Details

sample72.0ms

Algorithm

intervals

Results

52.0ms

275×

body

valid

simplify84.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	80
5	80
4	76
3	56
2	40
1	21
0	11

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize44.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma d d (* c c))
0.5b	(- (* b c) (* a d))
27.2b	(/ (- (* b c) (* a d)) (fma d d (* c c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
5×	`add-cbrt-cube` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `pow1` `associate-/r` `insert-posit16` `log1p-expm1-u` `associate-/l`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `fma-udef` `div-inv`

Counts

3 → 61

Calls

3 calls:

0.0ms	(fma d d (* c c))
8.0ms	(- (* b c) (* a d))
32.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

series236.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(fma d d (* c c))
67.0ms	(- (* b c) (* a d))
125.0ms	(/ (- (* b c) (* a d)) (fma d d (* c c)))

simplify1.0s

Counts

70 → 70

Iterations

Iter	Nodes
done	2007
3	2007
2	862
1	233
0	98

prune911.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 26.8b

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* b c) (* a d))
14.4b	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
31.8b	(sqrt (fma d d (* c c)))
31.8b	(sqrt (fma d d (* c c)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
21×	`*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac` `sqrt-prod`
6×	`pow1` `associate-/r*` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `flip3--` `pow1/2` `fma-udef` `hypot-def` `flip--` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `sub-neg` `frac-2neg` `fma-neg` `diff-log` `div-sub` `div-exp` `prod-diff` `div-inv`

Counts

4 → 96

Calls

4 calls:

16.0ms	(- (* b c) (* a d))
34.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
3.0ms	(sqrt (fma d d (* c c)))
2.0ms	(sqrt (fma d d (* c c)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* b c) (* a d))
175.0ms	(/ (- (* b c) (* a d)) (sqrt (fma d d (* c c))))
72.0ms	(sqrt (fma d d (* c c)))
60.0ms	(sqrt (fma d d (* c c)))

simplify841.0ms

Counts

108 → 108

Iterations

Iter	Nodes
done	2003
3	2003
2	778
1	266
0	115

prune1.2s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 24.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
0.5b	(- (* b c) (* a d))
14.4b	(/ (- (* b c) (* a d)) (hypot d c))
31.8b	(sqrt (fma d d (* c c)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac`
91×	`add-sqr-sqrt`
90×	`*-un-lft-identity` `add-cube-cbrt`
45×	`sqrt-prod`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r*` `div-inv`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `fma-udef` `hypot-def`

Counts

4 → 183

Calls

4 calls:

16.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
14.0ms	(- (* b c) (* a d))
30.0ms	(/ (- (* b c) (* a d)) (hypot d c))
1.0ms	(sqrt (fma d d (* c c)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

210.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (sqrt (fma d d (* c c))))
55.0ms	(- (* b c) (* a d))
146.0ms	(/ (- (* b c) (* a d)) (hypot d c))
77.0ms	(sqrt (fma d d (* c c)))

simplify1.2s

Counts

195 → 195

Iterations

Iter	Nodes
done	2008
3	2008
2	1647
1	593
0	256

prune2.5s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot d c)
0.1b	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
0.5b	(- (* b c) (* a d))
14.4b	(/ (- (* b c) (* a d)) (hypot d c))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
54×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
11×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv` `add-log-exp`
4×	`expm1-log1p-u` `pow1` `cbrt-undiv` `div-exp` `insert-posit16` `log1p-expm1-u`
3×	`div-sub` `associate-/l/`
2×	`clear-num` `frac-2neg` `flip3--` `flip--`
1×	`hypot-udef` `sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 135

Calls

4 calls:

0.0ms	(hypot d c)
15.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
8.0ms	(- (* b c) (* a d))
21.0ms	(/ (- (* b c) (* a d)) (hypot d c))

series357.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(hypot d c)
138.0ms	(/ (/ (- (* b c) (* a d)) (hypot d c)) (hypot d c))
47.0ms	(- (* b c) (* a d))
121.0ms	(/ (- (* b c) (* a d)) (hypot d c))

simplify1.1s

Counts

147 → 147

Iterations

Iter	Nodes
done	2007
3	2007
2	1474
1	470
0	196

prune1.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.6b

regimes246.0ms

Accuracy

32.4% (7.2b remaining)

Error of 12.8b against oracle of 5.5b and baseline of 16.2b

bsearch87.0ms

Steps

Iters	Range		Point
7	8.240977246969897e+91	1.9142861966646984e+93	1.8584161242035747e+93
7	-1.542727211461463e+154	-3.8584650617426363e+152	-1.4037038847053747e+154

simplify3.0ms

Iterations

Iter	Nodes
done	26
1	26
0	21

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.3s

8499×

body

valid