Details

sample127.0ms

Algorithm

intervals

Results

27.0ms	186×	body	80	valid
21.0ms	29×	body	2560	valid
18.0ms	24×	body	1280	valid
18.0ms	17×	body	640	valid
11.0ms	88×	body	80	nan
5.0ms	10×	body	320	valid
3.0ms	3×	body	5120	valid

simplify143.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
1.0b	(- (sqrt (fma b b (* (* a -4) c))) b)
2.0b	(fma b b (* (* a -4) c))
24.4b	(sqrt (fma b b (* (* a -4) c)))

rewrite37.0ms

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:

26.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
8.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
0.0ms	(fma b b (* (* a -4) c))
1.0ms	(sqrt (fma b b (* (* a -4) c)))

series503.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
125.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
91.0ms	(fma b b (* (* a -4) c))
137.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
3	2655
2	951
1	407
0	180

prune1.6s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 5.4b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
1.0b	(- (sqrt (fma b b (* (* a -4) c))) b)
2.0b	(fma b b (* (* a -4) c))
24.4b	(sqrt (fma b b (* (* a -4) c)))

rewrite38.0ms

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 b b (* (* a -4) c))) b)))
8.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
0.0ms	(fma b b (* (* a -4) c))
1.0ms	(sqrt (fma b b (* (* a -4) c)))

series468.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
116.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
70.0ms	(fma b b (* (* a -4) c))
108.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.7s

Counts

204 → 204

Iterations

Iter	Nodes
3	4409
2	1665
1	647
0	284

prune2.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.4b

localize51.0ms

Local error

Found 4 expressions with local error:

2.0b	(fma b b (* (* a -4) c))
24.4b	(sqrt (fma b b (* (* a -4) c)))
24.4b	(sqrt (fma b b (* (* a -4) c)))
24.4b	(sqrt (fma b b (* (* a -4) c)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma b b (* (* a -4) c))
2.0ms	(sqrt (fma b b (* (* a -4) c)))
2.0ms	(sqrt (fma b b (* (* a -4) c)))
3.0ms	(sqrt (fma b b (* (* a -4) c)))

series444.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(fma b b (* (* a -4) c))
109.0ms	(sqrt (fma b b (* (* a -4) c)))
134.0ms	(sqrt (fma b b (* (* a -4) c)))
128.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify817.0ms

Counts

71 → 71

Iterations

Iter	Nodes
4	2301
3	635
2	218
1	94
0	49

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 5.4b

localize37.0ms

Local error

Found 4 expressions with local error:

2.0b	(fma b b (* (* a -4) c))
24.4b	(sqrt (fma b b (* (* a -4) c)))
24.4b	(sqrt (fma b b (* (* a -4) c)))
24.4b	(sqrt (fma b b (* (* a -4) c)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 59

Calls

4 calls:

0.0ms	(fma b b (* (* a -4) c))
1.0ms	(sqrt (fma b b (* (* a -4) c)))
1.0ms	(sqrt (fma b b (* (* a -4) c)))
2.0ms	(sqrt (fma b b (* (* a -4) c)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(fma b b (* (* a -4) c))
99.0ms	(sqrt (fma b b (* (* a -4) c)))
104.0ms	(sqrt (fma b b (* (* a -4) c)))
100.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify795.0ms

Counts

71 → 71

Iterations

Iter	Nodes
4	2301
3	635
2	218
1	94
0	49

prune987.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 5.4b

regimes349.0ms

Accuracy

83.9% (4.5b remaining)

Error of 10.4b against oracle of 5.9b and baseline of 34.1b

bsearch211.0ms

Steps

Iters	Range		Point
9	2.5177836961106285e-119	1.1213560046341023e-113	1.1094847447691107e-113
9	-3.5217276407607985e+80	-1.118546872525465e+73	-2.541338025369698e+80

simplify6.0ms

Iterations

Iter	Nodes
2	34
1	34
0	28

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.2s	912×	body	1280	valid
921.0ms	1091×	body	2560	valid
850.0ms	5839×	body	80	valid
340.0ms	2909×	body	80	nan
278.0ms	461×	body	640	valid
127.0ms	226×	body	320	valid
102.0ms	126×	body	5120	valid
23.0ms	98×	body	160	valid