Details

sample151.0ms

Algorithm

intervals

Results

36.0ms	198×	body	80	valid
36.0ms	29×	body	1280	valid
18.0ms	17×	body	2560	valid
13.0ms	82×	body	80	nan
9.0ms	13×	body	640	valid
5.0ms	10×	body	320	valid
5.0ms	4×	body	5120	valid
3.0ms	10×	body	160	valid

simplify119.0ms

Counts

1 → 1

Iterations

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

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.4b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
1.5b	(fma b b (* (* a -4) c))
2.7b	(- (sqrt (fma b b (* (* a -4) c))) b)
22.2b	(sqrt (fma b b (* (* a -4) c)))

rewrite29.0ms

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:

17.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
0.0ms	(fma b b (* (* a -4) c))
8.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
1.0ms	(sqrt (fma b b (* (* a -4) c)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

180.0ms	(/ (- (sqrt (fma b b (* (* a -4) c))) b) a)
72.0ms	(fma b b (* (* a -4) c))
128.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
125.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
3	2656
2	950
1	407
0	180

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 6.3b

localize52.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
1.5b	(fma b b (* (* a -4) c))
2.7b	(- (sqrt (fma b b (* (* a -4) c))) b)
22.2b	(sqrt (fma b b (* (* a -4) c)))

rewrite27.0ms

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:

13.0ms	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
0.0ms	(fma b b (* (* a -4) c))
8.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
2.0ms	(sqrt (fma b b (* (* a -4) c)))

series515.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/ 1 (/ a (- (sqrt (fma b b (* (* a -4) c))) b)))
90.0ms	(fma b b (* (* a -4) c))
124.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
110.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.9s

Counts

204 → 204

Iterations

Iter	Nodes
3	4300
2	1646
1	647
0	284

prune2.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 6.3b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (fma b b (* (* a -4) c))) a)
1.5b	(fma b b (* (* a -4) c))
7.1b	(- (/ (sqrt (fma b b (* (* a -4) c))) a) (/ b a))
22.2b	(sqrt (fma b b (* (* a -4) c)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

481×	`times-frac`
378×	`add-sqr-sqrt`
366×	`*-un-lft-identity`
358×	`add-cube-cbrt`
286×	`prod-diff`
143×	`sqrt-prod`
39×	`div-inv`
22×	`fma-neg`
6×	`add-cbrt-cube` `add-exp-log` `associate-/l*` `add-log-exp` `difference-of-squares`
5×	`pow1`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate-/r*`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `flip3--` `distribute-rgt-out--` `pow1/2` `diff-log` `div-exp` `frac-sub` `fma-udef` `flip--` `sub-div`

Counts

4 → 405

Calls

4 calls:

16.0ms	(/ (sqrt (fma b b (* (* a -4) c))) a)
0.0ms	(fma b b (* (* a -4) c))
20.0ms	(- (/ (sqrt (fma b b (* (* a -4) c))) a) (/ b a))
1.0ms	(sqrt (fma b b (* (* a -4) c)))

series490.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (sqrt (fma b b (* (* a -4) c))) a)
64.0ms	(fma b b (* (* a -4) c))
154.0ms	(- (/ (sqrt (fma b b (* (* a -4) c))) a) (/ b a))
123.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify929.0ms

Counts

417 → 417

Iterations

Iter	Nodes
2	2348
1	1064
0	479

prune6.1s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 6.3b

localize45.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
1.5b	(fma b b (* (* a -4) c))
3.7b	(- (/ (sqrt (fma b b (* (* a -4) c))) (cbrt a)) (/ b (cbrt a)))
22.2b	(sqrt (fma b b (* (* a -4) c)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

1582×	`times-frac`
1158×	`add-sqr-sqrt`
1119×	`*-un-lft-identity`
1105×	`add-cube-cbrt`
880×	`prod-diff`
794×	`cbrt-prod`
423×	`sqrt-prod`
65×	`div-inv`
40×	`fma-neg`
15×	`difference-of-squares`
7×	`distribute-lft-out--`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `distribute-rgt-out--` `pow1/2` `pow1/3` `diff-log` `frac-sub` `fma-udef` `flip--` `sub-div`

Counts

4 → 1001

Calls

4 calls:

1.0ms	(cbrt a)
0.0ms	(fma b b (* (* a -4) c))
58.0ms	(- (/ (sqrt (fma b b (* (* a -4) c))) (cbrt a)) (/ b (cbrt a)))
1.0ms	(sqrt (fma b b (* (* a -4) c)))

series1.3s

Counts

4 → 12

Calls

4 calls:

291.0ms	(cbrt a)
68.0ms	(fma b b (* (* a -4) c))
777.0ms	(- (/ (sqrt (fma b b (* (* a -4) c))) (cbrt a)) (/ b (cbrt a)))
138.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.7s

Counts

1013 → 1013

Iterations

Iter	Nodes
1	2273
0	1055

prune18.8s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 6.2b

regimes526.0ms

Accuracy

78.1% (6.1b remaining)

Error of 11.9b against oracle of 5.8b and baseline of 33.5b

bsearch395.0ms

Steps

Iters	Range		Point
3	1.897422751335727e-16	2.3824489835354504e-16	1.922674299151799e-16
7	4.1266326978064226e-111	9.799836324706106e-110	4.664677641347216e-111
8	9.808312070140145e-191	3.260010576758525e-187	3.207624111695675e-187
10	-4.8388360275630777e+135	-9.113678877832951e+119	-1.3725796156555912e+127

simplify10.0ms

Iterations

Iter	Nodes
2	53
1	53
0	43

end0.0ms

sample4.9s

Algorithm

intervals

Results

1.5s	1043×	body	2560	valid
1.2s	5930×	body	80	valid
716.0ms	886×	body	1280	valid
482.0ms	2880×	body	80	nan
318.0ms	495×	body	640	valid
147.0ms	121×	body	5120	valid
79.0ms	202×	body	320	valid
30.0ms	116×	body	160	valid