Details

sample150.0ms

Algorithm

intervals

Results

46.0ms	180×	body	80	valid
28.0ms	37×	body	1280	valid
22.0ms	24×	body	2560	valid
13.0ms	93×	body	80	nan
11.0ms	18×	body	640	valid
4.0ms	4×	body	5120	valid
3.0ms	6×	body	320	valid
1.0ms	4×	body	160	valid

simplify112.0ms

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 32.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a -4) c)
0.5b	(fma b b (* (* a -4) c))
1.6b	(- (sqrt (fma b b (* (* a -4) c))) b)
21.3b	(sqrt (fma b b (* (* a -4) c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

27.0ms	(* (* a -4) c)
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)))

series328.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* a -4) c)
72.0ms	(fma b b (* (* a -4) c))
110.0ms	(- (sqrt (fma b b (* (* a -4) c))) b)
123.0ms	(sqrt (fma b b (* (* a -4) c)))

simplify1.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	2002
3	2002
2	915
1	335
0	146

prune511.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.3b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c (* a -4))
0.5b	(fma b b (* c (* a -4)))
1.6b	(- (sqrt (fma b b (* c (* a -4)))) b)
21.3b	(sqrt (fma b b (* c (* a -4))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

14.0ms	(* c (* a -4))
0.0ms	(fma b b (* c (* a -4)))
8.0ms	(- (sqrt (fma b b (* c (* a -4)))) b)
1.0ms	(sqrt (fma b b (* c (* a -4))))

series366.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* c (* a -4))
65.0ms	(fma b b (* c (* a -4)))
146.0ms	(- (sqrt (fma b b (* c (* a -4)))) b)
121.0ms	(sqrt (fma b b (* c (* a -4))))

simplify1.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	2012
3	2012
2	816
1	321
0	144

prune588.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.3b

localize42.0ms

Local error

Found 4 expressions with local error:

11.7b	(- (* (sqrt (* (cbrt (fma b b (* c (* a -4)))) (cbrt (fma b b (* c (* a -4)))))) (sqrt (cbrt (fma b b (* c (* a -4)))))) b)
22.1b	(cbrt (fma b b (* c (* a -4))))
22.1b	(cbrt (fma b b (* c (* a -4))))
22.1b	(cbrt (fma b b (* c (* a -4))))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
8×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
6×	`add-log-exp`
4×	`expm1-log1p-u` `pow1` `add-cbrt-cube` `add-exp-log` `insert-posit16` `log1p-expm1-u`
3×	`pow1/3` `prod-diff`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--`

Counts

4 → 61

Calls

4 calls:

59.0ms	(- (* (sqrt (* (cbrt (fma b b (* c (* a -4)))) (cbrt (fma b b (* c (* a -4)))))) (sqrt (cbrt (fma b b (* c (* a -4)))))) b)
1.0ms	(cbrt (fma b b (* c (* a -4))))
1.0ms	(cbrt (fma b b (* c (* a -4))))
2.0ms	(cbrt (fma b b (* c (* a -4))))

series581.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(- (* (sqrt (* (cbrt (fma b b (* c (* a -4)))) (cbrt (fma b b (* c (* a -4)))))) (sqrt (cbrt (fma b b (* c (* a -4)))))) b)
133.0ms	(cbrt (fma b b (* c (* a -4))))
151.0ms	(cbrt (fma b b (* c (* a -4))))
148.0ms	(cbrt (fma b b (* c (* a -4))))

simplify1.6s

Counts

73 → 73

Iterations

Iter	Nodes
done	2002
4	2002
3	1540
2	604
1	253
0	107

prune657.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.3b

localize57.0ms

Local error

Found 4 expressions with local error:

0.5b	(fma b b (* (* a -4) c))
21.3b	(sqrt (fma b b (* (* a -4) c)))
21.3b	(sqrt (fma b b (* (* a -4) c)))
22.7b	(fma (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c)))) (- b))

rewrite6.0ms

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

series476.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma b b (* (* a -4) c))
111.0ms	(sqrt (fma b b (* (* a -4) c)))
125.0ms	(sqrt (fma b b (* (* a -4) c)))
163.0ms	(fma (sqrt (sqrt (fma b b (* (* a -4) c)))) (sqrt (sqrt (fma b b (* (* a -4) c)))) (- b))

simplify1.2s

Counts

66 → 66

Iterations

Iter	Nodes
done	2001
4	2001
3	695
2	264
1	122
0	67

prune498.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 11.3b

regimes380.0ms

Accuracy

86.4% (3.1b remaining)

Error of 13.8b against oracle of 10.8b and baseline of 33.3b

bsearch259.0ms

Steps

Iters	Range		Point
9	1.9857735944483347e-57	1.377205241174095e-49	1.502588793204478e-55
9	-9.632418191944025e+160	-8.091671749741088e+152	-1.2957079292059776e+154

simplify5.0ms

Iterations

Iter	Nodes
done	32
1	32
0	27

end0.0ms

sample5.5s

Algorithm

intervals

Results

1.4s	5860×	body	80	valid
1.3s	1060×	body	2560	valid
896.0ms	910×	body	1280	valid
558.0ms	225×	body	320	valid
551.0ms	3006×	body	80	nan
286.0ms	471×	body	640	valid
121.0ms	108×	body	5120	valid
31.0ms	103×	body	160	valid