Details

sample537.0ms

Algorithm

intervals

Results

134.0ms	164×	body	80	valid
102.0ms	42×	body	1280	valid
84.0ms	54×	body	640	valid
38.0ms	29×	body	320	valid
25.0ms	66×	body	80	nan
5.0ms	7×	body	160	valid

simplify399.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

398.0ms

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

prune24.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.9b

localize71.0ms

Local error

Found 4 expressions with local error:

15.7b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.1b	(/ x (tan B))

rewrite165.0ms

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

75.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
58.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
25.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
5.0ms	(/ x (tan B))

series594.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

202.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
144.0ms	(/ x (tan B))
135.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
112.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify10.3s

Counts

79 → 109

Calls

79 calls:

Slowest

880.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
571.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
526.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
520.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
490.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.7s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize84.0ms

Local error

Found 4 expressions with local error:

15.7b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b	(/ (* x (cos B)) (sin B))

rewrite200.0ms

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

100.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
42.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
38.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
19.0ms	(/ (* x (cos B)) (sin B))

series536.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

206.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
133.0ms	(/ (* x (cos B)) (sin B))
102.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
95.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify9.9s

Counts

66 → 102

Calls

66 calls:

Slowest

582.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
563.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
560.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
547.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
460.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

15.7b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.2b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b	(* (/ x (sin B)) (cos B))

rewrite169.0ms

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

85.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
48.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
20.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
15.0ms	(* (/ x (sin B)) (cos B))

series589.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

224.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
142.0ms	(* (/ x (sin B)) (cos B))
113.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
109.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify10.8s

Counts

77 → 113

Calls

77 calls:

Slowest

586.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
576.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
568.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
530.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
514.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune2.1s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize89.0ms

Local error

Found 4 expressions with local error:

15.7b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b	(* (* x (cos B)) (/ 1 (sin B)))
0.2b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

rewrite235.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

Slowest

127.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
54.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
27.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
24.0ms	(* (* x (cos B)) (/ 1 (sin B)))

series532.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

197.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
137.0ms	(* (* x (cos B)) (/ 1 (sin B)))
105.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
92.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify12.2s

Counts

82 → 119

Calls

82 calls:

Slowest

679.0ms	(* (* (* (* x x) x) (* (* (cos B) (cos B)) (cos B))) (* (* (/ 1 (sin B)) (/ 1 (sin B))) (/ 1 (sin B))))
635.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
616.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
569.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
548.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))

prune1.8s

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

regimes483.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 10.9b

bsearch695.0ms

end0.0ms

sample14.2s

Algorithm

intervals

Results

4.9s	1665×	body	1280	valid
3.7s	1423×	body	640	valid
3.2s	4812×	body	80	valid
958.0ms	664×	body	320	valid
687.0ms	1624×	body	80	nan
311.0ms	320×	body	160	valid