Details

sample253.0ms

Algorithm: halfpoints

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	7
1	47	7
2	84	7
3	121	7
4	206	7
5	410	7
6	1017	7
7	2074	7
8	5001	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.1b

localize35.0ms

Local error

Found 2 expressions with local error:

0.3b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
58.3b	(- (exp x) (exp (- x)))

rewrite20.0ms

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:

13.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
5.0ms	(- (exp x) (exp (- x)))

series114.0ms

Counts

2 → 6

Calls

2 calls:

79.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
34.0ms	(- (exp x) (exp (- x)))

simplify102.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	293	506
1	893	449
2	3855	448
3	5001	448

prune158.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.3b

localize25.0ms

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

rewrite36.0ms

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:

8.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
5.0ms	(* 1/60 (pow x 5))
14.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
6.0ms	(* 1/3 (pow x 3))

series232.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
50.0ms	(* 1/60 (pow x 5))
88.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
35.0ms	(* 1/3 (pow x 3))

simplify57.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	465	830
1	1991	734
2	5002	734

prune321.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.3b

localize28.0ms

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))

rewrite54.0ms

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:

16.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
17.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
11.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
4.0ms	(/ 1 (sqrt 2.0))

series495.0ms

Counts

4 → 10

Calls

4 calls:

158.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
217.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
121.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify92.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	684	2589
1	3667	2213
2	5002	2104

prune559.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.2b

localize39.0ms

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))
0.3b	(* (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))

rewrite50.0ms

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-l/` `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×	`neg-sub0` `frac-times` `pow-neg` `div-inv` `associate-/l/` `pow-sub`
1×	`cube-mult` `frac-2neg` `flip3-+` `unpow3` `associate-*r/` `pow-prod-down` `clear-num` `flip-+`

Counts

4 → 147

Calls

4 calls:

6.0ms	(* 1/3 (pow x 3))
13.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
14.0ms	(* (pow 2.0 (- 1/2)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
11.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

series549.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* 1/3 (pow x 3))
159.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
224.0ms	(* (pow 2.0 (- 1/2)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
126.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))

simplify94.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	683	2107
1	3351	1871
2	5001	1867

prune514.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.2b

regimes100.0ms

Accuracy

0% (0.8b remaining)

Error of 0.9b against oracle of 0.1b and baseline of 0.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	10
1	24	10

end0.0ms

sample6.1s

Algorithm: halfpoints