Details

sample159.0ms

Algorithm

intervals

Results

42.0ms	37×	body	1280	valid
33.0ms	180×	body	80	valid
25.0ms	24×	body	2560	valid
15.0ms	93×	body	80	nan
13.0ms	18×	body	640	valid
5.0ms	4×	body	5120	valid
3.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify143.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.4b	(fma (* a c) -4 (* b b))
1.6b	(- (sqrt (fma (* a c) -4 (* b b))) b)
21.3b	(sqrt (fma (* a c) -4 (* b b)))

rewrite42.0ms

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:

28.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.0ms	(fma (* a c) -4 (* b b))
10.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series485.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
68.0ms	(fma (* a c) -4 (* b b))
116.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
115.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.4s

Counts

126 → 126

Iterations

Iter	Nodes
done	2002
3	2002
2	773
1	335
0	156

prune721.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.5b

localize49.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.6b	(- (sqrt (fma (* a c) -4 (* b b))) b)
21.3b	(sqrt (fma (* a c) -4 (* b b)))
21.3b	(sqrt (fma (* a c) -4 (* b b)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
32×	`sqrt-prod`
12×	`fma-neg`
8×	`add-log-exp`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 116

Calls

4 calls:

16.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
15.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
2.0ms	(sqrt (fma (* a c) -4 (* b b)))
2.0ms	(sqrt (fma (* a c) -4 (* b b)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
116.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
126.0ms	(sqrt (fma (* a c) -4 (* b b)))
111.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.4s

Counts

128 → 128

Iterations

Iter	Nodes
done	2003
4	2003
3	925
2	319
1	173
0	86

prune988.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 21.5b

localize94.0ms

Local error

Found 4 expressions with local error:

21.3b	(sqrt (fma (* a c) -4 (* b b)))
22.1b	(cbrt (fma (* a c) -4 (* b b)))
22.1b	(cbrt (fma (* a c) -4 (* b b)))
22.1b	(cbrt (fma (* a c) -4 (* b b)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

2.0ms	(sqrt (fma (* a c) -4 (* b b)))
1.0ms	(cbrt (fma (* a c) -4 (* b b)))
10.0ms	(cbrt (fma (* a c) -4 (* b b)))
1.0ms	(cbrt (fma (* a c) -4 (* b b)))

series951.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(sqrt (fma (* a c) -4 (* b b)))
292.0ms	(cbrt (fma (* a c) -4 (* b b)))
283.0ms	(cbrt (fma (* a c) -4 (* b b)))
245.0ms	(cbrt (fma (* a c) -4 (* b b)))

simplify1.1s

Counts

70 → 70

Iterations

Iter	Nodes
done	2002
4	2002
3	829
2	280
1	122
0	67

prune728.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 21.5b

localize134.0ms

Local error

Found 4 expressions with local error:

22.1b	(cbrt (fma (* a c) -4 (* b b)))
22.1b	(cbrt (fma (* a c) -4 (* b b)))
22.1b	(cbrt (fma (* a c) -4 (* b b)))
22.1b	(cbrt (fma (* a c) -4 (* b b)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `pow1/3` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`

Counts

4 → 56

Calls

4 calls:

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

series1.2s

Counts

4 → 12

Calls

4 calls:

300.0ms	(cbrt (fma (* a c) -4 (* b b)))
271.0ms	(cbrt (fma (* a c) -4 (* b b)))
300.0ms	(cbrt (fma (* a c) -4 (* b b)))
282.0ms	(cbrt (fma (* a c) -4 (* b b)))

simplify1.2s

Counts

68 → 68

Iterations

Iter	Nodes
done	2030
4	2030
3	781
2	251
1	103
0	52

prune834.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 21.5b

regimes419.0ms

Accuracy

98.3% (0.2b remaining)

Error of 22.1b against oracle of 22.0b and baseline of 33.3b

bsearch125.0ms

Steps

Iters	Range		Point
8	5.73444593407656e-233	2.8713645357407407e-228	3.49222195256563e-230

simplify7.0ms

Iterations

Iter	Nodes
done	23
1	23
0	21

end0.0ms

sample5.4s

Algorithm

intervals

Results

1.6s	1060×	body	2560	valid
1.2s	910×	body	1280	valid
1.1s	5860×	body	80	valid
509.0ms	3006×	body	80	nan
345.0ms	471×	body	640	valid
221.0ms	108×	body	5120	valid
102.0ms	225×	body	320	valid
30.0ms	103×	body	160	valid