Details

sample301.0ms

Algorithm

intervals

Results

149.0ms	235×	body	10240	exit
21.0ms	413×	body	80	nan
12.0ms	226×	body	80	valid
4.0ms	33×	body	160	valid

simplify880.0ms

Counts

1 → 1

Iterations

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

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.5b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp x) 2.0)
0.0b	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
6.6b	(- (pow (exp x) 2.0) 1.0)
6.7b	(- (exp x) 1.0)

rewrite122.0ms

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:

7.0ms	(pow (exp x) 2.0)
77.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
17.0ms	(- (pow (exp x) 2.0) 1.0)
11.0ms	(- (exp x) 1.0)

series299.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(pow (exp x) 2.0)
92.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
36.0ms	(- (pow (exp x) 2.0) 1.0)
36.0ms	(- (exp x) 1.0)

simplify869.0ms

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1607
1	463
0	183

prune597.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize30.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* (+ (sqrt 1.0) (pow (exp x) (/ 2.0 2))) (/ (- (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) (- (exp x) 1.0))))
0.0b	(+ (sqrt 1.0) (pow (exp x) (/ 2.0 2)))
6.7b	(- (exp x) 1.0)
6.7b	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity` `add-log-exp`
7×	`pow1` `difference-of-squares`
5×	`sqrt-div`
4×	`add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `sqrt-prod`
3×	`flip3-+` `flip-+`
2×	`frac-times` `sub-neg` `unpow-prod-down` `sqrt-pow1` `flip3--` `diff-log` `associate-*l/` `flip--` `distribute-lft-out--` `sqr-pow`
1×	`+-commutative` `sum-log` `pow1/2` `pow-prod-down` `associate-*r/` `distribute-lft-out`

Counts

4 → 61

Calls

4 calls:

53.0ms	(sqrt (* (+ (sqrt 1.0) (pow (exp x) (/ 2.0 2))) (/ (- (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) (- (exp x) 1.0))))
22.0ms	(+ (sqrt 1.0) (pow (exp x) (/ 2.0 2)))
17.0ms	(- (exp x) 1.0)
44.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))

series483.0ms

Counts

4 → 12

Calls

4 calls:

394.0ms	(sqrt (* (+ (sqrt 1.0) (pow (exp x) (/ 2.0 2))) (/ (- (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) (- (exp x) 1.0))))
31.0ms	(+ (sqrt 1.0) (pow (exp x) (/ 2.0 2)))
17.0ms	(- (exp x) 1.0)
40.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))

simplify888.0ms

Counts

73 → 73

Iterations

Iter	Nodes
done	5000
2	1900
1	462
0	191

prune383.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (pow (exp x) (/ 2.0 2)) 3)
6.7b	(- (exp x) 1.0)
6.7b	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
6.7b	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

5.0ms	(pow (pow (exp x) (/ 2.0 2)) 3)
8.0ms	(- (exp x) 1.0)
35.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
38.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))

series298.0ms

Counts

4 → 12

Calls

4 calls:

176.0ms	(pow (pow (exp x) (/ 2.0 2)) 3)
21.0ms	(- (exp x) 1.0)
54.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
47.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))

simplify870.0ms

Counts

97 → 97

Iterations

Iter	Nodes
done	5000
2	1256
1	339
0	128

prune533.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (+ (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) 3))
0.1b	(pow (+ (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) 3)
6.7b	(- (exp x) 1.0)
6.7b	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

31.0ms	(cbrt (pow (+ (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) 3))
30.0ms	(pow (+ (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) 3)
8.0ms	(- (exp x) 1.0)
19.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))

series227.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(cbrt (pow (+ (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) 3))
129.0ms	(pow (+ (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) 3)
15.0ms	(- (exp x) 1.0)
34.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))

simplify1.4s

Counts

97 → 97

Iterations

Iter	Nodes
done	5002
2	2163
1	453
0	163

prune446.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes64.0ms

Accuracy

77.1% (0.7b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.2b

bsearch94.0ms

Steps

Iters	Range		Point
9	-22.455199697559465	-3.034734332568842e-06	-1.3366795942010554e-05

simplify9.0ms

Iterations

Iter	Nodes
done	36
1	36
0	29

end0.0ms

sample7.5s

Algorithm

intervals

Results

4.2s	6649×	body	10240	exit
1.4s	12634×	body	80	nan
1.0s	7388×	body	80	valid
164.0ms	752×	body	160	valid