Details

sample49.0ms

Algorithm

intervals

Results

26.0ms

668×

body

valid

simplify2.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
7	2733
6	751
5	308
4	183
3	84
2	39
1	18
0	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.3b

localize15.0ms

Local error

Found 3 expressions with local error:

0.0b	(cosh x)
0.0b	(* (cosh x) (/ y x))
6.9b	(/ (* (cosh x) (/ y x)) z)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
17×	`add-cbrt-cube` `add-exp-log`
13×	`-un-lft-identity` `times-frac` `associate-r*` `add-cube-cbrt`
5×	`pow1` `cbrt-undiv` `cosh-def` `div-exp`
4×	`prod-exp` `cbrt-unprod`
3×	`associate-/r` `associate-l*` `add-log-exp` `associate-/l/`
2×	`frac-times` `associate-l/` `associate-r/` `div-inv` `unswap-sqr`
1×	`clear-num` `frac-2neg` `pow-prod-down` `-commutative` `associate-/l`

Counts

3 → 68

Calls

3 calls:

1.0ms	(cosh x)
19.0ms	(* (cosh x) (/ y x))
14.0ms	(/ (* (cosh x) (/ y x)) z)

series357.0ms

Counts

3 → 9

Calls

3 calls:

77.0ms	(cosh x)
118.0ms	(* (cosh x) (/ y x))
162.0ms	(/ (* (cosh x) (/ y x)) z)

simplify1.5s

Counts

77 → 77

Iterations

Iter	Nodes
done	5001
2	1402
1	377
0	150

prune487.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1/2 (exp x)) (* (exp x) 1/2))
0.0b	(/ (+ (/ 1/2 (exp x)) (* (exp x) 1/2)) x)
0.0b	(/ 1/2 (exp x))
4.9b	(* (/ (+ (/ 1/2 (exp x)) (* (exp x) 1/2)) x) (/ y z))

rewrite199.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`times-frac`
34×	`*-un-lft-identity` `add-cube-cbrt`
20×	`add-cbrt-cube`
19×	`add-exp-log`
13×	`associate-r` `associate-l`
6×	`pow1` `cbrt-undiv` `associate-/r` `div-exp` `associate-/l` `add-log-exp`
4×	`prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
2×	`clear-num` `frac-2neg` `flip3-+` `flip-+` `associate-/l/`
1×	`frac-times` `+-commutative` `sum-log` `pow-prod-down` `associate-l/` `associate-r/` `*-commutative`

Counts

4 → 117

Calls

4 calls:

34.0ms	(+ (/ 1/2 (exp x)) (* (exp x) 1/2))
67.0ms	(/ (+ (/ 1/2 (exp x)) (* (exp x) 1/2)) x)
7.0ms	(/ 1/2 (exp x))
84.0ms	(* (/ (+ (/ 1/2 (exp x)) (* (exp x) 1/2)) x) (/ y z))

series417.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(+ (/ 1/2 (exp x)) (* (exp x) 1/2))
133.0ms	(/ (+ (/ 1/2 (exp x)) (* (exp x) 1/2)) x)
19.0ms	(/ 1/2 (exp x))
201.0ms	(* (/ (+ (/ 1/2 (exp x)) (* (exp x) 1/2)) x) (/ y z))

simplify1.9s

Counts

129 → 129

Iterations

Iter	Nodes
done	5002
2	2016
1	604
0	218

prune779.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(cosh x)
0.0b	(/ y (/ x (cosh x)))
0.0b	(/ x (cosh x))
6.9b	(/ (/ y (/ x (cosh x))) z)

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

504×	`times-frac`
247×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
53×	`associate-/l*`
23×	`div-inv`
22×	`associate-/r/`
20×	`associate-/r*` `add-cbrt-cube` `add-exp-log`
18×	`cosh-def`
10×	`cbrt-undiv` `div-exp`
4×	`pow1` `add-log-exp`
3×	`clear-num` `frac-2neg`
1×	`associate-/l/`

Counts

4 → 318

Calls

4 calls:

2.0ms	(cosh x)
17.0ms	(/ y (/ x (cosh x)))
7.0ms	(/ x (cosh x))
38.0ms	(/ (/ y (/ x (cosh x))) z)

series557.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(cosh x)
163.0ms	(/ y (/ x (cosh x)))
126.0ms	(/ x (cosh x))
216.0ms	(/ (/ y (/ x (cosh x))) z)

simplify2.1s

Counts

330 → 330

Iterations

Iter	Nodes
done	5014
2	3900
1	1382
0	548

prune2.0s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(cosh x)
0.0b	(/ z (* (cosh x) y))
0.0b	(* (cosh x) y)
5.4b	(/ (/ 1 x) (/ z (* (cosh x) y)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

230×	`times-frac`
101×	`add-sqr-sqrt`
99×	`*-un-lft-identity` `add-cube-cbrt`
50×	`add-exp-log`
32×	`add-cbrt-cube`
28×	`div-exp`
25×	`div-inv`
17×	`cosh-def`
16×	`associate-l/` `associate-/r/` `associate-/l`
15×	`cbrt-undiv`
9×	`associate-/r*`
6×	`pow1` `prod-exp`
4×	`cbrt-unprod` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-r` `associate-l`
2×	`clear-num` `frac-2neg`
1×	`pow-prod-down` `*-commutative` `unswap-sqr` `associate-/l/`

Counts

4 → 204

Calls

4 calls:

2.0ms	(cosh x)
11.0ms	(/ z (* (cosh x) y))
10.0ms	(* (cosh x) y)
17.0ms	(/ (/ 1 x) (/ z (* (cosh x) y)))

series476.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(cosh x)
117.0ms	(/ z (* (cosh x) y))
89.0ms	(* (cosh x) y)
218.0ms	(/ (/ 1 x) (/ z (* (cosh x) y)))

simplify1.6s

Counts

216 → 216

Iterations

Iter	Nodes
done	5003
2	2983
1	1073
0	380

prune946.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes237.0ms

Accuracy

95.4% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 7.0b

bsearch128.0ms

Steps

Iters	Range		Point
9	8.335998337471322e-09	20.852008069825544	2.0355402558790256e-06
6	-6.808591309772948e-33	-9.52971775302429e-34	-6.394362921332223e-33

simplify6.0ms

Iterations

Iter	Nodes
done	26
1	26
0	18

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.7s

22172×

body

valid