Details

sample546.0ms

Algorithm

intervals

Results

128.0ms	68×	body	1280	valid
123.0ms	127×	body	80	valid
60.0ms	41×	body	640	valid
24.0ms	19×	body	320	valid
17.0ms	66×	body	80	nan
9.0ms	15×	body	160	valid

simplify1.4s

Counts: 1 → 1

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize44.0ms

Local error

Found 4 expressions with local error:

17.5b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
6.9b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
0.2b	(/ x (tan B))
0.1b	(/ F (sin B))

rewrite180.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

Slowest

130.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
34.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
6.0ms	(/ F (sin B))
5.0ms	(/ x (tan B))

series568.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

232.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) (/ F (sin B)))
128.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
120.0ms	(/ x (tan B))
87.0ms	(/ F (sin B))

simplify1.8s

Counts: 131 → 131

prune1.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize72.0ms

Local error

Found 4 expressions with local error:

17.5b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.8b	(/ (* (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))

rewrite210.0ms

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

95.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
64.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
44.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
5.0ms	(/ x (tan B))

series621.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

222.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
169.0ms	(/ x (tan B))
125.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
105.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify2.6s

Counts: 109 → 109

prune1.7s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize56.0ms

Local error

Found 4 expressions with local error:

18.0b	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
18.0b	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
0.8b	(/ (* (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))

rewrite401.0ms

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

222.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))
121.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))
36.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
18.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))

series586.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

208.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F)) (sin B))
149.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))
117.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) (* (pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2)) F))
112.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) (/ -1/2 2))

simplify1.1s

Counts: 133 → 133

prune2.3s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize73.0ms

Local error

Found 4 expressions with local error:

17.5b	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
0.8b	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
0.3b	(/ 1 (/ (tan B) x))
0.3b	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

rewrite194.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 145

Calls

4 calls:

Slowest

109.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)
38.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
35.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
7.0ms	(/ 1 (/ (tan B) x))

series602.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

246.0ms	(/ (* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F) (sin B))
128.0ms	(/ 1 (/ (tan B) x))
118.0ms	(pow (+ (+ 2 (* F F)) (* 2 x)) -1/2)
110.0ms	(* (pow (+ (+ 2 (* F F)) (* 2 x)) -1/2) F)

simplify1.0s

Counts: 157 → 157

prune2.3s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes313.0ms

Accuracy

97% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 10.6b

bsearch506.0ms

end0.0ms

sample14.4s

Algorithm

intervals

Results

4.9s	1709×	body	1280	valid
3.2s	4765×	body	80	valid
2.8s	1323×	body	640	valid
2.0s	712×	body	320	valid
678.0ms	1624×	body	80	nan
394.0ms	333×	body	160	valid