Details

sample544.0ms

Algorithm

intervals

Results

152.0ms	52×	body	1280	valid
93.0ms	49×	body	640	valid
68.0ms	61×	body	80	nan
68.0ms	149×	body	80	valid
17.0ms	15×	body	320	valid
14.0ms	17×	body	160	valid

simplify357.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

356.0ms

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

prune41.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.5b

localize76.0ms

Local error

Found 4 expressions with local error:

14.9b	(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))

rewrite261.0ms

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

145.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
63.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
39.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
10.0ms	(/ x (tan B))

series645.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

222.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
158.0ms	(/ x (tan B))
135.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
130.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify10.8s

Counts

79 → 109

Calls

79 calls:

Slowest

953.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
575.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
570.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
495.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
454.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.5s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize39.0ms

Local error

Found 4 expressions with local error:

14.9b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b	(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b	(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 131

Calls

4 calls:

Slowest

78.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
78.0ms	(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
37.0ms	(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
24.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

series630.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

228.0ms	(/ 1 (/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
208.0ms	(/ (sin B) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
99.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
95.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify26.3s

Counts

117 → 143

Calls

117 calls:

Slowest

837.0ms	(- (pow 2 -1/2) (+ (* 1/2 (* (pow F 2) (sqrt 1/8))) (* 1/2 (* x (sqrt 1/2)))))
798.0ms	(/ 1 (/ 1 (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))
625.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
618.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
605.0ms	(/ (sqrt 1) (/ 1 (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)))

prune2.1s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize64.0ms

Local error

Found 4 expressions with local error:

14.9b	(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 (sin B)) (cos B))

rewrite184.0ms

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

80.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
55.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
25.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
23.0ms	(* (/ x (sin B)) (cos B))

series555.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

216.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
145.0ms	(* (/ x (sin B)) (cos B))
100.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
94.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify10.5s

Counts

77 → 113

Calls

77 calls:

Slowest

656.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
570.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
561.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
501.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (sqrt F))
498.0ms	(/ (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) 1)

prune1.6s

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize45.0ms

Local error

Found 4 expressions with local error:

14.9b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
0.2b	(* (/ 1 (sin B)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
0.2b	(/ x (tan B))

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-exp-log`
31×	`prod-exp`
29×	`add-sqr-sqrt`
24×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube` `associate-l`
18×	`times-frac`
9×	`div-exp`
7×	`pow1` `unpow-prod-down` `cbrt-unprod`
6×	`pow-to-exp` `pow-exp`
4×	`rec-exp` `1-exp` `associate-r` `insert-posit16` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-/r` `associate-/l` `unswap-sqr` `sqr-pow`
2×	`*-commutative` `div-inv`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `tan-quot` `associate-/r/`

Counts

4 → 118

Calls

4 calls:

Slowest

104.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
93.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
19.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
10.0ms	(/ x (tan B))

series575.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

203.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
161.0ms	(/ x (tan B))
110.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
102.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)

simplify14.6s

Counts

96 → 130

Calls

96 calls:

Slowest

577.0ms	(+ (- (log 1) (log (sin B))) (log (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)))
572.0ms	(* (/ 1 (sin B)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F))
555.0ms	(* (pow (sqrt (+ (+ 2 (* F F)) (* 2 x))) -1/2) (sqrt F))
553.0ms	(+ (- (log (sin B))) (+ (log (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)) (log F)))
505.0ms	(* (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

regimes377.0ms

Accuracy

98.5% (0.2b remaining)

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

bsearch1.1s

end0.0ms

sample13.9s

Algorithm

intervals

Results

4.8s	1678×	body	1280	valid
3.4s	1427×	body	640	valid
2.6s	4739×	body	80	valid
1.5s	680×	body	320	valid
863.0ms	1664×	body	80	nan
412.0ms	331×	body	160	valid