Details

sample516.0ms

Algorithm: halfpoints

simplify1.0s

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.7b

localize58.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.8b	(- (exp x) (exp (- x)))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`*-un-lft-identity`
19×	`associate-l`
16×	`times-frac`
12×	`add-cube-cbrt`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-r`
2×	`prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip--` `div-inv`

Counts

2 → 52

Calls

2 calls:

79.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
18.0ms	(- (exp x) (exp (- x)))

series176.0ms

Counts

2 → 6

Calls

2 calls:

120.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
56.0ms	(- (exp x) (exp (- x)))

simplify805.0ms

Counts

58 → 58

Iterations

Useful iterations: 2 (206.0ms)

Iter	Nodes	Cost
0	121	770
1	307	755
2	1228	669
done	5001	669

prune215.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize57.0ms

Local error

Found 4 expressions with local error:

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

rewrite190.0ms

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×	`add-log-exp` `unswap-sqr`
8×	`unpow-prod-down` `prod-exp`
6×	`pow1`
4×	`cube-prod` `cbrt-unprod` `sqr-pow`
3×	`sum-log` `*-commutative`
2×	`pow-to-exp` `pow-exp`
1×	`cbrt-undiv` `+-commutative` `cube-mult` `associate-+r+` `flip3-+` `unpow3` `div-exp` `pow-prod-down` `associate-*l/` `flip-+` `div-inv`

Counts

4 → 101

Calls

4 calls:

39.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
13.0ms	(* 1/60 (pow x 5))
18.0ms	(* 1/3 (pow x 3))
117.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

series342.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
87.0ms	(* 1/60 (pow x 5))
46.0ms	(* 1/3 (pow x 3))
119.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

simplify1.4s

Counts

113 → 113

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	192	1718
1	497	1616
2	2228	1442
done	5001	1441

prune529.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
0.4b	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
0.4b	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
1.0b	(/ 1 (sqrt 2.0))

rewrite472.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
69×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
54×	`add-exp-log`
44×	`associate-l`
43×	`sqrt-prod`
34×	`add-cbrt-cube`
22×	`prod-exp`
14×	`div-exp`
13×	`pow1`
12×	`associate-/r*` `cbrt-unprod`
8×	`cbrt-undiv`
6×	`associate-/l*`
4×	`rec-exp` `1-exp` `associate-r` `pow-prod-down` `associate-*l/` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative` `associate-/l/`
1×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `flip-+` `inv-pow`

Counts

4 → 182

Calls

4 calls:

171.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
184.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
101.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
9.0ms	(/ 1 (sqrt 2.0))

series758.0ms

Counts

4 → 10

Calls

4 calls:

238.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
331.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
188.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify3.2s

Counts

192 → 192

Iterations

Useful iterations: 2 (773.0ms)

Iter	Nodes	Cost
0	256	4878
1	730	4621
2	4438	4014
done	5000	4014

prune921.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize90.0ms

Local error

Found 4 expressions with local error:

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

rewrite366.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt`
40×	`add-exp-log`
39×	`add-cube-cbrt` `*-un-lft-identity`
38×	`times-frac`
32×	`associate-l`
22×	`sqrt-prod` `add-cbrt-cube`
20×	`prod-exp`
16×	`associate-r`
8×	`cbrt-unprod`
7×	`unpow-prod-down` `unswap-sqr`
6×	`pow1` `associate-/r*`
5×	`div-exp`
4×	`pow-to-exp` `cube-prod` `pow-exp` `add-log-exp`
3×	`cbrt-undiv` `-commutative` `associate-/l` `sqr-pow`
2×	`associate-*l/` `div-inv` `associate-/l/`
1×	`cube-mult` `frac-2neg` `flip3-+` `unpow3` `associate-*r/` `pow-prod-down` `clear-num` `flip-+`

Counts

4 → 143

Calls

4 calls:

15.0ms	(* 1/3 (pow x 3))
91.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
126.0ms	(* (pow 2.0 -1/2) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
128.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

series843.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* 1/3 (pow x 3))
290.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
333.0ms	(* (pow 2.0 -1/2) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
162.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

simplify2.0s

Counts

155 → 155

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	260	3877
1	697	3736
2	3308	3357
done	5002	3356

prune867.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes115.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	20
1	24	20
done	24	20

end0.0ms

sample12.8s

Algorithm: halfpoints