Details

analyze1.0ms

Algorithm: search

sample36.0ms

Algorithm

intervals

Results

19.0ms	87×	body	1280	valid
5.0ms	134×	body	80	valid
3.0ms	19×	body	640	valid
2.0ms	14×	body	320	valid
0.0ms	2×	body	160	valid

simplify9.0ms

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

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: 14.6b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
1.3b	(- 1.0 (sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x))))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `*-un-lft-identity`
11×	`add-cube-cbrt`
9×	`times-frac`
6×	`pow1`
5×	`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

3 → 54

Calls

3 calls:

3.0ms	(/ 1.0 (hypot 1.0 x))
7.0ms	(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))))))

series31.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
12.0ms	(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))))))

simplify60.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	200	410
1	601	393
2	1983	391
3	5001	391

prune107.0ms

Filtered

45 candidates to 63 candidates (-40.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	2	64

Merged error: 14.1b

Counts

64 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(/ 1.0 (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.8b	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 85

Calls

4 calls:

3.0ms	(/ 1.0 (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)))))
8.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

series27.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/ 1.0 (hypot 1.0 x))
4.0ms	(/ 1.0 (hypot 1.0 x))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(- (* 1.0 (- 1.0 0.5)) (* 0.5 (/ 1.0 (hypot 1.0 x))))

simplify39.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	299	576
1	1026	547
2	5001	541

prune219.0ms

Filtered

70 candidates to 97 candidates (-38.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	97	2	99

Merged error: 14.1b

Counts

99 → 2

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (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)))))
0.8b	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-exp-log` `add-cbrt-cube`
16×	`associate-*r/`
12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
10×	`times-frac` `associate-*l/`
8×	`frac-sub`
7×	`pow1`
6×	`flip3--` `flip3-+` `flip--` `flip-+` `associate-/l/` `add-log-exp`
5×	`cbrt-undiv` `div-exp`
4×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l`
2×	`frac-2neg` `sqrt-pow1` `sqrt-div` `clear-num` `associate-/r/` `div-inv` `associate--r+`
1×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow1/2` `diff-log` `pow-prod-down` `sqrt-prod`

Counts

4 → 87

Calls

4 calls:

17.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (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)))))
6.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

series30.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ (* 1.0 (- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))) (* (+ 1.0 0.5) (hypot 1.0 x)))
4.0ms	(/ 1.0 (hypot 1.0 x))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
3.0ms	(- (* (- (* 1.0 1.0) (* 0.5 0.5)) (hypot 1.0 x)) (* 0.5 (+ 0.5 1.0)))

simplify80.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	616	1130
1	3179	964
2	5002	964

prune314.0ms

Filtered

73 candidates to 99 candidates (-35.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	99	2	101

Merged error: 14.1b

Counts

101 → 2

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (+ 1.0 0.5) (hypot 1.0 x))
0.0b	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
0.1b	(/ (+ (* (neg (+ (* (* 0.5 0.5) (+ (* 0.5 0.5) (* 1.0 1.0))) (* (pow 1.0 3) 1.0))) (* 0.5 (- (* 0.5 0.5) (* 1.0 1.0)))) (* (* (- (pow (* 1.0 1.0) 3) (pow (* 0.5 0.5) 3)) (hypot 1.0 x)) (- 0.5 1.0))) (* (- 0.5 1.0) (+ (* (* 0.5 0.5) (+ (* 0.5 0.5) (* 1.0 1.0))) (* (pow 1.0 3) 1.0))))
0.8b	(+ (* (neg (+ (* (* 0.5 0.5) (+ (* 0.5 0.5) (* 1.0 1.0))) (* (pow 1.0 3) 1.0))) (* 0.5 (- (* 0.5 0.5) (* 1.0 1.0)))) (* (* (- (pow (* 1.0 1.0) 3) (pow (* 0.5 0.5) 3)) (hypot 1.0 x)) (- 0.5 1.0)))

rewrite101.0ms

Algorithm

rewrite-expression-head

Rules

164×	`associate-r/` `associate-l/`
147×	`flip3--` `flip--`
132×	`frac-times`
128×	`frac-add`
96×	`distribute-neg-frac`
66×	`associate-/l/`
55×	`flip3-+` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
10×	`distribute-rgt-in` `add-sqr-sqrt` `*-un-lft-identity` `distribute-lft-in`
9×	`pow1`
8×	`add-cube-cbrt` `associate-+l+` `associate-/r/`
6×	`sub-neg` `add-log-exp`
4×	`associate-+r+` `associate-l`
3×	`times-frac` `associate-r` `associate-/l*`
2×	`cbrt-undiv` `sqrt-pow1` `sqrt-div` `div-exp` `pow-prod-down` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `pow1/2` `clear-num` `associate-/r` `sum-log` `sqrt-prod` `-commutative` `div-inv` `distribute-lft-out` `unswap-sqr`

