Details

sample59.0ms

Algorithm

intervals

Results

21.0ms	88×	body	1280	valid
12.0ms	23×	body	320	valid
5.0ms	172×	body	80	valid
5.0ms	37×	body	640	valid
1.0ms	18×	body	160	valid

simplify3.7s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	11	6
2	18	6
3	26	6
4	49	6
5	113	6
6	440	6
7	3314	6
done	5002	6

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
4.6b	(- (exp (* a x)) 1.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 24

Calls

2 calls:

8.0ms	(exp (* a x))
26.0ms	(- (exp (* a x)) 1.0)

series93.0ms

Counts

2 → 6

Calls

2 calls:

25.0ms	(exp (* a x))
68.0ms	(- (exp (* a x)) 1.0)

simplify1.6s

Counts

30 → 30

Iterations

Useful iterations: 3 (517.0ms)

Iter	Nodes	Cost
0	53	263
1	116	248
2	388	232
3	2010	228
done	5001	228

prune153.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 8.8b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
0.0b	(* 2 (* a x))
0.0b	(+ (exp (* a x)) 1.0)
4.5b	(- (exp (* 2 (* a x))) (* 1.0 1.0))

rewrite174.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
16×	`times-frac`
15×	`add-cube-cbrt`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-log-exp`
6×	`distribute-lft-out` `difference-of-squares`
4×	`associate-/r` `associate-/l`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-r` `clear-num` `sum-log` `*-commutative` `div-inv`

Counts

4 → 84

Calls

4 calls:

99.0ms	(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
42.0ms	(* 2 (* a x))
10.0ms	(+ (exp (* a x)) 1.0)
20.0ms	(- (exp (* 2 (* a x))) (* 1.0 1.0))

series181.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
25.0ms	(* 2 (* a x))
19.0ms	(+ (exp (* a x)) 1.0)
55.0ms	(- (exp (* 2 (* a x))) (* 1.0 1.0))

simplify1.0s

Counts

96 → 96

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	157	1763
1	412	1705
2	1700	1563
done	5001	1511

prune818.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 8.8b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* a x)) 1.0)
0.0b	(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (* 1.0 1.0) (exp (* 2 (* a x)))))
0.0b	(* (* a x) 4)
4.5b	(- (exp (* (* a x) 4)) (pow 1.0 4))

rewrite169.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
29×	`*-un-lft-identity`
21×	`times-frac`
17×	`add-cube-cbrt`
15×	`difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
8×	`add-log-exp`
7×	`associate-/l*`
5×	`unpow-prod-down` `distribute-lft-out--` `sqr-pow`
3×	`associate-r` `pow-prod-down` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `frac-2neg` `diff-log` `div-sub` `div-exp` `associate-l` `clear-num` `sum-log` `*-commutative` `div-inv` `distribute-lft-out`

Counts

4 → 94

Calls

4 calls:

20.0ms	(+ (exp (* a x)) 1.0)
94.0ms	(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (* 1.0 1.0) (exp (* 2 (* a x)))))
18.0ms	(* (* a x) 4)
29.0ms	(- (exp (* (* a x) 4)) (pow 1.0 4))

series213.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (exp (* a x)) 1.0)
115.0ms	(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (* 1.0 1.0) (exp (* 2 (* a x)))))
21.0ms	(* (* a x) 4)
55.0ms	(- (exp (* (* a x) 4)) (pow 1.0 4))

simplify1.7s

Counts

106 → 106

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	202	2414
1	532	2335
2	2480	2173
done	5001	2163

prune687.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 8.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (+ (* 1.0 1.0) (exp (* 2 (* a x)))))
0.6b	(cbrt (+ (* 1.0 1.0) (exp (* 2 (* a x)))))
0.6b	(cbrt (+ (* 1.0 1.0) (exp (* 2 (* a x)))))
4.5b	(- (exp (* (* a x) 4)) (pow 1.0 4))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`cbrt-prod` `*-un-lft-identity`
7×	`add-cube-cbrt`
6×	`cbrt-div` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`flip3-+` `pow1/3` `flip-+` `difference-of-squares`
1×	`sub-neg` `unpow-prod-down` `flip3--` `diff-log` `flip--` `distribute-lft-out--` `sqr-pow`

Counts

4 → 55

Calls

4 calls:

10.0ms	(cbrt (+ (* 1.0 1.0) (exp (* 2 (* a x)))))
18.0ms	(cbrt (+ (* 1.0 1.0) (exp (* 2 (* a x)))))
20.0ms	(cbrt (+ (* 1.0 1.0) (exp (* 2 (* a x)))))
23.0ms	(- (exp (* (* a x) 4)) (pow 1.0 4))

series602.0ms

Counts

4 → 12

Calls

4 calls:

203.0ms	(cbrt (+ (* 1.0 1.0) (exp (* 2 (* a x)))))
163.0ms	(cbrt (+ (* 1.0 1.0) (exp (* 2 (* a x)))))
168.0ms	(cbrt (+ (* 1.0 1.0) (exp (* 2 (* a x)))))
69.0ms	(- (exp (* (* a x) 4)) (pow 1.0 4))

simplify692.0ms

Counts

67 → 67

Iterations

Useful iterations: done (688.0ms)

Iter	Nodes	Cost
0	103	1295
1	251	1238
2	939	1089
done	5000	1067

prune563.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.8b

regimes410.0ms

Accuracy

94.7% (1.2b remaining)

Error of 9.1b against oracle of 7.9b and baseline of 29.8b

bsearch2.0ms

simplify8.0ms

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	42	92
1	54	92
done	54	92

end0.0ms

sample2.1s

Algorithm

intervals

Results

848.0ms	2756×	body	1280	valid
264.0ms	5402×	body	80	valid
248.0ms	1365×	body	640	valid
226.0ms	751×	body	320	valid
29.0ms	355×	body	160	valid