Details

sample426.0ms

Algorithm

intervals

Results

96.0ms	49×	body	1280	valid
76.0ms	140×	body	80	valid
68.0ms	48×	body	640	valid
21.0ms	22×	body	320	valid
14.0ms	55×	body	80	nan
8.0ms	12×	body	160	valid

simplify344.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

343.0ms

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

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.4b

localize45.0ms

Local error

Found 4 expressions with local error:

17.3b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.6b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b	(/ x (tan B))

rewrite207.0ms

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

98.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
69.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
32.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
5.0ms	(/ x (tan B))

series575.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

203.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
136.0ms	(/ x (tan B))
128.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
108.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify10.7s

Counts

79 → 109

Calls

79 calls:

Slowest

655.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
584.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
552.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
551.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
444.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

17.3b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.6b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b	(* (/ x (sin B)) (cos B))

rewrite208.0ms

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

93.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
50.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
34.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
29.0ms	(* (/ x (sin B)) (cos B))

series547.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

209.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
135.0ms	(* (/ x (sin B)) (cos B))
107.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
96.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify10.8s

Counts

77 → 113

Calls

77 calls:

Slowest

591.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
578.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
549.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
455.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)
447.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

17.3b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.6b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b	(/ (* x (cos B)) (sin B))

rewrite202.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

Slowest

104.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
42.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
30.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
24.0ms	(/ (* x (cos B)) (sin B))

series584.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

228.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
137.0ms	(/ (* x (cos B)) (sin B))
110.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
109.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify10.3s

Counts

66 → 102

Calls

66 calls:

Slowest

551.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
544.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)
533.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
507.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
505.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))

prune1.6s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize47.0ms

Local error

Found 4 expressions with local error:

17.3b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.6b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.3b	(* x (/ (cos B) (sin B)))

rewrite262.0ms

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

132.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
63.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
43.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
21.0ms	(* x (/ (cos B) (sin B)))

series505.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

189.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
122.0ms	(* x (/ (cos B) (sin B)))
98.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
96.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify10.2s

Counts

78 → 113

Calls

78 calls:

Slowest

571.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
564.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
560.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
532.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
470.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.6s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes523.0ms

Accuracy

98.2% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.4b

bsearch1.1s

end0.0ms

sample13.5s

Algorithm

intervals

Results

5.7s	1744×	body	1280	valid
2.8s	1363×	body	640	valid
2.3s	4754×	body	80	valid
1.4s	642×	body	320	valid
642.0ms	1557×	body	80	nan
341.0ms	363×	body	160	valid