Details

sample442.0ms

Algorithm: halfpoints

simplify4.4s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
8	2574
7	1165
6	432
5	178
4	111
3	79
2	48
1	30
0	16

prune13.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 41.7b

localize89.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.0b	(+ (exp x) (exp (- x)))
0.2b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.3b	(- (exp x) (exp (- x)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt`
39×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac`
23×	`add-cube-cbrt`
14×	`add-cbrt-cube` `add-exp-log`
8×	`pow1` `add-log-exp`
6×	`associate-r`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `flip-+` `flip--`

Counts

4 → 99

Calls

4 calls:

53.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
17.0ms	(+ (exp x) (exp (- x)))
70.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
17.0ms	(- (exp x) (exp (- x)))

series233.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
24.0ms	(+ (exp x) (exp (- x)))
93.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
47.0ms	(- (exp x) (exp (- x)))

simplify1.5s

Counts

111 → 111

Iterations

Iter	Nodes
done	5001
2	1780
1	517
0	199

prune798.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

localize125.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (* 1/3 (* x x)) 2))
0.0b	(* 1/60 (pow x 5))
0.1b	(* (/ (+ (* x (+ (* 1/3 (* x x)) 2)) (* 1/60 (pow x 5))) 2.0) (sin y))
0.2b	(* 1/3 (* x x))

rewrite173.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
22×	`associate-l`
21×	`add-exp-log`
18×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
14×	`associate-r`
13×	`pow1`
10×	`times-frac`
9×	`prod-exp`
7×	`cbrt-unprod` `unswap-sqr`
5×	`pow-prod-down`
4×	`unpow-prod-down` `*-commutative` `add-log-exp`
2×	`associate-*r/` `sqr-pow`
1×	`distribute-rgt-in` `pow-to-exp` `cbrt-undiv` `distribute-lft-in` `flip3-+` `div-exp` `associate-*l/` `pow-exp` `flip-+` `div-inv`

Counts

4 → 98

Calls

4 calls:

59.0ms	(* x (+ (* 1/3 (* x x)) 2))
9.0ms	(* 1/60 (pow x 5))
80.0ms	(* (/ (+ (* x (+ (* 1/3 (* x x)) 2)) (* 1/60 (pow x 5))) 2.0) (sin y))
21.0ms	(* 1/3 (* x x))

series303.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(* x (+ (* 1/3 (* x x)) 2))
58.0ms	(* 1/60 (pow x 5))
107.0ms	(* (/ (+ (* x (+ (* 1/3 (* x x)) 2)) (* 1/60 (pow x 5))) 2.0) (sin y))
41.0ms	(* 1/3 (* x x))

simplify1.5s

Counts

110 → 110

Iterations

Iter	Nodes
done	5002
2	1990
1	545
0	195

prune1.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 0.0b

localize149.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/3 (* x x))
0.2b	(* 1/3 (* x x))
0.4b	(* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (+ (* 1/3 (* x x)) 2)))
0.5b	(* x (sqrt (+ (* 1/3 (* x x)) 2)))

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1` `add-cbrt-cube` `add-exp-log`
17×	`add-sqr-sqrt`
14×	`sqrt-div` `associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
10×	`associate-l` `pow-prod-down` `prod-exp` `associate-*r/` `cbrt-unprod`
7×	`flip3-+` `sqrt-prod` `flip-+`
4×	`frac-times` `*-commutative` `add-log-exp` `unswap-sqr`
2×	`associate-*l/`

Counts

4 → 91

Calls

4 calls:

25.0ms	(* 1/3 (* x x))
25.0ms	(* 1/3 (* x x))
156.0ms	(* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (+ (* 1/3 (* x x)) 2)))
68.0ms	(* x (sqrt (+ (* 1/3 (* x x)) 2)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* 1/3 (* x x))
32.0ms	(* 1/3 (* x x))
132.0ms	(* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (+ (* 1/3 (* x x)) 2)))
154.0ms	(* x (sqrt (+ (* 1/3 (* x x)) 2)))

simplify1.8s

Counts

103 → 103

Iterations

Iter	Nodes
done	5015
2	1807
1	409
0	139

prune957.0ms

Pruning

13 alts after pruning (11 fresh and 2 done)

Merged error: 0.0b

localize122.0ms

Local error

Found 4 expressions with local error:

0.2b	(* 1/3 (* x x))
0.2b	(* (* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (sqrt (+ (* 1/3 (* x x)) 2)))) (sqrt (sqrt (+ (* 1/3 (* x x)) 2))))
0.4b	(* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (sqrt (+ (* 1/3 (* x x)) 2))))
0.5b	(* x (sqrt (+ (* 1/3 (* x x)) 2)))

rewrite750.0ms

Algorithm

rewrite-expression-head

Rules

110×	`sqrt-div`
36×	`associate-*r/`
34×	`flip3-+` `flip-+`
32×	`frac-times`
25×	`pow1` `add-cbrt-cube` `associate-r` `add-exp-log`
22×	`sqrt-prod`
19×	`add-sqr-sqrt`
16×	`associate-*l/`
14×	`*-un-lft-identity` `add-cube-cbrt`
13×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`associate-l`
4×	`*-commutative` `add-log-exp`
3×	`unswap-sqr`

Counts

4 → 128

Calls

4 calls:

23.0ms	(* 1/3 (* x x))
489.0ms	(* (* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (sqrt (+ (* 1/3 (* x x)) 2)))) (sqrt (sqrt (+ (* 1/3 (* x x)) 2))))
166.0ms	(* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (sqrt (+ (* 1/3 (* x x)) 2))))
66.0ms	(* x (sqrt (+ (* 1/3 (* x x)) 2)))

series659.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* 1/3 (* x x))
115.0ms	(* (* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (sqrt (+ (* 1/3 (* x x)) 2)))) (sqrt (sqrt (+ (* 1/3 (* x x)) 2))))
307.0ms	(* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (sqrt (+ (* 1/3 (* x x)) 2))))
190.0ms	(* x (sqrt (+ (* 1/3 (* x x)) 2)))

simplify3.0s

Counts

140 → 140

Iterations

Iter	Nodes
done	5002
2	2741
1	731
0	258

prune1.4s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.0b

regimes331.0ms

Accuracy

0% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 0.8b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	34
1	34
0	26

end0.0ms

sample13.1s

Algorithm: halfpoints