Details

sample105.0ms

Algorithm

intervals

Results

31.0ms	37×	body	2560	valid
17.0ms	190×	body	80	valid
9.0ms	23×	body	1280	valid
7.0ms	90×	body	80	nan
5.0ms	15×	body	640	valid
1.0ms	6×	body	160	valid
1.0ms	3×	body	320	valid
1.0ms	1×	body	5120	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize35.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite309.0ms

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:

161.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
20.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
43.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series488.0ms

Counts

4 → 12

Calls

4 calls:

167.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
65.0ms	(- (* b_2 b_2) (* a c))
135.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
120.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

183 → 183

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	242	5993
1	578	4337
2	2130	3551
done	5000	3006

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 7.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite333.0ms

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×	`add-exp-log` `associate-r`
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×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 169

Calls

4 calls:

201.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
26.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series519.0ms

Counts

4 → 12

Calls

4 calls:

171.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
75.0ms	(- (* b_2 b_2) (* a c))
141.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
131.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify7.3s

Counts

181 → 181

Iterations

Useful iterations: done (7.3s)

Iter	Nodes	Cost
0	261	5917
1	645	4200
2	3562	3317
done	5000	3316

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 7.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (pow b_2 2) (* c a))))))
0.8b	(- (pow b_2 2) (* c a))
1.1b	(- (- b_2) (sqrt (- (pow b_2 2) (* c a))))
23.4b	(sqrt (- (pow b_2 2) (* c a)))

rewrite350.0ms

Algorithm

rewrite-expression-head

Rules

175×	`add-sqr-sqrt`
174×	`*-un-lft-identity`
165×	`times-frac`
122×	`add-cube-cbrt`
68×	`prod-diff`
46×	`sqrt-prod`
34×	`distribute-rgt-neg-in`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
21×	`distribute-lft-neg-in`
18×	`fma-neg`
15×	`add-exp-log`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1` `unpow-prod-down`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp` `unpow2` `sqr-pow`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 271

Calls

4 calls:

139.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (pow b_2 2) (* c a))))))
39.0ms	(- (pow b_2 2) (* c a))
106.0ms	(- (- b_2) (sqrt (- (pow b_2 2) (* c a))))
34.0ms	(sqrt (- (pow b_2 2) (* c a)))

series535.0ms

Counts

4 → 12

Calls

4 calls:

195.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (pow b_2 2) (* c a))))))
65.0ms	(- (pow b_2 2) (* c a))
148.0ms	(- (- b_2) (sqrt (- (pow b_2 2) (* c a))))
127.0ms	(sqrt (- (pow b_2 2) (* c a)))

simplify3.8s

Counts

283 → 283

Iterations

Useful iterations: done (3.8s)

Iter	Nodes	Cost
0	366	8832
1	902	6686
2	4179	5856
done	5000	5855

prune1.3s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 7.6b

localize53.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
2.7b	(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
12.5b	(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
23.4b	(sqrt (fma (- c) a (* b_2 b_2)))

rewrite214.0ms

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

Counts

4 → 217

Calls

4 calls:

24.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
98.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
66.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
4.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

series1.0s

Counts

4 → 12

Calls

4 calls:

156.0ms	(- (sqrt (fma (- c) a (* b_2 b_2))) b_2)
304.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2)) a)
380.0ms	(/ (+ 0 (* a c)) (- (sqrt (fma (- c) a (* b_2 b_2))) b_2))
162.0ms	(sqrt (fma (- c) a (* b_2 b_2)))

simplify2.8s

Counts

229 → 229

Iterations

Useful iterations: done (2.8s)

Iter	Nodes	Cost
0	313	6352
1	752	5415
2	3626	5099
done	5000	5039

prune1.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 7.6b

regimes460.0ms

Accuracy

84.1% (4.5b remaining)

Error of 9.9b against oracle of 5.4b and baseline of 33.8b

bsearch136.0ms

Steps

Iters	Range		Point
8	4.049254448328916e+76	2.3057443967677173e+80	2.2766902918844874e+80
5	-1.2210963557284012e-33	-3.582918381276583e-34	-3.8424248185280593e-34

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	33
1	30	33
done	30	33

end0.0ms

sample3.4s

Algorithm

intervals

Results

1.2s	5910×	body	80	valid
594.0ms	1110×	body	2560	valid
345.0ms	904×	body	1280	valid
238.0ms	3011×	body	80	nan
193.0ms	432×	body	640	valid
53.0ms	106×	body	5120	valid
46.0ms	220×	body	320	valid
14.0ms	110×	body	160	valid