Details

sample3.2s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.457764%

Guaranteed chance to sample good point: 29.278313%

Results

29.0ms	81×	body	1280	valid
13.0ms	52×	body	640	valid
5.0ms	30×	body	320	valid
4.0ms	92×	body	80	overflowed
4.0ms	77×	body	80	valid
2.0ms	16×	body	160	valid

simplify401.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	7
1	28	7
2	40	7
3	73	7
4	176	7
5	559	7
6	2626	7
7	5001	7

prune5.0ms

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: 43.9b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.0b	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.8b	(- (exp (* 2.0 x)) 1.0)
3.9b	(- (exp x) 1.0)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
51×	`times-frac`
31×	`sqrt-prod`
27×	`add-cube-cbrt`
24×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-/r` `flip--` `associate-/l`
4×	`associate-/r/`
2×	`sub-neg` `rem-sqrt-square` `diff-log` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `div-sub` `div-exp` `clear-num`

Counts

4 → 123

Calls

4 calls:

9.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
8.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
4.0ms	(- (exp (* 2.0 x)) 1.0)
6.0ms	(- (exp x) 1.0)

series32.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
8.0ms	(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.0ms	(- (exp (* 2.0 x)) 1.0)
10.0ms	(- (exp x) 1.0)

simplify120.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 3 (105.0ms)

Iter	Nodes	Cost
0	387	1380
1	1054	1314
2	4265	1301
3	5001	1293

prune255.0ms

Filtered

92 candidates to 135 candidates (-46.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	132	4	136

Merged error: 0.0b

Counts

136 → 4

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(* x (+ 1.0 (* 0.5 x)))
8.2b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube`
3×	`associate-r` `associate-l` `sqrt-prod`
2×	`flip3-+` `sqrt-div` `associate-*r/` `flip-+` `add-log-exp`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

2 → 37

Calls

2 calls:

5.0ms	(* x (+ 1.0 (* 0.5 x)))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series11.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(* x (+ 1.0 (* 0.5 x)))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify38.0ms

Algorithm

egg-herbie

Counts

43 → 43

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	279	280
1	1132	268
2	5002	256

prune73.0ms

Filtered

31 candidates to 43 candidates (-38.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	42	1	43
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	42	5	47

Merged error: 0.0b

Counts

47 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0)))
0.9b	(* (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))) (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))))
8.2b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))
8.2b	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

82×	`sqrt-prod`
54×	`add-sqr-sqrt`
38×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
20×	`add-cube-cbrt` `*-un-lft-identity` `pow1/2`
15×	`swap-sqr`
9×	`flip3-+` `associate-r` `associate-l` `pow-prod-up` `flip-+` `unswap-sqr`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
2×	`associate-r/` `associate-l/`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 134

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0)))
17.0ms	(* (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))) (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series25.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0)))
5.0ms	(* (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))) (sqrt (sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))
5.0ms	(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	427	1491
1	1763	1403
2	5002	1383

prune251.0ms

Filtered

80 candidates to 146 candidates (-82.5%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	146	5	151

Merged error: 0.0b

Counts

151 → 5

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (+ (sqrt (exp x)) (sqrt 1.0))) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0))))
0.0b	(/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (+ (sqrt (exp x)) (sqrt 1.0)))
3.9b	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
4.0b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

218×	`add-sqr-sqrt`
214×	`*-un-lft-identity`
164×	`sqrt-prod`
135×	`times-frac`
87×	`associate-r`
80×	`difference-of-squares`
46×	`add-cube-cbrt`
44×	`distribute-lft-out`
40×	`distribute-lft-out--`
31×	`associate-l`
18×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`pow1` `associate-/r/`
5×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l`
4×	`prod-exp` `cbrt-unprod` `unswap-sqr`
3×	`flip3--` `flip3-+` `flip--` `flip-+` `div-inv`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 229

Calls

4 calls:

64.0ms	(* (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (+ (sqrt (exp x)) (sqrt 1.0))) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0))))
13.0ms	(/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (+ (sqrt (exp x)) (sqrt 1.0)))
6.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
6.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series53.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (+ (sqrt (exp x)) (sqrt 1.0))) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0))))
13.0ms	(/ (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (+ (sqrt (exp x)) (sqrt 1.0)))
5.0ms	(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
5.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify108.0ms

Algorithm

egg-herbie

Counts

241 → 241

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	753	4573
1	3694	3975
2	5002	3890

prune601.0ms

Filtered

127 candidates to 241 candidates (-89.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	240	1	241
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	241	5	246

Merged error: 0.0b

Counts

246 → 5

regimes54.0ms

Accuracy

98.5% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 21.2b

bsearch22.0ms

Steps

Iters	Range		Point
9	-0.02049104390072357	-4.517264162674723e-10	-0.00013445133628746207

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	19
1	38	19

end0.0ms

sample4.8s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0.457764%

Guaranteed chance to sample good point: 29.278313%

Results

835.0ms	2290×	body	1280	valid
383.0ms	1648×	body	640	valid
127.0ms	2849×	body	80	valid
122.0ms	789×	body	320	valid
106.0ms	2614×	body	80	overflowed
42.0ms	424×	body	160	valid
0.0ms	1×	body	80	invalid

Details

sample3.2s

simplify401.0ms

prune5.0ms

localize24.0ms

rewrite32.0ms

series32.0ms

simplify120.0ms

prune255.0ms

localize7.0ms

rewrite11.0ms

series11.0ms

simplify38.0ms

prune73.0ms

localize11.0ms

rewrite38.0ms

series25.0ms

simplify67.0ms

prune251.0ms

localize17.0ms

rewrite106.0ms

series53.0ms

simplify108.0ms

prune601.0ms

regimes54.0ms

bsearch22.0ms

simplify2.0ms

end0.0ms

sample4.8s

Profiling