Details

sample168.0ms

Algorithm

intervals

Results

59.0ms	177×	body	80	valid
21.0ms	37×	body	2560	valid
12.0ms	25×	body	1280	valid
6.0ms	18×	body	640	valid
6.0ms	81×	body	80	nan
2.0ms	9×	body	320	valid
2.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify57.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	49
4	49
3	46
2	33
1	19
0	10

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite156.0ms

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--` `insert-posit16` `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 → 175

Calls

4 calls:

63.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
38.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(- (* b_2 b_2) (* a c))
35.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
88.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
44.0ms	(- (* b_2 b_2) (* a c))
102.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

187 → 187

Iterations

Iter	Nodes
3	4198
2	1440
1	577
0	248

prune2.5s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.1b

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
165×	`times-frac`
118×	`add-cube-cbrt`
61×	`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`
15×	`add-exp-log`
11×	`fma-neg`
10×	`add-log-exp`
9×	`add-cbrt-cube` `associate-/r/`
7×	`neg-mul-1` `flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `pow-flip` `inv-pow`

Counts

4 → 261

Calls

4 calls:

61.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
39.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series418.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
103.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
50.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify918.0ms

Counts

273 → 273

Iterations

Iter	Nodes
2	2126
1	834
0	355

prune3.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 a) (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
1.1b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite207.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
16×	`add-cube-cbrt`
13×	`associate-l` `add-exp-log`
12×	`associate-r`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`distribute-lft-neg-in` `expm1-log1p-u` `distribute-rgt-neg-in` `prod-exp` `insert-posit16` `log1p-expm1-u` `distribute-neg-frac`
3×	`fma-def` `flip3-+` `sqrt-prod` `flip-+` `distribute-lft-out` `unswap-sqr`
2×	`frac-times` `distribute-neg-in` `flip3--` `sqrt-div` `div-exp` `associate-*r/` `cbrt-unprod` `flip--`
1×	`distribute-rgt-in` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `neg-mul-1` `sum-log` `sub-neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `1-exp` `prod-diff` `pow-prod-down` `associate-l/` `-commutative` `distribute-rgt-neg-out` `div-inv`

Counts

4 → 107

Calls

4 calls:

149.0ms	(* (/ 1 a) (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
30.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(* (/ 1 a) (- (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
109.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
51.0ms	(- (* b_2 b_2) (* a c))
94.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.7s

Counts

119 → 119

Iterations

Iter	Nodes
3	5099
2	1620
1	546
0	194

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))) a)
1.1b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `distribute-lft-out`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*`
3×	`associate-/r*` `fma-def` `sqrt-prod`
2×	`flip3-+` `flip3--` `sqrt-div` `flip-+` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-exp` `prod-diff` `div-inv`

Counts

4 → 89

Calls

4 calls:

60.0ms	(/ (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))) a)
22.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series372.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))) a)
90.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
49.0ms	(- (* b_2 b_2) (* a c))
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.1s

Counts

101 → 101

Iterations

Iter	Nodes
3	2910
2	956
1	350
0	149

prune1.1s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.1b

regimes506.0ms

Accuracy

85.3% (4.2b remaining)

Error of 9.9b against oracle of 5.8b and baseline of 34.1b

bsearch180.0ms

Steps

Iters	Range		Point
6	1.890398075878753e+149	8.723340275486535e+149	5.121074390969514e+149
11	-5.190492772730695e-87	-3.518766096303871e-111	-4.32337788234514e-89

simplify6.0ms

Iterations

Iter	Nodes
3	34
2	34
1	30
0	25

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.3s	1121×	body	2560	valid
711.0ms	5782×	body	80	valid
613.0ms	902×	body	1280	valid
408.0ms	2858×	body	80	nan
248.0ms	474×	body	640	valid
101.0ms	128×	body	5120	valid
73.0ms	225×	body	320	valid
63.0ms	108×	body	160	valid