Details

sample255.0ms

Algorithm

intervals

Results

83.0ms	208×	body	10240	exit
81.0ms	451×	body	80	nan
14.0ms	232×	body	80	valid
4.0ms	26×	body	160	valid

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	40	12
4	74	12
5	175	12
6	479	12
7	1665	12
done	5000	12

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.4b	(- (exp (* 2.0 x)) 1.0)
5.6b	(- (exp x) 1.0)

rewrite172.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

58.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
75.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
13.0ms	(- (exp (* 2.0 x)) 1.0)
13.0ms	(- (exp x) 1.0)

series372.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
106.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
56.0ms	(- (exp (* 2.0 x)) 1.0)
40.0ms	(- (exp x) 1.0)

simplify1.7s

Counts

135 → 135

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	904	2169
3	2293	2156
done	5001	2154

prune484.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (exp x) 1.0))
0.0b	(+ (exp x) 1.0)
5.4b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-prod` `add-cbrt-cube`
3×	`difference-of-squares`
2×	`sub-neg` `flip3--` `flip3-+` `sqrt-div` `diff-log` `flip--` `flip-+` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `exp-sum` `sum-log` `distribute-lft-out--`

Counts

4 → 56

Calls

4 calls:

18.0ms	(sqrt (+ (exp x) 1.0))
9.0ms	(+ (exp x) 1.0)
14.0ms	(- (exp (* 2.0 x)) 1.0)
103.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series110.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(sqrt (+ (exp x) 1.0))
9.0ms	(+ (exp x) 1.0)
28.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.5s

Counts

68 → 68

Iterations

Useful iterations: 3 (532.0ms)

Iter	Nodes	Cost
0	127	697
1	276	657
2	718	598
3	2083	585
done	5002	585

prune367.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp x) 3)
5.4b	(- (exp (* 2.0 x)) 1.0)
5.4b	(- (exp (+ x x)) (* 1.0 1.0))
5.6b	(- 1.0 (exp x))

rewrite141.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`add-cube-cbrt`
5×	`pow1` `add-cbrt-cube`
4×	`add-exp-log` `pow-pow` `difference-of-squares`
3×	`sub-neg` `unpow-prod-down` `pow-unpow` `exp-prod` `flip3--` `diff-log` `cube-prod` `flip--`
2×	`distribute-lft-out--`
1×	`cube-mult` `pow-to-exp` `unpow3` `exp-sum` `pow-exp` `rem-cube-cbrt` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

9.0ms	(pow (exp x) 3)
25.0ms	(- (exp (* 2.0 x)) 1.0)
90.0ms	(- (exp (+ x x)) (* 1.0 1.0))
13.0ms	(- 1.0 (exp x))

series121.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(pow (exp x) 3)
30.0ms	(- (exp (* 2.0 x)) 1.0)
40.0ms	(- (exp (+ x x)) (* 1.0 1.0))
25.0ms	(- 1.0 (exp x))

simplify4.4s

Counts

80 → 80

Iterations

Useful iterations: 3 (1.6s)

Iter	Nodes	Cost
0	142	727
1	305	659
2	903	597
3	4842	586
done	5000	586

prune492.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ (* 0.5 x) 1.0))
24.1b	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sqrt-prod`
2×	`flip3-+` `sqrt-div` `associate-*r/` `flip-+` `add-log-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 37

Calls

2 calls:

52.0ms	(* x (+ (* 0.5 x) 1.0))
11.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

series238.0ms

Counts

2 → 6

Calls

2 calls:

96.0ms	(* x (+ (* 0.5 x) 1.0))
142.0ms	(sqrt (+ 2.0 (* x (+ (* 0.5 x) 1.0))))

simplify2.8s

Counts

43 → 43

Iterations

Useful iterations: 3 (943.0ms)

Iter	Nodes	Cost
0	106	598
1	280	541
2	885	507
3	3334	498
done	5002	498

prune147.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes49.0ms

Accuracy

72.3% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.0b

bsearch80.0ms

Steps

Iters	Range		Point
8	-0.0004704452395047321	-1.5977204101010247e-06	-1.2886839166735242e-05

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	36
1	32	36
done	32	36

end0.0ms

sample7.2s

Algorithm

intervals

Results

3.4s	6651×	body	10240	exit
1.9s	12526×	body	80	nan
951.0ms	7404×	body	80	valid
108.0ms	747×	body	160	valid