Details

sample34.0ms

Algorithm

intervals

Results

17.0ms	103×	body	1280	valid
5.0ms	23×	body	640	valid
3.0ms	121×	body	80	valid
1.0ms	6×	body	320	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	6
1	26	6
2	33	6
3	35	6
4	41	6
5	44	6
6	44	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: 15.3b

Counts

2 → 1

localize7.0ms

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))
1.3b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

2×	`flip3-+` `sqrt-div` `associate-*r/` `sqrt-prod` `flip-+`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `pow1/2` `clear-num` `*-commutative` `flip--` `div-inv`

Counts

4 → 15

Calls

4 calls:

2.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
4.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

series850.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(+ 1.0 (/ 1.0 (hypot 1.0 x)))
264.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
107.0ms	(/ 1.0 (hypot 1.0 x))
355.0ms	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

simplify35.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	355	358
1	1216	340
2	5001	326

prune108.0ms

Filtered

27 candidates to 26 candidates (96.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	23	4	27
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	23	5	28

Merged error: 14.8b

Counts

28 → 5

localize12.0ms

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))
0.9b	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

2×	`frac-2neg` `clear-num` `div-inv`
1×	`+-commutative` `flip3-+` `flip-+` `fma-udef`

Counts

4 → 10

Calls

4 calls:

3.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
2.0ms	(/ 1.0 (hypot 1.0 x))
2.0ms	(/ 1.0 (hypot 1.0 x))
1.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

series679.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(+ 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))
107.0ms	(/ 1.0 (hypot 1.0 x))
108.0ms	(/ 1.0 (hypot 1.0 x))
146.0ms	(fma 1.0 1.0 (* (- 0.5) (+ 1.0 (/ 1.0 (hypot 1.0 x)))))

simplify33.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	308	238
1	1096	222
2	5001	216

prune113.0ms

Filtered

22 candidates to 22 candidates (100.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	2	1	3
Picked	0	1	1
Done	0	1	1
Total	22	5	27

Merged error: 0.2b

Counts

27 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 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)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 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)
0.9b	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`sqr-pow`
8×	`unpow3` `prod-diff`
6×	`unpow-prod-down` `sqrt-prod`
3×	`*-commutative`
2×	`difference-cubes` `flip3--` `fma-neg` `flip--` `associate-/l/` `associate-/l*` `difference-of-squares`
1×	`pow-to-exp` `sub-neg` `pow-pow` `frac-2neg` `pow1/2` `div-sub` `clear-num` `sqrt-pow2` `fma-udef` `div-inv`

Counts

4 → 32

Calls

4 calls:

1.0ms	(fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
8.0ms	(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
3.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
6.0ms	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

series8.4s

Counts

4 → 12

Calls

4 calls:

602.0ms	(fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))))
5.7s	(/ (- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)) (fma 1.0 1.0 (fma 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))) (* 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))))))
691.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
1.4s	(- (pow 1.0 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3))

simplify67.0ms

Algorithm

egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1799	2551
1	5001	2445

prune414.0ms

Filtered

44 candidates to 36 candidates (81.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	41	3	44
Fresh	0	2	2
Picked	1	0	1
Done	2	0	2
Total	44	5	49

Merged error: 0.2b

Counts

49 → 5

localize23.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.5b	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
0.8b	(- (* (pow 1.0 3) (pow 1.0 3)) (* (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

185×	`sqr-pow`
135×	`prod-diff`
103×	`unpow3`
78×	`unpow-prod-down` `sqrt-prod`
76×	`swap-sqr`
72×	`*-commutative`
68×	`associate-r` `associate-l`
33×	`unswap-sqr`
16×	`difference-of-squares`
9×	`fma-neg`
3×	`pow-to-exp` `pow-pow` `pow1/2` `sqrt-pow2`
2×	`pow-prod-down`
1×	`difference-cubes` `sub-neg` `flip3--` `flip--`

Counts

4 → 186

Calls

4 calls:

3.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
3.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
3.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
28.0ms	(- (* (pow 1.0 3) (pow 1.0 3)) (* (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)))

series3.1s

Counts

4 → 12

Calls

4 calls:

701.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
710.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
700.0ms	(pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)
993.0ms	(- (* (pow 1.0 3) (pow 1.0 3)) (* (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3) (pow (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))) 3)))

simplify141.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	851	8597
1	3140	4689
2	5002	4683

prune315.0ms

Filtered

198 candidates to 45 candidates (22.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	196	2	198
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	198	5	203

Merged error: 0.2b

Counts

203 → 5

regimes231.0ms

Accuracy

99.4% (0.1b remaining)

Error of 0.3b against oracle of 0.2b and baseline of 14.6b

bsearch161.0ms

Steps

Iters	Range		Point
8	3.88064682879673e-06	0.018000635171863108	0.0031563808817272844
10	-1421.6155834850151	-1.485944467815708e-07	-0.9591038128874348

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	71
1	67	71

end0.0ms

sample819.0ms

Algorithm

intervals

Results

474.0ms	2872×	body	1280	valid
122.0ms	4069×	body	80	valid
79.0ms	590×	body	640	valid
27.0ms	302×	body	320	valid
10.0ms	167×	body	160	valid