Details

sample584.0ms

Algorithm

intervals

Results

152.0ms	55×	body	1280	valid
145.0ms	52×	body	640	valid
88.0ms	137×	body	80	valid
34.0ms	23×	body	320	valid
20.0ms	50×	body	80	nan
10.0ms	12×	body	160	valid

simplify333.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

332.0ms

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

prune37.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 10.7b

localize79.0ms

Local error

Found 4 expressions with local error:

19.4b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b	(/ (* (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))

rewrite162.0ms

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

84.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
41.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
24.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
10.0ms	(/ x (tan B))

series576.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

206.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
152.0ms	(/ x (tan B))
122.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
95.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify11.6s

Counts

79 → 109

Calls

79 calls:

Slowest

1.1s	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
714.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
683.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
669.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)
650.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

19.4b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b	(/ (* (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))

rewrite210.0ms

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

107.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
53.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
37.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
12.0ms	(/ (* x (cos B)) (sin B))

series598.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

230.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
144.0ms	(/ (* x (cos B)) (sin B))
114.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
110.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify11.4s

Counts

66 → 102

Calls

66 calls:

Slowest

697.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
681.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)
680.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
620.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
609.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))

prune1.6s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize59.0ms

Local error

Found 4 expressions with local error:

20.0b	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
20.0b	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
0.3b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))

rewrite432.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

Slowest

194.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))
160.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))
44.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
29.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))

series606.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

230.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))
150.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
136.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
91.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))

simplify16.6s

Counts

94 → 133

Calls

94 calls:

Slowest

920.0ms	(/ (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))) (* (* (sin B) (sin B)) (sin B)))
712.0ms	(/ (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (* (* F F) F))) (* (* (sin B) (sin B)) (sin B)))
635.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) 1)
629.0ms	(/ (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))) (* (* (sin B) (sin B)) (sin B)))
625.0ms	(+ (* (log (+ (+ 2 (* F F)) (* 2 x))) (/ -1/2 2)) (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)))

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize83.0ms

Local error

Found 4 expressions with local error:

20.0b	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
19.4b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.4b	(pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2)
0.3b	(/ (* (pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))

rewrite286.0ms

Algorithm

rewrite-expression-head

Rules

72×	`add-exp-log`
35×	`prod-exp`
27×	`pow-exp`
21×	`div-exp`
19×	`add-sqr-sqrt` `pow-unpow` `*-un-lft-identity` `add-cube-cbrt`
17×	`pow-to-exp`
16×	`unpow-prod-down`
13×	`add-cbrt-cube`
12×	`times-frac`
6×	`pow1`
4×	`insert-posit16` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `associate-/r*` `pow-pow` `cbrt-unprod`
2×	`div-inv`
1×	`clear-num` `frac-2neg` `associate-/l*` `unpow1/2`

Counts

4 → 113

Calls

4 calls:

Slowest

187.0ms	(/ (* (pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))
41.0ms	(pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2)
35.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
22.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))

series682.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

255.0ms	(/ (* (pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))
195.0ms	(pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2)
129.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
103.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify15.7s

Counts

84 → 125

Calls

84 calls:

Slowest

1.0s	(/ (* (* (* (pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2) (pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2)) (pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2)) (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))) (* (* F F) F))) (* (* (sin B) (sin B)) (sin B)))
959.0ms	(/ (* (* (* (pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2) (pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2)) (pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2)) (* (* (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))) (* (* (sin B) (sin B)) (sin B)))
847.0ms	(/ (* (* (* (pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (* (pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))) (* (pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))) (* (* (sin B) (sin B)) (sin B)))
446.0ms	(- (log (* (pow (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1/2) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))) (log (sin B)))
445.0ms	(* (log (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) 1/2)

prune2.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes445.0ms

Accuracy

98.5% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.5b

bsearch723.0ms

end0.0ms

sample14.5s

Algorithm

intervals

Results

5.8s	1691×	body	1280	valid
3.3s	1368×	body	640	valid
2.5s	4698×	body	80	valid
1.4s	703×	body	320	valid
748.0ms	1637×	body	80	nan
347.0ms	382×	body	160	valid