Details

sample40.0ms

Algorithm

intervals

Results

14.0ms	74×	body	1280	valid
5.0ms	179×	body	80	valid
5.0ms	38×	body	640	valid
2.0ms	29×	body	320	valid
1.0ms	17×	body	160	valid

simplify3.5s

Counts

1 → 1

Iterations

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize17.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.0b	(- (exp (* a x)) 1.0)

rewrite32.0ms

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))
25.0ms	(- (exp (* a x)) 1.0)

series85.0ms

Counts

2 → 6

Calls

2 calls:

22.0ms	(exp (* a x))
62.0ms	(- (exp (* a x)) 1.0)

simplify2.1s

Counts

46 → 46

Iterations

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

prune153.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 a)
1.1b	(* (* 1/6 a) (* (* x a) (* x a)))
1.7b	(* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))
12.5b	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1` `add-cbrt-cube` `add-exp-log`
33×	`pow-prod-down` `prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-cube-cbrt`
7×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
2×	`associate-*r/` `unswap-sqr`
1×	`distribute-rgt-in` `distribute-lft-in` `flip3-+` `flip-+` `fma-udef`

Counts

4 → 96

Calls

4 calls:

10.0ms	(* 1/6 a)
126.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
17.0ms	(* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))
0.0ms	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))

series401.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* 1/6 a)
81.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
152.0ms	(* x (+ a (* (* 1/6 a) (* (* x a) (* x a)))))
150.0ms	(fma 1/2 (* (* x a) (* x a)) (* x (+ a (* (* 1/6 a) (* (* x a) (* x a))))))

simplify2.5s

Counts

108 → 108

Iterations

Iter	Nodes
done	5002
2	2797
1	447
0	147

prune464.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 a)
1.1b	(* (* 1/6 a) (* (* x a) (* x a)))
2.9b	(* x (* (* 1/6 a) (* (* x a) (* x a))))
12.5b	(fma 1/2 (* (* x a) (* x a)) (+ (* x a) (* x (* (* 1/6 a) (* (* x a) (* x a))))))

rewrite389.0ms

Algorithm

rewrite-expression-head

Rules

100×	`pow1` `add-cbrt-cube` `add-exp-log`
74×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`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`
1×	`fma-udef` `unswap-sqr`

Counts

4 → 119

Calls

4 calls:

5.0ms	(* 1/6 a)
97.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
279.0ms	(* x (* (* 1/6 a) (* (* x a) (* x a))))
1.0ms	(fma 1/2 (* (* x a) (* x a)) (+ (* x a) (* x (* (* 1/6 a) (* (* x a) (* x a))))))

series357.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* 1/6 a)
67.0ms	(* (* 1/6 a) (* (* x a) (* x a)))
95.0ms	(* x (* (* 1/6 a) (* (* x a) (* x a))))
169.0ms	(fma 1/2 (* (* x a) (* x a)) (+ (* x a) (* x (* (* 1/6 a) (* (* x a) (* x a))))))

simplify2.9s

Counts

131 → 131

Iterations

Iter	Nodes
done	5002
2	3098
1	459
0	151

prune534.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (exp (* a x)) 1.0))
4.0b	(- (exp (* a x)) 1.0)
4.0b	(- (exp (* a x)) 1.0)
4.0b	(- (exp (* a x)) 1.0)

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`prod-diff`
26×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`fma-neg`
5×	`cbrt-prod`
4×	`expm1-log1p-u` `pow1` `flip3--` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 101

Calls

4 calls:

11.0ms	(cbrt (- (exp (* a x)) 1.0))
21.0ms	(- (exp (* a x)) 1.0)
25.0ms	(- (exp (* a x)) 1.0)
22.0ms	(- (exp (* a x)) 1.0)

series341.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(cbrt (- (exp (* a x)) 1.0))
61.0ms	(- (exp (* a x)) 1.0)
67.0ms	(- (exp (* a x)) 1.0)
59.0ms	(- (exp (* a x)) 1.0)

simplify2.4s

Counts

113 → 113

Iterations

Iter	Nodes
done	5000
3	4379
2	794
1	239
0	105

prune566.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes381.0ms

Accuracy

98% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 21.1b

bsearch1.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	36
3	36
2	34
1	31
0	24

end0.0ms

sample1.8s

Algorithm

intervals

Results

875.0ms	2706×	body	1280	valid
317.0ms	1357×	body	640	valid
220.0ms	5424×	body	80	valid
87.0ms	758×	body	320	valid
30.0ms	391×	body	160	valid