Details

sample340.0ms

Algorithm

intervals

Results

49.0ms	214×	body	10240	exit
16.0ms	457×	body	80	nan
9.0ms	231×	body	80	valid
3.0ms	30×	body	160	valid

simplify1.1s

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	171	12
6	484	12
7	1947	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
0.3b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
5.8b	(- (exp (* 2.0 x)) 1.0)
5.9b	(- (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:

20.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
13.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series195.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
91.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
25.0ms	(- (exp (* 2.0 x)) 1.0)
23.0ms	(- (exp x) 1.0)

simplify1.6s

Counts

135 → 135

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	1037	2169
3	3969	2156
done	5001	2154

prune321.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
0.3b	(sqrt (+ (exp x) 1.0))
5.8b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
25×	`times-frac`
21×	`difference-of-squares`
17×	`add-cube-cbrt`
8×	`add-log-exp`
7×	`exp-sum` `distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `associate-/r` `associate-/l`
4×	`flip3--` `sqrt-prod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 96

Calls

4 calls:

40.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
5.0ms	(sqrt (+ (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
26.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series228.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp (+ x x)) (* 1.0 1.0)))
32.0ms	(sqrt (+ (exp x) 1.0))
23.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify435.0ms

Counts

108 → 108

Iterations

Useful iterations: done (431.0ms)

Iter	Nodes	Cost
0	184	1906
1	425	1852
2	1314	1709
done	5002	1694

prune358.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (- (exp (+ x x)) (* 1.0 1.0)) 3)))
0.3b	(sqrt (+ (exp x) 1.0))
5.8b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

105×	`add-sqr-sqrt`
96×	`cbrt-prod`
95×	`times-frac`
93×	`*-un-lft-identity`
49×	`add-cube-cbrt`
47×	`difference-of-squares`
30×	`unpow-prod-down` `cube-prod`
21×	`distribute-lft-out--`
19×	`associate-/r*`
13×	`exp-sum`
8×	`add-log-exp`
6×	`add-exp-log` `cube-mult` `unpow3` `sqr-pow`
5×	`pow1` `add-cbrt-cube` `associate-/l*`
4×	`flip3--` `sqrt-prod` `flip--`
2×	`cube-div` `sub-neg` `cbrt-div` `sqrt-div` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 180

Calls

4 calls:

76.0ms	(/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (- (exp (+ x x)) (* 1.0 1.0)) 3)))
5.0ms	(sqrt (+ (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
26.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series234.0ms

Counts

4 → 12

Calls

4 calls:

156.0ms	(/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (- (exp (+ x x)) (* 1.0 1.0)) 3)))
35.0ms	(sqrt (+ (exp x) 1.0))
24.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify800.0ms

Counts

192 → 192

Iterations

Useful iterations: done (793.0ms)

Iter	Nodes	Cost
0	278	5128
1	632	4405
2	2113	4058
done	5000	4056

prune500.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (cbrt (pow (- (exp (+ x x)) (* 1.0 1.0)) 3)) 3)))
0.3b	(sqrt (+ (exp x) 1.0))
5.8b	(- (exp (* 2.0 x)) 1.0)
5.8b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

456×	`cbrt-prod`
237×	`add-sqr-sqrt`
235×	`times-frac`
213×	`*-un-lft-identity`
174×	`unpow-prod-down` `cube-prod`
113×	`add-cube-cbrt`
99×	`difference-of-squares`
49×	`distribute-lft-out--`
47×	`associate-/r*`
25×	`exp-sum`
18×	`cube-mult` `unpow3` `sqr-pow`
8×	`add-log-exp`
6×	`add-exp-log`
5×	`pow1` `add-cbrt-cube` `associate-/l*`
4×	`cube-div` `cbrt-div` `flip3--` `sqrt-prod` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 348

Calls

4 calls:

140.0ms	(/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (cbrt (pow (- (exp (+ x x)) (* 1.0 1.0)) 3)) 3)))
8.0ms	(sqrt (+ (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
26.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series239.0ms

Counts

4 → 12

Calls

4 calls:

159.0ms	(/ (- (exp (* 2.0 x)) 1.0) (cbrt (pow (cbrt (pow (- (exp (+ x x)) (* 1.0 1.0)) 3)) 3)))
30.0ms	(sqrt (+ (exp x) 1.0))
30.0ms	(- (exp (* 2.0 x)) 1.0)
19.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.0s

Counts

360 → 360

Iterations

Useful iterations: done (993.0ms)

Iter	Nodes	Cost
0	384	12786
1	868	9589
2	2381	8850
done	5001	8848

prune553.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes25.0ms

Accuracy

78.6% (0.6b remaining)

Error of 0.7b against oracle of 0.2b and baseline of 2.8b

bsearch38.0ms

Steps

Iters	Range		Point
5	-4.022447873684564e-15	-1.6668736937815573e-15	-2.5679454952614643e-15

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	51
1	43	51
done	43	51

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.4s	6643×	body	10240	exit
428.0ms	12688×	body	80	nan
275.0ms	7478×	body	80	valid
55.0ms	664×	body	160	valid