Details

sample236.0ms

Algorithm

intervals

Results

25.0ms	193×	body	80	valid
24.0ms	30×	body	2560	valid
21.0ms	31×	body	1280	valid
13.0ms	91×	body	80	nan
6.0ms	14×	body	640	valid
3.0ms	10×	body	320	valid
3.0ms	3×	body	5120	valid
0.0ms	1×	body	160	valid

simplify58.0ms

Counts

1 → 1

Iterations

Iter	Nodes
5	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: 31.1b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite223.0ms

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:

107.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(- (* b_2 b_2) (* a c))
31.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
184.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
87.0ms	(- (* b_2 b_2) (* a c))
159.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.3s

Counts

187 → 187

Iterations

Iter	Nodes
3	4198
2	1440
1	577
0	248

prune2.4s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite197.0ms

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` `insert-posit16` `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 → 173

Calls

4 calls:

116.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
38.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
113.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
53.0ms	(- (* b_2 b_2) (* a c))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.8s

Counts

185 → 185

Iterations

Iter	Nodes
3	4463
2	1610
1	638
0	267

prune2.0s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite164.0ms

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:

93.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
44.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(- (* b_2 b_2) (* a c))
10.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
109.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
72.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

187 → 187

Iterations

Iter	Nodes
3	4198
2	1440
1	577
0	248

prune2.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.1b

localize39.0ms

Local error

Found 4 expressions with local error:

2.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.3b	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) a)
17.8b	(- (* b_2 b_2) (* b_2 b_2))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite156.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`add-cube-cbrt`
10×	`fma-def` `add-log-exp`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `insert-posit16` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-/r` `sqrt-prod` `associate-/l`
2×	`sum-log` `flip3-+` `flip3--` `sqrt-div` `associate-+l-` `flip-+` `flip--` `distribute-lft-out` `associate-/l/`
1×	`neg-sub0` `cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `neg-mul-1` `sub-neg` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `+-inverses` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `neg-log` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 100

Calls

4 calls:

28.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
101.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) a)
15.0ms	(- (* b_2 b_2) (* b_2 b_2))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
10.0ms	(/ (+ (- (* b_2 b_2) (* b_2 b_2)) (* a c)) a)
1.0ms	(- (* b_2 b_2) (* b_2 b_2))
82.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.6s

Counts

112 → 112

Iterations

Iter	Nodes
3	2821
2	993
1	401
0	168

prune1.2s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.1b

regimes409.0ms

Accuracy

93.6% (1.5b remaining)

Error of 6.9b against oracle of 5.4b and baseline of 29.4b

bsearch271.0ms

Steps

Iters	Range	Point
9	2.1762368803982262e+45	1.3534154308951418e+51	5.646875521171257e+50
10	-1.42643309478481e-241	-6.497739978200133e-255	-6.590101287064612e-255
8	-1.7996802595953755e+64	-1.2634430355867738e+61	-2.6063173736106266e+63

Iters

Range

Point

2.1762368803982262e+45

1.3534154308951418e+51

5.646875521171257e+50

-1.42643309478481e-241

-6.497739978200133e-255

-6.590101287064612e-255

-1.7996802595953755e+64

-1.2634430355867738e+61

-2.6063173736106266e+63

simplify5.0ms

Iterations

Iter	Nodes
2	33
1	33
0	29

end0.0ms

sample3.7s

Algorithm

intervals

Results

1.2s	5884×	body	80	valid
873.0ms	1016×	body	2560	valid
612.0ms	908×	body	1280	valid
328.0ms	2869×	body	80	nan
183.0ms	441×	body	640	valid
121.0ms	239×	body	320	valid
95.0ms	122×	body	5120	valid
24.0ms	113×	body	160	valid