Details

sample45.0ms

Algorithm

intervals

Results

22.0ms

273×

body

valid

simplify15.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	21
2	21
1	17
0	11

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.0b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma d d (* c c))
1.3b	(fma a c (* b d))
25.6b	(/ (fma a c (* b d)) (fma d d (* c c)))

rewrite5.0ms

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`
3×	`expm1-log1p-u` `pow1` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`fma-udef`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

3 → 49

Calls

3 calls:

0.0ms	(fma d d (* c c))
0.0ms	(fma a c (* b d))
4.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

series248.0ms

Counts

3 → 9

Calls

3 calls:

61.0ms	(fma d d (* c c))
56.0ms	(fma a c (* b d))
131.0ms	(/ (fma a c (* b d)) (fma d d (* c c)))

simplify2.4s

Counts

58 → 58

Iterations

Iter	Nodes
done	5000
4	3252
3	990
2	315
1	120
0	72

prune493.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 25.2b

localize28.0ms

Local error

Found 4 expressions with local error:

1.3b	(fma a c (* b d))
16.3b	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
30.5b	(sqrt (fma d d (* c c)))
30.5b	(sqrt (fma d d (* c c)))

rewrite10.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 83

Calls

4 calls:

0.0ms	(fma a c (* b d))
5.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
1.0ms	(sqrt (fma d d (* c c)))
1.0ms	(sqrt (fma d d (* c c)))

series366.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(fma a c (* b d))
165.0ms	(/ (fma a c (* b d)) (sqrt (fma d d (* c c))))
63.0ms	(sqrt (fma d d (* c c)))
77.0ms	(sqrt (fma d d (* c c)))

simplify3.0s

Counts

95 → 95

Iterations

Iter	Nodes
done	5020
4	2674
3	979
2	299
1	143
0	88

prune782.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 22.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
1.3b	(fma a c (* b d))
16.3b	(/ (fma a c (* b d)) (hypot d c))
30.5b	(sqrt (fma d d (* c c)))

rewrite30.0ms

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`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-undiv` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg` `fma-udef`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `hypot-def` `associate-/l/`

Counts

4 → 169

Calls

4 calls:

13.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
0.0ms	(fma a c (* b d))
7.0ms	(/ (fma a c (* b d)) (hypot d c))
3.0ms	(sqrt (fma d d (* c c)))

series616.0ms

Counts

4 → 12

Calls

4 calls:

280.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (sqrt (fma d d (* c c))))
63.0ms	(fma a c (* b d))
203.0ms	(/ (fma a c (* b d)) (hypot d c))
70.0ms	(sqrt (fma d d (* c c)))

simplify2.4s

Counts

181 → 181

Iterations

Iter	Nodes
done	5003
3	3287
2	1039
1	466
0	226

prune1.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 14.2b

localize31.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
1.3b	(fma a c (* b d))
16.3b	(/ (fma a c (* b d)) (hypot d c))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
53×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
16×	`associate-/l*`
10×	`add-cbrt-cube` `add-exp-log`
6×	`associate-/r*` `div-inv`
4×	`cbrt-undiv` `div-exp`
3×	`expm1-log1p-u` `pow1` `log1p-expm1-u` `add-log-exp`
2×	`clear-num` `frac-2neg`
1×	`fma-udef` `associate-/l/`

Counts

3 → 111

Calls

3 calls:

22.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
1.0ms	(fma a c (* b d))
8.0ms	(/ (fma a c (* b d)) (hypot d c))

series425.0ms

Counts

3 → 9

Calls

3 calls:

189.0ms	(/ (/ (fma a c (* b d)) (hypot d c)) (hypot d c))
65.0ms	(fma a c (* b d))
171.0ms	(/ (fma a c (* b d)) (hypot d c))

simplify2.1s

Counts

120 → 120

Iterations

Iter	Nodes
done	5050
3	3650
2	922
1	342
0	159

prune689.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.3b

regimes411.0ms

Accuracy

32.5% (7.8b remaining)

Error of 13.6b against oracle of 5.8b and baseline of 17.4b

bsearch80.0ms

Steps

Iters	Range		Point
9	6.36185677957703e+145	5.205407902564929e+153	1.8016086380156584e+148
5	-2.2871888563215003e+52	-5.952772209436251e+51	-2.2512419148347823e+52

simplify4.0ms

Iterations

Iter	Nodes
done	20
1	20
0	18

end0.0ms

sample864.0ms

Algorithm

intervals

Results

607.0ms

8459×

body

valid