Details

sample45.0ms

Algorithm

intervals

Results

18.0ms	83×	body	1280	valid
6.0ms	48×	body	640	valid
5.0ms	165×	body	80	valid
2.0ms	27×	body	320	valid
1.0ms	12×	body	160	valid

simplify3.0s

Counts

1 → 1

Iterations

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 29.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.1b	(exp (* a x))
3.6b	(- (exp (* a x)) 1.0)

rewrite22.0ms

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:

6.0ms	(exp (* a x))
14.0ms	(- (exp (* a x)) 1.0)

series86.0ms

Counts

2 → 6

Calls

2 calls:

15.0ms	(exp (* a x))
71.0ms	(- (exp (* a x)) 1.0)

simplify1.9s

Counts

46 → 46

Iterations

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

prune211.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 5.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (* (pow a 3) x))
4.7b	(* (pow a 3) x)
9.1b	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))
12.9b	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))

rewrite61.0ms

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:

28.0ms	(* 1/6 (* (pow a 3) x))
11.0ms	(* (pow a 3) x)
0.0ms	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))
18.0ms	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* 1/6 (* (pow a 3) x))
29.0ms	(* (pow a 3) x)
90.0ms	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))
172.0ms	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))

simplify1.3s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	2167
1	341
0	127

prune533.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize23.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (pow a 3) (* x 1/6))
7.0b	(* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6))))
7.9b	(pow (exp x) (* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))))
9.1b	(fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))

rewrite51.0ms

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:

31.0ms	(* (pow a 3) (* x 1/6))
11.0ms	(* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6))))
6.0ms	(pow (exp x) (* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))))
0.0ms	(fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))

series338.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (pow a 3) (* x 1/6))
149.0ms	(* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6))))
83.0ms	(pow (exp x) (* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))))
63.0ms	(fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))

simplify1.0s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	1982
1	381
0	137

prune735.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize40.0ms

Local error

Found 4 expressions with local error:

0.1b	(* a (* a (* a x)))
0.1b	(* 1/6 (* a (* a (* a x))))
9.1b	(fma 1/2 (* a a) (* 1/6 (* a (* a (* a x)))))
12.9b	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* a (* a (* a x))))))

rewrite238.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1` `add-cbrt-cube` `add-exp-log`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-l*` `add-cube-cbrt`
5×	`associate-r`
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 → 82

Calls

4 calls:

65.0ms	(* a (* a (* a x)))
140.0ms	(* 1/6 (* a (* a (* a x))))
0.0ms	(fma 1/2 (* a a) (* 1/6 (* a (* a (* a x)))))
28.0ms	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* a (* a (* a x))))))

series328.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* a (* a (* a x)))
30.0ms	(* 1/6 (* a (* a (* a x))))
82.0ms	(fma 1/2 (* a a) (* 1/6 (* a (* a (* a x)))))
177.0ms	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* a (* a (* a x))))))

simplify1.8s

Counts

94 → 94

Iterations

Iter	Nodes
done	5001
2	2590
1	367
0	126

prune476.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

regimes425.0ms

Accuracy

79.3% (5.0b remaining)

Error of 5.2b against oracle of 0.2b and baseline of 24.5b

bsearch1.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	24
1	24
0	19

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.3s	2657×	body	1280	valid
254.0ms	5490×	body	80	valid
246.0ms	1373×	body	640	valid
152.0ms	753×	body	320	valid
36.0ms	400×	body	160	valid