Details

sample47.0ms

Algorithm

intervals

Results

20.0ms	90×	body	1280	valid
5.0ms	39×	body	640	valid
4.0ms	163×	body	80	valid
2.0ms	24×	body	320	valid
1.0ms	12×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	3485
6	450
5	118
4	51
3	27
2	18
1	11
0	6

prune22.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.6b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.6b	(- (exp (* a x)) 1.0)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 40

Calls

2 calls:

3.0ms	(exp (* a x))
11.0ms	(- (exp (* a x)) 1.0)

series82.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(exp (* a x))
59.0ms	(- (exp (* a x)) 1.0)

simplify1.8s

Counts

46 → 46

Iterations

Iter	Nodes
done	5000
3	3404
2	600
1	183
0	79

prune228.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.6b

localize38.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (* (pow a 3) x))
6.5b	(* (pow a 3) x)
9.8b	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))
14.3b	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

20.0ms	(* 1/6 (* (pow a 3) x))
10.0ms	(* (pow a 3) x)
0.0ms	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))
25.0ms	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 1/6 (* (pow a 3) x))
31.0ms	(* (pow a 3) x)
85.0ms	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))
146.0ms	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))

simplify1.5s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	2167
1	341
0	127

prune470.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

6.1b	(* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6))))
6.6b	(pow (exp x) (* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))))
6.6b	(* (pow a 3) (* x 1/6))
9.8b	(fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

6.0ms	(* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6))))
16.0ms	(pow (exp x) (* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))))
35.0ms	(* (pow a 3) (* x 1/6))
1.0ms	(fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6))))
68.0ms	(pow (exp x) (* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))))
41.0ms	(* (pow a 3) (* x 1/6))
90.0ms	(fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))

simplify1.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1972
1	378
0	137

prune733.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (* (* a a) (* a x)))
1.8b	(* (* a a) (* a x))
9.8b	(fma 1/2 (* a a) (* 1/6 (* (* a a) (* a x))))
14.3b	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (* a a) (* a x)))))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow1` `add-cbrt-cube` `add-exp-log`
24×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `fma-udef`
1×	`distribute-rgt-in` `distribute-lft-in` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

87.0ms	(* 1/6 (* (* a a) (* a x)))
21.0ms	(* (* a a) (* a x))
0.0ms	(fma 1/2 (* a a) (* 1/6 (* (* a a) (* a x))))
24.0ms	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (* a a) (* a x)))))

series304.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 1/6 (* (* a a) (* a x)))
42.0ms	(* (* a a) (* a x))
79.0ms	(fma 1/2 (* a a) (* 1/6 (* (* a a) (* a x))))
146.0ms	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (* a a) (* a x)))))

simplify2.1s

Counts

98 → 98

Iterations

Iter	Nodes
done	5001
2	2892
1	378
0	124

prune396.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes414.0ms

Accuracy

86.9% (3.2b remaining)

Error of 3.4b against oracle of 0.2b and baseline of 24.5b

bsearch1.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	26
1	26
0	22

end0.0ms

sample2.4s

Algorithm

intervals

Results

884.0ms	2701×	body	1280	valid
791.0ms	5509×	body	80	valid
242.0ms	1304×	body	640	valid
101.0ms	804×	body	320	valid
32.0ms	387×	body	160	valid