Details

sample40.0ms

Algorithm

intervals

Results

22.0ms	97×	body	1280	valid
5.0ms	124×	body	80	valid
4.0ms	20×	body	640	valid
1.0ms	11×	body	320	valid
0.0ms	4×	body	160	valid

simplify8.0ms

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

prune7.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 15.5b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(/ 1.0 (hypot 1.0 x))
1.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 48

Calls

3 calls:

1.0ms	(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))))))

series19.0ms

Counts

3 → 9

Calls

3 calls:

1.0ms	(hypot 1.0 x)
4.0ms	(/ 1.0 (hypot 1.0 x))
14.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify43.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 2 (11.0ms)

Iter	Nodes	Cost
0	158	331
1	485	306
2	1396	304
3	5002	304

prune106.0ms

Filtered

57 candidates to 41 candidates (28.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	53	4	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	4	58

Merged error: 15.0b

Counts

58 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
1.1b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite17.0ms

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:

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

series30.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
7.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify137.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	306	616
1	1080	568
2	4837	560
3	5001	560

prune213.0ms

Filtered

96 candidates to 69 candidates (28.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	96	4	100

Merged error: 15.0b

Counts

100 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (+ (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.1b	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

165×	`add-sqr-sqrt`
95×	`*-un-lft-identity`
84×	`times-frac`
80×	`difference-of-squares`
64×	`unpow-prod-down` `cube-prod`
45×	`add-cube-cbrt`
41×	`sqr-pow`
28×	`associate-/l*`
25×	`distribute-lft-out--`
10×	`associate-*r/`
9×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+` `add-log-exp`
5×	`difference-cubes`
4×	`pow-pow` `frac-add`
3×	`pow-unpow`
2×	`cbrt-undiv` `cube-div` `flip3--` `frac-2neg` `sqrt-pow1` `sqrt-div` `div-exp` `clear-num` `sqrt-prod` `flip--` `div-inv` `associate-/l/`
1×	`cube-mult` `pow-to-exp` `sub-neg` `pow1/2` `diff-log` `unpow3` `div-sub` `pow-prod-down` `pow-exp` `sqrt-pow2` `rem-cube-cbrt`

Counts

4 → 216

Calls

4 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
22.0ms	(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (+ (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
8.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
12.0ms	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

series141.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(/ 1.0 (hypot 1.0 x))
83.0ms	(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (+ (* 1.0 (+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))) (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
21.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
31.0ms	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

simplify135.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 2 (85.0ms)

Iter	Nodes	Cost
0	819	5692
1	3572	5550
2	5001	5471

prune913.0ms

Filtered

228 candidates to 124 candidates (45.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	226	2	228
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	228	4	232

Merged error: 15.0b

Counts

232 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
1.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
1.5b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`add-log-exp`
5×	`cbrt-prod` `add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 57

Calls

4 calls:

3.0ms	(cbrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
3.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
4.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(cbrt (- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))
14.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
15.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
14.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify73.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 4 (64.0ms)

Iter	Nodes	Cost
0	109	739
1	236	685
2	719	677
3	2317	675
4	5002	669

prune229.0ms

Filtered

69 candidates to 49 candidates (29.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	69	4	73

Merged error: 15.0b

Counts

73 → 4

regimes331.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	13
1	19	13

end0.0ms

sample1.1s

Algorithm

intervals

Results

630.0ms	2858×	body	1280	valid
167.0ms	4069×	body	80	valid
105.0ms	606×	body	640	valid
38.0ms	320×	body	320	valid
11.0ms	147×	body	160	valid

Details

sample40.0ms

simplify8.0ms

prune7.0ms

localize8.0ms

rewrite8.0ms

series19.0ms

simplify43.0ms

prune106.0ms

localize13.0ms

rewrite17.0ms

series30.0ms

simplify137.0ms

prune213.0ms

localize14.0ms

rewrite58.0ms

series141.0ms

simplify135.0ms

prune913.0ms

localize12.0ms

rewrite14.0ms

series86.0ms

simplify73.0ms

prune229.0ms

regimes331.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling