Details

sample294.0ms

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	5001	7

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 44.2b

Counts

2 → 1

localize36.0ms

Local error

Found 2 expressions with local error:

0.1b	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
57.5b	(- (exp x) (exp (- x)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
19×	`associate-l`
16×	`times-frac`
14×	`add-cube-cbrt`
13×	`associate-*l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`pow1` `add-log-exp`
3×	`associate-r` `associate-/r*`
2×	`flip3--` `prod-exp` `flip--` `cbrt-unprod` `associate-/l/` `unswap-sqr`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `pow-prod-down` `clear-num` `*-commutative` `div-inv`

Counts

2 → 64

Calls

2 calls:

12.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
5.0ms	(- (exp x) (exp (- x)))

series126.0ms

Counts

2 → 6

Calls

2 calls:

85.0ms	(* (/ (- (exp x) (exp (- x))) 2.0) (sin y))
41.0ms	(- (exp x) (exp (- x)))

simplify39.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	321	585
1	1307	528
2	5002	526

prune155.0ms

Filtered

70 candidates to 51 candidates (27.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	4	71

Merged error: 0.1b

Counts

71 → 4

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/3 (pow x 3)) (+ (* 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))
0.2b	(* 1/3 (pow x 3))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

170×	`*-un-lft-identity`
114×	`associate-l`
90×	`distribute-lft-out`
45×	`add-sqr-sqrt`
40×	`times-frac`
30×	`add-cube-cbrt`
21×	`associate-*l/`
19×	`add-exp-log`
18×	`associate-r`
13×	`add-cbrt-cube` `associate-/l*`
10×	`pow1`
9×	`add-log-exp`
8×	`unpow-prod-down` `prod-exp` `unswap-sqr`
4×	`cbrt-unprod` `sqr-pow`
3×	`pow-prod-down` `associate-/r` `sum-log` `-commutative`
2×	`+-commutative` `pow-to-exp` `associate-+r+` `flip3-+` `pow-exp` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `unpow3` `div-exp` `clear-num` `div-inv`

Counts

4 → 159

Calls

4 calls:

34.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
6.0ms	(* 1/60 (pow x 5))
45.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
7.0ms	(* 1/3 (pow x 3))

series245.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
52.0ms	(* 1/60 (pow x 5))
94.0ms	(* (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) 2.0) (sin y))
38.0ms	(* 1/3 (pow x 3))

simplify68.0ms

Algorithm

egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	480	1322
1	2293	1232
2	5003	1232

prune294.0ms

Filtered

171 candidates to 84 candidates (50.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	165	6	171
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	165	10	175

Merged error: 0.0b

Counts

175 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
0.1b	(* 1/60 (pow x 5))
0.2b	(* 1/3 (pow x 3))
0.3b	(/ (sin y) (/ 2.0 (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))))

rewrite112.0ms

Algorithm

rewrite-expression-head

Rules

518×	`*-un-lft-identity`
291×	`times-frac`
252×	`distribute-lft-out`
188×	`associate-l`
136×	`add-sqr-sqrt`
126×	`add-cube-cbrt`
58×	`associate-/r*`
27×	`associate-/r/`
19×	`add-exp-log`
15×	`associate-r`
13×	`add-cbrt-cube`
9×	`add-log-exp`
8×	`pow1` `unpow-prod-down`
6×	`prod-exp` `associate-/l*` `unswap-sqr`
5×	`flip3-+` `flip-+` `div-inv`
4×	`sqr-pow`
3×	`cbrt-undiv` `div-exp` `sum-log`
2×	`+-commutative` `pow-to-exp` `associate-+r+` `frac-2neg` `pow-prod-down` `pow-exp` `clear-num` `*-commutative` `cbrt-unprod`
1×	`unpow3`

Counts

4 → 293

Calls

4 calls:

30.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
6.0ms	(* 1/60 (pow x 5))
6.0ms	(* 1/3 (pow x 3))
44.0ms	(/ (sin y) (/ 2.0 (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))))

series349.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))
50.0ms	(* 1/60 (pow x 5))
43.0ms	(* 1/3 (pow x 3))
193.0ms	(/ (sin y) (/ 2.0 (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x)))))

simplify108.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	672	3602
1	3474	3489
2	5002	3487

prune451.0ms

Filtered

305 candidates to 124 candidates (59.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	300	5	305
Fresh	5	2	7
Picked	0	1	1
Done	0	2	2
Total	305	10	315

Merged error: 0.0b

Counts

315 → 10

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite193.0ms

Algorithm

rewrite-expression-head

Rules

974×	`*-un-lft-identity`
486×	`distribute-lft-out`
376×	`associate-l`
288×	`frac-times`
271×	`associate-/l*`
252×	`add-sqr-sqrt`
240×	`associate-/r*`
222×	`sqrt-prod`
217×	`add-cube-cbrt`
204×	`times-frac`
90×	`associate-r`
41×	`clear-num`
40×	`frac-2neg`
28×	`associate-/l/`
25×	`add-exp-log`
24×	`associate-*r/`
22×	`add-cbrt-cube`
14×	`flip3-+` `flip-+`
12×	`associate-*l/` `un-div-inv` `unswap-sqr`
8×	`pow1`
7×	`prod-exp`
6×	`cbrt-undiv` `div-exp`
5×	`cbrt-unprod`
4×	`unpow-prod-down` `div-inv` `add-log-exp`
2×	`pow-prod-down` `*-commutative` `sqr-pow`
1×	`pow-to-exp` `unpow3` `pow-exp`

Counts

4 → 643

Calls

4 calls:

6.0ms	(* 1/3 (pow x 3))
86.0ms	(* (/ (sin y) (sqrt 2.0)) (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)))
40.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
5.0ms	(/ (sin y) (sqrt 2.0))

series587.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* 1/3 (pow x 3))
345.0ms	(* (/ (sin y) (sqrt 2.0)) (/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0)))
128.0ms	(/ (+ (* 1/3 (pow x 3)) (+ (* 1/60 (pow x 5)) (* 2 x))) (sqrt 2.0))
69.0ms	(/ (sin y) (sqrt 2.0))

simplify130.0ms

Algorithm

egg-herbie

Counts

655 → 655

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1524	8879
1	5001	8515

prune770.0ms

Filtered

655 candidates to 202 candidates (69.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	653	2	655
Fresh	3	3	6
Picked	1	0	1
Done	1	2	3
Total	658	7	665

Merged error: 0.0b

Counts

665 → 7

regimes69.0ms

Accuracy

0% (0.6b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

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