Details

analyze949.0ms

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

sample31.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4960	37
1	4960	37

prune17.0ms

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: 23.7b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
0.1b	(* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
0.1b	(* x (+ (* x 4.16438922228) 78.6994924154))
23.6b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

rewrite63.0ms

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:

15.0ms	(* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
13.0ms	(* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
7.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
26.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

series55.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
9.0ms	(* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y))
6.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
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))

simplify58.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4960	2487
1	4960	2487

prune310.0ms

Filtered

80 candidates to 109 candidates (-36.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	7	109
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	103	8	111

Merged error: 0.0b

Counts

111 → 8

localize29.0ms

Local error

Found 4 expressions with local error:

8.4b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
8.4b	(sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
15.0b	(* (/ 1 (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (/ (+ (* 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))))
20.5b	(/ (+ (* 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)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

95×	`add-sqr-sqrt`
76×	`times-frac`
53×	`*-un-lft-identity`
47×	`add-cube-cbrt` `sqrt-prod`
28×	`add-exp-log`
24×	`associate-r` `associate-l`
18×	`add-cbrt-cube`
15×	`unswap-sqr`
10×	`sqrt-div`
9×	`div-exp`
8×	`pow1` `prod-exp`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
3×	`div-inv` `associate-/l*`
2×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 160

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))
54.0ms	(* (/ 1 (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (/ (+ (* 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))))
29.0ms	(/ (+ (* 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)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(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	(* (/ 1 (sqrt (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))) (/ (+ (* 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))))
55.0ms	(/ (+ (* 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)))

simplify90.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5075	7264

prune605.0ms

Filtered

108 candidates to 172 candidates (-59.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	172	8	180

Merged error: 0.0b

Counts

180 → 8

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
0.1b	(* x (+ (* x 4.16438922228) 78.6994924154))
0.1b	(/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
23.8b	(* (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 119

Calls

4 calls:

12.0ms	(* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
6.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
14.0ms	(/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
32.0ms	(* (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894))
6.0ms	(* x (+ (* x 4.16438922228) 78.6994924154))
10.0ms	(/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
36.0ms	(* (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (/ 1 (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))

simplify63.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4963	3035
1	4963	3035

prune284.0ms

Filtered

85 candidates to 131 candidates (-54.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	131	8	139

Merged error: 0.0b

Counts

139 → 8

localize33.0ms

Local error

Found 4 expressions with local error:

0.4b	(cbrt (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
23.6b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
23.6b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
23.6b	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

rewrite108.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

25.0ms	(cbrt (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606)))
27.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
27.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
27.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

series161.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(cbrt (/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* 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) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
35.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))
35.0ms	(/ (+ (* x (+ (* x (+ (* x (+ (* x 4.16438922228) 78.6994924154)) 137.519416416)) y)) z) (+ (* x (+ (* x (+ (* x (+ x 43.3400022514)) 263.505074721)) 313.399215894)) 47.066876606))

simplify62.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5368	5870

prune1.0s

Filtered

108 candidates to 129 candidates (-19.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	129	8	137

Merged error: 0.0b

Counts

137 → 8

regimes354.0ms

Accuracy

96.9% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 23.8b

bsearch54.0ms

Steps

Iters	Range		Point
9	9.437045504303476e+30	7.624797228158838e+38	8.162715924193877e+34
9	-6.635845190123966e+58	-7.560272595016306e+53	-1.1974823994661146e+57

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	202	81
1	202	81

end0.0ms

sample849.0ms

Algorithm

intervals

Results

661.0ms	8000×	body	80	valid
1.0ms	8×	body	80	invalid

Details

analyze949.0ms

sample31.0ms

simplify43.0ms

prune17.0ms

localize22.0ms

rewrite63.0ms

series55.0ms

simplify58.0ms

prune310.0ms

localize29.0ms

rewrite113.0ms

series106.0ms

simplify90.0ms

prune605.0ms

localize24.0ms

rewrite68.0ms

series56.0ms

simplify63.0ms

prune284.0ms

localize33.0ms

rewrite108.0ms

series161.0ms

simplify62.0ms

prune1.0s

regimes354.0ms

bsearch54.0ms

simplify3.0ms

end0.0ms

sample849.0ms

Profiling