Details

sample255.0ms

Algorithm

intervals

Results

76.0ms	87×	body	1280	valid
48.0ms	49×	body	320	valid
45.0ms	81×	body	640	valid
30.0ms	256×	body	80	valid
4.0ms	17×	body	160	valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	14	15
1	24	14
2	45	14
3	91	14
4	222	14
5	605	14
6	2946	14
done	5000	14

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize45.0ms

Local error

Found 3 expressions with local error:

0.0b	(* J (- (exp l) (exp (- l))))
0.0b	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
6.3b	(- (exp l) (exp (- l)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
27×	`prod-diff`
24×	`add-cube-cbrt`
11×	`distribute-rgt-in` `distribute-lft-in`
5×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `sub-neg` `fma-neg` `associate-l` `log1p-expm1-u`
2×	`flip3--` `associate-*r/` `flip--` `distribute-lft-out--` `difference-of-squares`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

3 → 84

Calls

3 calls:

50.0ms	(* J (- (exp l) (exp (- l))))
0.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
26.0ms	(- (exp l) (exp (- l)))

series396.0ms

Counts

3 → 9

Calls

3 calls:

107.0ms	(* J (- (exp l) (exp (- l))))
246.0ms	(fma (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0)) U)
43.0ms	(- (exp l) (exp (- l)))

simplify1.0s

Counts

93 → 93

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	160	1865
1	360	1447
2	1501	1134
done	5002	964

prune600.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(* J (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5)))))
0.0b	(* 1/60 (pow l 5))
0.1b	(fma (* J (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5))))) (cos (/ K 2.0)) U)
0.1b	(fma 1/3 (pow l 3) (* 1/60 (pow l 5)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
11×	`add-exp-log`
10×	`associate-r`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`add-cbrt-cube`
6×	`pow1` `associate-l`
4×	`expm1-log1p-u` `unpow-prod-down` `prod-exp` `fma-udef` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`*-commutative` `cbrt-unprod` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `distribute-lft-in` `pow-prod-down` `pow-exp`

Counts

4 → 69

Calls

4 calls:

6.0ms	(* J (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5)))))
9.0ms	(* 1/60 (pow l 5))
0.0ms	(fma (* J (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5))))) (cos (/ K 2.0)) U)
0.0ms	(fma 1/3 (pow l 3) (* 1/60 (pow l 5)))

series848.0ms

Counts

4 → 12

Calls

4 calls:

204.0ms	(* J (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5)))))
74.0ms	(* 1/60 (pow l 5))
323.0ms	(fma (* J (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5))))) (cos (/ K 2.0)) U)
247.0ms	(fma 1/3 (pow l 3) (* 1/60 (pow l 5)))

simplify2.4s

Counts

81 → 81

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	136	1227
1	288	1186
2	906	1059
3	4629	1035
done	5000	1035

prune718.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (cbrt (pow (* (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5)))) J) 3)) (cos (/ K 2.0)) U)
0.1b	(fma 1/3 (pow l 3) (* 1/60 (pow l 5)))
0.2b	(pow (* (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5)))) J) 3)
29.3b	(cbrt (pow (* (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5)))) J) 3))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`cbrt-prod`
7×	`pow1` `add-cbrt-cube` `add-exp-log`
6×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow`
2×	`cube-mult` `unpow-prod-down` `pow-pow` `unpow3` `cube-prod` `pow-exp` `fma-udef` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `pow1/3` `pow-prod-down` `prod-exp` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 63

Calls

4 calls:

0.0ms	(fma (cbrt (pow (* (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5)))) J) 3)) (cos (/ K 2.0)) U)
1.0ms	(fma 1/3 (pow l 3) (* 1/60 (pow l 5)))
9.0ms	(pow (* (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5)))) J) 3)
5.0ms	(cbrt (pow (* (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5)))) J) 3))

series829.0ms

Counts

4 → 12

Calls

4 calls:

294.0ms	(fma (cbrt (pow (* (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5)))) J) 3)) (cos (/ K 2.0)) U)
217.0ms	(fma 1/3 (pow l 3) (* 1/60 (pow l 5)))
170.0ms	(pow (* (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5)))) J) 3)
148.0ms	(cbrt (pow (* (fma 2 l (fma 1/3 (pow l 3) (* 1/60 (pow l 5)))) J) 3))

simplify618.0ms

Counts

75 → 75

Iterations

Useful iterations: done (615.0ms)

Iter	Nodes	Cost
0	148	1679
1	364	1523
2	1486	1330
done	5002	1325

prune656.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

0.0b	(* J (/ (- (exp (+ l l)) (exp (* l -2))) (+ (exp (- l)) (exp l))))
0.0b	(fma (* J (/ (- (exp (+ l l)) (exp (* l -2))) (+ (exp (- l)) (exp l)))) (cos (/ K 2.0)) U)
0.0b	(/ (- (exp (+ l l)) (exp (* l -2))) (+ (exp (- l)) (exp l)))
6.2b	(- (exp (+ l l)) (exp (* l -2)))

rewrite522.0ms

Algorithm

rewrite-expression-head

Rules

82×	`*-un-lft-identity`
71×	`add-sqr-sqrt`
49×	`times-frac`
36×	`add-cube-cbrt`
30×	`associate-r`
20×	`difference-of-squares`
14×	`exp-sum`
13×	`distribute-lft-out`
12×	`prod-diff`
11×	`add-cbrt-cube` `add-exp-log`
10×	`distribute-lft-out--`
6×	`pow1` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `associate-/r*` `fma-neg` `associate-/r/` `log1p-expm1-u`
3×	`associate-l`
2×	`cbrt-undiv` `flip3-+` `flip3--` `div-exp` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `flip--` `unswap-sqr` `associate-/l/`
1×	`clear-num` `sub-neg` `frac-2neg` `diff-log` `div-sub` `pow-prod-down` `associate-r/` `-commutative` `fma-udef`

Counts

4 → 147

Calls

4 calls:

232.0ms	(* J (/ (- (exp (+ l l)) (exp (* l -2))) (+ (exp (- l)) (exp l))))
1.0ms	(fma (* J (/ (- (exp (+ l l)) (exp (* l -2))) (+ (exp (- l)) (exp l)))) (cos (/ K 2.0)) U)
205.0ms	(/ (- (exp (+ l l)) (exp (* l -2))) (+ (exp (- l)) (exp l)))
79.0ms	(- (exp (+ l l)) (exp (* l -2)))

series854.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* J (/ (- (exp (+ l l)) (exp (* l -2))) (+ (exp (- l)) (exp l))))
429.0ms	(fma (* J (/ (- (exp (+ l l)) (exp (* l -2))) (+ (exp (- l)) (exp l)))) (cos (/ K 2.0)) U)
152.0ms	(/ (- (exp (+ l l)) (exp (* l -2))) (+ (exp (- l)) (exp l)))
71.0ms	(- (exp (+ l l)) (exp (* l -2)))

simplify1.2s

Counts

159 → 159

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	252	3834
1	644	3524
2	2775	3111
done	5002	3045

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes680.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	21
1	21	21
done	21	21

end0.0ms

sample8.7s

Algorithm

intervals

Results

3.6s	2673×	body	1280	valid
2.2s	2610×	body	640	valid
1.2s	8566×	body	80	valid
533.0ms	1392×	body	320	valid
221.0ms	774×	body	160	valid