Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	79×	body	1280	valid
4.0ms	42×	body	640	valid
4.0ms	185×	body	80	valid
1.0ms	24×	body	320	valid
1.0ms	17×	body	160	valid

simplify3.5s

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	270	6
7	751	6
8	2509	6
done	5000	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)

series55.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(exp (* a x))
42.0ms	(- (exp (* a x)) 1.0)

simplify1.2s

Counts

46 → 46

Iterations

Useful iterations: 3 (237.0ms)

Iter	Nodes	Cost
0	79	557
1	175	457
2	436	386
3	1572	346
done	5001	346

prune97.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (pow a 3))
4.0b	(* (* 1/6 (pow a 3)) x)
9.2b	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
16.5b	(* (pow x 2) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

rewrite75.0ms

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))
11.0ms	(* (* 1/6 (pow a 3)) x)
10.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
44.0ms	(* (pow x 2) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

series263.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 1/6 (pow a 3))
32.0ms	(* (* 1/6 (pow a 3)) x)
61.0ms	(+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2)))
132.0ms	(* (pow x 2) (+ (* (* 1/6 (pow a 3)) x) (* 1/2 (pow a 2))))

simplify1.3s

Counts

113 → 113

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	156	1654
1	437	1463
2	1953	1314
done	5000	1313

prune323.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (pow a 3))
4.0b	(* (* 1/6 (pow a 3)) x)
9.2b	(fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x))
10.2b	(pow (exp (* x x)) (fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

7.0ms	(* 1/6 (pow a 3))
10.0ms	(* (* 1/6 (pow a 3)) x)
0.0ms	(fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x))
2.0ms	(pow (exp (* x x)) (fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x)))

series181.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 1/6 (pow a 3))
27.0ms	(* (* 1/6 (pow a 3)) x)
61.0ms	(fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x))
56.0ms	(pow (exp (* x x)) (fma 1/2 (* a a) (* (* 1/6 (pow a 3)) x)))

simplify951.0ms

Counts

98 → 98

Iterations

Useful iterations: done (948.0ms)

Iter	Nodes	Cost
0	131	1267
1	294	1159
2	1014	1083
done	5000	1081

prune298.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

1.0ms	(exp (* a x))
1.0ms	(sqrt (exp (* a x)))
1.0ms	(sqrt (exp (* a x)))
0.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

series143.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(exp (* a x))
22.0ms	(sqrt (exp (* a x)))
22.0ms	(sqrt (exp (* a x)))
86.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

simplify1.4s

Counts

68 → 68

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	63	589
1	123	455
2	345	430
3	1254	429
done	5000	423

prune150.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.2b

regimes123.0ms

Accuracy

86.4% (3.3b remaining)

Error of 3.6b against oracle of 0.3b and baseline of 24.6b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	40
1	27	40
done	27	40

end0.0ms

sample914.0ms

Algorithm

intervals

Results

410.0ms	2649×	body	1280	valid
137.0ms	1371×	body	640	valid
109.0ms	5510×	body	80	valid
49.0ms	781×	body	320	valid
17.0ms	391×	body	160	valid