Details

sample103.0ms

Algorithm

intervals

Results

24.0ms	40×	body	2560	valid
20.0ms	186×	body	80	valid
14.0ms	28×	body	1280	valid
9.0ms	91×	body	80	nan
7.0ms	4×	body	160	valid
4.0ms	10×	body	640	valid
2.0ms	8×	body	320	valid
2.0ms	3×	body	5120	valid

simplify126.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	105
7	105
6	104
5	102
4	94
3	77
2	44
1	25
0	14

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
1.3b	(fma b b (* (* a -4) c))
1.3b	(- (sqrt (fma b b (* (* a -4) c))) b)
21.9b	(sqrt (fma b b (* (* a -4) c)))

rewrite54.0ms

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:

32.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.0ms	(fma b b (* (* a -4) c))
16.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
2.0ms	(sqrt (fma b b (* (* a -4) c)))

series531.0ms

Counts

4 → 12

Calls

4 calls:

178.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
84.0ms	(fma b b (* (* a -4) c))
143.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
126.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
3	2689
2	950
1	405
0	180

prune1.4s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.8b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) a)
1.3b	(- (sqrt (fma c (* -4 a) (* b b))) b)
21.9b	(sqrt (fma c (* -4 a) (* b b)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
29×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`fma-neg` `associate-/l*`
5×	`add-cbrt-cube` `add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`expm1-log1p-u` `associate-/r*` `insert-posit16` `log1p-expm1-u`
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` `div-inv`

Counts

3 → 103

Calls

3 calls:

17.0ms	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) a)
9.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
2.0ms	(sqrt (fma c (* -4 a) (* b b)))

series343.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(/ (- (sqrt (fma c (* -4 a) (* b b))) b) a)
130.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
114.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify2.1s

Counts

112 → 112

Iterations

Iter	Nodes
4	4407
3	1733
2	645
1	295
0	144

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.8b

localize24.0ms

Local error

Found 3 expressions with local error:

0.2b	(* (- (sqrt (fma c (* -4 a) (* b b))) b) (/ 1 a))
1.3b	(- (sqrt (fma c (* -4 a) (* b b))) b)
21.9b	(sqrt (fma c (* -4 a) (* b b)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
26×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r`
12×	`add-exp-log`
11×	`times-frac`
8×	`add-cbrt-cube`
6×	`pow1` `fma-neg` `associate-l`
5×	`add-log-exp`
4×	`prod-exp` `difference-of-squares`
3×	`expm1-log1p-u` `flip3--` `insert-posit16` `log1p-expm1-u` `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` `div-inv`

Counts

3 → 104

Calls

3 calls:

36.0ms	(* (- (sqrt (fma c (* -4 a) (* b b))) b) (/ 1 a))
10.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series305.0ms

Counts

3 → 9

Calls

3 calls:

106.0ms	(* (- (sqrt (fma c (* -4 a) (* b b))) b) (/ 1 a))
104.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
95.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify2.0s

Counts

113 → 113

Iterations

Iter	Nodes
3	2355
2	984
1	359
0	163

prune1.3s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.7b

localize36.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.3b	(- (sqrt (fma c (* -4 a) (* b b))) b)
21.9b	(sqrt (fma c (* -4 a) (* b b)))
21.9b	(sqrt (fma c (* -4 a) (* b b)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

8.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
8.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
1.0ms	(sqrt (fma c (* -4 a) (* b b)))
1.0ms	(sqrt (fma c (* -4 a) (* b b)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
116.0ms	(- (sqrt (fma c (* -4 a) (* b b))) b)
103.0ms	(sqrt (fma c (* -4 a) (* b b)))
125.0ms	(sqrt (fma c (* -4 a) (* b b)))

simplify1.1s

Counts

128 → 128

Iterations

Iter	Nodes
4	2478
3	903
2	292
1	153
0	85

prune1.7s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 4.7b

regimes393.0ms

Accuracy

84.7% (4.3b remaining)

Error of 9.8b against oracle of 5.4b and baseline of 33.7b

bsearch225.0ms

Steps

Iters	Range		Point
8	6.256891986679925e-86	3.543466061308676e-83	4.6659701943749105e-84
8	-6.435448379097954e+123	-1.4863434806956936e+121	-4.694684309811035e+121

simplify5.0ms

Iterations

Iter	Nodes
2	32
1	32
0	28

end0.0ms

sample4.7s

Algorithm

intervals

Results

1.4s	1106×	body	2560	valid
1.1s	935×	body	1280	valid
894.0ms	5845×	body	80	valid
525.0ms	2919×	body	80	nan
218.0ms	453×	body	640	valid
133.0ms	111×	body	5120	valid
79.0ms	212×	body	320	valid
55.0ms	113×	body	160	valid