Details

sample400.0ms

Algorithm

intervals

Results

221.0ms	193×	body	10240	exit
57.0ms	413×	body	80	nan
18.0ms	236×	body	80	valid
4.0ms	24×	body	160	valid

simplify981.0ms

Counts

1 → 1

Iterations

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

prune26.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
0.2b	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
4.5b	(- (pow (exp x) 2.0) 1.0)
4.7b	(- (exp x) 1.0)

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
87×	`*-un-lft-identity`
71×	`times-frac`
52×	`difference-of-squares`
41×	`sqrt-prod`
31×	`add-cube-cbrt`
28×	`distribute-lft-out--`
12×	`unpow-prod-down` `sqr-pow`
8×	`add-log-exp`
7×	`associate-/l*`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r*` `flip3--` `flip--`
4×	`associate-/r/`
2×	`rem-sqrt-square` `sub-neg` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp`

Counts

4 → 147

Calls

4 calls:

61.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
63.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
37.0ms	(- (pow (exp x) 2.0) 1.0)
19.0ms	(- (exp x) 1.0)

series255.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0))
109.0ms	(sqrt (/ (- (pow (exp x) 2.0) 1.0) (- (exp x) 1.0)))
44.0ms	(- (pow (exp x) 2.0) 1.0)
34.0ms	(- (exp x) 1.0)

simplify757.0ms

Counts

159 → 159

Iterations

Iter	Nodes
done	5000
2	1477
1	475
0	231

prune800.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) (- (exp x) 1.0))
0.2b	(sqrt (+ (sqrt 1.0) (pow (exp x) (/ 2.0 2))))
4.7b	(- (exp x) 1.0)
4.7b	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

117×	`add-sqr-sqrt`
62×	`*-un-lft-identity`
54×	`difference-of-squares`
50×	`times-frac`
25×	`sqrt-prod`
22×	`add-cube-cbrt`
19×	`distribute-lft-out--`
14×	`unpow-prod-down` `sqr-pow`
10×	`associate-/l*`
8×	`add-log-exp`
6×	`add-cbrt-cube` `add-exp-log`
5×	`pow1` `associate-/r*`
4×	`flip3--` `flip--`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `div-exp` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 131

Calls

4 calls:

79.0ms	(/ (- (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) (- (exp x) 1.0))
27.0ms	(sqrt (+ (sqrt 1.0) (pow (exp x) (/ 2.0 2))))
13.0ms	(- (exp x) 1.0)
34.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))

series240.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/ (- (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) (- (exp x) 1.0))
77.0ms	(sqrt (+ (sqrt 1.0) (pow (exp x) (/ 2.0 2))))
18.0ms	(- (exp x) 1.0)
36.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))

simplify777.0ms

Counts

143 → 143

Iterations

Iter	Nodes
done	5000
2	1576
1	496
0	212

prune696.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (cbrt (pow (- (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) 3)) (- (exp x) 1.0))
0.2b	(sqrt (+ (sqrt 1.0) (pow (exp x) (/ 2.0 2))))
4.7b	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
4.7b	(- (exp x) 1.0)

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

252×	`add-sqr-sqrt`
156×	`cbrt-prod`
149×	`*-un-lft-identity`
145×	`times-frac`
109×	`difference-of-squares`
86×	`unpow-prod-down`
60×	`cube-prod`
59×	`add-cube-cbrt`
44×	`distribute-lft-out--`
43×	`sqrt-prod`
32×	`sqr-pow`
29×	`associate-/l*`
8×	`add-log-exp`
6×	`cube-mult` `unpow3` `add-exp-log`
5×	`pow1` `associate-/r*` `add-cbrt-cube`
4×	`flip3--` `flip--`
2×	`cube-div` `cbrt-div` `sub-neg` `sqrt-div` `diff-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-exp` `flip-+` `div-inv` `distribute-lft-out`

Counts

4 → 244

Calls

4 calls:

125.0ms	(/ (cbrt (pow (- (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) 3)) (- (exp x) 1.0))
21.0ms	(sqrt (+ (sqrt 1.0) (pow (exp x) (/ 2.0 2))))
28.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
15.0ms	(- (exp x) 1.0)

series304.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(/ (cbrt (pow (- (pow (exp x) (/ 2.0 2)) (sqrt 1.0)) 3)) (- (exp x) 1.0))
106.0ms	(sqrt (+ (sqrt 1.0) (pow (exp x) (/ 2.0 2))))
52.0ms	(- (pow (exp x) (/ 2.0 2)) (sqrt 1.0))
27.0ms	(- (exp x) 1.0)

simplify1.4s

Counts

256 → 256

Iterations

Iter	Nodes
done	5004
2	2699
1	643
0	310

prune1.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (/ (* 1/2 x) (sqrt 2)) (* (/ (* x x) (sqrt 2)) (- 1/4 1/16))) (sqrt 2))
0.2b	(* (/ (* x x) (sqrt 2)) (- 1/4 1/16))
0.2b	(/ (* x x) (sqrt 2))
0.4b	(/ (* 1/2 x) (sqrt 2))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
23×	`add-cbrt-cube` `add-exp-log`
20×	`*-un-lft-identity` `times-frac`
16×	`add-cube-cbrt` `sqrt-prod`
12×	`associate-/r*`
10×	`associate-l`
9×	`add-log-exp`
6×	`pow1` `cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
5×	`associate-r`
3×	`sum-log` `div-inv` `unswap-sqr`
2×	`distribute-rgt-in` `frac-times` `clear-num` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3--` `associate-r/` `flip--` `associate-/l`
1×	`+-commutative` `associate-+l+` `flip3-+` `pow-prod-down` `associate-l/` `-commutative` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 110

Calls

4 calls:

118.0ms	(+ (+ (/ (* 1/2 x) (sqrt 2)) (* (/ (* x x) (sqrt 2)) (- 1/4 1/16))) (sqrt 2))
49.0ms	(* (/ (* x x) (sqrt 2)) (- 1/4 1/16))
10.0ms	(/ (* x x) (sqrt 2))
9.0ms	(/ (* 1/2 x) (sqrt 2))

series374.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (+ (/ (* 1/2 x) (sqrt 2)) (* (/ (* x x) (sqrt 2)) (- 1/4 1/16))) (sqrt 2))
90.0ms	(* (/ (* x x) (sqrt 2)) (- 1/4 1/16))
88.0ms	(/ (* x x) (sqrt 2))
93.0ms	(/ (* 1/2 x) (sqrt 2))

simplify1.7s

Counts

122 → 122

Iterations

Iter	Nodes
done	5002
2	3454
1	556
0	180

prune532.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

regimes95.0ms

Accuracy

72.1% (0.8b remaining)

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

bsearch87.0ms

Steps

Iters	Range		Point
9	-0.0007095347148853646	-6.590418748316962e-09	-3.392149690240269e-07

simplify6.0ms

Iterations

Iter	Nodes
done	45
1	45
0	36

end0.0ms

sample7.7s

Algorithm

intervals

Results

4.6s	6821×	body	10240	exit
1.2s	12777×	body	80	nan
1.1s	7393×	body	80	valid
156.0ms	723×	body	160	valid