Details

sample43.0ms

Algorithm

intervals

Results

25.0ms

256×

body

valid

simplify4.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	2355
11	2355
10	2345
9	1929
8	1425
7	1158
6	1017
5	710
4	386
3	167
2	72
1	38
0	18

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0b	(fma (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x)
0.1b	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
16.1b	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 63

Calls

4 calls:

0.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
0.0ms	(fma (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x)
0.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
5.0ms	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

series329.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(fma (+ z 6.012459259764103) z 3.350343815022304)
174.0ms	(fma (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x)
34.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
92.0ms	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify1.6s

Counts

75 → 75

Iterations

Iter	Nodes
done	5004
3	1949
2	535
1	233
0	122

prune555.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
15.4b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.4b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.5b	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))

rewrite14.0ms

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` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `fma-udef` `div-inv`

Counts

4 → 85

Calls

4 calls:

0.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
6.0ms	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
95.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
74.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
167.0ms	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304)))

simplify2.3s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
3	2771
2	791
1	305
0	147

prune908.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize49.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
15.4b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
15.4b	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
16.0b	(* (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt`
22×	`-un-lft-identity` `times-frac` `associate-r*`
20×	`add-cube-cbrt`
17×	`sqrt-prod`
13×	`add-exp-log`
9×	`add-cbrt-cube`
8×	`pow1`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `fma-udef` `div-inv`

Counts

4 → 93

Calls

4 calls:

0.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
2.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
26.0ms	(* (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))

series853.0ms

Counts

4 → 12

Calls

4 calls:

461.0ms	(fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525)
91.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
83.0ms	(sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))
217.0ms	(* (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (/ 1 (sqrt (fma (+ z 6.012459259764103) z 3.350343815022304))))

simplify2.5s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
3	4244
2	1119
1	411
0	171

prune568.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (fma (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x))
16.1b	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))
16.1b	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))
16.1b	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
27×	`times-frac`
10×	`add-cbrt-cube` `add-exp-log`
9×	`associate-/r` `associate-/l`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`
1×	`pow1/3`

Counts

4 → 104

Calls

4 calls:

1.0ms	(cbrt (fma (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x))
7.0ms	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))
6.0ms	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))
5.0ms	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

series992.0ms

Counts

4 → 12

Calls

4 calls:

707.0ms	(cbrt (fma (/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304)) y x))
101.0ms	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))
96.0ms	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))
87.0ms	(/ (fma (fma 0.0692910599291889 z 0.4917317610505968) z 0.279195317918525) (fma (+ z 6.012459259764103) z 3.350343815022304))

simplify2.0s

Counts

116 → 116

Iterations

Iter	Nodes
done	5003
3	2489
2	737
1	283
0	144

prune903.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

regimes411.0ms

Accuracy

96.2% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 15.7b

bsearch172.0ms

Steps

Iters	Range		Point
8	6.0329627772416755e-24	8.874871730790149e-20	8.728612712058619e-20
6	-6.085229541487145e+16	-8098743939100131.0	-8200451688083493.0

simplify5.0ms

Iterations

Iter	Nodes
done	30
1	30
0	26

end0.0ms

sample1.4s

Algorithm

intervals

Results

1.1s

8000×

body

valid