a c))
45.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.0ms	(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)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
79.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
108.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

183 → 183

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	244	92638
1	574	82163
2	1513	74224
done	5001	62934

prune854.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
13.7b	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`fma-neg` `prod-diff`
10×	`add-log-exp`
6×	`distribute-lft-neg-in` `pow1` `distribute-rgt-neg-in` `sqrt-prod`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `sqrt-div` `add-exp-log` `log1p-expm1-u` `flip--`
3×	`diff-log`
2×	`rem-sqrt-square` `neg-mul-1` `sub-neg` `sqrt-pow1` `pow1/2`
1×	`associate--l-` `neg-sub0` `neg-log` `difference-of-squares`

Counts

4 → 87

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series339.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b_2 b_2) (* a c))
92.0ms	(- (- b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))
103.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify4.0s

Counts

99 → 99

Iterations

Useful iterations: done (4.0s)

Iter	Nodes	Cost
0	128	34548
1	304	27190
2	864	26651
3	2825	26341
done	5000	25996

prune621.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.5b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.2b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

164×	`add-sqr-sqrt`
162×	`times-frac`
129×	`*-un-lft-identity`
95×	`add-cube-cbrt`
34×	`difference-of-squares`
32×	`sqrt-prod`
27×	`associate-/l*`
18×	`prod-diff`
17×	`distribute-lft-out--`
11×	`add-cbrt-cube` `add-exp-log`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`fma-neg` `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` `diff-log` `flip-+`

Counts

4 → 219

Calls

4 calls:

46.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
144.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
94.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series763.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
235.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
339.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.5s

Counts

231 → 231

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	340	123759
1	851	107125
2	2480	102659
done	5012	102584

prune1.2s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.6b

localize33.0ms

Local error

Found 4 expressions with local error:

11.1b	(/ (+ 0 (* a c)) (fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2)))
15.7b	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 75

Calls

4 calls:

15.0ms	(/ (+ 0 (* a c)) (fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2)))
0.0ms	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series950.0ms

Counts

4 → 12

Calls

4 calls:

601.0ms	(/ (+ 0 (* a c)) (fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2)))
160.0ms	(fma (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (- b_2))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))
95.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.5s

Counts

87 → 87

Iterations

Useful iterations: done (3.5s)

Iter	Nodes	Cost
0	156	34690
1	373	27811
2	1059	25605
3	3870	25246
done	5001	25131

prune579.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.6b

regimes479.0ms

Accuracy

87.2% (3.5b remaining)

Error of 9.2b against oracle of 5.8b and baseline of 32.7b

bsearch231.0ms

Steps

Iters	Range	Point
10	7.868349732386487e+96	4.727011775790926e+114	1.6738516635749796e+107
6	-1.8486478600700203e-204	-1.2771142337683854e-205	-1.6070748188691203e-204
9	-1.5616592422619596e-10	-4.8623869860036984e-17	-5.2605709473303605e-14

Iters

Range

Point

7.868349732386487e+96

4.727011775790926e+114

1.6738516635749796e+107

-1.8486478600700203e-204

-1.2771142337683854e-205

-1.6070748188691203e-204

-1.5616592422619596e-10

-4.8623869860036984e-17

-5.2605709473303605e-14

simplify31.0ms

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	34	1150
1	40	1149
2	45	1149
done	45	1149

end0.0ms

sample2.6s

Algorithm

intervals

Results

898.0ms	5866×	body	80	valid
466.0ms	1040×	body	2560	valid
331.0ms	916×	body	1280	valid
232.0ms	2929×	body	80	nan
139.0ms	462×	body	640	valid
96.0ms	110×	body	5120	valid
37.0ms	220×	body	320	valid
13.0ms	113×	body	160	valid