Details

sample776.0ms

Algorithm

intervals

Results

238.0ms	53×	body	1280	valid
109.0ms	149×	body	80	valid
109.0ms	47×	body	640	valid
61.0ms	61×	body	80	nan
33.0ms	20×	body	320	valid
10.0ms	9×	body	160	valid

simplify1.2s

Counts: 1 → 1

prune27.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 12.5b

localize48.0ms

Local error

Found 4 expressions with local error:

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

rewrite202.0ms

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×	`insert-posit16` `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 → 119

Calls

4 calls:

Slowest

148.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
40.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
6.0ms	(/ x (tan B))
5.0ms	(/ F (sin B))

series579.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

250.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
150.0ms	(/ x (tan B))
112.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
67.0ms	(/ F (sin B))

simplify2.3s

Counts: 131 → 131

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

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

rewrite214.0ms

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×	`insert-posit16` `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 → 97

Calls

4 calls:

Slowest

111.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
48.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
43.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
11.0ms	(/ x (tan B))

series513.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

189.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
144.0ms	(/ x (tan B))
91.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
88.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify2.1s

Counts: 109 → 109

prune1.5s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

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

rewrite226.0ms

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×	`cbrt-unprod` `insert-posit16` `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 → 101

Calls

4 calls:

Slowest

108.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
64.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
38.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
15.0ms	(* (/ x (sin B)) (cos B))

series533.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

202.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
121.0ms	(* (/ x (sin B)) (cos B))
106.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
104.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify635.0ms

Counts: 113 → 113

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize85.0ms

Local error

Found 4 expressions with local error:

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

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`add-exp-log`
19×	`*-un-lft-identity` `add-cube-cbrt`
16×	`add-cbrt-cube` `associate-r`
13×	`times-frac`
10×	`associate-l`
8×	`prod-exp`
7×	`pow1` `unpow-prod-down`
5×	`div-exp` `unswap-sqr`
4×	`cbrt-unprod` `insert-posit16` `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-r/` `associate-/l`

Counts

4 → 101

Calls

4 calls:

Slowest

93.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
68.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
34.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
22.0ms	(* x (/ (cos B) (sin B)))

series625.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

220.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
169.0ms	(* x (/ (cos B) (sin B)))
133.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
103.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify642.0ms

Counts: 113 → 113

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

regimes214.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.6b

bsearch847.0ms

end0.0ms

sample14.5s

Algorithm

intervals

Results

5.9s	1735×	body	1280	valid
3.5s	1382×	body	640	valid
2.6s	4722×	body	80	valid
1.1s	732×	body	320	valid
791.0ms	1651×	body	80	nan
265.0ms	320×	body	160	valid