Details

sample34.0ms

Algorithm

intervals

Results

16.0ms	97×	body	1280	valid
4.0ms	45×	body	640	valid
3.0ms	158×	body	80	valid
1.0ms	15×	body	320	valid
1.0ms	16×	body	160	valid

simplify4.6s

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	110	6
6	272	6
7	1155	6
8	4059	6
done	5000	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.7b

localize4.0ms

Local error

Found 1 expressions with local error:

3.5b	(- (exp (* a x)) 1.0)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 28

Calls

1 calls:

5.0ms

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

series33.0ms

Counts

1 → 3

Calls

1 calls:

33.0ms

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

simplify1.4s

Counts

31 → 31

Iterations

Useful iterations: 3 (259.0ms)

Iter	Nodes	Cost
0	72	472
1	169	384
2	536	304
3	2521	255
done	5000	255

prune70.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (pow a 3))
4.6b	(* (* 1/6 (pow a 3)) x)
10.7b	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
13.9b	(* (pow x 2) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
24×	`add-exp-log`
18×	`associate-r`
13×	`prod-exp` `add-cbrt-cube`
12×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
8×	`unpow-prod-down` `unswap-sqr`
6×	`pow1` `add-log-exp`
5×	`cbrt-unprod`
4×	`expm1-log1p-u` `cube-prod` `log1p-expm1-u` `sqr-pow`
3×	`pow-to-exp` `pow-exp` `*-commutative`
2×	`flip3-+` `associate-*r/` `flip-+` `unpow2`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `fma-def` `distribute-lft-in` `unpow3` `pow-prod-down` `sum-log`

Counts

4 → 101

Calls

4 calls:

7.0ms	(* 1/6 (pow a 3))
10.0ms	(* (* 1/6 (pow a 3)) x)
9.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
41.0ms	(* (pow x 2) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

series243.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(* 1/6 (pow a 3))
28.0ms	(* (* 1/6 (pow a 3)) x)
58.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
122.0ms	(* (pow x 2) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

simplify1.2s

Counts

113 → 113

Iterations

Useful iterations: 2 (205.0ms)

Iter	Nodes	Cost
0	156	1654
1	446	1463
2	2329	1314
done	5001	1314

prune290.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(log (pow (exp (* x x)) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))))
0.1b	(* 1/6 (pow a 3))
7.9b	(pow (exp (* x x)) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))))
14.7b	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

2.0ms	(log (pow (exp (* x x)) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))))
7.0ms	(* 1/6 (pow a 3))
2.0ms	(pow (exp (* x x)) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))))
0.0ms	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(log (pow (exp (* x x)) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))))
34.0ms	(* 1/6 (pow a 3))
52.0ms	(pow (exp (* x x)) (fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2))))
56.0ms	(fma (* 1/6 (pow a 3)) x (* 1/2 (pow a 2)))

simplify611.0ms

Counts

98 → 98

Iterations

Useful iterations: 2 (95.0ms)

Iter	Nodes	Cost
0	128	1559
1	268	1427
2	1062	1322
done	5001	1322

prune321.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp (* a x)))
0.0b	(sqrt (exp (* a x)))
0.0b	(+ (sqrt (exp (* a x))) (sqrt 1.0))
3.5b	(- (sqrt (exp (* a x))) (sqrt 1.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

56×	`sqrt-prod`
44×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
10×	`add-log-exp`
6×	`pow1` `fma-def` `sqrt-pow1` `fma-neg`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `difference-of-squares`
2×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `pow1/2` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `diff-log` `sum-log` `flip--` `flip-+`

Counts

4 → 117

Calls

4 calls:

1.0ms	(sqrt (exp (* a x)))
1.0ms	(sqrt (exp (* a x)))
7.0ms	(+ (sqrt (exp (* a x))) (sqrt 1.0))
10.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

series151.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(sqrt (exp (* a x)))
21.0ms	(sqrt (exp (* a x)))
46.0ms	(+ (sqrt (exp (* a x))) (sqrt 1.0))
59.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

simplify1.9s

Counts

129 → 129

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	124	2204
1	270	1698
2	771	1382
3	3065	1220
done	5000	1214

prune240.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes128.0ms

Accuracy

86.3% (3.3b remaining)

Error of 3.6b against oracle of 0.3b and baseline of 24.7b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	65
1	36	65
done	36	65

end0.0ms

sample913.0ms

Algorithm

intervals

Results

428.0ms	2708×	body	1280	valid
127.0ms	1309×	body	640	valid
108.0ms	5401×	body	80	valid
49.0ms	756×	body	320	valid
18.0ms	409×	body	160	valid