Details

sample504.0ms

Algorithm

intervals

Results

197.0ms	53×	body	1280	valid
80.0ms	47×	body	640	valid
58.0ms	149×	body	80	valid
49.0ms	20×	body	320	valid
24.0ms	61×	body	80	nan
8.0ms	9×	body	160	valid

simplify1.2s

Counts: 1 → 1

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize72.0ms

Local error

Found 4 expressions with local error:

19.0b	(pow (fma 2 x (fma F F 2)) -1/2)
4.8b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
0.2b	(/ x (tan B))
0.2b	(/ F (sin B))

rewrite60.0ms

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

28.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
10.0ms	(/ x (tan B))
9.0ms	(/ F (sin B))
8.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series696.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

277.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
222.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
127.0ms	(/ x (tan B))
70.0ms	(/ F (sin B))

simplify2.6s

Counts: 139 → 139

prune2.2s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 9.8b

localize43.0ms

Local error

Found 4 expressions with local error:

19.0b	(pow (fma 2 x (fma F F 2)) -1/2)
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
0.2b	(/ x (tan B))

rewrite35.0ms

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

15.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
10.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
5.0ms	(/ x (tan B))
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series799.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

286.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
225.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
148.0ms	(/ x (tan B))
140.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify2.7s

Counts: 117 → 117

prune1.8s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.8b

localize51.0ms

Local error

Found 4 expressions with local error:

19.0b	(pow (fma 2 x (fma F F 2)) -1/2)
0.2b	(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)
0.2b	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))

rewrite36.0ms

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

25.0ms	(* (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))
4.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
1.0ms	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

591.0ms	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
232.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
188.0ms	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))
139.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify1.7s

Counts: 102 → 102

prune1.9s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 9.8b

localize58.0ms

Local error

Found 4 expressions with local error:

19.0b	(pow (fma 2 x (fma F F 2)) -1/2)
0.2b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
0.2b	(* (/ x (sin B)) (cos B))

rewrite44.0ms

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

19.0ms	(* (/ x (sin B)) (cos B))
11.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
9.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
3.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series843.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

315.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
236.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
151.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
141.0ms	(* (/ x (sin B)) (cos B))

simplify866.0ms

Counts: 121 → 121

prune1.8s

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 9.8b

regimes344.0ms

Accuracy

0% (0.6b remaining)

Error of 10.5b against oracle of 9.9b and baseline of 10.5b

bsearch4.0ms

end0.0ms

sample14.3s

Algorithm

intervals

Results

6.1s	1735×	body	1280	valid
2.9s	1382×	body	640	valid
2.6s	4722×	body	80	valid
1.1s	1651×	body	80	nan
984.0ms	732×	body	320	valid
322.0ms	320×	body	160	valid