Details

sample135.0ms

Algorithm

intervals

Results

37.0ms	198×	body	80	valid
30.0ms	34×	body	2560	valid
22.0ms	29×	body	1280	valid
14.0ms	91×	body	80	nan
5.0ms	8×	body	640	valid
3.0ms	7×	body	320	valid
2.0ms	2×	body	5120	valid
2.0ms	6×	body	160	valid

simplify166.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	101
7	101
6	100
5	98
4	90
3	74
2	44
1	25
0	14

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 37.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
1.2b	(fma (* a c) -4 (* b b))
1.3b	(- (sqrt (fma (* a c) -4 (* b b))) b)
27.8b	(sqrt (fma (* a c) -4 (* b b)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

33.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.0ms	(fma (* a c) -4 (* b b))
11.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series402.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
66.0ms	(fma (* a c) -4 (* b b))
90.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
104.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify940.0ms

Counts

126 → 126

Iterations

Iter	Nodes
3	2003
2	718
1	319
0	156

prune1.2s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 32.0b

localize45.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1 a))
1.2b	(fma (* a c) -4 (* b b))
1.3b	(- (sqrt (fma (* a c) -4 (* b b))) b)
27.8b	(sqrt (fma (* a c) -4 (* b b)))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 115

Calls

4 calls:

58.0ms	(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1 a))
0.0ms	(fma (* a c) -4 (* b b))
16.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
3.0ms	(sqrt (fma (* a c) -4 (* b b)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1 a))
84.0ms	(fma (* a c) -4 (* b b))
111.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
92.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify2.9s

Counts

127 → 127

Iterations

Iter	Nodes
3	2457
2	936
1	380
0	175

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 32.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (fma (* a c) -4 (* b b))) b)))
1.2b	(fma (* a c) -4 (* b b))
1.3b	(- (sqrt (fma (* a c) -4 (* b b))) b)
27.8b	(sqrt (fma (* a c) -4 (* b b)))

rewrite44.0ms

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*`
18×	`prod-diff`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube` `associate-/r/`
7×	`div-exp`
6×	`pow1` `fma-neg` `add-log-exp`
5×	`flip3--` `div-inv` `flip--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-undiv` `associate-/l*`
2×	`rec-exp` `1-exp`
1×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `fma-udef` `pow-flip` `inv-pow`

Counts

4 → 192

Calls

4 calls:

24.0ms	(/ 1 (/ a (- (sqrt (fma (* a c) -4 (* b b))) b)))
0.0ms	(fma (* a c) -4 (* b b))
12.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series439.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(/ 1 (/ a (- (sqrt (fma (* a c) -4 (* b b))) b)))
66.0ms	(fma (* a c) -4 (* b b))
119.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
121.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify5.8s

Counts

204 → 204

Iterations

Iter	Nodes
3	4042
2	1442
1	601
0	271

prune1.6s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 25.4b

localize60.0ms

Local error

Found 4 expressions with local error:

1.2b	(fma (* a c) -4 (* b b))
1.6b	(+ (sqrt (fma (* a c) -4 (* b b))) b)
14.7b	(/ (fma a (* -4 c) 0) a)
27.8b	(sqrt (fma (* a c) -4 (* b b)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

17×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
9×	`times-frac`
6×	`fma-def` `add-cbrt-cube` `add-exp-log` `sqrt-prod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r` `associate-/l`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `clear-num` `sum-log` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `flip-+` `fma-udef` `div-inv` `distribute-lft-out`

Counts

4 → 78

Calls

4 calls:

0.0ms	(fma (* a c) -4 (* b b))
6.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
4.0ms	(/ (fma a (* -4 c) 0) a)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(fma (* a c) -4 (* b b))
137.0ms	(+ (sqrt (fma (* a c) -4 (* b b))) b)
64.0ms	(/ (fma a (* -4 c) 0) a)
98.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify4.2s

Counts

90 → 90

Iterations

Iter	Nodes
4	7211
3	1349
2	491
1	211
0	116

prune980.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.7b

regimes391.0ms

Accuracy

96.4% (0.5b remaining)

Error of 14.6b against oracle of 14.0b and baseline of 29.3b

bsearch307.0ms

Steps

Iters	Range		Point
8	9.577178113063194e+87	1.3835948343101812e+92	1.3483090680597456e+92
9	-1.2934161330812669e-259	-3.5211401479992753e-265	-5.229623884976429e-265

simplify10.0ms

Iterations

Iter	Nodes
2	38
1	38
0	33

end0.0ms

sample4.6s

Algorithm

intervals

Results

1.5s	5886×	body	80	valid
1.1s	1054×	body	2560	valid
756.0ms	908×	body	1280	valid
416.0ms	2993×	body	80	nan
240.0ms	446×	body	640	valid
126.0ms	232×	body	320	valid
112.0ms	110×	body	5120	valid
30.0ms	113×	body	160	valid