Details

sample13.0ms

Algorithm

intervals

Results

4.0ms	239×	body	80	valid
0.0ms	7×	body	640	valid
0.0ms	4×	body	1280	valid
0.0ms	3×	body	2560	valid
0.0ms	2×	body	160	valid
0.0ms	1×	body	320	valid

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	3
1	19	3
2	29	3
3	41	3
4	51	3
5	79	3
6	134	3
7	169	3
8	185	3
9	213	3
10	226	3
11	226	3

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+ x (/ (- x y) 2.0))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `+-commutative` `add-sqr-sqrt` `add-cube-cbrt` `associate-+r-` `flip3-+` `div-sub` `sum-log` `add-cbrt-cube` `flip-+` `distribute-lft-out`

Counts

1 → 13

Calls

1 calls:

23.0ms

(+ x (/ (- x y) 2.0))

series35.0ms

Counts

1 → 3

Calls

1 calls:

35.0ms

(+ x (/ (- x y) 2.0))

simplify79.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	91	81
1	242	74
2	704	74
3	3412	74
4	5001	74

prune36.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (+ x (/ (- x y) 2.0))) (cbrt (+ x (/ (- x y) 2.0))))
0.5b	(cbrt (+ x (/ (- x y) 2.0)))
0.5b	(cbrt (+ x (/ (- x y) 2.0)))
0.5b	(cbrt (+ x (/ (- x y) 2.0)))

rewrite230.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod`
35×	`*-un-lft-identity`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt`
11×	`pow1`
9×	`flip3-+` `pow1/3` `swap-sqr` `flip-+` `distribute-lft-out`
7×	`associate-r` `associate-l`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

166.0ms	(* (cbrt (+ x (/ (- x y) 2.0))) (cbrt (+ x (/ (- x y) 2.0))))
21.0ms	(cbrt (+ x (/ (- x y) 2.0)))
19.0ms	(cbrt (+ x (/ (- x y) 2.0)))
20.0ms	(cbrt (+ x (/ (- x y) 2.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

355.0ms	(* (cbrt (+ x (/ (- x y) 2.0))) (cbrt (+ x (/ (- x y) 2.0))))
371.0ms	(cbrt (+ x (/ (- x y) 2.0)))
370.0ms	(cbrt (+ x (/ (- x y) 2.0)))
378.0ms	(cbrt (+ x (/ (- x y) 2.0)))

simplify71.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	263	1109
1	751	1044
2	2594	956
3	5002	940

prune262.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (+ x (/ (- x y) 2.0)))
0.5b	(cbrt (+ x (/ (- x y) 2.0)))
0.6b	(cbrt (* (cbrt (+ x (/ (- x y) 2.0))) (cbrt (+ x (/ (- x y) 2.0)))))
0.9b	(pow (cbrt (cbrt (+ x (/ (- x y) 2.0)))) 4)

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

24×	`cbrt-div`
20×	`cbrt-prod`
16×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down`
8×	`flip3-+` `flip-+`
5×	`pow1` `add-exp-log`
4×	`frac-times` `pow1/3` `add-cbrt-cube` `add-log-exp`
3×	`pow-unpow` `distribute-lft-out`
2×	`pow-pow` `associate-r/` `associate-l/`
1×	`pow-to-exp` `pow-exp` `sqr-pow`

Counts

4 → 70

Calls

4 calls:

21.0ms	(cbrt (+ x (/ (- x y) 2.0)))
19.0ms	(cbrt (+ x (/ (- x y) 2.0)))
47.0ms	(cbrt (* (cbrt (+ x (/ (- x y) 2.0))) (cbrt (+ x (/ (- x y) 2.0)))))
42.0ms	(pow (cbrt (cbrt (+ x (/ (- x y) 2.0)))) 4)

series1.7s

Counts

4 → 12

Calls

4 calls:

388.0ms	(cbrt (+ x (/ (- x y) 2.0)))
393.0ms	(cbrt (+ x (/ (- x y) 2.0)))
370.0ms	(cbrt (* (cbrt (+ x (/ (- x y) 2.0))) (cbrt (+ x (/ (- x y) 2.0)))))
572.0ms	(pow (cbrt (cbrt (+ x (/ (- x y) 2.0)))) 4)

simplify118.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	404	943
1	1069	879
2	3744	852
3	5002	841

prune301.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (- x y) 2.0) (/ (- x y) 2.0))
0.0b	(- x (/ (- x y) 2.0))
12.1b	(- (* x x) (* (/ (- x y) 2.0) (/ (- x y) 2.0)))
28.3b	(/ (- (* x x) (* (/ (- x y) 2.0) (/ (- x y) 2.0))) (- x (/ (- x y) 2.0)))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-sqr-sqrt`
110×	`*-un-lft-identity`
106×	`times-frac`
56×	`add-cube-cbrt`
32×	`difference-of-squares`
25×	`swap-sqr`
24×	`distribute-lft-out--`
19×	`associate-r` `associate-l`
18×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
8×	`add-log-exp`
6×	`associate-/r*`
5×	`cbrt-undiv` `div-exp` `div-inv`
4×	`flip3--` `prod-exp` `flip--` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`sub-neg` `diff-log` `div-sub` `associate-/r/` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up` `associate--r-`

Counts

4 → 171

Calls

4 calls:

53.0ms	(* (/ (- x y) 2.0) (/ (- x y) 2.0))
20.0ms	(- x (/ (- x y) 2.0))
9.0ms	(- (* x x) (* (/ (- x y) 2.0) (/ (- x y) 2.0)))
63.0ms	(/ (- (* x x) (* (/ (- x y) 2.0) (/ (- x y) 2.0))) (- x (/ (- x y) 2.0)))

series180.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* (/ (- x y) 2.0) (/ (- x y) 2.0))
35.0ms	(- x (/ (- x y) 2.0))
29.0ms	(- (* x x) (* (/ (- x y) 2.0) (/ (- x y) 2.0)))
94.0ms	(/ (- (* x x) (* (/ (- x y) 2.0) (/ (- x y) 2.0))) (- x (/ (- x y) 2.0)))

simplify119.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 2 (100.0ms)

Iter	Nodes	Cost
0	767	1986
1	4021	1797
2	5001	1766

prune373.0ms

Pruning

9 alts after pruning (5 fresh and 4 done)

Merged error: 0.0b

regimes101.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	3
1	7	3

end0.0ms

sample339.0ms

Algorithm

intervals

Results

131.0ms	7385×	body	80	valid
15.0ms	204×	body	1280	valid
14.0ms	174×	body	640	valid
9.0ms	101×	body	2560	valid
4.0ms	95×	body	320	valid
1.0ms	42×	body	160	valid