Details

sample811.0ms

Algorithm

intervals

Results

463.0ms	41×	body	640	valid
106.0ms	48×	body	1280	valid
68.0ms	28×	body	320	valid
66.0ms	171×	body	80	valid
20.0ms	60×	body	80	nan
4.0ms	5×	body	160	valid

simplify137.0ms

Calls

1 calls:

Slowest

137.0ms

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

prune25.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 16.1b

localize42.0ms

Local error

Found 4 expressions with local error:

18.3b	(pow (fma 2 x (fma F F 2)) -1/2)
9.0b	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
0.1b	(/ x (tan B))
0.1b	(/ F (sin B))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity` `add-exp-log` `add-cube-cbrt`
6×	`associate-/r` `unpow-prod-down` `add-cbrt-cube` `associate-l*`
5×	`pow1`
4×	`expm1-log1p-u` `associate-r` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `div-inv`
2×	`pow-to-exp` `clear-num` `frac-2neg` `pow-exp`
1×	`pow-pow` `tan-quot` `associate-r/` `associate-/r/` `-commutative` `cbrt-unprod`

Calls

4 calls:

Slowest

6.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
3.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
1.0ms	(/ x (tan B))
1.0ms	(/ F (sin B))

series584.0ms

Calls

4 calls:

Slowest

219.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
165.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) (/ F (sin B)))
140.0ms	(/ x (tan B))
60.0ms	(/ F (sin B))

simplify2.1s

Calls

38 calls:

Slowest

327.0ms	(- (+ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) (* 3/8 (/ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) (pow x 2)))) (* 1/2 (/ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) x)))
264.0ms	(- (+ (* 3/8 (/ (exp (* -1/2 (- (log 2) (log (/ 1 x))))) (pow x 2))) (exp (* -1/2 (- (log 2) (log (/ 1 x)))))) (* 1/2 (/ (exp (* -1/2 (- (log 2) (log (/ 1 x))))) x)))
234.0ms	(* (* (* (pow (fma 2 x (fma F F 2)) -1/2) (pow (fma 2 x (fma F F 2)) -1/2)) (pow (fma 2 x (fma F F 2)) -1/2)) (* (* (/ F (sin B)) (/ F (sin B))) (/ F (sin B))))
218.0ms	(- (+ (* 3/2 (/ (* (sqrt 1/32) (* (pow x 2) F)) B)) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))
170.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))

prune1.4s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 12.7b

localize17.0ms

Local error

Found 4 expressions with local error:

18.3b	(pow (fma 2 x (fma F F 2)) -1/2)
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
0.1b	(/ x (tan B))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Calls

4 calls:

Slowest

15.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
8.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
3.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
1.0ms	(/ x (tan B))

series543.0ms

Calls

4 calls:

Slowest

194.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
155.0ms	(/ (* (pow (fma 2 x (fma F F 2)) -1/2) F) (sin B))
131.0ms	(/ x (tan B))
63.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify2.3s

Calls

38 calls:

Slowest

274.0ms	(- (+ (* 3/8 (/ (exp (* -1/2 (- (log 2) (log (/ 1 x))))) (pow x 2))) (exp (* -1/2 (- (log 2) (log (/ 1 x)))))) (* 1/2 (/ (exp (* -1/2 (- (log 2) (log (/ 1 x))))) x)))
271.0ms	(- (+ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) (* 3/8 (/ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) (pow x 2)))) (* 1/2 (/ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) x)))
244.0ms	(/ (* (* (* (pow (fma 2 x (fma F F 2)) -1/2) F) (* (pow (fma 2 x (fma F F 2)) -1/2) F)) (* (pow (fma 2 x (fma F F 2)) -1/2) F)) (* (* (sin B) (sin B)) (sin B)))
228.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
220.0ms	(- (+ (* 3/2 (/ (* (sqrt 1/32) (* (pow x 2) F)) B)) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))

prune1.3s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.7b

localize19.0ms

Local error

Found 4 expressions with local error:

18.3b	(pow (fma 2 x (fma F F 2)) -1/2)
0.3b	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
0.2b	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))
0.2b	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
7×	`add-exp-log`
6×	`unpow-prod-down` `add-cbrt-cube` `associate-l`
5×	`pow1` `log1p-expm1-u`
4×	`expm1-log1p-u` `insert-posit16` `add-log-exp`
3×	`associate-/r` `associate-/l`
1×	`pow-to-exp` `cbrt-undiv` `expm1-log1p` `clear-num` `pow-pow` `frac-2neg` `div-exp` `pow-exp` `*-commutative` `div-inv` `expm1-udef`

