Details

sample296.0ms

Algorithm

intervals

Results

14.0ms	813×	body	80	nan
5.0ms	255×	body	80	valid
0.0ms	1×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.5b

Counts

2 → 1

localize7.0ms

Local error

Found 1 expressions with local error:

0.5b	(* (sqrt (- x 1.0)) (sqrt x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`sqrt-prod`
8×	`associate-l`
7×	`*-un-lft-identity`
6×	`associate-r`
5×	`pow1` `add-cube-cbrt`
4×	`unswap-sqr`
3×	`add-exp-log` `pow-prod-down` `add-cbrt-cube`
2×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-*l/`
1×	`expm1-log1p-u` `flip3--` `sqrt-unprod` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`

Counts

1 → 36

Calls

1 calls:

12.0ms

(* (sqrt (- x 1.0)) (sqrt x))

series90.0ms

Counts

1 → 3

Calls

1 calls:

90.0ms

(* (sqrt (- x 1.0)) (sqrt x))

simplify75.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 2 (18.0ms)

Iter	Nodes	Cost
0	186	226
1	622	215
2	2584	210
3	5001	210

prune63.0ms

Filtered

39 candidates to 27 candidates (69.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	36	3	39
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	3	40

Merged error: 0b

Counts

40 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(- x (fma 0.125 (/ 1 x) 0.5))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `fma-udef` `log1p-expm1-u` `associate--r+` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 29

Calls

1 calls:

4.0ms

(- x (fma 0.125 (/ 1 x) 0.5))

series29.0ms

Counts

1 → 3

Calls

1 calls:

29.0ms

(- x (fma 0.125 (/ 1 x) 0.5))

simplify70.0ms

Algorithm

egg-herbie

Counts

32 → 32

Iterations

Useful iterations: 3 (65.0ms)

Iter	Nodes	Cost
0	128	313
1	361	194
2	2402	188
3	5002	133

prune37.0ms

Filtered

32 candidates to 18 candidates (56.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	32	3	35

Merged error: 0b

Counts

35 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sqrt x)) (cbrt (sqrt x)))
0.5b	(cbrt (sqrt x))
0.5b	(cbrt (sqrt x))
0.5b	(cbrt (sqrt x))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 109

Calls

4 calls:

7.0ms	(* (cbrt (sqrt x)) (cbrt (sqrt x)))
2.0ms	(cbrt (sqrt x))
2.0ms	(cbrt (sqrt x))
2.0ms	(cbrt (sqrt x))

series617.0ms

Counts

4 → 12

Calls

4 calls:

155.0ms	(* (cbrt (sqrt x)) (cbrt (sqrt x)))
153.0ms	(cbrt (sqrt x))
153.0ms	(cbrt (sqrt x))
156.0ms	(cbrt (sqrt x))

simplify108.0ms

Algorithm

egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 3 (100.0ms)

Iter	Nodes	Cost
0	162	756
1	602	698
2	3313	615
3	5002	584

prune191.0ms

Filtered

121 candidates to 78 candidates (64.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	121	3	124

Merged error: 0b

Counts

124 → 3

localize4.0ms

Local error

Found 1 expressions with local error:

28.0b

(sqrt (* (- x 1.0) x))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

14×	`sqrt-prod`
11×	`add-sqr-sqrt`
6×	`*-un-lft-identity`
5×	`associate-l`
4×	`pow1` `add-cube-cbrt`
3×	`associate-r`
2×	`rem-sqrt-square` `sqrt-pow1` `sqrt-div` `associate-*l/` `unswap-sqr`
1×	`add-exp-log` `expm1-log1p-u` `flip3--` `pow1/2` `pow-prod-down` `*-commutative` `add-cbrt-cube` `flip--` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`

Counts

1 → 30

Calls

1 calls:

10.0ms

(sqrt (* (- x 1.0) x))

series42.0ms

Counts

1 → 3

Calls

1 calls:

42.0ms

(sqrt (* (- x 1.0) x))

simplify47.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	161	163
1	415	158
2	1813	152
3	5002	151

prune46.0ms

Filtered

33 candidates to 25 candidates (75.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	33	3	36

Merged error: 0b

Counts

36 → 3

regimes15.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	3
1	9	3

end0.0ms

sample833.0ms

Algorithm

intervals

Results

373.0ms	23991×	body	80	nan
151.0ms	7991×	body	80	valid
0.0ms	9×	body	160	valid