Details

sample42.0ms

Algorithm

intervals

Results

16.0ms	88×	body	1280	valid
7.0ms	45×	body	640	valid
4.0ms	169×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	13×	body	160	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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 28.5b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.1b	(- (exp (* a x)) 1.0)

rewrite19.0ms

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

series79.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(exp (* a x))
55.0ms	(- (exp (* a x)) 1.0)

simplify1.7s

Counts

46 → 46

Iterations

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

prune197.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 6.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/6 (* (pow a 3) x))
4.1b	(* (pow a 3) x)
10.1b	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))
15.8b	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))

rewrite48.0ms

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:

16.0ms	(* 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)))
19.0ms	(* (* x x) (fma 1/2 (* a a) (* 1/6 (* (pow a 3) x))))

series332.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* 1/6 (* (pow a 3) x))
34.0ms	(* (pow a 3) x)
88.0ms	(fma 1/2 (* a a) (* 1/6 (* (pow a 3) x)))
159.0ms	(* (* 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

prune578.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

4.1b	(* (pow a 3) (* x 1/6))
5.9b	(pow (exp x) (* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))))
7.0b	(* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6))))
10.1b	(fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))

rewrite49.0ms

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:

25.0ms	(* (pow a 3) (* x 1/6))
8.0ms	(pow (exp x) (* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))))
13.0ms	(* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6))))
1.0ms	(fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))

series361.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(* (pow a 3) (* x 1/6))
63.0ms	(pow (exp x) (* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))))
168.0ms	(* x (fma (* a a) 1/2 (* (pow a 3) (* x 1/6))))
101.0ms	(fma (* a a) 1/2 (* (pow a 3) (* x 1/6)))

simplify1.1s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	1988
1	381
0	137

prune660.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (* a x))
0.2b	(sqrt (exp (* a x)))
0.2b	(sqrt (exp (* a x)))
3.2b	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

rewrite16.0ms

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:

6.0ms	(exp (* a x))
5.0ms	(sqrt (exp (* a x)))
3.0ms	(sqrt (exp (* a x)))
0.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

series168.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(exp (* a x))
26.0ms	(sqrt (exp (* a x)))
24.0ms	(sqrt (exp (* a x)))
99.0ms	(fma (sqrt (exp (* a x))) (sqrt (exp (* a x))) (- 1.0))

simplify2.3s

Counts

68 → 68

Iterations

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

prune308.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.1b

regimes429.0ms

Accuracy

85.9% (3.5b remaining)

Error of 3.8b against oracle of 0.2b and baseline of 25.1b

bsearch1.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	30
1	30
0	25

end0.0ms

sample2.1s

Algorithm

intervals

Results

731.0ms	2681×	body	1280	valid
693.0ms	5474×	body	80	valid
241.0ms	1318×	body	640	valid
78.0ms	731×	body	320	valid
29.0ms	385×	body	160	valid