Details

sample90.0ms

Algorithm

intervals

Results

50.0ms	279×	body	80	valid
15.0ms	96×	body	80	nan

simplify183.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	170
7	170
6	168
5	164
4	157
3	132
2	76
1	39
0	20

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.6b

localize136.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (sqrt (fma c (* a -4) (* b b))) b)
1.4b	(- (- b) (sqrt (fma c (* a -4) (* b b))))
19.8b	(sqrt (fma c (* a -4) (* b b)))
19.8b	(sqrt (fma c (* a -4) (* b b)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

78×	`prod-diff`
71×	`add-sqr-sqrt`
67×	`*-un-lft-identity`
61×	`add-cube-cbrt`
50×	`sqrt-prod`
22×	`distribute-rgt-neg-in`
21×	`distribute-lft-neg-in`
16×	`fma-neg`
10×	`add-log-exp`
7×	`neg-mul-1`
6×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `difference-of-squares`
3×	`diff-log` `distribute-lft-out--`
2×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `flip--`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 161

Calls

4 calls:

13.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
18.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
2.0ms	(sqrt (fma c (* a -4) (* b b)))
2.0ms	(sqrt (fma c (* a -4) (* b b)))

series403.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(- (sqrt (fma c (* a -4) (* b b))) b)
90.0ms	(- (- b) (sqrt (fma c (* a -4) (* b b))))
119.0ms	(sqrt (fma c (* a -4) (* b b)))
100.0ms	(sqrt (fma c (* a -4) (* b b)))

simplify1.1s

Counts

173 → 173

Iterations

Iter	Nodes
3	2297
2	877
1	414
0	191

prune2.9s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.3b

localize152.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (- (sqrt (fma (* c a) -4 (* b b)))) b)
19.8b	(sqrt (fma c (* a -4) (* b b)))
19.8b	(sqrt (fma (* c a) -4 (* b b)))
19.8b	(sqrt (fma (* c a) -4 (* b b)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt` `prod-diff`
47×	`*-un-lft-identity`
43×	`add-cube-cbrt`
33×	`sqrt-prod`
25×	`distribute-rgt-neg-in`
24×	`distribute-lft-neg-in`
16×	`fma-neg`
8×	`add-log-exp`
7×	`pow1`
4×	`expm1-log1p-u` `neg-mul-1` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log` `distribute-lft-out--`
1×	`associate--l-` `neg-sub0` `sub-neg` `flip3--` `neg-log` `flip--` `difference-of-squares`

Counts

4 → 128

Calls

4 calls:

24.0ms	(- (- (sqrt (fma (* c a) -4 (* b b)))) b)
2.0ms	(sqrt (fma c (* a -4) (* b b)))
2.0ms	(sqrt (fma (* c a) -4 (* b b)))
2.0ms	(sqrt (fma (* c a) -4 (* b b)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(- (- (sqrt (fma (* c a) -4 (* b b)))) b)
110.0ms	(sqrt (fma c (* a -4) (* b b)))
134.0ms	(sqrt (fma (* c a) -4 (* b b)))
133.0ms	(sqrt (fma (* c a) -4 (* b b)))

simplify2.9s

Counts

140 → 140

Iterations

Iter	Nodes
4	4114
3	1242
2	464
1	264
0	141

prune2.8s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.2b

localize202.0ms

Local error

Found 4 expressions with local error:

19.8b	(sqrt (fma c (* a -4) (* b b)))
20.6b	(cbrt (fma c (* a -4) (* b b)))
20.6b	(cbrt (fma c (* a -4) (* b b)))
20.6b	(cbrt (fma c (* a -4) (* b b)))

rewrite4.0ms

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` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 54

Calls

4 calls:

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

series913.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt (fma c (* a -4) (* b b)))
252.0ms	(cbrt (fma c (* a -4) (* b b)))
284.0ms	(cbrt (fma c (* a -4) (* b b)))
265.0ms	(cbrt (fma c (* a -4) (* b b)))

simplify3.8s

Counts

66 → 66

Iterations

Iter	Nodes
5	6417
4	1982
3	660
2	253
1	121
0	66

prune1.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 11.2b

localize216.0ms

Local error

Found 4 expressions with local error:

19.8b	(sqrt (fma c (* a -4) (* b b)))
19.8b	(sqrt (fma c (* a -4) (* b b)))
20.6b	(cbrt (fma c (* a -4) (* b b)))
20.6b	(cbrt (fma c (* a -4) (* b b)))

rewrite4.0ms

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` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

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

series731.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(sqrt (fma c (* a -4) (* b b)))
110.0ms	(sqrt (fma c (* a -4) (* b b)))
277.0ms	(cbrt (fma c (* a -4) (* b b)))
231.0ms	(cbrt (fma c (* a -4) (* b b)))

simplify3.2s

Counts

68 → 68

Iterations

Iter	Nodes
5	6417
4	1982
3	660
2	253
1	121
0	66

prune1.4s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 11.2b

regimes295.0ms

Accuracy

90.3% (0.7b remaining)

Error of 13.3b against oracle of 12.7b and baseline of 19.5b

bsearch129.0ms

Steps

Iters	Range		Point
9	1.5347927881719531e+137	5.414027326126016e+143	2.3543665697229833e+137

simplify11.0ms

Iterations

Iter	Nodes
3	50
2	50
1	46
0	38

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.5s	8738×	body	80	valid
937.0ms	2886×	body	80	nan