Details

sample73.0ms

Algorithm

intervals

Results

38.0ms	78×	body	1280	valid
11.0ms	39×	body	640	valid
8.0ms	22×	body	2560	valid
4.0ms	24×	body	320	valid
3.0ms	83×	body	80	valid
1.0ms	10×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	5
1	10	5

prune2.0ms

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: 50.9b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.8b	(+ x (sqrt (+ (* x x) 1.0)))
3.2b	(log (+ x (sqrt (+ (* x x) 1.0))))
15.9b	(sqrt (+ (* x x) 1.0))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity`
8×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
5×	`pow1` `add-log-exp`
4×	`add-exp-log` `log-prod`
3×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`log-div` `sqrt-div` `distribute-lft-out`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `log-pow` `hypot-def`

Counts

3 → 52

Calls

3 calls:

10.0ms	(+ x (sqrt (+ (* x x) 1.0)))
6.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
4.0ms	(sqrt (+ (* x x) 1.0))

series270.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(+ x (sqrt (+ (* x x) 1.0)))
170.0ms	(log (+ x (sqrt (+ (* x x) 1.0))))
41.0ms	(sqrt (+ (* x x) 1.0))

simplify40.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	331	422
1	1127	385
2	5002	366

prune167.0ms

Filtered

61 candidates to 55 candidates (90.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	56	5	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	5	62

Merged error: 0.0b

Counts

62 → 5

localize12.0ms

Local error

Found 1 expressions with local error:

0.1b	(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

240×	`times-frac`
220×	`associate-r`
181×	`add-sqr-sqrt`
140×	`unpow-prod-down` `cube-prod`
117×	`add-cube-cbrt` `*-un-lft-identity`
80×	`sqrt-prod`
40×	`sqr-pow`
30×	`cube-mult` `unpow3`
25×	`unswap-sqr`
24×	`add-exp-log`
10×	`prod-exp`
9×	`div-exp`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube`
3×	`pow1` `associate-l`
2×	`cbrt-unprod`
1×	`cbrt-undiv` `expm1-log1p-u` `associate-r/` `pow-prod-down` `-commutative` `log1p-expm1-u` `div-inv` `add-log-exp`

Counts

1 → 272

Calls

1 calls:

59.0ms

(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

series132.0ms

Counts

1 → 3

Calls

1 calls:

132.0ms

(* 1/6 (/ (pow x 3) (pow (sqrt 1.0) 3)))

simplify90.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	729	1769
1	3838	1380
2	5003	1380

prune315.0ms

Filtered

275 candidates to 97 candidates (35.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	275	0	275
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	275	5	280

Merged error: 0.0b

Counts

280 → 5

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot x (sqrt 1.0))
0.8b	(+ x (hypot x (sqrt 1.0)))
3.2b	(log (+ x (hypot x (sqrt 1.0))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity`
5×	`add-sqr-sqrt` `add-cube-cbrt` `add-log-exp`
4×	`pow1` `add-exp-log` `log-prod`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3-+` `flip-+` `distribute-lft-out`
1×	`+-commutative` `hypot-udef` `rem-log-exp` `sum-log` `log-pow`

Counts

3 → 44

Calls

3 calls:

1.0ms	(hypot x (sqrt 1.0))
3.0ms	(+ x (hypot x (sqrt 1.0)))
3.0ms	(log (+ x (hypot x (sqrt 1.0))))

series478.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(hypot x (sqrt 1.0))
122.0ms	(+ x (hypot x (sqrt 1.0)))
264.0ms	(log (+ x (hypot x (sqrt 1.0))))

simplify87.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	268	349
1	886	321
2	3696	305
3	5001	303

prune121.0ms

Filtered

53 candidates to 46 candidates (86.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	53	5	58

Merged error: 0.0b

Counts

58 → 5

localize8.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ x (hypot x (sqrt 1.0)))
0.8b	(+ x (hypot x (sqrt 1.0)))
3.2b	(log (+ x (hypot x (sqrt 1.0))))
3.2b	(log (+ x (hypot x (sqrt 1.0))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
8×	`add-sqr-sqrt` `add-cube-cbrt` `log-prod` `add-log-exp`
6×	`pow1` `add-exp-log` `fma-def`
4×	`expm1-log1p-u` `log-div` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `distribute-lft-out`
2×	`+-commutative` `rem-log-exp` `sum-log` `log-pow`

Counts

4 → 68

Calls

4 calls:

3.0ms	(+ x (hypot x (sqrt 1.0)))
3.0ms	(+ x (hypot x (sqrt 1.0)))
3.0ms	(log (+ x (hypot x (sqrt 1.0))))
3.0ms	(log (+ x (hypot x (sqrt 1.0))))

series794.0ms

Counts

4 → 12

Calls

4 calls:

129.0ms	(+ x (hypot x (sqrt 1.0)))
127.0ms	(+ x (hypot x (sqrt 1.0)))
270.0ms	(log (+ x (hypot x (sqrt 1.0))))
266.0ms	(log (+ x (hypot x (sqrt 1.0))))

simplify82.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	238	568
1	786	510
2	3259	494
3	5001	490

prune232.0ms

Filtered

80 candidates to 68 candidates (85.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	80	5	85

Merged error: 0.0b

Counts

85 → 5

regimes33.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 32.0b

bsearch79.0ms

Steps

Iters	Range		Point
7	4.240483494528851e-05	0.005370866090842012	0.0009503988119469446
10	-3.4402871636077537	-5.738045557766166e-18	-1.0185275619862584

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	24
1	39	24

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.1s	2327×	body	1280	valid
456.0ms	1593×	body	640	valid
275.0ms	782×	body	2560	valid
136.0ms	797×	body	320	valid
88.0ms	2083×	body	80	valid
43.0ms	418×	body	160	valid