Details

sample333.0ms

Algorithm

intervals

Results

44.0ms	213×	body	10240	exit
13.0ms	389×	body	80	nan
8.0ms	233×	body	80	valid
2.0ms	25×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	19	12
2	28	12
3	40	12
4	74	12
5	170	12
6	464	12
7	1492	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp x) 1.0)

rewrite50.0ms

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:

14.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
15.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
7.0ms	(- (exp x) 1.0)

series200.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
60.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
25.0ms	(- (exp (* 2.0 x)) 1.0)
24.0ms	(- (exp x) 1.0)

simplify1.1s

Counts

135 → 135

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	896	2169
3	2386	2156
done	5001	2154

prune324.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (exp x) 1.0))
0.0b	(+ (exp x) 1.0)
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite44.0ms

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:

6.0ms	(sqrt (+ (exp x) 1.0))
4.0ms	(+ (exp x) 1.0)
4.0ms	(- (exp (* 2.0 x)) 1.0)
30.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series88.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(sqrt (+ (exp x) 1.0))
8.0ms	(+ (exp x) 1.0)
25.0ms	(- (exp (* 2.0 x)) 1.0)
20.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify886.0ms

Counts

68 → 68

Iterations

Useful iterations: 3 (275.0ms)

Iter	Nodes	Cost
0	127	697
1	278	657
2	721	598
3	2095	585
done	5000	585

prune220.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (exp (* 2.0 x)) 1.0) 3)
0.1b	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

6.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
6.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
4.0ms	(- (exp (* 2.0 x)) 1.0)
26.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series129.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
24.0ms	(cbrt (pow (- (exp (* 2.0 x)) 1.0) 3))
28.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify2.0s

Counts

96 → 96

Iterations

Useful iterations: 3 (527.0ms)

Iter	Nodes	Cost
0	140	1353
1	318	1136
2	923	1025
3	4278	1017
done	5000	1017

prune284.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (exp x) 3)
5.7b	(- (exp (* 2.0 x)) 1.0)
5.7b	(- (exp (+ x x)) (* 1.0 1.0))
5.8b	(- 1.0 (exp x))

rewrite37.0ms

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:

2.0ms	(pow (exp x) 3)
4.0ms	(- (exp (* 2.0 x)) 1.0)
27.0ms	(- (exp (+ x x)) (* 1.0 1.0))
3.0ms	(- 1.0 (exp x))

series83.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow (exp x) 3)
24.0ms	(- (exp (* 2.0 x)) 1.0)
22.0ms	(- (exp (+ x x)) (* 1.0 1.0))
13.0ms	(- 1.0 (exp x))

simplify2.5s

Counts

80 → 80

Iterations

Useful iterations: 3 (771.0ms)

Iter	Nodes	Cost
0	142	727
1	305	659
2	924	597
3	4535	590
done	5000	590

prune321.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes29.0ms

Accuracy

74% (0.7b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 2.9b

bsearch46.0ms

Steps

Iters	Range		Point
8	-0.0008391074150366579	-8.849834202292668e-07	-1.2887874422510308e-05

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	6739×	body	10240	exit
420.0ms	12781×	body	80	nan
263.0ms	7403×	body	80	valid
60.0ms	711×	body	160	valid