Details

sample525.0ms

Algorithm

intervals

Results

159.0ms	50×	body	1280	valid
91.0ms	54×	body	640	valid
77.0ms	28×	body	320	valid
57.0ms	146×	body	80	valid
15.0ms	44×	body	80	nan
7.0ms	8×	body	160	valid

simplify1.1s

Counts

1 → 1

Iterations

Iter	Nodes
6	2046
5	644
4	269
3	138
2	87
1	45
0	20

prune34.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.1b

localize73.0ms

Local error

Found 4 expressions with local error:

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

rewrite61.0ms

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:

10.0ms	(/ F (sin B))
10.0ms	(/ x (tan B))
29.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
7.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series753.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(/ F (sin B))
162.0ms	(/ x (tan B))
209.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
312.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.3s

Counts

139 → 139

Iterations

Iter	Nodes
3	4408
2	1378
1	517
0	244

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.2b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

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:

10.0ms	(/ x (tan B))
19.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
23.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
5.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series867.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ x (tan B))
161.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
263.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
302.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify3.1s

Counts

117 → 117

Iterations

Iter	Nodes
3	4742
2	1239
1	456
0	220

prune951.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.2b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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:

17.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.0ms	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))
5.0ms	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
2.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series1.1s

Counts

4 → 12

Calls

4 calls:

141.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
187.0ms	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))
506.0ms	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
295.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

simplify2.0s

Counts

102 → 102

Iterations

Iter	Nodes
3	3473
2	995
1	385
0	190

prune840.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.2b

localize74.0ms

Local error

Found 4 expressions with local error:

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

rewrite45.0ms

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:

32.0ms	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2))
6.0ms	(/ (log1p (expm1 (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) F))) (sin B))
1.0ms	(sqrt (fma 2 x (fma F F 2)))
1.0ms	(sqrt (fma 2 x (fma F F 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

114.0ms	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2))
636.0ms	(/ (log1p (expm1 (* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) F))) (sin B))
172.0ms	(sqrt (fma 2 x (fma F F 2)))
153.0ms	(sqrt (fma 2 x (fma F F 2)))

simplify2.3s

Counts

147 → 147

Iterations

Iter	Nodes
3	4805
2	1102
1	374
0	185

prune934.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.2b

regimes846.0ms

Accuracy

0% (0.6b remaining)

Error of 10.9b against oracle of 10.3b and baseline of 10.9b

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
1	15
0	15

end0.0ms

sample13.6s

Algorithm

intervals

Results

5.5s	1575×	body	1280	valid
3.2s	1430×	body	640	valid
2.3s	4800×	body	80	valid
1.2s	722×	body	320	valid
817.0ms	1614×	body	80	nan
362.0ms	374×	body	160	valid