Details

sample302.0ms

Algorithm

intervals

Results

139.0ms	179×	body	10240	exit
28.0ms	351×	body	80	nan
16.0ms	241×	body	80	valid
3.0ms	19×	body	160	valid

simplify1.3s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	752
5	179
4	74
3	40
2	28
1	19
0	10

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 3.4b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
0.0b	(pow (exp x) 2.0)
4.0b	(- (pow (exp x) 2.0) 1.0)
4.0b	(- (exp x) 1.0)

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

74×	`add-sqr-sqrt`
53×	`*-un-lft-identity`
35×	`times-frac`
30×	`difference-of-squares`
21×	`add-cube-cbrt`
16×	`distribute-lft-out--`
10×	`unpow-prod-down`
8×	`add-log-exp` `sqr-pow`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r*`
4×	`pow-pow` `flip3--` `flip--`
3×	`pow-unpow` `exp-prod`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`pow-to-exp` `cbrt-undiv` `clear-num` `frac-2neg` `div-sub` `div-exp` `pow-exp` `div-inv`

Counts

4 → 114

Calls

4 calls:

76.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
6.0ms	(pow (exp x) 2.0)
32.0ms	(- (pow (exp x) 2.0) 1.0)
18.0ms	(- (exp x) 1.0)

series240.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
94.0ms	(pow (exp x) 2.0)
34.0ms	(- (pow (exp x) 2.0) 1.0)
27.0ms	(- (exp x) 1.0)

simplify824.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1608
1	463
0	183

prune712.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2.0)
0.0b	(pow (exp x) 2.0)
4.0b	(- (sqrt (pow (exp x) 2.0)) (sqrt 1.0))
4.0b	(- (exp x) 1.0)

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
12×	`sqrt-prod`
10×	`add-cube-cbrt`
9×	`difference-of-squares`
8×	`unpow-prod-down` `pow-pow` `add-log-exp`
6×	`pow1` `pow-unpow` `exp-prod`
4×	`add-cbrt-cube` `add-exp-log` `sqr-pow`
3×	`distribute-lft-out--`
2×	`pow-to-exp` `sub-neg` `flip3--` `diff-log` `pow-exp` `flip--`

Counts

4 → 76

Calls

4 calls:

5.0ms	(pow (exp x) 2.0)
7.0ms	(pow (exp x) 2.0)
29.0ms	(- (sqrt (pow (exp x) 2.0)) (sqrt 1.0))
11.0ms	(- (exp x) 1.0)

series289.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(pow (exp x) 2.0)
140.0ms	(pow (exp x) 2.0)
31.0ms	(- (sqrt (pow (exp x) 2.0)) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

simplify1.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5002
3	3262
2	897
1	270
0	112

prune507.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- (exp x) 1.0) 3)
0.1b	(cbrt (pow (- (exp x) 1.0) 3))
4.0b	(- (sqrt (pow (exp x) 2.0)) (sqrt 1.0))
4.0b	(- (exp x) 1.0)

rewrite122.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 92

Calls

4 calls:

23.0ms	(pow (- (exp x) 1.0) 3)
22.0ms	(cbrt (pow (- (exp x) 1.0) 3))
55.0ms	(- (sqrt (pow (exp x) 2.0)) (sqrt 1.0))
16.0ms	(- (exp x) 1.0)

series141.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(pow (- (exp x) 1.0) 3)
20.0ms	(cbrt (pow (- (exp x) 1.0) 3))
51.0ms	(- (sqrt (pow (exp x) 2.0)) (sqrt 1.0))
27.0ms	(- (exp x) 1.0)

simplify1.2s

Counts

104 → 104

Iterations

Iter	Nodes
done	5002
2	1786
1	379
0	141

prune545.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize19.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* (* 1/2 x) x) x)
25.8b	(sqrt (+ 2 (+ (* (* 1/2 x) x) x)))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `sqrt-prod` `add-log-exp`
3×	`pow1` `add-cube-cbrt`
2×	`flip3-+` `add-cbrt-cube` `sqrt-div` `add-exp-log` `flip-+`
1×	`+-commutative` `rem-sqrt-square` `sum-log` `distribute-lft1-in` `sqrt-pow1` `distribute-rgt-out` `pow1/2` `distribute-lft-out`

Counts

2 → 29

Calls

2 calls:

21.0ms	(+ (* (* 1/2 x) x) x)
90.0ms	(sqrt (+ 2 (+ (* (* 1/2 x) x) x)))

series167.0ms

Counts

2 → 6

Calls

2 calls:

69.0ms	(+ (* (* 1/2 x) x) x)
98.0ms	(sqrt (+ 2 (+ (* (* 1/2 x) x) x)))

simplify609.0ms

Counts

35 → 35

Iterations

Iter	Nodes
done	5000
2	1094
1	229
0	86

prune118.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes41.0ms

Accuracy

73.9% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 3.1b

bsearch63.0ms

Steps

Iters	Range		Point
8	-0.00028809610572707044	-1.3580961426078482e-07	-1.7510472603446805e-05

simplify3.0ms

Iterations

Iter	Nodes
done	31
1	31
0	26

end0.0ms

sample7.4s

Algorithm

intervals

Results

4.4s	6632×	body	10240	exit
1.4s	12660×	body	80	nan
750.0ms	7383×	body	80	valid
166.0ms	756×	body	160	valid