Details

analyze979.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
37.4%	62.4%	0.1%	10
43.7%	56.2%	0.1%	11
43.7%	56.2%	0.1%	12
43.7%	56.2%	0.1%	13
61.7%	38.2%	0.1%	14

sample34.0ms

Algorithm

intervals

Results

24.0ms

256×

body

valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5321	37

prune12.0ms

Filtered

1 candidates to 1 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: 27.2b

Counts

2 → 2

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (+ (* x 4.16438922228) 78.6994924154))
0.0b	(* x (+ (* x (+ x 43.3400022514)) 263.505074721))
0.1b	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
26.4b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
18×	`add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`times-frac` `associate-r` `associate-l`
6×	`associate-*r/`
5×	`flip3-+` `flip-+`
4×	`add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `associate-/r` `-commutative` `cbrt-unprod` `associate-/l*` `unswap-sqr`
2×	`associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 97

Calls

4 calls:

7.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
9.0ms	(* x (+ (* x (+ x 43.3400022514)) 263.505074721))
10.0ms	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
29.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

series49.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
4.0ms	(* x (+ (* x (+ x 43.3400022514)) 263.505074721))
4.0ms	(* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416))
36.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

simplify52.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5007	2277

prune241.0ms

Filtered

76 candidates to 109 candidates (-43.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	103	6	109
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	105	6	111

Merged error: 0.0b

Counts

111 → 6

localize28.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
26.4b	(/ (+ (* x (+ (* (* (cbrt x) (cbrt x)) (* (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416) (cbrt x))) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 64

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
32.0ms	(/ (+ (* x (+ (* (* (cbrt x) (cbrt x)) (* (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416) (cbrt x))) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

series113.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(cbrt x)
21.0ms	(cbrt x)
22.0ms	(cbrt x)
47.0ms	(/ (+ (* x (+ (* (* (cbrt x) (cbrt x)) (* (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416) (cbrt x))) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

simplify56.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4942	1629
1	4942	1629

prune144.0ms

Filtered

56 candidates to 76 candidates (-35.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	76	6	82

Merged error: 0.0b

Counts

82 → 6

localize29.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
26.5b	(* (+ (* x (+ (* (* (cbrt x) (cbrt x)) (* (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416) (cbrt x))) y)) z) (/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`add-cube-cbrt` `associate-r`
13×	`add-exp-log`
11×	`times-frac`
9×	`cbrt-prod` `add-cbrt-cube`
6×	`pow1`
4×	`prod-exp` `add-log-exp`
3×	`flip3-+` `pow1/3` `associate-l` `flip-+` `unswap-sqr`
2×	`frac-times` `div-exp` `associate-*l/` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `1-exp` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 75

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
41.0ms	(* (+ (* x (+ (* (* (cbrt x) (cbrt x)) (* (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416) (cbrt x))) y)) z) (/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

series115.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(cbrt x)
22.0ms	(cbrt x)
26.0ms	(cbrt x)
45.0ms	(* (+ (* x (+ (* (* (cbrt x) (cbrt x)) (* (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416) (cbrt x))) y)) z) (/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

simplify56.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4990	1780
1	4990	1780

prune156.0ms

Filtered

61 candidates to 87 candidates (-42.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	87	6	93

Merged error: 0.0b

Counts

93 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

6.5b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
6.5b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
19.6b	(/ (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
22.6b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 264

Calls

4 calls:

12.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
12.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
49.0ms	(/ (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
28.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

series103.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
6.0ms	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
37.0ms	(/ (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
53.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

simplify147.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5067	17965

prune786.0ms

Filtered

145 candidates to 276 candidates (-90.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	275	1	276
Fresh	1	2	3
Picked	0	1	1
Done	0	2	2
Total	276	6	282

Merged error: 0.0b

Counts

282 → 6

regimes318.0ms

Accuracy

97.7% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 24.8b

bsearch41.0ms

Steps

Iters	Range		Point
4	2.1164136049873296e+37	3.199571344413006e+37	2.82367765051812e+37
10	-1.047981098738211e+70	-5.3755956991885364e+57	-1.6570490193562163e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	68
1	93	68

end0.0ms

sample862.0ms

Algorithm

intervals

Results

671.0ms	8000×	body	80	valid
1.0ms	7×	body	80	invalid

Details

analyze979.0ms

sample34.0ms

simplify36.0ms

prune12.0ms

localize24.0ms

rewrite58.0ms

series49.0ms

simplify52.0ms

prune241.0ms

localize28.0ms

rewrite37.0ms

series113.0ms

simplify56.0ms

prune144.0ms

localize29.0ms

rewrite47.0ms

series115.0ms

simplify56.0ms

prune156.0ms

localize27.0ms

rewrite115.0ms

series103.0ms

simplify147.0ms

prune786.0ms

regimes318.0ms

bsearch41.0ms

simplify2.0ms

end0.0ms

sample862.0ms

Profiling