Details

sample459.0ms

Algorithm

intervals

Results

163.0ms	55×	body	1280	valid
102.0ms	47×	body	640	valid
53.0ms	136×	body	80	valid
27.0ms	26×	body	320	valid
13.0ms	39×	body	80	nan
10.0ms	13×	body	160	valid

simplify1.1s

Counts: 1 → 1

prune42.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.4b

localize47.0ms

Local error

Found 4 expressions with local error:

15.7b	(pow (fma 2 x (fma F F 2)) -1/2)
6.4b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
0.1b	(/ x (tan B))
0.1b	(/ F (sin B))

rewrite38.0ms

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:

Slowest

14.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
5.0ms	(/ x (tan B))
5.0ms	(/ F (sin B))
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series729.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

281.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
215.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
153.0ms	(/ x (tan B))
80.0ms	(/ F (sin B))

simplify2.8s

Counts: 139 → 139

prune2.2s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 7.4b

localize52.0ms

Local error

Found 4 expressions with local error:

15.7b	(pow (fma 2 x (fma F F 2)) -1/2)
0.7b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.1b	(/ x (tan B))

rewrite62.0ms

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:

Slowest

22.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
16.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
12.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
10.0ms	(/ x (tan B))

series784.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

251.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
247.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
158.0ms	(/ x (tan B))
127.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify2.6s

Counts: 117 → 117

prune1.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 7.4b

localize54.0ms

Local error

Found 4 expressions with local error:

15.7b	(pow (fma 2 x (fma F F 2)) -1/2)
0.7b	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
0.3b	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

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:

Slowest

9.0ms	(* (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)
0.0ms	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))

series1.2s

Counts

4 → 12

Calls

4 calls:

Slowest

549.0ms	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
242.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
212.0ms	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))
171.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify2.0s

Counts: 102 → 102

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.4b

localize46.0ms

Local error

Found 4 expressions with local error:

15.7b	(pow (fma 2 x (fma F F 2)) -1/2)
0.7b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b	(* (/ x (sin B)) (cos B))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

Slowest

24.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
21.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
14.0ms	(* (/ x (sin B)) (cos B))
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series782.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

256.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
226.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
168.0ms	(* (/ x (sin B)) (cos B))
131.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify779.0ms

Counts: 121 → 121

prune2.0s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.4b

regimes296.0ms

Accuracy

0% (0.6b remaining)

Error of 10.2b against oracle of 9.6b and baseline of 10.2b

bsearch3.0ms

end0.0ms

sample14.7s

Algorithm

intervals

Results

6.0s	1688×	body	1280	valid
3.9s	1417×	body	640	valid
2.1s	4789×	body	80	valid
962.0ms	672×	body	320	valid
796.0ms	1672×	body	80	nan
475.0ms	378×	body	160	valid