Details

sample273.0ms

Algorithm: halfpoints

simplify3.5s

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	16	24
1	30	11
2	46	11
3	81	11
4	113	11
5	181	11
6	310	11
7	597	11
8	982	11
9	1505	11
10	1702	11
11	1839	11
12	1865	11
done	1865	11

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.3b

localize36.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.1b	(- (exp x) (exp (- x)))

rewrite37.0ms

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:

26.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
6.0ms	(- (exp x) (exp (- x)))

series115.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
36.0ms	(- (exp x) (exp (- x)))

simplify1.0s

Counts

58 → 58

Iterations

Useful iterations: 3 (389.0ms)

Iter	Nodes	Cost
0	121	770
1	295	755
2	774	669
3	2499	668
done	5000	668

prune155.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 3 expressions with local error:

0.1b	(* 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))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

35×	`add-sqr-sqrt`
22×	`associate-r`
19×	`associate-l`
18×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
12×	`add-cbrt-cube`
10×	`times-frac`
9×	`unswap-sqr`
8×	`unpow-prod-down` `prod-exp`
5×	`pow1`
4×	`cube-prod` `cbrt-unprod` `sqr-pow`
3×	`*-commutative` `add-log-exp`
2×	`pow-to-exp` `pow-exp`
1×	`cbrt-undiv` `cube-mult` `unpow3` `div-exp` `pow-prod-down` `associate-*l/` `div-inv`

Counts

3 → 88

Calls

3 calls:

5.0ms	(* 1/60 (pow x 5))
37.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
7.0ms	(* 1/3 (pow x 3))

series170.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* 1/60 (pow x 5))
86.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
36.0ms	(* 1/3 (pow x 3))

simplify527.0ms

Counts

97 → 97

Iterations

Useful iterations: 2 (163.0ms)

Iter	Nodes	Cost
0	174	1355
1	408	1282
2	1199	1134
done	5000	1134

prune272.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

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))
0.3b	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
0.5b	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
1.0b	(/ 1 (sqrt 2.0))

rewrite130.0ms

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:

40.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
49.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
28.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
3.0ms	(/ 1 (sqrt 2.0))

series487.0ms

Counts

4 → 10

Calls

4 calls:

153.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
215.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
119.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify964.0ms

Counts

192 → 192

Iterations

Useful iterations: done (954.0ms)

Iter	Nodes	Cost
0	256	4878
1	686	4529
2	2316	3874
done	5000	3832

prune721.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize32.0ms

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))
0.3b	(* (cbrt (/ 1 (* 2.0 (sqrt 2.0)))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
0.5b	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
1.0b	(/ 1 (* 2.0 (sqrt 2.0)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

47×	`add-sqr-sqrt`
44×	`times-frac`
38×	`add-cube-cbrt` `*-un-lft-identity`
32×	`associate-l`
31×	`add-exp-log`
22×	`sqrt-prod` `add-cbrt-cube`
17×	`pow1`
10×	`prod-exp`
8×	`cbrt-unprod`
7×	`cbrt-prod` `div-exp` `associate-/r*`
6×	`associate-/l*`
5×	`cbrt-undiv` `pow-flip` `pow-prod-down`
4×	`associate-r` `associate-*l/` `div-inv` `add-log-exp`
3×	`unswap-sqr`
2×	`rec-exp` `cbrt-div` `frac-2neg` `1-exp` `clear-num` `*-commutative` `pow-prod-up` `associate-/l/`
1×	`frac-times` `sqrt-pow1` `flip3-+` `pow1/2` `associate-*r/` `pow3` `flip-+` `inv-pow`

Counts

4 → 144

Calls

4 calls:

40.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
44.0ms	(* (cbrt (/ 1 (* 2.0 (sqrt 2.0)))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
29.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
6.0ms	(/ 1 (* 2.0 (sqrt 2.0)))

series825.0ms

Counts

4 → 10

Calls

4 calls:

161.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
543.0ms	(* (cbrt (/ 1 (* 2.0 (sqrt 2.0)))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
120.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (* 2.0 (sqrt 2.0)))

simplify929.0ms

Counts

154 → 154

Iterations

Useful iterations: done (924.0ms)

Iter	Nodes	Cost
0	253	3983
1	646	3849
2	2118	3433
done	5000	3417

prune539.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

0% (0.3b remaining)

Error of 0.7b against oracle of 0.4b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample6.1s

Algorithm: halfpoints