Details

sample261.0ms

Algorithm

intervals

Results

28.0ms	34×	body	2560	valid
27.0ms	198×	body	80	valid
20.0ms	29×	body	1280	valid
14.0ms	91×	body	80	nan
4.0ms	8×	body	640	valid
3.0ms	7×	body	320	valid
2.0ms	6×	body	160	valid
2.0ms	2×	body	5120	valid

simplify53.0ms

Counts

1 → 1

Iterations

Iter	Nodes
6	34
5	34
4	32
3	30
2	23
1	15
0	10

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.2b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
27.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 122

Calls

4 calls:

132.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
8.0ms	(- (* b_2 b_2) (* a c))
38.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
19.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
53.0ms	(- (* b_2 b_2) (* a c))
87.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
109.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

134 → 134

Iterations

Iter	Nodes
3	3530
2	1175
1	462
0	199

prune856.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 7.7b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.2b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
27.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
137×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
84×	`add-cube-cbrt`
28×	`sqrt-prod`
26×	`difference-of-squares`
24×	`associate-/r*`
19×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
8×	`add-log-exp`
7×	`flip3--` `fma-neg` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `sub-neg` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `pow-flip` `inv-pow`

Counts

4 → 200

Calls

4 calls:

59.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
16.0ms	(- (* b_2 b_2) (* a c))
59.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
54.0ms	(- (* b_2 b_2) (* a c))
119.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
107.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify6.1s

Counts

212 → 212

Iterations

Iter	Nodes
3	5808
2	1851
1	711
0	303

prune1.3s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 7.7b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.2b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
27.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite239.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
19×	`prod-diff`
18×	`times-frac`
10×	`difference-of-squares`
8×	`add-log-exp`
7×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `div-inv`

Counts

4 → 122

Calls

4 calls:

127.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
18.0ms	(- (* b_2 b_2) (* a c))
74.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
18.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series360.0ms

Counts

4 → 12

Calls

4 calls:

111.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
42.0ms	(- (* b_2 b_2) (* a c))
118.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
89.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify1.9s

Counts

134 → 134

Iterations

Iter	Nodes
3	3530
2	1175
1	462
0	199

prune914.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 7.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
1.2b	(- (* b_2 b_2) (* a c))
1.4b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
27.8b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
19×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1` `fma-neg`
6×	`associate-l`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`unswap-sqr`
2×	`frac-times` `sub-neg` `sqrt-div` `diff-log` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 123

Calls

4 calls:

108.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
8.0ms	(- (* b_2 b_2) (* a c))
45.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series301.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
40.0ms	(- (* b_2 b_2) (* a c))
83.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify3.7s

Counts

135 → 135

Iterations

Iter	Nodes
3	4054
2	1372
1	527
0	219

prune981.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 7.7b

regimes328.0ms

Accuracy

82.3% (4.9b remaining)

Error of 10.5b against oracle of 5.6b and baseline of 33.5b

bsearch192.0ms

Steps

Iters	Range		Point
8	2.764110880089542e-64	2.3245141193625934e-60	2.0617732603635578e-61
9	-229886301330938.94	-710549284.1101115	-227369802444031.66

simplify8.0ms

Iterations

Iter	Nodes
2	31
1	31
0	26

end0.0ms

sample4.1s

Algorithm

intervals

Results

1.3s	1057×	body	2560	valid
930.0ms	5887×	body	80	valid
668.0ms	908×	body	1280	valid
325.0ms	2988×	body	80	nan
258.0ms	444×	body	640	valid
169.0ms	111×	body	5120	valid
83.0ms	231×	body	320	valid
51.0ms	113×	body	160	valid