Details

sample32.0ms

Algorithm

intervals

Results

12.0ms	79×	body	1280	valid
4.0ms	42×	body	640	valid
4.0ms	185×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	17×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	27	6
4	51	6
5	109	6
6	256	6
7	719	6
8	2457	6
done	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.5b	(- (exp (* a x)) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`add-cube-cbrt` `prod-diff`
6×	`add-log-exp`
3×	`fma-neg`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `diff-log` `flip--` `rem-exp-log` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 40

Calls

2 calls:

1.0ms	(exp (* a x))
5.0ms	(- (exp (* a x)) 1.0)

series50.0ms

Counts

2 → 6

Calls

2 calls:

12.0ms	(exp (* a x))
38.0ms	(- (exp (* a x)) 1.0)

simplify1.2s

Counts

46 → 46

Iterations

Useful iterations: 3 (226.0ms)

Iter	Nodes	Cost
0	79	557
1	171	457
2	431	386
3	1574	346
done	5001	346

prune101.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 9.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2 (* x a))
0.0b	(exp (* 2 (* x a)))
0.0b	(/ (- (exp (* 2 (* x a))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
4.5b	(- (exp (* 2 (* x a))) (* 1.0 1.0))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
17×	`add-cube-cbrt`
16×	`times-frac`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-log-exp`
6×	`difference-of-squares`
5×	`distribute-lft-out`
4×	`expm1-log1p-u` `associate-/r` `log1p-expm1-u` `associate-/l`
3×	`fma-neg` `associate-l` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `exp-prod` `exp-to-pow` `frac-2neg` `flip3-+` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `*-commutative` `flip-+` `div-inv` `rem-exp-log`

Counts

4 → 96

Calls

4 calls:

6.0ms	(* 2 (* x a))
2.0ms	(exp (* 2 (* x a)))
17.0ms	(/ (- (exp (* 2 (* x a))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
6.0ms	(- (exp (* 2 (* x a))) (* 1.0 1.0))

series146.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* 2 (* x a))
17.0ms	(exp (* 2 (* x a)))
66.0ms	(/ (- (exp (* 2 (* x a))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
46.0ms	(- (exp (* 2 (* x a))) (* 1.0 1.0))

simplify912.0ms

Counts

108 → 108

Iterations

Useful iterations: done (908.0ms)

Iter	Nodes	Cost
0	167	1879
1	420	1810
2	1273	1654
done	5000	1628

prune302.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* a x) (+ (* 0.5 (* a x)) 1.0))
0.1b	(* (pow (* a x) 3) 0.16666666666666663)
0.3b	(pow (* a x) 3)
12.1b	(+ (* (* a x) (+ (* 0.5 (* a x)) 1.0)) (* (pow (* a x) 3) 0.16666666666666663))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log`
14×	`add-cbrt-cube`
12×	`pow1`
11×	`add-sqr-sqrt`
9×	`associate-l` `prod-exp`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`associate-r` `add-log-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `pow-prod-down` `pow-exp` `log1p-expm1-u`
3×	`pow-unpow` `sqr-pow`
2×	`distribute-rgt-in` `cube-mult` `pow-to-exp` `unpow-prod-down` `associate-+l+` `pow-pow` `distribute-lft-in` `flip3-+` `unpow3` `cube-prod` `associate-r/` `-commutative` `flip-+` `rem-cube-cbrt` `unswap-sqr`
1×	`+-commutative` `fma-def` `sum-log`

Counts

4 → 92

Calls

4 calls:

22.0ms	(* (* a x) (+ (* 0.5 (* a x)) 1.0))
6.0ms	(* (pow (* a x) 3) 0.16666666666666663)
2.0ms	(pow (* a x) 3)
14.0ms	(+ (* (* a x) (+ (* 0.5 (* a x)) 1.0)) (* (pow (* a x) 3) 0.16666666666666663))

series305.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(* (* a x) (+ (* 0.5 (* a x)) 1.0))
73.0ms	(* (pow (* a x) 3) 0.16666666666666663)
50.0ms	(pow (* a x) 3)
119.0ms	(+ (* (* a x) (+ (* 0.5 (* a x)) 1.0)) (* (pow (* a x) 3) 0.16666666666666663))

simplify998.0ms

Counts

104 → 104

Iterations

Useful iterations: 2 (250.0ms)

Iter	Nodes	Cost
0	142	1380
1	396	1160
2	2118	1069
done	5000	1069

prune268.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 0.5 (* x a) 1.0)
0.1b	(* (pow (* a x) 3) 0.16666666666666663)
0.3b	(pow (* a x) 3)
4.8b	(fma (* x a) (fma 0.5 (* x a) 1.0) (* (pow (* a x) 3) 0.16666666666666663))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

0.0ms	(fma 0.5 (* x a) 1.0)
6.0ms	(* (pow (* a x) 3) 0.16666666666666663)
2.0ms	(pow (* a x) 3)
0.0ms	(fma (* x a) (fma 0.5 (* x a) 1.0) (* (pow (* a x) 3) 0.16666666666666663))

series249.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(fma 0.5 (* x a) 1.0)
69.0ms	(* (pow (* a x) 3) 0.16666666666666663)
50.0ms	(pow (* a x) 3)
99.0ms	(fma (* x a) (fma 0.5 (* x a) 1.0) (* (pow (* a x) 3) 0.16666666666666663))

simplify654.0ms

Counts

84 → 84

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	103	882
1	216	804
2	868	718
done	5001	718

prune213.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes97.0ms

Accuracy

99.1% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 21.2b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	42
1	28	42
done	28	42

end0.0ms

sample996.0ms

Algorithm

intervals

Results

448.0ms	2649×	body	1280	valid
149.0ms	1371×	body	640	valid
123.0ms	5510×	body	80	valid
56.0ms	781×	body	320	valid
19.0ms	391×	body	160	valid