Details

sample35.0ms

Algorithm

intervals

Results

18.0ms	80×	body	1280	valid
6.0ms	144×	body	80	valid
2.0ms	12×	body	640	valid
1.0ms	10×	body	320	valid
1.0ms	10×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	24	6
2	28	6
3	30	6
4	35	6
5	37	6
6	37	6

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: 15.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.0b	(/ 1.0 (hypot 1.0 x))
3.1b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
12×	`add-cube-cbrt`
9×	`times-frac`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log` `add-cbrt-cube`
3×	`associate-/r` `associate-/l`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*r/` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `diff-log` `div-exp` `pow-prod-down` `clear-num` `sum-log` `sqrt-prod` `flip--` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
7.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series189.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
73.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
5.0ms	(/ 1.0 (hypot 1.0 x))
84.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	221	492
1	697	465
2	2325	463
3	5001	463

prune137.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	2	79

Merged error: 14.7b

Counts

79 → 2

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
2.4b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`associate-/r` `associate-/l`
4×	`pow1` `associate-*r/` `associate--l+`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `flip3--` `frac-2neg` `distribute-lft-in` `div-exp` `clear-num` `frac-sub` `flip--` `div-inv`
1×	`+-commutative` `flip3-+` `diff-log` `sum-log` `flip-+` `distribute-lft-out`

Counts

4 → 84

Calls

4 calls:

6.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
3.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
5.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(/ 1.0 (hypot 1.0 x))
32.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify147.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	288	547
1	1035	512
2	4960	506
3	5001	506

prune208.0ms

Filtered

96 candidates to 68 candidates (70.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	91	5	96
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	93	5	98

Merged error: 14.6b

Counts

98 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.2b	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
2.4b	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

87×	`associate-*r/`
44×	`add-exp-log` `add-cbrt-cube`
43×	`pow1`
24×	`frac-sub`
21×	`frac-times` `prod-exp` `cbrt-unprod`
20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
19×	`flip3--` `flip--`
18×	`times-frac`
17×	`pow-prod-down`
15×	`associate-*l/`
8×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp` `associate--l+`
6×	`associate-/r` `associate-/l` `add-log-exp`
5×	`sub-neg`
4×	`pow-sqr` `pow-prod-up`
2×	`frac-2neg` `pow-plus` `clear-num` `div-inv`
1×	`pow2` `diff-log` `swap-sqr` `associate-r` `associate-l` `*-commutative` `difference-of-squares`

Counts

4 → 146

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
3.0ms	(/ 1.0 (hypot 1.0 x))
11.0ms	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
15.0ms	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

series93.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
10.0ms	(/ 1.0 (hypot 1.0 x))
24.0ms	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
54.0ms	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

simplify103.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	706	1704
1	3591	1480
2	5001	1479

prune330.0ms

Filtered

158 candidates to 82 candidates (51.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	153	5	158
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	158	5	163

Merged error: 14.3b

Counts

163 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.2b	(exp (log (- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))))
0.2b	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
2.4b	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

169×	`associate-*r/`
48×	`frac-sub`
44×	`pow1`
42×	`add-exp-log` `add-cbrt-cube`
41×	`frac-times`
38×	`flip3--` `flip--`
29×	`associate-*l/`
26×	`log-div` `exp-diff`
21×	`prod-exp` `cbrt-unprod`
17×	`pow-prod-down`
14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`distribute-rgt-in` `distribute-lft-in` `associate--l+`
7×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`sub-neg`
4×	`log-prod` `exp-prod` `exp-sum` `pow-sqr` `pow-prod-up`
3×	`associate-/r` `associate-/l`
2×	`pow-plus` `difference-of-squares`
1×	`pow2` `frac-2neg` `diff-log` `swap-sqr` `associate-r` `associate-l` `clear-num` `log-pow` `*-commutative` `div-inv` `rem-exp-log`

Counts

4 → 161

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
22.0ms	(exp (log (- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))))
11.0ms	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
16.0ms	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

series143.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
54.0ms	(exp (log (- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))))
30.0ms	(* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x))))
54.0ms	(- (* (* 1.0 (- 1.0 0.5)) (* 1.0 (- 1.0 0.5))) (* (* 0.5 (/ 1.0 (hypot 1.0 x))) (* 0.5 (/ 1.0 (hypot 1.0 x)))))

simplify117.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	838	2651
1	3826	2371
2	5001	2334

prune365.0ms

Filtered

173 candidates to 83 candidates (48.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	171	7	178

Merged error: 14.3b

Counts

178 → 7

regimes160.0ms

Accuracy

0% (0.4b remaining)

Error of 14.9b against oracle of 14.5b and baseline of 14.9b

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	54
1	72	54
2	80	54
3	86	54
4	95	54
5	96	54
6	96	54

end0.0ms

sample1.1s

Algorithm

intervals

Results

613.0ms	2855×	body	1280	valid
167.0ms	4050×	body	80	valid
109.0ms	625×	body	640	valid
39.0ms	322×	body	320	valid
12.0ms	148×	body	160	valid

Details

sample35.0ms

simplify10.0ms

prune2.0ms

localize11.0ms

rewrite21.0ms

series189.0ms

simplify68.0ms

prune137.0ms

localize12.0ms

rewrite24.0ms

series69.0ms

simplify147.0ms

prune208.0ms

localize17.0ms

rewrite43.0ms

series93.0ms

simplify103.0ms

prune330.0ms

localize21.0ms

rewrite63.0ms

series143.0ms

simplify117.0ms

prune365.0ms

regimes160.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample1.1s

Profiling