Details

sample806.0ms

Algorithm: halfpoints

simplify5.4s

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	117	11
5	188	11
6	331	11
7	556	11
8	1006	11
9	1375	11
10	1691	11
11	1775	11
12	1795	11
done	1795	11

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.9b

localize75.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
59.0b	(- (exp x) (exp (- x)))

rewrite99.0ms

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:

81.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
16.0ms	(- (exp x) (exp (- x)))

series171.0ms

Counts

2 → 6

Calls

2 calls:

115.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
56.0ms	(- (exp x) (exp (- x)))

simplify2.1s

Counts

58 → 58

Iterations

Useful iterations: 3 (829.0ms)

Iter	Nodes	Cost
0	121	770
1	290	755
2	749	669
3	2404	668
done	5001	668

prune287.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite231.0ms

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:

40.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
24.0ms	(* 1/60 (pow x 5))
26.0ms	(* 1/3 (pow x 3))
135.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

series347.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
69.0ms	(* 1/60 (pow x 5))
54.0ms	(* 1/3 (pow x 3))
132.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))

simplify961.0ms

Counts

113 → 113

Iterations

Useful iterations: done (958.0ms)

Iter	Nodes	Cost
0	192	1718
1	467	1618
2	1503	1442
done	5000	1441

prune460.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.0b

localize36.0ms

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

rewrite411.0ms

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:

116.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
128.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
135.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
24.0ms	(/ 1 (sqrt 2.0))

series743.0ms

Counts

4 → 10

Calls

4 calls:

237.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
327.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
179.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify1.7s

Counts

192 → 192

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	256	4878
1	653	4529
2	2340	3872
done	5001	3848

prune777.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

localize36.0ms

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

rewrite434.0ms

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:

132.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
123.0ms	(* (cbrt (/ 1 (* 2.0 (sqrt 2.0)))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
147.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
18.0ms	(/ 1 (* 2.0 (sqrt 2.0)))

series1.2s

Counts

4 → 10

Calls

4 calls:

212.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
830.0ms	(* (cbrt (/ 1 (* 2.0 (sqrt 2.0)))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
178.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (* 2.0 (sqrt 2.0)))

simplify1.4s

Counts

154 → 154

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	253	3983
1	630	3849
2	2122	3433
done	5001	3421

prune909.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0b

regimes117.0ms

Accuracy

0% (0.6b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample12.5s

Algorithm: halfpoints