Details

sample57.0ms

Algorithm

intervals

Results

12.0ms	198×	body	80	valid
9.0ms	29×	body	2560	valid
9.0ms	34×	body	1280	valid
5.0ms	92×	body	80	nan
3.0ms	12×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	4×	body	160	valid
0.0ms	1×	body	5120	valid

simplify44.0ms

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: 33.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.2b	(- (* b_2 b_2) (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite198.0ms

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:

115.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
25.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(- (* b_2 b_2) (* a c))
35.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
88.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
45.0ms	(- (* b_2 b_2) (* a c))
85.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.1s

Counts

183 → 183

Iterations

Iter	Nodes
done	5000
2	1505
1	573
0	244

prune744.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.5b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.2b	(- (* b_2 b_2) (* a c))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite166.0ms

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:

101.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
40.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series327.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
86.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
38.0ms	(- (* b_2 b_2) (* a c))
76.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify2.5s

Counts

181 → 181

Iterations

Iter	Nodes
done	5000
2	1786
1	639
0	263

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.4b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
2.2b	(- (* b_2 b_2) (* a c))
5.2b	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite224.0ms

Algorithm

rewrite-expression-head

Rules

1339×	`times-frac`
946×	`add-sqr-sqrt`
940×	`*-un-lft-identity`
926×	`add-cube-cbrt`
749×	`prod-diff`
323×	`sqrt-prod`
210×	`distribute-rgt-neg-in`
207×	`distribute-lft-neg-in`
69×	`neg-mul-1`
60×	`div-inv`
35×	`fma-neg`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `flip3--` `sqrt-div` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`associate--l-` `neg-sub0` `cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `distribute-rgt-out--` `pow1/2` `div-sub` `div-exp` `frac-sub` `sub-div`

Counts

4 → 889

Calls

4 calls:

14.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
7.0ms	(- (* b_2 b_2) (* a c))
96.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

170.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
58.0ms	(- (* b_2 b_2) (* a c))
108.0ms	(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
79.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.2s

Counts

901 → 901

Iterations

Iter	Nodes
done	5000
2	4288
1	2002
0	903

prune4.4s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.4b

localize122.0ms

Local error

Found 4 expressions with local error:

13.2b	(- (* (/ b_2 (cbrt a)) (/ (/ -1 (cbrt a)) (cbrt a))) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
23.2b	(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)))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
22×	`prod-diff`
20×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
7×	`pow1`
6×	`sqrt-div` `add-log-exp`
4×	`expm1-log1p-u` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `frac-sub`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `associate-l/` `associate-r/` `div-inv`

Counts

4 → 91

Calls

4 calls:

57.0ms	(- (* (/ b_2 (cbrt a)) (/ (/ -1 (cbrt a)) (cbrt a))) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))
11.0ms	(sqrt (- (* b_2 b_2) (* a c)))
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series461.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(- (* (/ b_2 (cbrt a)) (/ (/ -1 (cbrt a)) (cbrt a))) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
106.0ms	(sqrt (- (* b_2 b_2) (* a c)))
100.0ms	(sqrt (- (* b_2 b_2) (* a c)))
93.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.8s

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1923
1	639
0	231

prune830.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.4b

regimes463.0ms

Accuracy

84.1% (4.6b remaining)

Error of 10.3b against oracle of 5.8b and baseline of 34.4b

bsearch135.0ms

Steps

Iters	Range		Point
5	6.972240796235003e+85	2.4695855038465726e+86	2.3609083740516956e+86
10	-3.3499769700489724e-75	-6.612186054126484e-88	-2.0687874539246598e-76

simplify10.0ms

Iterations

Iter	Nodes
done	34
1	34
0	28

end0.0ms

sample2.5s

Algorithm

intervals

Results

674.0ms	902×	body	1280	valid
495.0ms	5857×	body	80	valid
488.0ms	1086×	body	2560	valid
185.0ms	2952×	body	80	nan
143.0ms	484×	body	640	valid
59.0ms	187×	body	320	valid
41.0ms	98×	body	5120	valid
12.0ms	112×	body	160	valid