Details

sample457.0ms

Algorithm: halfpoints

simplify1.2s

Counts

1 → 1

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	16	24
1	30	11
2	48	11
3	83	11
4	128	11
5	247	11
6	1037	11
done	5001	11

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.0b

localize67.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.8b	(- (exp x) (exp (- x)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
27×	`*-un-lft-identity`
19×	`add-cube-cbrt` `associate-l`
16×	`times-frac`
9×	`prod-diff`
7×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`fma-neg` `associate-r`
2×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `flip3--` `diff-log` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `flip--` `div-inv`

Counts

2 → 68

Calls

2 calls:

74.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
18.0ms	(- (exp x) (exp (- x)))

series192.0ms

Counts

2 → 6

Calls

2 calls:

132.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
59.0ms	(- (exp x) (exp (- x)))

simplify1.1s

Counts

74 → 74

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	149	1156
1	365	1007
2	1505	847
done	5000	789

prune325.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 3 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
13×	`associate-l`
11×	`add-cube-cbrt` `*-un-lft-identity`
10×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
2×	`prod-exp` `cbrt-unprod` `fma-udef` `unswap-sqr`
1×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate-l/` `-commutative` `div-inv`

Counts

3 → 54

Calls

3 calls:

0.0ms	(fma 1/60 (pow x 5) (* 2 x))
0.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
20.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

series371.0ms

Counts

3 → 9

Calls

3 calls:

175.0ms	(fma 1/60 (pow x 5) (* 2 x))
83.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
112.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) 2.0) (sin y))

simplify956.0ms

Counts

63 → 63

Iterations

Useful iterations: done (953.0ms)

Iter	Nodes	Cost
0	109	1189
1	248	1175
2	1215	1025
done	5000	1015

prune321.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 0.0b

localize61.0ms

Local error

Found 4 expressions with local error:

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

rewrite139.0ms

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×	`expm1-log1p-u` `rec-exp` `1-exp` `associate-r` `pow-prod-down` `associate-*l/` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-flip` `unswap-sqr`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `sqrt-pow1` `pow1/2` `associate-*r/` `inv-pow`

Counts

4 → 188

Calls

4 calls:

23.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
91.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
10.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
7.0ms	(/ 1 (sqrt 2.0))

series687.0ms

Counts

4 → 10

Calls

4 calls:

266.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
267.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
154.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify3.0s

Counts

198 → 198

Iterations

Useful iterations: done (3.0s)

Iter	Nodes	Cost
0	254	4584
1	664	4327
2	3882	3773
done	5001	3735

prune891.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0b

localize72.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
0.2b	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
0.4b	(* (pow 2.0 -1/2) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
0.4b	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))

rewrite110.0ms

Algorithm

rewrite-expression-head

Rules

43×	`add-sqr-sqrt`
38×	`times-frac`
35×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity`
29×	`associate-l`
22×	`sqrt-prod`
20×	`add-cbrt-cube`
17×	`prod-exp`
7×	`cbrt-unprod`
6×	`pow1` `associate-/r*`
5×	`div-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-to-exp` `unpow-prod-down` `pow-exp` `associate-/l*` `unswap-sqr`
2×	`associate-l/` `-commutative` `div-inv`
1×	`frac-2neg` `associate-*r/` `pow-prod-down` `clear-num` `fma-udef` `sqr-pow`

Counts

4 → 126

Calls

4 calls:

0.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
37.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
51.0ms	(* (pow 2.0 -1/2) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
17.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))

series1.3s

Counts

4 → 12

Calls

4 calls:

86.0ms	(fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x)))
208.0ms	(* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y))
774.0ms	(* (pow 2.0 -1/2) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
213.0ms	(/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0))

simplify1.9s

Counts

138 → 138

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	220	3590
1	554	3495
2	2607	3141
done	5000	3132

prune876.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes113.0ms

Accuracy

0% (0.7b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	18
1	18	18
done	18	18

end0.0ms

sample11.8s

Algorithm: halfpoints