Details

sample924.0ms

Algorithm

intervals

Results

651.0ms	48×	body	1280	valid
87.0ms	50×	body	640	valid
66.0ms	154×	body	80	valid
30.0ms	22×	body	320	valid
14.0ms	39×	body	80	nan
13.0ms	13×	body	160	valid

simplify449.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

448.0ms

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

prune20.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.2b

localize43.0ms

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

rewrite212.0ms

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

94.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
62.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
43.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
9.0ms	(/ x (tan B))

series606.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

227.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
153.0ms	(/ x (tan B))
115.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
111.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify10.1s

Counts

79 → 109

Calls

79 calls:

Slowest

633.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
622.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
547.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
536.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
443.0ms	(/ (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

localize37.0ms

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

rewrite199.0ms

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

98.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
61.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
21.0ms	(/ (* x (cos B)) (sin B))
17.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

series602.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

230.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
133.0ms	(/ (* x (cos B)) (sin B))
121.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
118.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify9.9s

Counts

66 → 102

Calls

66 calls:

Slowest

598.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
556.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)
529.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
485.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
477.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))

prune1.5s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

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

rewrite217.0ms

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

95.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
61.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
31.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
27.0ms	(* (/ x (sin B)) (cos B))

series580.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

242.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
131.0ms	(* (/ x (sin B)) (cos B))
121.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
85.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify10.6s

Counts

77 → 113

Calls

77 calls:

Slowest

630.0ms	(* (sqrt (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (sqrt F))
604.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
518.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
507.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
498.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))

prune1.7s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

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

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-exp-log`
36×	`times-frac`
32×	`add-sqr-sqrt`
27×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube`
16×	`div-exp`
10×	`associate-/r*`
9×	`prod-exp`
7×	`cbrt-undiv` `unpow-prod-down` `associate-l`
6×	`pow1` `div-inv`
4×	`insert-posit16` `associate-/l*` `add-log-exp`
3×	`pow-to-exp` `rec-exp` `pow-unpow` `1-exp` `associate-r` `pow-exp` `cbrt-unprod` `unswap-sqr` `sqr-pow`
2×	`clear-num` `frac-2neg`
1×	`pow-pow` `associate-/r/` `*-commutative` `pow-flip` `inv-pow`

Counts

4 → 125

Calls

4 calls:

Slowest

127.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
61.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
22.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
17.0ms	(/ 1 (/ (sin B) (* x (cos B))))

series555.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

242.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
114.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
106.0ms	(/ 1 (/ (sin B) (* x (cos B))))
93.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify13.3s

Counts

115 → 137

Calls

115 calls:

Slowest

627.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
614.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
608.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
520.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)
489.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))

prune2.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes348.0ms

Accuracy

98.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 10.8b

bsearch524.0ms

end0.0ms

sample13.6s

Algorithm

intervals

Results

5.2s	1658×	body	1280	valid
3.8s	1380×	body	640	valid
2.0s	4823×	body	80	valid
1.0s	711×	body	320	valid
986.0ms	1607×	body	80	nan
296.0ms	364×	body	160	valid