Details

sample68.0ms

Algorithm

intervals

Results

27.0ms	88×	body	1280	valid
8.0ms	180×	body	80	valid
8.0ms	42×	body	640	valid
4.0ms	26×	body	320	valid
1.0ms	13×	body	160	valid

simplify4.0s

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.6b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(exp (* a x))
3.7b	(- (exp (* a x)) 1.0)

rewrite25.0ms

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:

6.0ms	(exp (* a x))
19.0ms	(- (exp (* a x)) 1.0)

series65.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(exp (* a x))
49.0ms	(- (exp (* a x)) 1.0)

simplify1.6s

Counts

30 → 30

Iterations

Useful iterations: 3 (508.0ms)

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

prune95.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 9.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* a x)) 1.0)
0.0b	(exp (* 2 (* a x)))
0.0b	(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
3.9b	(- (exp (* 2 (* a x))) (* 1.0 1.0))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
16×	`times-frac`
14×	`add-cube-cbrt`
10×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out` `difference-of-squares`
4×	`pow1` `associate-/r` `associate-/l`
2×	`flip3--` `flip3-+` `associate-/r/` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `exp-prod` `exp-to-pow` `frac-2neg` `diff-log` `div-sub` `div-exp` `clear-num` `sum-log` `div-inv` `rem-exp-log`

Counts

4 → 76

Calls

4 calls:

10.0ms	(+ (exp (* a x)) 1.0)
9.0ms	(exp (* 2 (* a x)))
79.0ms	(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
32.0ms	(- (exp (* 2 (* a x))) (* 1.0 1.0))

series218.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(+ (exp (* a x)) 1.0)
36.0ms	(exp (* 2 (* a x)))
96.0ms	(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
61.0ms	(- (exp (* 2 (* a x))) (* 1.0 1.0))

simplify838.0ms

Counts

88 → 88

Iterations

Useful iterations: done (835.0ms)

Iter	Nodes	Cost
0	135	1710
1	351	1655
2	1310	1527
done	5000	1469

prune336.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 9.8b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (* a x) 4)
0.0b	(/ (/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (* 1.0 1.0) (pow (exp 2) (* a x)))) (+ (exp (* a x)) 1.0))
0.0b	(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (* 1.0 1.0) (pow (exp 2) (* a x))))
3.8b	(- (exp (* (* a x) 4)) (pow 1.0 4))

rewrite315.0ms

Algorithm

rewrite-expression-head

Rules

234×	`times-frac`
200×	`add-sqr-sqrt`
196×	`*-un-lft-identity`
100×	`add-cube-cbrt`
60×	`difference-of-squares`
34×	`associate-/l*`
28×	`distribute-lft-out`
20×	`unpow-prod-down` `distribute-lft-out--` `sqr-pow`
16×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/r/`
9×	`pow1`
7×	`flip3-+` `associate-/r*` `flip-+` `div-inv`
6×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`div-sub` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `associate-/l/`
2×	`flip3--` `frac-2neg` `clear-num` `flip--`
1×	`sub-neg` `diff-log` `associate-l` `*-commutative`

Counts

4 → 239

Calls

4 calls:

29.0ms	(* (* a x) 4)
123.0ms	(/ (/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (* 1.0 1.0) (pow (exp 2) (* a x)))) (+ (exp (* a x)) 1.0))
88.0ms	(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (* 1.0 1.0) (pow (exp 2) (* a x))))
44.0ms	(- (exp (* (* a x) 4)) (pow 1.0 4))

series480.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (* a x) 4)
201.0ms	(/ (/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (* 1.0 1.0) (pow (exp 2) (* a x)))) (+ (exp (* a x)) 1.0))
174.0ms	(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (+ (* 1.0 1.0) (pow (exp 2) (* a x))))
78.0ms	(- (exp (* (* a x) 4)) (pow 1.0 4))

simplify689.0ms

Counts

251 → 251

Iterations

Useful iterations: done (678.0ms)

Iter	Nodes	Cost
0	386	10396
1	1021	10019
done	5000	9691

prune1.5s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.8b

localize67.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp (* (* a x) 4)) 3) (pow (pow 1.0 4) 3)) (+ (+ (pow 1.0 8) (pow (exp (* a x)) 8)) (* (exp (* (* a x) 4)) (pow 1.0 4))))
0.0b	(pow (exp (* (* a x) 4)) 3)
0.1b	(pow (exp (* a x)) 8)
3.8b	(- (pow (exp (* (* a x) 4)) 3) (pow (pow 1.0 4) 3))

rewrite500.0ms

Algorithm

rewrite-expression-head

Rules

275×	`add-sqr-sqrt`
166×	`unpow-prod-down`
160×	`difference-of-squares`
123×	`times-frac` `cube-prod`
105×	`*-un-lft-identity`
102×	`sqr-pow`
55×	`add-cube-cbrt`
41×	`associate-/l*`
25×	`distribute-lft-out--`
8×	`add-log-exp`
7×	`add-cbrt-cube`
6×	`pow1` `add-exp-log` `pow-unpow` `pow-pow`
5×	`difference-cubes`
3×	`associate-/r*`
2×	`pow-to-exp` `exp-prod` `flip3--` `exp-to-pow` `pow-exp` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `cube-mult` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `unpow3` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv` `rem-cube-cbrt`

Counts

4 → 278

Calls

4 calls:

351.0ms	(/ (- (pow (exp (* (* a x) 4)) 3) (pow (pow 1.0 4) 3)) (+ (+ (pow 1.0 8) (pow (exp (* a x)) 8)) (* (exp (* (* a x) 4)) (pow 1.0 4))))
23.0ms	(pow (exp (* (* a x) 4)) 3)
19.0ms	(pow (exp (* a x)) 8)
88.0ms	(- (pow (exp (* (* a x) 4)) 3) (pow (pow 1.0 4) 3))

series477.0ms

Counts

4 → 12

Calls

4 calls:

239.0ms	(/ (- (pow (exp (* (* a x) 4)) 3) (pow (pow 1.0 4) 3)) (+ (+ (pow 1.0 8) (pow (exp (* a x)) 8)) (* (exp (* (* a x) 4)) (pow 1.0 4))))
54.0ms	(pow (exp (* (* a x) 4)) 3)
64.0ms	(pow (exp (* a x)) 8)
119.0ms	(- (pow (exp (* (* a x) 4)) 3) (pow (pow 1.0 4) 3))

simplify3.2s

Counts

290 → 290

Iterations

Useful iterations: done (3.2s)

Iter	Nodes	Cost
0	343	14201
1	912	13540
2	4141	13331
done	5001	12933

prune1.6s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 9.8b

regimes412.0ms

Accuracy

94.3% (1.2b remaining)

Error of 9.3b against oracle of 8.1b and baseline of 29.6b

bsearch1.0ms

simplify11.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	156
1	65	156
done	65	156

end0.0ms

sample2.2s

Algorithm

intervals

Results

770.0ms	2685×	body	1280	valid
657.0ms	1343×	body	640	valid
295.0ms	5567×	body	80	valid
84.0ms	717×	body	320	valid
32.0ms	411×	body	160	valid