Details

sample726.0ms

Algorithm

intervals

Results

269.0ms	56×	body	1280	valid
138.0ms	43×	body	640	valid
108.0ms	153×	body	80	valid
65.0ms	59×	body	80	nan
30.0ms	20×	body	320	valid
9.0ms	9×	body	160	valid

simplify464.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

463.0ms

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

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.5b

localize60.0ms

Local error

Found 4 expressions with local error:

17.3b	(pow (fma 2 x (fma F F 2)) -1/2)
7.9b	(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.2b	(/ x (tan B))
0.1b	(/ (sin B) F)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

181×	`times-frac`
106×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
45×	`unpow-prod-down`
22×	`add-exp-log`
19×	`associate-/r*`
15×	`sqr-pow`
13×	`add-cbrt-cube` `associate-/l*`
11×	`div-exp` `div-inv`
5×	`pow1` `cbrt-undiv`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-unpow` `clear-num` `frac-2neg` `pow-exp`
2×	`associate-/r/`
1×	`pow-pow` `tan-quot`

Counts

4 → 214

Calls

4 calls:

Slowest

12.0ms	(/ (sin B) F)
11.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
8.0ms	(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
5.0ms	(/ x (tan B))

series732.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

306.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
219.0ms	(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
166.0ms	(/ x (tan B))
40.0ms	(/ (sin B) F)

simplify1.1m

Counts

342 → 226

Calls

342 calls:

Slowest

709.0ms	(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
708.0ms	(/ (sqrt (pow (fma 2 x (fma F F 2)) -1/2)) (sin B))
658.0ms	(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ (* (cbrt (sin B)) (cbrt (sin B))) (sqrt F)))
640.0ms	(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) 1)
637.0ms	(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ (sqrt (sin B)) 1))

prune3.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 10.9b

localize34.0ms

Local error

Found 4 expressions with local error:

17.3b	(pow (fma x 2 (fma F F 2)) -1/2)
0.8b	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
0.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
0.2b	(/ x (tan B))

rewrite48.0ms

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×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-r` `insert-posit16` `log1p-expm1-u` `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 → 126

Calls

4 calls:

Slowest

29.0ms	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
8.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
6.0ms	(/ x (tan B))
2.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series749.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

262.0ms	(pow (fma x 2 (fma F F 2)) -1/2)
174.0ms	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
164.0ms	(/ x (tan B))
149.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)

simplify33.7s

Counts

153 → 138

Calls

153 calls:

Slowest

753.0ms	(/ (* (* x x) x) (* (* (tan B) (tan B)) (tan B)))
647.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
619.0ms	(sqrt (* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F)))
612.0ms	(* (/ 1 (sqrt (sin B))) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
611.0ms	(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))

prune2.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 10.9b

localize50.0ms

Local error

Found 4 expressions with local error:

17.3b	(pow (fma x 2 (fma F F 2)) -1/2)
0.4b	(/ (pow (fma x 2 (fma F F 2)) -1/2) (sin B))
0.2b	(* (/ (pow (fma x 2 (fma F F 2)) -1/2) (sin B)) F)
0.2b	(/ x (tan B))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

55×	`add-sqr-sqrt`
54×	`times-frac`
45×	`*-un-lft-identity` `add-cube-cbrt`
25×	`unpow-prod-down` `associate-l`
22×	`add-exp-log`
13×	`add-cbrt-cube`
10×	`associate-/l*`
9×	`sqr-pow`
7×	`pow1` `div-exp`
6×	`associate-/r*`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`pow-to-exp` `cbrt-undiv` `pow-unpow` `associate-r` `pow-exp` `div-inv`
2×	`clear-num` `frac-2neg` `cbrt-unprod`
1×	`pow-pow` `pow-prod-down` `associate-l/` `tan-quot` `associate-/r/` `-commutative`

Counts

4 → 150

Calls

4 calls:

Slowest

13.0ms	(* (/ (pow (fma x 2 (fma F F 2)) -1/2) (sin B)) F)
9.0ms	(/ x (tan B))
7.0ms	(/ (pow (fma x 2 (fma F F 2)) -1/2) (sin B))
2.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series799.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

