Details

sample77.0ms

Algorithm

intervals

Results

37.0ms	93×	body	1280	valid
9.0ms	177×	body	80	valid
7.0ms	34×	body	640	valid
3.0ms	24×	body	320	valid
0.0ms	5×	body	160	valid

simplify2.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5090
8	2971
7	747
6	218
5	94
4	45
3	24
2	16
1	11
0	6

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.8b

localize11.0ms

Local error

Found 1 expressions with local error:

2.2b	(- (exp (* a x)) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 28

Calls

1 calls:

11.0ms

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

series59.0ms

Counts

1 → 3

Calls

1 calls:

59.0ms

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

simplify3.6s

Counts

31 → 31

Iterations

Iter	Nodes
done	5000
4	4637
3	1429
2	396
1	171
0	72

prune188.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (* a x) (* a x)) (* a x))
0.2b	(* (* a x) (* a x))
0.2b	(* (* a x) (* a x))
14.3b	(fma 1/2 (* (* a x) (* a x)) (fma (* (* (* a x) (* a x)) (* a x)) 1/6 (* a x)))

rewrite212.0ms

Algorithm

rewrite-expression-head

Rules

237×	`pow1`
103×	`pow-prod-down`
69×	`add-cbrt-cube` `add-exp-log`
47×	`prod-exp` `cbrt-unprod`
42×	`pow-prod-up`
21×	`pow-plus`
20×	`pow-sqr`
5×	`pow2`
4×	`add-sqr-sqrt` `expm1-log1p-u` `*-un-lft-identity` `add-cube-cbrt` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-l` `*-commutative`
2×	`swap-sqr`
1×	`pow3` `fma-udef`

Counts

4 → 158

Calls

4 calls:

122.0ms	(* (* (* a x) (* a x)) (* a x))
36.0ms	(* (* a x) (* a x))
46.0ms	(* (* a x) (* a x))
1.0ms	(fma 1/2 (* (* a x) (* a x)) (fma (* (* (* a x) (* a x)) (* a x)) 1/6 (* a x)))

series364.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* (* (* a x) (* a x)) (* a x))
49.0ms	(* (* a x) (* a x))
51.0ms	(* (* a x) (* a x))
161.0ms	(fma 1/2 (* (* a x) (* a x)) (fma (* (* (* a x) (* a x)) (* a x)) 1/6 (* a x)))

simplify1.8s

Counts

170 → 170

Iterations

Iter	Nodes
done	5000
2	892
1	243
0	94

prune459.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 1 expressions with local error:

2.2b	(- (exp (* a x)) 1.0)

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

1 → 28

Calls

1 calls:

11.0ms

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

series51.0ms

Counts

1 → 3

Calls

1 calls:

51.0ms

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

simplify3.3s

Counts

31 → 31

Iterations

Iter	Nodes
done	5000
4	4637
3	1429
2	396
1	171
0	72

prune191.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize44.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (exp (* a x))) (sqrt 1.0))
0.0b	(sqrt (exp (* a x)))
0.0b	(sqrt (exp (* a x)))
2.2b	(- (sqrt (exp (* a x))) (sqrt 1.0))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

56×	`sqrt-prod`
44×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
36×	`prod-diff`
34×	`add-cube-cbrt`
10×	`add-log-exp`
6×	`pow1` `fma-def` `sqrt-pow1` `fma-neg`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `difference-of-squares`
2×	`rem-sqrt-square` `exp-prod` `exp-to-pow` `pow1/2` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 117

Calls

4 calls:

31.0ms	(+ (sqrt (exp (* a x))) (sqrt 1.0))
5.0ms	(sqrt (exp (* a x)))
5.0ms	(sqrt (exp (* a x)))
33.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

series240.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (sqrt (exp (* a x))) (sqrt 1.0))
42.0ms	(sqrt (exp (* a x)))
44.0ms	(sqrt (exp (* a x)))
66.0ms	(- (sqrt (exp (* a x))) (sqrt 1.0))

simplify2.8s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
3	2333
2	713
1	276
0	125

prune674.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes223.0ms

Accuracy

99.5% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 22.0b

bsearch62.0ms

Steps

Iters	Range		Point
9	-0.0026744779238242673	-1.8483037069943186e-10	-0.00018199215103143304

simplify7.0ms

Iterations

Iter	Nodes
done	33
1	33
0	26

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.3s	2619×	body	1280	valid
268.0ms	1346×	body	640	valid
188.0ms	5536×	body	80	valid
109.0ms	749×	body	320	valid
29.0ms	381×	body	160	valid