Details

sample287.0ms

Algorithm: halfpoints

simplify60.0ms

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	5002	7

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.3b

localize35.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.7b	(- (exp x) (exp (- x)))

rewrite36.0ms

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:

28.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
6.0ms	(- (exp x) (exp (- x)))

series119.0ms

Counts

2 → 6

Calls

2 calls:

78.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
41.0ms	(- (exp x) (exp (- x)))

simplify109.0ms

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

prune172.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/60 (pow x 5)) (* 2 x))
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))

rewrite58.0ms

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

Counts

4 → 99

Calls

4 calls:

3.0ms	(+ (* 1/60 (pow x 5)) (* 2 x))
8.0ms	(* 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))

series328.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(+ (* 1/60 (pow x 5)) (* 2 x))
54.0ms	(* 1/60 (pow x 5))
95.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
38.0ms	(* 1/3 (pow x 3))

simplify57.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	468	756
1	1975	665
2	5001	664

prune322.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

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))

rewrite131.0ms

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:

41.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
50.0ms	(* (/ 1 (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))
3.0ms	(/ 1 (sqrt 2.0))

series528.0ms

Counts

4 → 10

Calls

4 calls:

167.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
228.0ms	(* (/ 1 (sqrt 2.0)) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
132.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ 1 (sqrt 2.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (69.0ms)

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

prune548.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0b

localize30.0ms

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))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

311×	`times-frac`
188×	`add-sqr-sqrt`
180×	`add-cube-cbrt` `*-un-lft-identity`
107×	`associate-l`
103×	`sqrt-prod`
82×	`cbrt-prod`
29×	`add-exp-log`
22×	`add-cbrt-cube`
17×	`div-inv`
16×	`associate-/l*`
15×	`pow1`
12×	`associate-/r*`
9×	`div-exp`
7×	`prod-exp` `cbrt-unprod`
6×	`cbrt-undiv`
4×	`associate-r` `pow-prod-down` `associate-*l/` `add-log-exp` `pow-div`
3×	`associate-/l/` `unswap-sqr`
2×	`cbrt-div` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `*-commutative` `inv-pow`
1×	`frac-times` `rec-exp` `flip3-+` `1-exp` `associate-*r/` `flip-+`

Counts

4 → 306

Calls

4 calls:

43.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
79.0ms	(* (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))
8.0ms	(/ (/ 1 2.0) (sqrt 2.0))

series905.0ms

Counts

4 → 10

Calls

4 calls:

164.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y))
605.0ms	(* (cbrt (/ (/ 1 2.0) (sqrt 2.0))) (* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)) (sin y)))
136.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
0.0ms	(/ (/ 1 2.0) (sqrt 2.0))

simplify125.0ms

Algorithm

egg-herbie

Counts

316 → 316

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1111	4318
1	4829	3959
2	5001	3959

prune1.1s

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0b

regimes99.0ms

Accuracy

48% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.8b

bsearch250.0ms

Steps

Iters	Range		Point
8	-0.48869560230416215	-0.0008391074150366579	-0.017784394852257208

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	29
1	42	29

end0.0ms

sample6.0s

Algorithm: halfpoints