Details

sample46.0ms

Algorithm

intervals

Results

15.0ms	81×	body	1280	valid
6.0ms	13×	body	160	valid
5.0ms	46×	body	640	valid
4.0ms	165×	body	80	valid
2.0ms	23×	body	320	valid

simplify2.8s

Counts

1 → 1

Iterations

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 30.0b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.3b	(- (exp (* a x)) 1.0)

rewrite25.0ms

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))
17.0ms	(- (exp (* a x)) 1.0)

series71.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(exp (* a x))
48.0ms	(- (exp (* a x)) 1.0)

simplify2.0s

Counts

46 → 46

Iterations

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

prune199.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.6b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (* (pow a 3) x))
6.2b	(* (pow a 3) x)
10.8b	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))
13.8b	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))

rewrite70.0ms

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))
20.0ms	(* (pow a 3) x)
0.0ms	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))
27.0ms	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* 1/6 (* (pow a 3) x))
43.0ms	(* (pow a 3) x)
80.0ms	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))
185.0ms	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))

simplify1.4s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	2167
1	341
0	127

prune478.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize53.0ms

Local error

Found 4 expressions with local error:

3.9b	(pow (exp x) (* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))))
5.4b	(* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6))))
6.2b	(* (pow a 3) (* x 1/6))
10.8b	(fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))

rewrite59.0ms

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:

9.0ms	(pow (exp x) (* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))))
11.0ms	(* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6))))
34.0ms	(* (pow a 3) (* x 1/6))
1.0ms	(fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))

series411.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(pow (exp x) (* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))))
169.0ms	(* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6))))
49.0ms	(* (pow a 3) (* x 1/6))
110.0ms	(fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))

simplify1.2s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	1982
1	378
0	137

prune705.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

localize20.0ms

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)))
4.3b	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `*-un-lft-identity` `sqrt-pow1` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `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:

3.0ms	(exp (* a x))
3.0ms	(sqrt (exp (* a x)))
3.0ms	(sqrt (exp (* a x)))
0.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

series228.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(exp (* a x))
43.0ms	(sqrt (exp (* a x)))
36.0ms	(sqrt (exp (* a x)))
127.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

simplify2.1s

Counts

68 → 68

Iterations

Iter	Nodes
done	5004
3	2291
2	426
1	124
0	63

prune329.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes464.0ms

Accuracy

86.5% (3.2b remaining)

Error of 3.4b against oracle of 0.2b and baseline of 23.8b

bsearch2.0ms

simplify9.0ms

Iterations

Iter	Nodes
done	46
1	46
0	39

end0.0ms

sample2.4s

Algorithm

intervals

Results

936.0ms	2713×	body	1280	valid
641.0ms	5337×	body	80	valid
319.0ms	1382×	body	640	valid
102.0ms	775×	body	320	valid
34.0ms	400×	body	160	valid