276.0ms	(pow (fma x 2 (fma F F 2)) -1/2)
224.0ms	(* (/ (pow (fma x 2 (fma F F 2)) -1/2) (sin B)) F)
164.0ms	(/ (pow (fma x 2 (fma F F 2)) -1/2) (sin B))
135.0ms	(/ x (tan B))

simplify36.7s

Counts

201 → 162

Calls

201 calls:

Slowest

1.0s	(* (* (* (/ (pow (fma x 2 (fma F F 2)) -1/2) (sin B)) F) (* (/ (pow (fma x 2 (fma F F 2)) -1/2) (sin B)) F)) (* (/ (pow (fma x 2 (fma F F 2)) -1/2) (sin B)) F))
820.0ms	(* (* (* (/ (pow (fma x 2 (fma F F 2)) -1/2) (sin B)) (/ (pow (fma x 2 (fma F F 2)) -1/2) (sin B))) (/ (pow (fma x 2 (fma F F 2)) -1/2) (sin B))) (* (* F F) F))
776.0ms	(/ (* (* (pow (fma x 2 (fma F F 2)) -1/2) (pow (fma x 2 (fma F F 2)) -1/2)) (pow (fma x 2 (fma F F 2)) -1/2)) (* (* (sin B) (sin B)) (sin B)))
650.0ms	(/ (pow (* (cbrt (fma x 2 (fma F F 2))) (cbrt (fma x 2 (fma F F 2)))) -1/2) 1)
619.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))

prune2.5s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.9b

localize85.0ms

Local error

Found 4 expressions with local error:

17.3b	(pow (fma x 2 (fma F F 2)) -1/2)
0.8b	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
0.2b	(/ 1 (/ (tan B) x))
0.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
65×	`add-exp-log`
63×	`add-sqr-sqrt`
58×	`*-un-lft-identity` `add-cube-cbrt`
31×	`prod-exp`
23×	`add-cbrt-cube`
20×	`associate-l`
15×	`div-exp`
13×	`associate-/r*`
8×	`pow1`
7×	`unpow-prod-down` `cbrt-unprod`
6×	`pow-to-exp` `rec-exp` `1-exp` `pow-exp` `div-inv`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `associate-/l*` `unswap-sqr` `sqr-pow`
2×	`*-commutative`
1×	`clear-num` `pow-pow` `frac-2neg` `pow-prod-down` `associate-*l/` `associate-/r/` `pow-flip` `inv-pow`

Counts

4 → 174

Calls

4 calls:

Slowest

33.0ms	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
16.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
6.0ms	(/ 1 (/ (tan B) x))
4.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series669.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

274.0ms	(pow (fma x 2 (fma F F 2)) -1/2)
146.0ms	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
129.0ms	(/ 1 (/ (tan B) x))
120.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)

simplify39.2s

Counts

230 → 186

Calls

230 calls:

Slowest

950.0ms	(* (/ (cbrt 1) (sqrt (sin B))) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
651.0ms	(real->posit16 (* (pow (fma x 2 (fma F F 2)) -1/2) F))
627.0ms	(sqrt (* (pow (fma x 2 (fma F F 2)) -1/2) F))
626.0ms	(* (cbrt (* (pow (fma x 2 (fma F F 2)) -1/2) F)) (cbrt (* (pow (fma x 2 (fma F F 2)) -1/2) F)))
625.0ms	(expm1 (* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F)))

prune2.9s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 10.9b

regimes473.0ms

Accuracy

0% (0.6b remaining)

Error of 10.4b against oracle of 9.8b and baseline of 10.4b

bsearch4.0ms

end0.0ms

sample14.0s

Algorithm

intervals

Results

6.0s	1650×	body	1280	valid
3.3s	1356×	body	640	valid
2.3s	4779×	body	80	valid
929.0ms	715×	body	320	valid
685.0ms	1629×	body	80	nan
459.0ms	354×	body	160	valid