Details

sample131.0ms

Algorithm

intervals

Results

41.0ms	188×	body	80	valid
28.0ms	39×	body	2560	valid
20.0ms	31×	body	1280	valid
10.0ms	87×	body	80	nan
6.0ms	13×	body	640	valid
3.0ms	3×	body	5120	valid
3.0ms	6×	body	320	valid
0.0ms	1×	body	160	valid

simplify135.0ms

Counts

1 → 1

Iterations

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

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.4b	(- (sqrt (fma b b (* (* a -4) c))) b)
0.5b	(fma b b (* (* a -4) c))
23.1b	(sqrt (fma b b (* (* a -4) c)))

rewrite55.0ms

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:

35.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
15.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
0.0ms	(fma b b (* (* a -4) c))
3.0ms	(sqrt (fma b b (* (* a -4) c)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
134.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
63.0ms	(fma b b (* (* a -4) c))
118.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify2.5s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
3	3517
2	1002
1	424
0	180

prune700.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.4b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
0.4b	(- (sqrt (fma b b (* (* a -4) c))) b)
0.5b	(fma b b (* (* a -4) c))
23.1b	(sqrt (fma b b (* (* a -4) c)))

rewrite33.0ms

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:

15.0ms	(/ 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))
2.0ms	(sqrt (fma b b (* (* a -4) c)))

series501.0ms

Counts

4 → 12

Calls

4 calls:

175.0ms	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
122.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
87.0ms	(fma b b (* (* a -4) c))
117.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify2.2s

Counts

204 → 204

Iterations

Iter	Nodes
done	5000
2	1831
1	661
0	284

prune988.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.4b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma b b (* (* a -4) c))
0.5b	(fma b b (* (* a -4) c))
23.1b	(sqrt (fma b b (* (* a -4) c)))
23.1b	(sqrt (fma b b (* (* a -4) c)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

0.0ms	(fma b b (* (* a -4) c))
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)))

series367.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(fma b b (* (* a -4) c))
74.0ms	(fma b b (* (* a -4) c))
111.0ms	(sqrt (fma b b (* (* a -4) c)))
108.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify2.8s

Counts

66 → 66

Iterations

Iter	Nodes
done	5001
4	3165
3	739
2	223
1	94
0	49

prune486.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 6.4b

localize62.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma b b (* (* a -4) c))
23.1b	(sqrt (fma b b (* (* a -4) c)))
23.1b	(sqrt (fma b b (* (* a -4) c)))
23.1b	(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))
3.0ms	(sqrt (fma b b (* (* a -4) c)))
2.0ms	(sqrt (fma b b (* (* a -4) c)))
2.0ms	(sqrt (fma b b (* (* a -4) c)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(fma b b (* (* a -4) c))
103.0ms	(sqrt (fma b b (* (* a -4) c)))
123.0ms	(sqrt (fma b b (* (* a -4) c)))
118.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify2.8s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
4	3165
3	739
2	223
1	94
0	49

prune539.0ms

Pruning

12 alts after pruning (9 fresh and 3 done)

Merged error: 6.4b

regimes569.0ms

Accuracy

83.5% (4.6b remaining)

Error of 10.4b against oracle of 5.9b and baseline of 33.7b

bsearch232.0ms

Steps

Iters	Range		Point
8	1.287554927770862e-68	8.304725640954512e-66	4.5810084990875205e-68
8	-3.370135567630554e+133	-1.481129451033522e+129	-2.1144981103869975e+131

simplify11.0ms

Iterations

Iter	Nodes
done	34
1	34
0	28

end0.0ms

sample4.8s

Algorithm

intervals

Results

1.5s	1064×	body	2560	valid
937.0ms	5890×	body	80	valid
653.0ms	901×	body	1280	valid
487.0ms	2854×	body	80	nan
475.0ms	207×	body	320	valid
296.0ms	447×	body	640	valid
135.0ms	95×	body	5120	valid
36.0ms	133×	body	160	valid