Details

sample67.0ms

Algorithm

intervals

Results

15.0ms	2×	body	5120	valid
11.0ms	37×	body	2560	valid
10.0ms	198×	body	80	valid
5.0ms	107×	body	80	nan
4.0ms	19×	body	1280	valid
3.0ms	13×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	4×	body	160	valid

simplify32.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(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:

74.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
40.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
51.0ms	(- (* b_2 b_2) (* a c))
108.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
97.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.0s

Counts

183 → 183

Iterations

Iter	Nodes
done	5001
2	1513
1	574
0	244

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite164.0ms

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:

92.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
10.0ms	(- (* b_2 b_2) (* a c))
37.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
53.0ms	(- (* b_2 b_2) (* a c))
117.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
77.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.4s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	1770
1	639
0	263

prune862.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite190.0ms

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:

118.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (* b_2 b_2) (* a c))
35.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

144.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
58.0ms	(- (* b_2 b_2) (* a c))
134.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
87.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

183 → 183

Iterations

Iter	Nodes
done	5001
2	1513
1	574
0	244

prune1.1s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 6.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.4b	(- (* b_2 b_2) (* a c))
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite151.0ms

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` `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 → 257

Calls

4 calls:

52.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
13.0ms	(- (* b_2 b_2) (* a c))
55.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
17.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series397.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
52.0ms	(- (* b_2 b_2) (* a c))
101.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
99.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

269 → 269

Iterations

Iter	Nodes
done	5004
2	2153
1	832
0	351

prune1.0s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 5.9b

regimes574.0ms

Accuracy

83.6% (4.6b remaining)

Error of 10.2b against oracle of 5.5b and baseline of 33.8b

bsearch109.0ms

Steps

Iters	Range		Point
6	4.2942163002471454e+116	2.920461936675284e+117	2.865381670376961e+117
9	-2.9209995635511727e-62	-5.172501488366762e-68	-2.5694949190681246e-64

simplify4.0ms

Iterations

Iter	Nodes
done	25
1	25
0	22

end0.0ms

sample2.4s

Algorithm

intervals

Results

784.0ms	5910×	body	80	valid
541.0ms	1038×	body	2560	valid
256.0ms	909×	body	1280	valid
232.0ms	2910×	body	80	nan
89.0ms	444×	body	640	valid
73.0ms	110×	body	5120	valid
35.0ms	238×	body	320	valid
12.0ms	108×	body	160	valid