Details

sample12.0ms

Algorithm

intervals

Results

5.0ms	246×	body	80	valid
0.0ms	4×	body	640	valid
0.0ms	3×	body	2560	valid
0.0ms	3×	body	1280	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	4
1	11	4
2	11	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity`
3×	`fma-def` `add-log-exp`
2×	`add-sqr-sqrt` `add-cube-cbrt`
1×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `sum-log` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`

Counts

1 → 17

Calls

1 calls:

10.0ms

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

series25.0ms

Counts

1 → 3

Calls

1 calls:

25.0ms

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

simplify65.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	88	110
1	226	97
2	540	97
3	1522	97
4	5001	97

prune55.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt x) (cbrt x))
0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cbrt x) (cbrt x))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)

series731.0ms

Counts

4 → 12

Calls

4 calls:

200.0ms	(* (cbrt x) (cbrt x))
173.0ms	(cbrt x)
181.0ms	(cbrt x)
177.0ms	(cbrt x)

simplify89.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	119	308
1	477	281
2	2972	258
3	5001	256

prune243.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))
0.0b	(- x (/ (fabs (- y x)) 2.0))
11.9b	(- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0)))
28.6b	(/ (- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))) (- x (/ (fabs (- y x)) 2.0)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

121×	`add-sqr-sqrt`
97×	`times-frac`
91×	`*-un-lft-identity`
79×	`add-cube-cbrt`
40×	`prod-diff`
20×	`difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`swap-sqr` `associate-r` `associate-l`
11×	`pow1`
8×	`div-inv` `add-log-exp`
6×	`associate-/r*` `distribute-lft-out--`
5×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `flip3--` `fma-neg` `prod-exp` `flip--` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `unswap-sqr`
2×	`sub-neg` `diff-log` `associate-/r/` `associate-/l/`
1×	`pow2` `frac-times` `frac-2neg` `pow-plus` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `pow-sqr` `*-commutative` `pow-prod-up`

Counts

4 → 198

Calls

4 calls:

10.0ms	(* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))
11.0ms	(- x (/ (fabs (- y x)) 2.0))
4.0ms	(- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0)))
12.0ms	(/ (- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))) (- x (/ (fabs (- y x)) 2.0)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))
18.0ms	(- x (/ (fabs (- y x)) 2.0))
32.0ms	(- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0)))
48.0ms	(/ (- (* x x) (* (/ (fabs (- y x)) 2.0) (/ (fabs (- y x)) 2.0))) (- x (/ (fabs (- y x)) 2.0)))

simplify151.0ms

Algorithm

egg-herbie

Counts

210 → 210

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	882	3559
1	4054	2716
2	5001	2673

prune446.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (- x (/ (fabs (- y x)) 2.0))) (cbrt (- x (/ (fabs (- y x)) 2.0))))
0.6b	(cbrt (- x (/ (fabs (- y x)) 2.0)))
0.6b	(cbrt (- x (/ (fabs (- y x)) 2.0)))
0.6b	(cbrt (- x (/ (fabs (- y x)) 2.0)))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-sqr-sqrt`
50×	`cbrt-prod`
35×	`*-un-lft-identity`
18×	`cbrt-div`
15×	`add-cube-cbrt`
14×	`difference-of-squares`
11×	`pow1` `swap-sqr`
9×	`flip3--` `pow1/3` `associate-r` `associate-l` `flip--` `distribute-lft-out--`
7×	`times-frac`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `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 → 115

Calls

4 calls:

17.0ms	(* (cbrt (- x (/ (fabs (- y x)) 2.0))) (cbrt (- x (/ (fabs (- y x)) 2.0))))
6.0ms	(cbrt (- x (/ (fabs (- y x)) 2.0)))
6.0ms	(cbrt (- x (/ (fabs (- y x)) 2.0)))
177.0ms	(cbrt (- x (/ (fabs (- y x)) 2.0)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(* (cbrt (- x (/ (fabs (- y x)) 2.0))) (cbrt (- x (/ (fabs (- y x)) 2.0))))
55.0ms	(cbrt (- x (/ (fabs (- y x)) 2.0)))
53.0ms	(cbrt (- x (/ (fabs (- y x)) 2.0)))
57.0ms	(cbrt (- x (/ (fabs (- y x)) 2.0)))

simplify53.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	443	1728
1	1467	1649
2	5001	1548

prune373.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes77.0ms

Accuracy

0% (0.0b 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	8	4
1	8	4

end0.0ms

sample283.0ms

Algorithm

intervals

Results

142.0ms	7683×	body	80	valid
9.0ms	110×	body	1280	valid
6.0ms	83×	body	640	valid
6.0ms	55×	body	2560	valid
2.0ms	48×	body	320	valid
1.0ms	22×	body	160	valid