Details

sample326.0ms

Algorithm

intervals

Results

32.0ms	173×	body	10240	exit
11.0ms	337×	body	80	nan
8.0ms	243×	body	80	valid
2.0ms	20×	body	160	valid

simplify1.5s

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	483	12
7	1538	12
done	5000	12

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.2b

localize12.0ms

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))
3.9b	(- (exp (* 2.0 x)) 1.0)
4.1b	(- (exp x) 1.0)

rewrite44.0ms

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:

13.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
14.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series207.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
60.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms	(- (exp (* 2.0 x)) 1.0)
30.0ms	(- (exp x) 1.0)

simplify1.2s

Counts

135 → 135

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	189	2376
1	388	2279
2	896	2169
3	2384	2156
done	5000	2154

prune321.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
0.1b	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
3.9b	(- (exp (* 2.0 x)) 1.0)
3.9b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

270×	`times-frac`
230×	`*-un-lft-identity`
188×	`add-sqr-sqrt`
102×	`add-cube-cbrt`
88×	`difference-of-squares`
36×	`distribute-lft-out`
30×	`exp-sum` `associate-/r*`
28×	`distribute-lft-out--`
15×	`associate-/r/`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/l*`
8×	`div-inv` `add-log-exp`
7×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `flip3--` `div-exp` `flip--` `associate-/l/`
2×	`sub-neg` `frac-2neg` `diff-log` `div-sub` `clear-num`

Counts

4 → 253

Calls

4 calls:

61.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
50.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
4.0ms	(- (exp (* 2.0 x)) 1.0)
25.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series183.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0))
92.0ms	(/ (- (exp (* 2.0 x)) 1.0) (/ (- (exp (+ x x)) (* 1.0 1.0)) (+ (exp x) 1.0)))
29.0ms	(- (exp (* 2.0 x)) 1.0)
21.0ms	(- (exp (+ x x)) (* 1.0 1.0))

simplify1.2s

Counts

265 → 265

Iterations

Useful iterations: 2 (547.0ms)

Iter	Nodes	Cost
0	360	8009
1	1036	7743
2	3591	7375
done	5000	7375

prune735.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize17.0ms

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))
3.9b	(- (exp (* 2.0 x)) 1.0)
3.9b	(- (exp (+ x x)) (* 1.0 1.0))

rewrite46.0ms

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)
28.0ms	(- (exp (+ x x)) (* 1.0 1.0))

series130.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(pow (- (exp (* 2.0 x)) 1.0) 3)
25.0ms	(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))

simplify2.2s

Counts

96 → 96

Iterations

Useful iterations: 3 (598.0ms)

Iter	Nodes	Cost
0	140	1353
1	319	1136
2	916	1025
3	4246	1017
done	5000	1017

prune270.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* 0.5 (pow x 2)) (+ (* 1.0 x) 2.0))
27.5b	(sqrt (+ (* 0.5 (pow x 2)) (+ (* 1.0 x) 2.0)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-log-exp`
4×	`add-sqr-sqrt`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sum-log` `sqrt-prod`
2×	`add-exp-log` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `associate-+r+` `sqrt-pow1` `pow1/2`

Counts

2 → 28

Calls

2 calls:

8.0ms	(+ (* 0.5 (pow x 2)) (+ (* 1.0 x) 2.0))
14.0ms	(sqrt (+ (* 0.5 (pow x 2)) (+ (* 1.0 x) 2.0)))

series107.0ms

Counts

2 → 6

Calls

2 calls:

26.0ms	(+ (* 0.5 (pow x 2)) (+ (* 1.0 x) 2.0))
80.0ms	(sqrt (+ (* 0.5 (pow x 2)) (+ (* 1.0 x) 2.0)))

simplify1.4s

Counts

34 → 34

Iterations

Useful iterations: 3 (376.0ms)

Iter	Nodes	Cost
0	79	664
1	219	619
2	735	559
3	3111	488
done	5001	488

prune74.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes26.0ms

Accuracy

99.5% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 2.8b

bsearch72.0ms

Steps

Iters	Range		Point
6	1.0433743232564454e-14	1.316736141892985e-13	1.1457866946809401e-14
7	-1.4191042175333267e-05	-5.670122129476186e-07	-1.2938199112682712e-05

simplify3.0ms

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	29	62
1	38	42
done	38	42

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	6619×	body	10240	exit
373.0ms	12562×	body	80	nan
241.0ms	7441×	body	80	valid
52.0ms	695×	body	160	valid