Details

sample552.0ms

Algorithm

intervals

Results

194.0ms	52×	body	1280	valid
106.0ms	151×	body	80	valid
92.0ms	44×	body	640	valid
31.0ms	22×	body	320	valid
21.0ms	51×	body	80	nan
6.0ms	8×	body	160	valid

simplify443.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

442.0ms

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

prune39.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.5b

localize79.0ms

Local error

Found 4 expressions with local error:

19.0b	(pow (fma 2 x (fma F F 2)) -1/2)
6.6b	(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
0.1b	(/ x (tan B))
0.1b	(/ (sin B) F)

rewrite35.0ms

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

9.0ms	(/ (sin B) F)
8.0ms	(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
5.0ms	(/ x (tan B))
3.0ms	(pow (fma 2 x (fma F F 2)) -1/2)

series689.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

279.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
233.0ms	(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
135.0ms	(/ x (tan B))
42.0ms	(/ (sin B) F)

simplify54.1s

Counts

278 → 226

Calls

278 calls:

Slowest

703.0ms	(- (+ (* 3/2 (/ (* (sqrt 1/32) (* (pow x 2) F)) B)) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))
699.0ms	(/ (pow (* (cbrt (fma 2 x (fma F F 2))) (cbrt (fma 2 x (fma F F 2)))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
643.0ms	(/ (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (/ 1 (* (cbrt F) (cbrt F))))
632.0ms	(/ (pow (fma 2 x (fma F F 2)) -1/2) (/ (sin B) F))
630.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))

prune3.7s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.2b

localize58.0ms

Local error

Found 4 expressions with local error:

19.0b	(pow (fma x 2 (fma F F 2)) -1/2)
0.6b	(* (/ 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)
0.1b	(/ x (tan B))

rewrite72.0ms

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

31.0ms	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
25.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
10.0ms	(/ x (tan B))
2.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series699.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

256.0ms	(pow (fma x 2 (fma F F 2)) -1/2)
151.0ms	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
149.0ms	(/ x (tan B))
142.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)

simplify12.8s

Counts

96 → 138

Calls

96 calls:

Slowest

556.0ms	(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))
537.0ms	(+ (- (log (sin B))) (+ (log (pow (fma x 2 (fma F F 2)) -1/2)) (log F)))
534.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
465.0ms	(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))
463.0ms	(+ (- (log 1) (log (sin B))) (log (* (pow (fma x 2 (fma F F 2)) -1/2) F)))

prune2.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.2b

localize64.0ms

Local error

Found 4 expressions with local error:

19.0b	(pow (fma x 2 (fma F F 2)) -1/2)
0.6b	(* (/ 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 (sin B)) (cos B))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-exp-log`
34×	`add-sqr-sqrt`
33×	`associate-l` `prod-exp`
24×	`*-un-lft-identity` `add-cube-cbrt`
23×	`add-cbrt-cube`
19×	`times-frac`
9×	`pow1` `div-exp` `cbrt-unprod`
7×	`unpow-prod-down` `associate-r`
6×	`pow-to-exp` `pow-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `*-commutative` `sqr-pow`
2×	`pow-prod-down` `associate-*l/` `div-inv`
1×	`pow-pow`

Counts

4 → 130

Calls

4 calls:

Slowest

29.0ms	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
18.0ms	(* (/ x (sin B)) (cos B))
8.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
4.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series666.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

268.0ms	(pow (fma x 2 (fma F F 2)) -1/2)
142.0ms	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
135.0ms	(* (/ x (sin B)) (cos B))
122.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)

simplify13.4s

Counts

94 → 142

Calls

94 calls:

Slowest

1.0s	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
507.0ms	(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))
492.0ms	(+ (- (log (sin B))) (+ (log (pow (fma x 2 (fma F F 2)) -1/2)) (log F)))
469.0ms	(+ (- (log 1) (log (sin B))) (+ (log (pow (fma x 2 (fma F F 2)) -1/2)) (log F)))
456.0ms	(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))

prune2.3s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.2b

localize72.0ms

Local error

Found 4 expressions with local error:

19.0b	(pow (fma x 2 (fma F F 2)) -1/2)
0.6b	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
0.3b	(* x (/ 1 (tan B)))
0.2b	(* (pow (fma x 2 (fma F F 2)) -1/2) F)

rewrite90.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-exp-log`
36×	`add-sqr-sqrt`
35×	`prod-exp`
25×	`*-un-lft-identity`
24×	`add-cube-cbrt`
23×	`add-cbrt-cube` `associate-l`
20×	`times-frac`
18×	`associate-r`
10×	`div-exp`
9×	`pow1` `cbrt-unprod`
7×	`unpow-prod-down`
6×	`pow-to-exp` `pow-exp` `unswap-sqr`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `*-commutative` `sqr-pow`
2×	`pow-prod-down` `div-inv`
1×	`pow-pow` `associate-l/` `tan-quot` `associate-r/` `associate-/r/` `un-div-inv`

Counts

4 → 135

Calls

4 calls:

Slowest

41.0ms	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
26.0ms	(* x (/ 1 (tan B)))
17.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)
2.0ms	(pow (fma x 2 (fma F F 2)) -1/2)

series759.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

312.0ms	(pow (fma x 2 (fma F F 2)) -1/2)
155.0ms	(* x (/ 1 (tan B)))
148.0ms	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
144.0ms	(* (pow (fma x 2 (fma F F 2)) -1/2) F)

simplify14.0s

Counts

101 → 147

Calls

101 calls:

Slowest

603.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
574.0ms	(* (/ 1 (sin B)) (* (pow (fma x 2 (fma F F 2)) -1/2) F))
546.0ms	(+ (- (log (sin B))) (+ (log (pow (fma x 2 (fma F F 2)) -1/2)) (log F)))
481.0ms	(+ (- (log 1) (log (sin B))) (+ (log (pow (fma x 2 (fma F F 2)) -1/2)) (log F)))
471.0ms	(* (pow (sqrt (fma x 2 (fma F F 2))) -1/2) (sqrt F))

prune2.5s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.2b

regimes549.0ms

Accuracy

0% (0.7b remaining)

Error of 10.6b against oracle of 10.0b and baseline of 10.6b

bsearch5.0ms

end0.0ms

sample14.8s

Algorithm

intervals

Results

5.3s	1686×	body	1280	valid
3.4s	1351×	body	640	valid
3.0s	4853×	body	80	valid
1.3s	1658×	body	80	nan
1.0s	677×	body	320	valid
447.0ms	311×	body	160	valid