Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample43.0ms

Algorithm

intervals

Results

26.0ms	99×	body	1280	valid
6.0ms	124×	body	80	valid
3.0ms	20×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	442	12
1	442	12

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 14.9b

Counts

2 → 1

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot 1.0 x)
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.6b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

1.0ms	(hypot 1.0 x)
3.0ms	(/ 1.0 (hypot 1.0 x))
6.0ms	(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))))))

series32.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot 1.0 x)
4.0ms	(/ 1.0 (hypot 1.0 x))
13.0ms	(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))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5551	757

prune129.0ms

Filtered

52 candidates to 72 candidates (-38.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	68	4	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	4	73

Merged error: 14.5b

Counts

73 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
26×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
19×	`times-frac`
11×	`add-log-exp`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
4×	`pow1`
3×	`diff-log` `distribute-lft-out--`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--` `div-inv` `distribute-lft-out` `difference-of-squares`
1×	`+-commutative` `associate--l-` `flip3-+` `associate--l+` `sum-log` `sqrt-prod` `flip-+`

Counts

4 → 87

Calls

4 calls:

3.0ms	(/ 0.5 (hypot 1.0 x))
3.0ms	(/ 0.5 (hypot 1.0 x))
3.0ms	(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
10.0ms	(- (- 1.0 0.5) (/ 0.5 (hypot 1.0 x)))

series30.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify47.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4931	1080
1	4931	1080

prune233.0ms

Filtered

74 candidates to 99 candidates (-33.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	96	3	99
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	98	5	103

Merged error: 14.2b

Counts

103 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 0.5 (hypot 1.0 x))
0.0b	(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
1.1b	(- (- 1.0 0.5) (log (exp (/ 0.5 (hypot 1.0 x)))))
3.8b	(log (exp (/ 0.5 (hypot 1.0 x))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

3.0ms	(/ 0.5 (hypot 1.0 x))
3.0ms	(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
13.0ms	(- (- 1.0 0.5) (log (exp (/ 0.5 (hypot 1.0 x)))))
4.0ms	(log (exp (/ 0.5 (hypot 1.0 x))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 0.5 (hypot 1.0 x))
16.0ms	(+ 1.0 (sqrt (* 1.0 (+ 0.5 (/ 0.5 (hypot 1.0 x))))))
6.0ms	(- (- 1.0 0.5) (log (exp (/ 0.5 (hypot 1.0 x)))))
4.0ms	(log (exp (/ 0.5 (hypot 1.0 x))))

simplify48.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5347	996

prune236.0ms

Filtered

73 candidates to 99 candidates (-35.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	99	0	99
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	99	5	104

Merged error: 14.2b

Counts

104 → 5

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sqrt 0.5) (sqrt (hypot 1.0 x)))
0.2b	(/ (sqrt 0.5) (sqrt (hypot 1.0 x)))
0.4b	(* (+ (sqrt (- 1.0 0.5)) (/ (sqrt 0.5) (sqrt (hypot 1.0 x)))) (- (sqrt (- 1.0 0.5)) (/ (sqrt 0.5) (sqrt (hypot 1.0 x)))))
1.2b	(- (sqrt (- 1.0 0.5)) (/ (sqrt 0.5) (sqrt (hypot 1.0 x))))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

120×	`add-sqr-sqrt`
110×	`sqrt-prod`
88×	`times-frac`
68×	`*-un-lft-identity`
62×	`add-cube-cbrt`
22×	`sqrt-div`
20×	`difference-of-squares`
17×	`flip3--` `flip--`
16×	`frac-times`
14×	`associate-r`
12×	`associate-/r` `frac-sub` `associate-/l`
10×	`add-exp-log` `frac-add` `add-cbrt-cube`
6×	`pow1` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-r/` `associate-l` `associate-l/`
3×	`sub-neg`
2×	`cbrt-undiv` `sqrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv` `distribute-lft-out--`
1×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

4 → 202

Calls

4 calls:

5.0ms	(/ (sqrt 0.5) (sqrt (hypot 1.0 x)))
5.0ms	(/ (sqrt 0.5) (sqrt (hypot 1.0 x)))
48.0ms	(* (+ (sqrt (- 1.0 0.5)) (/ (sqrt 0.5) (sqrt (hypot 1.0 x)))) (- (sqrt (- 1.0 0.5)) (/ (sqrt 0.5) (sqrt (hypot 1.0 x)))))
21.0ms	(- (sqrt (- 1.0 0.5)) (/ (sqrt 0.5) (sqrt (hypot 1.0 x))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (sqrt 0.5) (sqrt (hypot 1.0 x)))
9.0ms	(/ (sqrt 0.5) (sqrt (hypot 1.0 x)))
26.0ms	(* (+ (sqrt (- 1.0 0.5)) (/ (sqrt 0.5) (sqrt (hypot 1.0 x)))) (- (sqrt (- 1.0 0.5)) (/ (sqrt 0.5) (sqrt (hypot 1.0 x)))))
16.0ms	(- (sqrt (- 1.0 0.5)) (/ (sqrt 0.5) (sqrt (hypot 1.0 x))))

simplify74.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5034	4243

prune807.0ms

Filtered

126 candidates to 214 candidates (-69.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	214	5	219

Merged error: 14.2b

Counts

219 → 5

regimes83.0ms

Accuracy

0% (0.3b remaining)

Error of 14.7b against oracle of 14.5b and baseline of 14.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	26
1	37	26

end0.0ms

sample1.0s

Algorithm

intervals

Results

626.0ms	2853×	body	1280	valid
161.0ms	4086×	body	80	valid
106.0ms	603×	body	640	valid
38.0ms	311×	body	320	valid
11.0ms	147×	body	160	valid

Details

analyze1.0ms

sample43.0ms

simplify19.0ms

prune5.0ms

localize8.0ms

rewrite15.0ms

series32.0ms

simplify56.0ms

prune129.0ms

localize12.0ms

rewrite21.0ms

series30.0ms

simplify47.0ms

prune233.0ms

localize15.0ms

rewrite25.0ms

series30.0ms

simplify48.0ms

prune236.0ms

localize18.0ms

rewrite87.0ms

series60.0ms

simplify74.0ms

prune807.0ms

regimes83.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.0s

Profiling