Details

sample57.0ms

Algorithm

intervals

Results

23.0ms	288×	body	80	valid
5.0ms	81×	body	80	nan

simplify212.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	176
6	176
5	174
4	161
3	122
2	66
1	36
0	20

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.2b

localize149.0ms

Local error

Found 4 expressions with local error:

0.9b	(- (- b) (sqrt (fma (* c 4.0) (- a) (* b b))))
1.2b	(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
22.4b	(sqrt (fma (* c 4.0) (- a) (* b b)))
22.4b	(sqrt (fma (* c 4.0) (- a) (* b b)))

rewrite49.0ms

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:

22.0ms	(- (- b) (sqrt (fma (* c 4.0) (- a) (* b b))))
9.0ms	(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
1.0ms	(sqrt (fma (* c 4.0) (- a) (* b b)))
4.0ms	(sqrt (fma (* c 4.0) (- a) (* b b)))

series445.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(- (- b) (sqrt (fma (* c 4.0) (- a) (* b b))))
109.0ms	(- (sqrt (fma (* c 4.0) (- a) (* b b))) b)
117.0ms	(sqrt (fma (* c 4.0) (- a) (* b b)))
124.0ms	(sqrt (fma (* c 4.0) (- a) (* b b)))

simplify2.5s

Counts

173 → 173

Iterations

Iter	Nodes
done	5000
2	1829
1	425
0	193

prune979.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 11.9b

localize190.0ms

Local error

Found 4 expressions with local error:

22.4b	(sqrt (fma (* c 4.0) (- a) (* b b)))
22.4b	(sqrt (fma (* c 4.0) (- a) (* b b)))
22.4b	(sqrt (fma (* c 4.0) (- a) (* b b)))
23.3b	(fma (sqrt (sqrt (fma (* c 4.0) (- a) (* b b)))) (sqrt (sqrt (fma (* c 4.0) (- a) (* b b)))) (- b))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

2.0ms	(sqrt (fma (* c 4.0) (- a) (* b b)))
3.0ms	(sqrt (fma (* c 4.0) (- a) (* b b)))
3.0ms	(sqrt (fma (* c 4.0) (- a) (* b b)))
1.0ms	(fma (sqrt (sqrt (fma (* c 4.0) (- a) (* b b)))) (sqrt (sqrt (fma (* c 4.0) (- a) (* b b)))) (- b))

series1.1s

Counts

4 → 12

Calls

4 calls:

157.0ms	(sqrt (fma (* c 4.0) (- a) (* b b)))
135.0ms	(sqrt (fma (* c 4.0) (- a) (* b b)))
148.0ms	(sqrt (fma (* c 4.0) (- a) (* b b)))
673.0ms	(fma (sqrt (sqrt (fma (* c 4.0) (- a) (* b b)))) (sqrt (sqrt (fma (* c 4.0) (- a) (* b b)))) (- b))

simplify628.0ms

Counts

67 → 67

Iterations

Iter	Nodes
done	5001
3	1069
2	286
1	112
0	65

prune685.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.5b

localize224.0ms

Local error

Found 4 expressions with local error:

9.5b	(- (* (fabs (cbrt (fma 4.0 (* c (- a)) (* b b)))) (sqrt (cbrt (fma 4.0 (* c (- a)) (* b b))))) b)
22.4b	(sqrt (fma (* c 4.0) (- a) (* b b)))
23.1b	(cbrt (fma 4.0 (* c (- a)) (* b b)))
23.1b	(cbrt (fma 4.0 (* c (- a)) (* b b)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
6×	`cbrt-prod` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
3×	`prod-diff` `sqrt-prod`
2×	`pow1/3`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `flip3--` `pow1/2` `fma-neg` `diff-log` `flip--`

Counts

4 → 59

Calls

4 calls:

12.0ms	(- (* (fabs (cbrt (fma 4.0 (* c (- a)) (* b b)))) (sqrt (cbrt (fma 4.0 (* c (- a)) (* b b))))) b)
2.0ms	(sqrt (fma (* c 4.0) (- a) (* b b)))
1.0ms	(cbrt (fma 4.0 (* c (- a)) (* b b)))
1.0ms	(cbrt (fma 4.0 (* c (- a)) (* b b)))

series1.5s

Counts

4 → 12

Calls

4 calls:

638.0ms	(- (* (fabs (cbrt (fma 4.0 (* c (- a)) (* b b)))) (sqrt (cbrt (fma 4.0 (* c (- a)) (* b b))))) b)
121.0ms	(sqrt (fma (* c 4.0) (- a) (* b b)))
347.0ms	(cbrt (fma 4.0 (* c (- a)) (* b b)))
346.0ms	(cbrt (fma 4.0 (* c (- a)) (* b b)))

simplify685.0ms

Counts

71 → 71

Iterations

Iter	Nodes
done	5000
2	1202
1	341
0	145

prune882.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 11.5b

localize199.0ms

Local error

Found 4 expressions with local error:

23.1b	(cbrt (fma 4.0 (* c (- a)) (* b b)))
23.1b	(cbrt (fma (- (* a c)) 4.0 (* b b)))
23.1b	(cbrt (fma (- (* a c)) 4.0 (* b b)))
23.1b	(cbrt (fma (- (* a c)) 4.0 (* b b)))

rewrite4.0ms

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` `log1p-expm1-u` `add-log-exp`

Counts

4 → 52

Calls

4 calls:

1.0ms	(cbrt (fma 4.0 (* c (- a)) (* b b)))
1.0ms	(cbrt (fma (- (* a c)) 4.0 (* b b)))
1.0ms	(cbrt (fma (- (* a c)) 4.0 (* b b)))
1.0ms	(cbrt (fma (- (* a c)) 4.0 (* b b)))

series1.8s

Counts

4 → 12

Calls

4 calls:

358.0ms	(cbrt (fma 4.0 (* c (- a)) (* b b)))
726.0ms	(cbrt (fma (- (* a c)) 4.0 (* b b)))
346.0ms	(cbrt (fma (- (* a c)) 4.0 (* b b)))
357.0ms	(cbrt (fma (- (* a c)) 4.0 (* b b)))

simplify560.0ms

Counts

64 → 64

Iterations

Iter	Nodes
done	5000
3	1063
2	293
1	127
0	69

prune970.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 11.5b

regimes391.0ms

Accuracy

82% (1.4b remaining)

Error of 13.5b against oracle of 12.1b and baseline of 19.8b

bsearch166.0ms

Steps

Iters	Range		Point
9	3.768382185355077e+69	1.107955803311012e+78	2.284562987196845e+77

simplify6.0ms

Iterations

Iter	Nodes
done	32
1	32
0	30

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	8726×	body	80	valid
388.0ms	2814×	body	80	nan