Details

sample493.0ms

Algorithm: halfpoints

simplify1.1s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	16	24
1	30	11
2	48	11
3	83	11
4	118	11
5	231	11
6	979	11
done	5000	11

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.7b

localize58.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.9b	(- (exp x) (exp (- x)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
36×	`*-un-lft-identity`
35×	`associate-l`
29×	`times-frac`
22×	`add-cube-cbrt`
13×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-r`
5×	`add-log-exp`
4×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`distribute-lft-out`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 87

Calls

3 calls:

55.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
73.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
15.0ms	(- (exp x) (exp (- x)))

series289.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(* (/ (+ (exp x) (exp (- x))) 2.0) (cos y))
137.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
66.0ms	(- (exp x) (exp (- x)))

simplify1.5s

Counts

96 → 96

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	188	1322
1	496	1301
2	2273	1151
done	5002	1147

prune597.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize112.0ms

Local error

Found 4 expressions with local error:

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

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
22×	`associate-r`
19×	`add-exp-log` `add-cube-cbrt` `-un-lft-identity` `associate-l*`
13×	`add-cbrt-cube`
10×	`times-frac`
9×	`unswap-sqr`
8×	`unpow-prod-down` `prod-exp`
6×	`pow1` `add-log-exp`
4×	`cube-prod` `cbrt-unprod` `sqr-pow`
3×	`*-commutative`
2×	`pow-to-exp` `pow-exp`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `flip3-+` `unpow3` `div-exp` `pow-prod-down` `associate-*l/` `sum-log` `flip-+` `div-inv`

Counts

4 → 99

Calls

4 calls:

9.0ms	(+ (* 1/60 (pow x 5)) (* 2 x))
17.0ms	(* 1/60 (pow x 5))
136.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
26.0ms	(* 1/3 (pow x 3))

series513.0ms

Counts

4 → 12

Calls

4 calls:

243.0ms	(+ (* 1/60 (pow x 5)) (* 2 x))
62.0ms	(* 1/60 (pow x 5))
159.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
49.0ms	(* 1/3 (pow x 3))

simplify1.4s

Counts

111 → 111

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	193	1563
1	504	1469
2	2179	1303
done	5000	1302

prune796.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize111.0ms

Local error

Found 4 expressions with local error:

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

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
73×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
21×	`add-exp-log`
19×	`associate-r`
16×	`associate-/r*`
15×	`add-cbrt-cube`
8×	`unpow-prod-down`
7×	`unswap-sqr`
6×	`associate-l` `prod-exp` `div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv` `cube-prod` `div-exp` `add-log-exp` `sqr-pow`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `*-commutative` `cbrt-unprod` `associate-/l/`
1×	`cube-mult` `flip3-+` `unpow3` `associate-/r/` `flip-+`

Counts

4 → 155

Calls

4 calls:

17.0ms	(* 1/60 (pow x 5))
14.0ms	(* 1/3 (pow x 3))
6.0ms	(/ 2.0 (sin y))
128.0ms	(/ (+ (* 1/60 (pow x 5)) (+ (* 2 x) (* 1/3 (pow x 3)))) (/ 2.0 (sin y)))

series275.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* 1/60 (pow x 5))
67.0ms	(* 1/3 (pow x 3))
22.0ms	(/ 2.0 (sin y))
127.0ms	(/ (+ (* 1/60 (pow x 5)) (+ (* 2 x) (* 1/3 (pow x 3)))) (/ 2.0 (sin y)))

simplify2.1s

Counts

167 → 167

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	280	3432
1	736	3288
2	3654	3107
done	5000	3100

prune1.4s

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize91.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/3 (pow x 3))
0.2b	(/ (+ (* 1/60 (pow x 5)) (+ (* 2 x) (* 1/3 (pow x 3)))) (* (sqrt 2.0) (/ (sqrt 2.0) (sin y))))
0.4b	(* (sqrt 2.0) (/ (sqrt 2.0) (sin y)))
0.4b	(/ (sqrt 2.0) (sin y))

rewrite190.0ms

Algorithm

rewrite-expression-head

Rules

63×	`add-sqr-sqrt`
43×	`times-frac`
40×	`add-cube-cbrt` `*-un-lft-identity`
34×	`associate-r`
29×	`sqrt-prod`
25×	`add-exp-log`
22×	`add-cbrt-cube`
10×	`unswap-sqr`
9×	`associate-l` `associate-/l*`
7×	`prod-exp`
6×	`pow1` `cbrt-undiv` `div-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `cube-prod` `associate-/r*` `add-log-exp`
3×	`div-inv`
2×	`frac-2neg` `associate-r/` `clear-num` `-commutative` `associate-/l/` `sqr-pow`
1×	`cube-mult` `pow-to-exp` `flip3-+` `unpow3` `pow-prod-down` `pow-exp` `associate-/r/` `flip-+`

Counts

4 → 144

Calls

4 calls:

15.0ms	(* 1/3 (pow x 3))
113.0ms	(/ (+ (* 1/60 (pow x 5)) (+ (* 2 x) (* 1/3 (pow x 3)))) (* (sqrt 2.0) (/ (sqrt 2.0) (sin y))))
38.0ms	(* (sqrt 2.0) (/ (sqrt 2.0) (sin y)))
19.0ms	(/ (sqrt 2.0) (sin y))

series535.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* 1/3 (pow x 3))
286.0ms	(/ (+ (* 1/60 (pow x 5)) (+ (* 2 x) (* 1/3 (pow x 3)))) (* (sqrt 2.0) (/ (sqrt 2.0) (sin y))))
123.0ms	(* (sqrt 2.0) (/ (sqrt 2.0) (sin y)))
70.0ms	(/ (sqrt 2.0) (sin y))

simplify5.0s

Counts

156 → 156

Iterations

Useful iterations: 2 (1.8s)

Iter	Nodes	Cost
0	239	2363
1	643	2170
2	4520	1755
done	5000	1755

prune1.2s

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.0b

regimes323.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	33
1	35	33
done	35	33

end0.0ms

sample12.3s

Algorithm: halfpoints