Details

sample77.0ms

Algorithm

intervals

Results

34.0ms	86×	body	1280	valid
12.0ms	40×	body	640	valid
10.0ms	176×	body	80	valid
7.0ms	37×	body	320	valid
2.0ms	11×	body	160	valid

simplify1.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
6	646
5	161
4	64
3	32
2	21
1	14
0	6

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.6b

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b	(exp (* a x))
4.6b	(- (exp (* a x)) 1)

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt` `add-log-exp`
5×	`*-un-lft-identity`
2×	`pow1` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `insert-posit16` `difference-of-squares`
1×	`exp-prod` `sub-neg` `flip3--` `exp-to-pow` `diff-log` `difference-of-sqr-1` `flip--` `distribute-lft-out--` `rem-exp-log`

Counts

2 → 28

Calls

2 calls:

4.0ms	(exp (* a x))
14.0ms	(- (exp (* a x)) 1)

series51.0ms

Counts

2 → 6

Calls

2 calls:

13.0ms	(exp (* a x))
38.0ms	(- (exp (* a x)) 1)

simplify1.7s

Counts

34 → 34

Iterations

Iter	Nodes
done	5001
3	2459
2	448
1	134
0	56

prune144.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.3b	(* 1/6 a)
1.5b	(* (* (* x a) (* x a)) x)
4.4b	(* (* 1/6 a) (* (* (* x a) (* x a)) x))
9.1b	(+ (* (* x a) (* (* x a) 1/2)) (* (* 1/6 a) (* (* (* x a) (* x a)) x)))

rewrite488.0ms

Algorithm

rewrite-expression-head

Rules

80×	`pow1` `add-cbrt-cube` `add-exp-log`
58×	`pow-prod-down` `prod-exp` `cbrt-unprod`
10×	`add-sqr-sqrt`
7×	`-un-lft-identity` `associate-r*` `add-cube-cbrt`
6×	`add-log-exp`
5×	`associate-l`
4×	`insert-posit16`
3×	`*-commutative`
2×	`unswap-sqr`
1×	`+-commutative` `sum-log` `flip3-+` `flip-+`

Counts

4 → 107

Calls

4 calls:

10.0ms	(* 1/6 a)
105.0ms	(* (* (* x a) (* x a)) x)
271.0ms	(* (* 1/6 a) (* (* (* x a) (* x a)) x))
97.0ms	(+ (* (* x a) (* (* x a) 1/2)) (* (* 1/6 a) (* (* (* x a) (* x a)) x)))

series322.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* 1/6 a)
46.0ms	(* (* (* x a) (* x a)) x)
114.0ms	(* (* 1/6 a) (* (* (* x a) (* x a)) x))
145.0ms	(+ (* (* x a) (* (* x a) 1/2)) (* (* 1/6 a) (* (* (* x a) (* x a)) x)))

simplify3.0s

Counts

119 → 119

Iterations

Iter	Nodes
done	5002
2	3450
1	504
0	150

prune350.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (- (exp (* a x)) 1))
0.1b	(exp (* a x))
4.5b	(log (exp (- (exp (* a x)) 1)))
4.6b	(- (exp (* a x)) 1)

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`exp-prod`
11×	`add-log-exp`
8×	`log-pow`
7×	`add-cube-cbrt`
6×	`difference-of-squares`
5×	`pow1` `log-prod`
4×	`add-cbrt-cube` `exp-sum` `add-exp-log` `insert-posit16`
3×	`sub-neg` `difference-of-sqr-1` `distribute-lft-out--` `rem-exp-log`
2×	`exp-diff` `diff-log`
1×	`log-div` `flip3--` `exp-to-pow` `rem-log-exp` `flip--`

Counts

4 → 71

Calls

4 calls:

30.0ms	(exp (- (exp (* a x)) 1))
8.0ms	(exp (* a x))
48.0ms	(log (exp (- (exp (* a x)) 1)))
23.0ms	(- (exp (* a x)) 1)

series175.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(exp (- (exp (* a x)) 1))
21.0ms	(exp (* a x))
61.0ms	(log (exp (- (exp (* a x)) 1)))
51.0ms	(- (exp (* a x)) 1)

simplify1.9s

Counts

83 → 83

Iterations

Iter	Nodes
done	5001
3	3024
2	583
1	189
0	90

prune318.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize40.0ms

Local error

Found 4 expressions with local error:

1.2b	(* (* 1/6 a) (* (* a x) (* a x)))
2.9b	(* x (* (* 1/6 a) (* (* a x) (* a x))))
3.6b	(+ (* (* 1/2 (* a x)) (* a x)) (* a x))
9.1b	(+ (+ (* (* 1/2 (* a x)) (* a x)) (* a x)) (* x (* (* 1/6 a) (* (* a x) (* a x)))))

rewrite745.0ms

Algorithm

rewrite-expression-head

Rules

98×	`pow1` `add-cbrt-cube` `add-exp-log`
73×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-log-exp`
5×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
4×	`sum-log` `associate-l` `insert-posit16`
2×	`+-commutative` `flip3-+` `associate-r` `*-commutative` `flip-+`
1×	`associate-+l+` `distribute-lft1-in`

Counts

4 → 114

Calls

4 calls:

91.0ms	(* (* 1/6 a) (* (* a x) (* a x)))
214.0ms	(* x (* (* 1/6 a) (* (* a x) (* a x))))
64.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (* a x))
374.0ms	(+ (+ (* (* 1/2 (* a x)) (* a x)) (* a x)) (* x (* (* 1/6 a) (* (* a x) (* a x)))))

series370.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(* (* 1/6 a) (* (* a x) (* a x)))
91.0ms	(* x (* (* 1/6 a) (* (* a x) (* a x))))
85.0ms	(+ (* (* 1/2 (* a x)) (* a x)) (* a x))
133.0ms	(+ (+ (* (* 1/2 (* a x)) (* a x)) (* a x)) (* x (* (* 1/6 a) (* (* a x) (* a x)))))

simplify2.9s

Counts

126 → 126

Iterations

Iter	Nodes
done	5001
2	4422
1	562
0	163

prune281.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes378.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.5b

bsearch1.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	33
2	33
1	31
0	21

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	2560×	body	1280	valid
705.0ms	5475×	body	80	valid
351.0ms	1367×	body	640	valid
142.0ms	810×	body	320	valid
73.0ms	399×	body	160	valid