Details

sample107.0ms

Algorithm

intervals

Results

26.0ms	36×	body	2560	valid
25.0ms	26×	body	1280	valid
21.0ms	187×	body	80	valid
9.0ms	84×	body	80	nan
6.0ms	12×	body	640	valid
3.0ms	3×	body	5120	valid
2.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify94.0ms

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.1b

localize21.0ms

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)
1.3b	(fma b b (* (* a -4) c))
23.7b	(sqrt (fma b b (* (* a -4) c)))

rewrite36.0ms

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:

19.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
14.0ms	(- (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)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

158.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
98.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
66.0ms	(fma b b (* (* a -4) c))
130.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify911.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	2005
2	1002
1	424
0	180

prune783.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize26.0ms

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)
1.3b	(fma b b (* (* a -4) c))
23.7b	(sqrt (fma b b (* (* a -4) c)))

rewrite51.0ms

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:

29.0ms	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
14.0ms	(- (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)))

series482.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
118.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
78.0ms	(fma b b (* (* a -4) c))
126.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.1s

Counts

204 → 204

Iterations

Iter	Nodes
done	2000
2	1831
1	661
0	284

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 5.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (fma b b (* (* a c) -4))) b)))
1.0b	(- (sqrt (fma b b (* (* a c) -4))) b)
1.3b	(fma b b (* (* a c) -4))
23.7b	(sqrt (fma b b (* (* a c) -4)))

rewrite59.0ms

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:

30.0ms	(/ 1 (/ a (- (sqrt (fma b b (* (* a c) -4))) b)))
20.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
0.0ms	(fma b b (* (* a c) -4))
2.0ms	(sqrt (fma b b (* (* a c) -4)))

series545.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/ 1 (/ a (- (sqrt (fma b b (* (* a c) -4))) b)))
142.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
68.0ms	(fma b b (* (* a c) -4))
149.0ms	(sqrt (fma b b (* (* a c) -4)))

simplify743.0ms

Counts

204 → 204

Iterations

Iter	Nodes
done	2000
2	1770
1	659
0	283

prune927.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 5.1b

localize74.0ms

Local error

Found 4 expressions with local error:

1.3b	(fma b b (* (* a c) -4))
1.3b	(fma b b (* (* a c) -4))
23.7b	(sqrt (fma b b (* (* a c) -4)))
23.7b	(sqrt (fma b b (* (* a c) -4)))

rewrite5.0ms

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

series386.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(fma b b (* (* a c) -4))
61.0ms	(fma b b (* (* a c) -4))
97.0ms	(sqrt (fma b b (* (* a c) -4)))
134.0ms	(sqrt (fma b b (* (* a c) -4)))

simplify550.0ms

Counts

66 → 66

Iterations

Iter	Nodes
done	2001
3	736
2	223
1	92
0	48

prune442.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 5.1b

regimes307.0ms

Accuracy

84.6% (4.4b remaining)

Error of 9.7b against oracle of 5.3b and baseline of 33.9b

bsearch421.0ms

Steps

Iters	Range		Point
8	2.469533614662255e-16	6.384179586440732e-13	5.297236684235463e-16
9	2.201345904528094e-30	9.673336284784144e-25	1.8656332031849816e-25
10	5.0092461758030895e-88	5.0325836698121444e-76	1.739098950628615e-79
9	-7.806260788625035e+148	-1.2289413495061505e+143	-1.6257289292067596e+144

simplify12.0ms

Iterations

Iter	Nodes
done	49
3	49
2	46
1	43
0	34

end0.0ms

sample3.9s

Algorithm

intervals

Results

1.5s	5761×	body	80	valid
817.0ms	1103×	body	2560	valid
546.0ms	957×	body	1280	valid
383.0ms	2981×	body	80	nan
187.0ms	480×	body	640	valid
84.0ms	115×	body	5120	valid
64.0ms	223×	body	320	valid
54.0ms	128×	body	160	valid