Details

sample128.0ms

Algorithm

intervals

Results

31.0ms	36×	body	2560	valid
27.0ms	187×	body	80	valid
20.0ms	86×	body	80	nan
17.0ms	25×	body	1280	valid
10.0ms	17×	body	640	valid
3.0ms	8×	body	320	valid
1.0ms	4×	body	160	valid

simplify97.0ms

Counts

1 → 1

Iterations

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

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.8b	(fma (* a c) -4 (* b b))
0.9b	(- (sqrt (fma (* a c) -4 (* b b))) b)
23.5b	(sqrt (fma (* a c) -4 (* b b)))

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:

22.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
0.0ms	(fma (* a c) -4 (* b b))
8.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (- (sqrt (fma (* a c) -4 (* b b))) b) a)
71.0ms	(fma (* a c) -4 (* b b))
135.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
103.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.1s

Counts

126 → 126

Iterations

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

prune1.5s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 24.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1 a))
0.8b	(fma (* a c) -4 (* b b))
0.9b	(- (sqrt (fma (* a c) -4 (* b b))) b)
23.5b	(sqrt (fma (* a c) -4 (* b b)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
32×	`*-un-lft-identity`
27×	`add-cube-cbrt`
18×	`prod-diff`
17×	`sqrt-prod`
13×	`associate-r` `add-exp-log`
11×	`times-frac`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`fma-neg` `associate-l` `add-log-exp`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `difference-of-squares`
3×	`flip3--` `flip--` `unswap-sqr`
2×	`frac-times` `div-exp` `associate-*l/` `cbrt-unprod` `distribute-lft-out--`
1×	`cbrt-undiv` `rem-sqrt-square` `rec-exp` `sub-neg` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `div-inv`

Counts

4 → 115

Calls

4 calls:

43.0ms	(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1 a))
0.0ms	(fma (* a c) -4 (* b b))
8.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
1.0ms	(sqrt (fma (* a c) -4 (* b b)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

152.0ms	(* (- (sqrt (fma (* a c) -4 (* b b))) b) (/ 1 a))
79.0ms	(fma (* a c) -4 (* b b))
140.0ms	(- (sqrt (fma (* a c) -4 (* b b))) b)
91.0ms	(sqrt (fma (* a c) -4 (* b b)))

simplify1.1s

Counts

127 → 127

Iterations

Iter	Nodes
done	2001
3	2001
2	1007
1	397
0	175

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 24.0b

localize49.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt (* (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))) (cbrt (fma (* a c) -4 (* b b)))))
24.2b	(cbrt (fma (* a c) -4 (* b b)))
24.2b	(cbrt (fma (* a c) -4 (* b b)))
24.2b	(cbrt (fma (* a c) -4 (* b b)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

24×	`pow1`
15×	`sqrt-pow1`
12×	`pow1/3`
9×	`cbrt-prod` `pow-prod-up`
7×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow-plus`
5×	`pow-prod-down`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-sqr`
2×	`pow2`
1×	`pow1/2` `pow3` `sqrt-prod`

Counts

4 → 69

Calls

4 calls:

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

series903.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(sqrt (* (* (cbrt (fma (* a c) -4 (* b b))) (cbrt (fma (* a c) -4 (* b b)))) (cbrt (fma (* a c) -4 (* b b)))))
276.0ms	(cbrt (fma (* a c) -4 (* b b)))
279.0ms	(cbrt (fma (* a c) -4 (* b b)))
244.0ms	(cbrt (fma (* a c) -4 (* b b)))

simplify884.0ms

Counts

81 → 81

Iterations

Iter	Nodes
done	2000
4	2000
3	847
2	304
1	150
0	85

prune1.0s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 24.0b

localize37.0ms

Local error

Found 4 expressions with local error:

23.5b	(sqrt (fma (* a c) -4 (* b b)))
23.5b	(sqrt (fma (* a c) -4 (* b b)))
24.2b	(cbrt (fma (* a c) -4 (* b b)))
24.2b	(cbrt (fma (* a c) -4 (* b b)))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `pow1` `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` `pow1/3`

Counts

4 → 60

Calls

4 calls:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt (fma (* a c) -4 (* b b)))
118.0ms	(sqrt (fma (* a c) -4 (* b b)))
257.0ms	(cbrt (fma (* a c) -4 (* b b)))
584.0ms	(cbrt (fma (* a c) -4 (* b b)))

simplify940.0ms

Counts

72 → 72

Iterations

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

prune1.1s

Pruning

13 alts after pruning (10 fresh and 3 done)

Merged error: 24.0b

regimes429.0ms

Accuracy

97.7% (0.3b remaining)

Error of 21.8b against oracle of 21.5b and baseline of 32.9b

bsearch116.0ms

Steps

Iters	Range		Point
10	-1.9389773539313132e-256	-2.787376398831021e-273	-2.9388713619935654e-273

simplify7.0ms

Iterations

Iter	Nodes
done	25
1	25
0	23

end0.0ms

sample4.5s

Algorithm

intervals

Results

1.1s	881×	body	1280	valid
1.1s	1026×	body	2560	valid
1.0s	5891×	body	80	valid
409.0ms	2954×	body	80	nan
315.0ms	464×	body	640	valid
146.0ms	96×	body	5120	valid
99.0ms	237×	body	320	valid
29.0ms	104×	body	160	valid