Details

sample17.0ms

Algorithm

intervals

Results

5.0ms	207×	body	80	valid
2.0ms	18×	body	640	valid
1.0ms	17×	body	320	valid
1.0ms	5×	body	1280	valid
1.0ms	9×	body	160	valid

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	5
1	35	5
2	74	5
3	128	5
4	252	5
5	374	5
6	514	5
7	642	5
8	777	5
9	1010	5
10	1686	5
11	5001	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (- 1.0 x) y)
2.1b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.6b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 63

Calls

3 calls:

18.0ms	(* (- 1.0 x) y)
17.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
18.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series151.0ms

Counts

3 → 9

Calls

3 calls:

28.0ms	(* (- 1.0 x) y)
66.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
56.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	338	401
1	1456	359
2	5001	359

prune143.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

2.1b	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
6.6b	(/ (* (- 1.0 x) y) (+ y 1.0))
6.6b	(/ (* (- 1.0 x) y) (+ y 1.0))
6.6b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt` `times-frac` `associate-/r*`
10×	`add-cube-cbrt`
6×	`cbrt-undiv` `div-exp` `associate-*l/` `associate-/r/` `associate-/l/` `distribute-lft-out` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
3×	`frac-2neg` `flip3-+` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*`
1×	`sub-neg` `diff-log` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 95

Calls

4 calls:

10.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
10.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series203.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0)))
47.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
42.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
46.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	287	648
1	1151	575
2	5001	574

prune282.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

6.4b	(/ (- (* 1.0 1.0) (* (/ (* (- 1.0 x) y) (+ y 1.0)) (/ (* (- 1.0 x) y) (+ y 1.0)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))
6.6b	(/ (* (- 1.0 x) y) (+ y 1.0))
6.6b	(/ (* (- 1.0 x) y) (+ y 1.0))
6.6b	(/ (* (- 1.0 x) y) (+ y 1.0))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
28×	`times-frac`
21×	`add-exp-log` `add-cbrt-cube`
20×	`add-sqr-sqrt` `add-cube-cbrt`
16×	`associate-/r*`
11×	`distribute-lft-out`
8×	`associate-/r/` `associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
6×	`associate-*l/`
5×	`difference-of-squares`
4×	`pow1` `flip3--` `frac-2neg` `flip3-+` `clear-num` `flip--` `flip-+` `div-inv` `add-log-exp`
3×	`prod-exp` `cbrt-unprod`
1×	`div-sub`

Counts

4 → 122

Calls

4 calls:

30.0ms	(/ (- (* 1.0 1.0) (* (/ (* (- 1.0 x) y) (+ y 1.0)) (/ (* (- 1.0 x) y) (+ y 1.0)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))
10.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
9.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

series531.0ms

Counts

4 → 12

Calls

4 calls:

401.0ms	(/ (- (* 1.0 1.0) (* (/ (* (- 1.0 x) y) (+ y 1.0)) (/ (* (- 1.0 x) y) (+ y 1.0)))) (+ 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))
41.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
46.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))
42.0ms	(/ (* (- 1.0 x) y) (+ y 1.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	431	1543
1	2019	1406
2	5001	1406

prune286.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (- 1.0 x) y)
0.1b	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
3.6b	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
14.2b	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-exp-log` `add-cbrt-cube`
19×	`add-sqr-sqrt`
15×	`-un-lft-identity` `associate-l*`
11×	`add-cube-cbrt`
8×	`pow1` `times-frac` `associate-r`
7×	`flip3--` `flip--`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`sub-neg` `associate-*l/` `difference-of-squares`
4×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate-/r*` `associate-/r/` `associate--r+`
2×	`frac-times` `associate-r/` `pow-prod-down` `-commutative` `div-inv` `associate-/l/` `distribute-lft-out--` `unswap-sqr`
1×	`frac-2neg` `diff-log` `clear-num` `associate-/l*`

Counts

4 → 105

Calls

4 calls:

13.0ms	(* (- 1.0 x) y)
30.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
2.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
9.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (- 1.0 x) y)
77.0ms	(* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0))
150.0ms	(- 1.0 (* (/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0))) (- y 1.0)))
89.0ms	(/ (* (- 1.0 x) y) (- (* y y) (* 1.0 1.0)))

simplify82.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	567	1027
1	3078	900
2	5001	900

prune232.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

regimes245.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 24.5b

bsearch72.0ms

Steps

Iters	Range		Point
9	1610.1334651337936	217359335082.17374	106211441.56073992
6	-200803539.0671856	-48473935.98635021	-93297022.87967427

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	14
1	33	14

end0.0ms

sample457.0ms

Algorithm

intervals

Results

161.0ms	6119×	body	80	valid
60.0ms	664×	body	640	valid
41.0ms	553×	body	320	valid
41.0ms	365×	body	1280	valid
14.0ms	299×	body	160	valid