Details

sample445.0ms

Algorithm

intervals

Results

155.0ms	20×	body	640	valid
29.0ms	37×	body	2560	valid
22.0ms	186×	body	80	valid
20.0ms	28×	body	1280	valid
13.0ms	91×	body	80	nan
4.0ms	10×	body	320	valid
1.0ms	3×	body	160	valid

simplify61.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	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: 34.6b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite97.0ms

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:

52.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
9.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series305.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
40.0ms	(- (* b_2 b_2) (* a c))
85.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
84.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

187 → 187

Iterations

Iter	Nodes
done	2004
3	2004
2	1521
1	578
0	248

prune2.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite120.0ms

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:

62.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(- (* b_2 b_2) (* a c))
22.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
25.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
52.0ms	(- (* b_2 b_2) (* a c))
118.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
112.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.2s

Counts

187 → 187

Iterations

Iter	Nodes
done	2004
3	2004
2	1521
1	578
0	248

prune2.4s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.8b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(* -1/2 (/ c b_2))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`associate-r`
10×	`times-frac`
9×	`*-un-lft-identity` `add-cube-cbrt`
6×	`add-cbrt-cube` `add-exp-log`
3×	`pow1` `associate-l`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `pow-prod-down` `associate-r/` `-commutative` `insert-posit16` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 35

Calls

1 calls:

19.0ms

(* -1/2 (/ c b_2))

series32.0ms

Counts

1 → 3

Calls

1 calls:

32.0ms

(* -1/2 (/ c b_2))

simplify1.3s

Counts

38 → 38

Iterations

Iter	Nodes
done	2016
4	2016
3	1721
2	518
1	173
0	71

prune350.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 5.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt b_2) (cbrt b_2))
0.6b	(cbrt b_2)
0.6b	(cbrt b_2)
0.6b	(cbrt b_2)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
9×	`pow1/3`
6×	`swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

16.0ms	(* (cbrt b_2) (cbrt b_2))
1.0ms	(cbrt b_2)
2.0ms	(cbrt b_2)
2.0ms	(cbrt b_2)

series1.2s

Counts

4 → 12

Calls

4 calls:

331.0ms	(* (cbrt b_2) (cbrt b_2))
291.0ms	(cbrt b_2)
271.0ms	(cbrt b_2)
300.0ms	(cbrt b_2)

simplify1.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	2004
4	2004
3	1110
2	364
1	141
0	67

prune838.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.8b

regimes583.0ms

Accuracy

79.7% (5.7b remaining)

Error of 11.2b against oracle of 5.5b and baseline of 33.6b

bsearch213.0ms

Steps

Iters	Range		Point
8	6.45623811977989e+97	1.5556153764929518e+101	1.786204067849289e+100
10	-1.305087172727865e-183	-3.833210530916389e-194	-1.2890050783826923e-183

simplify8.0ms

Iterations

Iter	Nodes
done	27
1	27
0	25

end0.0ms

sample3.6s

Algorithm

intervals

Results

894.0ms	918×	body	1280	valid
868.0ms	1100×	body	2560	valid
739.0ms	5836×	body	80	valid
353.0ms	2972×	body	80	nan
197.0ms	497×	body	640	valid
182.0ms	107×	body	5120	valid
58.0ms	194×	body	320	valid
22.0ms	118×	body	160	valid