Calls

4 calls:

Slowest

5.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)
4.0ms	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
1.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
0.0ms	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))

series759.0ms

Calls

4 calls:

Slowest

386.0ms	(/ (log1p (expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))) (sin B))
194.0ms	(pow (fma 2 x (fma F F 2)) -1/2)
102.0ms	(expm1 (* (pow (fma 2 x (fma F F 2)) -1/2) F))
77.0ms	(* (pow (fma 2 x (fma F F 2)) -1/2) F)

simplify3.8s

Calls

48 calls:

Slowest

324.0ms	(- (+ (* 1/2 (* (pow F 2) (pow (sqrt 1/2) 2))) (* F (sqrt 1/2))) (* x (* F (sqrt 1/8))))
292.0ms	(- (+ (* 3/8 (/ (exp (* -1/2 (- (log 2) (log (/ 1 x))))) (pow x 2))) (exp (* -1/2 (- (log 2) (log (/ 1 x)))))) (* 1/2 (/ (exp (* -1/2 (- (log 2) (log (/ 1 x))))) x)))
287.0ms	(- (+ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) (* 3/8 (/ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) (pow x 2)))) (* 1/2 (/ (exp (* -1/2 (- (log -2) (log (/ -1 x))))) x)))
244.0ms	(- (+ (pow 2 -1/2) (* 3/2 (* (sqrt 1/32) (pow x 2)))) (* x (sqrt 1/8)))
221.0ms	(- (+ (* 3/2 (/ (* (sqrt 1/32) (* (pow x 2) F)) B)) (/ (* F (sqrt 1/2)) B)) (/ (* x (* F (sqrt 1/8))) B))

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.7b

localize25.0ms

Local error

Found 4 expressions with local error:

18.3b	(sqrt (fma 2 x (fma F F 2)))
18.3b	(sqrt (fma 2 x (fma F F 2)))
0.6b	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2))
0.3b	(* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) F)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-exp-log`
14×	`add-sqr-sqrt`
12×	`unpow-prod-down` `*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
10×	`associate-l`
9×	`associate-r` `prod-exp`
6×	`pow-to-exp` `add-cbrt-cube` `pow-exp`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `pow1/2` `*-commutative`
1×	`pow2` `pow-prod-down` `pow-prod-up` `cbrt-unprod`

Calls

4 calls:

Slowest

39.0ms	(* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) F)
15.0ms	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2))
1.0ms	(sqrt (fma 2 x (fma F F 2)))
1.0ms	(sqrt (fma 2 x (fma F F 2)))

series239.0ms

Calls

4 calls:

Slowest

79.0ms	(sqrt (fma 2 x (fma F F 2)))
59.0ms	(sqrt (fma 2 x (fma F F 2)))
56.0ms	(* (* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2)) F)
44.0ms	(* (pow (sqrt (fma 2 x (fma F F 2))) -1/2) (pow (sqrt (fma 2 x (fma F F 2))) -1/2))

simplify2.7s

Calls

51 calls:

Slowest

298.0ms	(- (+ (sqrt 2) (* x (sqrt 1/2))) (* 1/2 (* (pow x 2) (sqrt 1/8))))
238.0ms	(- (+ (sqrt 2) (* x (sqrt 1/2))) (* 1/2 (* (pow x 2) (sqrt 1/8))))
199.0ms	(- (+ (* 3/2 (* (sqrt 1/32) (* (pow x 2) F))) (* F (sqrt 1/2))) (* x (* F (sqrt 1/8))))
190.0ms	(- (+ (* 3/2 (* (sqrt 1/32) (pow x 2))) (sqrt 1/2)) (* x (sqrt 1/8)))
100.0ms	(+ (* (log (sqrt (fma 2 x (fma F F 2)))) -1/2) (* (log (sqrt (fma 2 x (fma F F 2)))) -1/2))

prune1.9s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.7b

regimes485.0ms

Accuracy

0% (0.7b remaining)

Error of 11.1b against oracle of 10.4b and baseline of 11.1b

bsearch8.0ms

end0.0ms

sample13.8s

Algorithm

intervals

Results

6.0s	1633×	body	1280	valid
3.2s	1421×	body	640	valid
2.2s	4788×	body	80	valid
1.0s	694×	body	320	valid
821.0ms	1621×	body	80	nan
341.0ms	325×	body	160	valid