Details

sample167.0ms

Algorithm

intervals

Results

37.0ms	40×	body	2560	valid
32.0ms	8×	body	320	valid
30.0ms	186×	body	80	valid
22.0ms	28×	body	1280	valid
13.0ms	91×	body	80	nan
6.0ms	10×	body	640	valid
3.0ms	3×	body	5120	valid
1.0ms	4×	body	160	valid

simplify122.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	101
7	101
6	100
5	98
4	90
3	74
2	44
1	25
0	14

prune17.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
1.0b	(fma (* a c) -4 (* b b))
1.3b	(- (sqrt (fma (* a c) -4 (* b b))) b)
21.9b	(sqrt (fma (* a c) -4 (* b b)))

rewrite41.0ms

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:

21.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.0ms	(fma (* a c) -4 (* b b))
15.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
3.0ms	(sqrt (fma (* a c) -4 (* b b)))

series473.0ms

Counts

4 → 12

Calls

4 calls:

162.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
63.0ms	(fma (* a c) -4 (* b b))
134.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
114.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify908.0ms

Counts

126 → 126

Iterations

Iter	Nodes
3	2003
2	718
1	319
0	156

prune1.6s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 28.5b

localize44.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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 c) -4))) b) a)
0.0ms	(fma b b (* (* a c) -4))
11.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
2.0ms	(sqrt (fma b b (* (* a c) -4)))

series374.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (- (sqrt (fma b b (* (* a c) -4))) b) a)
53.0ms	(fma b b (* (* a c) -4))
106.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
99.0ms	(sqrt (fma b b (* (* a c) -4)))

simplify1.2s

Counts

126 → 126

Iterations

Iter	Nodes
3	2643
2	950
1	403
0	179

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize51.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`sqrt-prod`
21×	`add-cube-cbrt`
18×	`prod-diff`
7×	`pow1`
6×	`fma-neg` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 90

Calls

4 calls:

16.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
3.0ms	(sqrt (fma b b (* (* a c) -4)))
2.0ms	(sqrt (fma b b (* (* a c) -4)))
2.0ms	(sqrt (fma b b (* (* a c) -4)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
91.0ms	(sqrt (fma b b (* (* a c) -4)))
101.0ms	(sqrt (fma b b (* (* a c) -4)))
105.0ms	(sqrt (fma b b (* (* a c) -4)))

simplify2.4s

Counts

102 → 102

Iterations

Iter	Nodes
4	3251
3	1240
2	439
1	207
0	99

prune1.6s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.8b

localize39.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
1.3b	(fma b b (* (* a c) -4))
1.3b	(- (sqrt (fma b b (* (* a c) -4))) b)
21.9b	(sqrt (fma b b (* (* a c) -4)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
16×	`sqrt-prod`
6×	`fma-neg` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`cbrt-prod`
2×	`difference-of-squares`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `pow1/3` `diff-log` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 83

Calls

4 calls:

1.0ms	(cbrt a)
0.0ms	(fma b b (* (* a c) -4))
12.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
1.0ms	(sqrt (fma b b (* (* a c) -4)))

series523.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(cbrt a)
61.0ms	(fma b b (* (* a c) -4))
113.0ms	(- (sqrt (fma b b (* (* a c) -4))) b)
83.0ms	(sqrt (fma b b (* (* a c) -4)))

simplify3.4s

Counts

95 → 95

Iterations

Iter	Nodes
4	5684
3	1712
2	596
1	265
0	134

prune1.2s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 4.7b

regimes504.0ms

Accuracy

85% (4.2b remaining)

Error of 9.6b against oracle of 5.4b and baseline of 33.6b

bsearch250.0ms

Steps

Iters	Range		Point
8	6.256891986679925e-86	3.543466061308676e-83	5.9878793504095505e-84
10	-1.0499721897563905e+163	-8.354690034354516e+151	-9.768773924260542e+151

simplify9.0ms

Iterations

Iter	Nodes
2	30
1	30
0	26

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.0s	1106×	body	2560	valid
1.0s	935×	body	1280	valid
971.0ms	5845×	body	80	valid
522.0ms	2919×	body	80	nan
304.0ms	453×	body	640	valid
114.0ms	111×	body	5120	valid
111.0ms	212×	body	320	valid
29.0ms	113×	body	160	valid