Details

sample583.0ms

Algorithm

intervals

Results

177.0ms	50×	body	1280	valid
162.0ms	54×	body	640	valid
72.0ms	146×	body	80	valid
42.0ms	28×	body	320	valid
20.0ms	44×	body	80	nan
9.0ms	8×	body	160	valid

simplify1.5s

Counts

1 → 1

Iterations

Iter	Nodes
done	2024
7	2024
6	1982
5	908
4	393
3	188
2	99
1	47
0	20

prune43.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ F (sin B))
0.2b	(/ x (tan B))
6.0b	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
19.2b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
31×	`*-un-lft-identity` `add-cube-cbrt`
30×	`times-frac`
22×	`add-exp-log`
13×	`add-cbrt-cube` `associate-r`
8×	`unpow-prod-down`
7×	`associate-l`
6×	`associate-/r` `prod-exp` `associate-/l` `unswap-sqr`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `pow-exp` `div-inv`
2×	`clear-num` `frac-2neg` `cbrt-unprod`
1×	`pow-pow` `tan-quot` `associate-r/` `associate-/r/` `-commutative`

Counts

4 → 127

Calls

4 calls:

5.0ms	(/ F (sin B))
5.0ms	(/ x (tan B))
23.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
4.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series728.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ F (sin B))
162.0ms	(/ x (tan B))
189.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) (/ F (sin B)))
288.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.5s

Counts

139 → 139

Iterations

Iter	Nodes
done	2005
3	2005
2	1645
1	547
0	244

prune2.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (tan B))
0.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.9b	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
19.2b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`add-exp-log`
19×	`*-un-lft-identity` `add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`times-frac`
7×	`unpow-prod-down` `associate-l`
6×	`associate-/r*` `prod-exp`
5×	`pow1` `div-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `associate-/l*` `add-log-exp`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-r` `pow-exp` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg` `cbrt-unprod` `div-inv`
1×	`pow-pow` `tan-quot` `associate-/r/` `*-commutative`

Counts

4 → 105

Calls

4 calls:

5.0ms	(/ x (tan B))
9.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
11.0ms	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
3.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series879.0ms

Counts

4 → 12

Calls

4 calls:

185.0ms	(/ x (tan B))
151.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
232.0ms	(/ (* (pow (fma x 2 (fma F F 2)) -1/2) F) (sin B))
310.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.3s

Counts

117 → 117

Iterations

Iter	Nodes
done	2000
3	2000
2	1351
1	481
0	220

prune1.8s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.3b	(expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))
0.9b	(/ (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))) (sin B))
19.2b	(pow (fma x 2 (fma F F 2)) -1/2)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity` `add-cube-cbrt`
12×	`add-exp-log`
9×	`times-frac`
8×	`add-cbrt-cube`
7×	`unpow-prod-down` `associate-l`
5×	`pow1` `log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`pow-unpow` `associate-/r` `associate-r` `prod-exp` `associate-/l` `unswap-sqr` `sqr-pow`
2×	`pow-to-exp` `pow-exp`
1×	`cbrt-undiv` `expm1-log1p` `clear-num` `pow-pow` `frac-2neg` `div-exp` `*-commutative` `cbrt-unprod` `div-inv` `expm1-udef`

Counts

4 → 90

Calls

4 calls:

9.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.0ms	(expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))
5.0ms	(/ (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))) (sin B))
2.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series1.3s

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
182.0ms	(expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))
665.0ms	(/ (log1p (expm1 (* (pow (fma x 2 (fma F F 2)) -1/2) F))) (sin B))
302.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

simplify1.1s

Counts

102 → 102

Iterations

Iter	Nodes
done	2004
3	2004
2	1006
1	406
0	190

prune1.9s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.2b

localize61.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
0.9b	(/ (log1p (expm1 (* (* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2)) F))) (sin B))
19.2b	(sqrt (fma x 2 (fma F F 2)))
19.2b	(sqrt (fma x 2 (fma F F 2)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt`
44×	`unpow-prod-down`
28×	`sqrt-prod`
26×	`*-un-lft-identity` `add-cube-cbrt`
18×	`add-exp-log`
16×	`unswap-sqr`
12×	`swap-sqr` `sqr-pow`
10×	`associate-r` `associate-l`
9×	`times-frac` `prod-exp`
8×	`add-cbrt-cube`
6×	`pow-to-exp` `pow1` `pow-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`pow2` `cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `cbrt-unprod` `div-inv`

Counts

4 → 135

Calls

4 calls:

21.0ms	(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
5.0ms	(/ (log1p (expm1 (* (* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2)) F))) (sin B))
1.0ms	(sqrt (fma x 2 (fma F F 2)))
1.0ms	(sqrt (fma x 2 (fma F F 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2))
649.0ms	(/ (log1p (expm1 (* (* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (pow (sqrt (fma x 2 (fma F F 2))) -1/2)) F))) (sin B))
175.0ms	(sqrt (fma x 2 (fma F F 2)))
154.0ms	(sqrt (fma x 2 (fma F F 2)))

simplify1.1s

Counts

147 → 147

Iterations

Iter	Nodes
done	2001
3	2001
2	1080
1	376
0	185

prune2.4s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.2b

regimes517.0ms

Accuracy

0% (0.7b remaining)

Error of 11.0b against oracle of 10.3b and baseline of 11.0b

bsearch0.0ms

simplify4.0ms

Iterations

Iter	Nodes
done	19
1	19
0	18

end0.0ms

sample13.1s

Algorithm

intervals

Results

4.6s	1575×	body	1280	valid
4.0s	1430×	body	640	valid
2.1s	4800×	body	80	valid
914.0ms	722×	body	320	valid
645.0ms	1614×	body	80	nan
371.0ms	374×	body	160	valid