Counts

4 → 216

Calls

4 calls:

11.0ms	(* (+ 1.0 0.5) (hypot 1.0 x))
6.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
39.0ms	(/ (+ (* (neg (+ (* (* 0.5 0.5) (+ (* 0.5 0.5) (* 1.0 1.0))) (* (pow 1.0 3) 1.0))) (* 0.5 (- (* 0.5 0.5) (* 1.0 1.0)))) (* (* (- (pow (* 1.0 1.0) 3) (pow (* 0.5 0.5) 3)) (hypot 1.0 x)) (- 0.5 1.0))) (* (- 0.5 1.0) (+ (* (* 0.5 0.5) (+ (* 0.5 0.5) (* 1.0 1.0))) (* (pow 1.0 3) 1.0))))
23.0ms	(+ (* (neg (+ (* (* 0.5 0.5) (+ (* 0.5 0.5) (* 1.0 1.0))) (* (pow 1.0 3) 1.0))) (* 0.5 (- (* 0.5 0.5) (* 1.0 1.0)))) (* (* (- (pow (* 1.0 1.0) 3) (pow (* 0.5 0.5) 3)) (hypot 1.0 x)) (- 0.5 1.0)))

series24.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(* (+ 1.0 0.5) (hypot 1.0 x))
12.0ms	(sqrt (* 0.5 (+ 1.0 (/ 1.0 (hypot 1.0 x)))))
6.0ms	(/ (+ (* (neg (+ (* (* 0.5 0.5) (+ (* 0.5 0.5) (* 1.0 1.0))) (* (pow 1.0 3) 1.0))) (* 0.5 (- (* 0.5 0.5) (* 1.0 1.0)))) (* (* (- (pow (* 1.0 1.0) 3) (pow (* 0.5 0.5) 3)) (hypot 1.0 x)) (- 0.5 1.0))) (* (- 0.5 1.0) (+ (* (* 0.5 0.5) (+ (* 0.5 0.5) (* 1.0 1.0))) (* (pow 1.0 3) 1.0))))
4.0ms	(+ (* (neg (+ (* (* 0.5 0.5) (+ (* 0.5 0.5) (* 1.0 1.0))) (* (pow 1.0 3) 1.0))) (* 0.5 (- (* 0.5 0.5) (* 1.0 1.0)))) (* (* (- (pow (* 1.0 1.0) 3) (pow (* 0.5 0.5) 3)) (hypot 1.0 x)) (- 0.5 1.0)))

simplify147.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 1 (49.0ms)

Iter	Nodes	Cost
0	2345	10433
1	5003	10208

prune8.0s

Filtered

202 candidates to 228 candidates (-12.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	226	2	228
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	227	3	230

Merged error: 14.1b

Counts

230 → 3

regimes105.0ms

Accuracy

0% (0.2b remaining)

Error of 15.1b against oracle of 14.9b and baseline of 15.1b

bsearch0.0ms

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	100
1	125	100
2	140	100
3	148	100
4	155	100
5	158	100
6	162	100
7	162	100

end0.0ms

analyze1.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

634.0ms	2866×	body	1280	valid
160.0ms	4027×	body	80	valid
107.0ms	622×	body	640	valid
43.0ms	332×	body	320	valid
12.0ms	153×	body	160	valid

Details

analyze1.0ms

sample36.0ms

simplify9.0ms

prune7.0ms

localize8.0ms

rewrite15.0ms

series31.0ms

simplify60.0ms

prune107.0ms

localize13.0ms

rewrite22.0ms

series27.0ms

simplify39.0ms

prune219.0ms

localize19.0ms

rewrite36.0ms

series30.0ms

simplify80.0ms

prune314.0ms

localize36.0ms

rewrite101.0ms

series24.0ms

simplify147.0ms

prune8.0s

regimes105.0ms

bsearch0.0ms

simplify7.0ms

end0.0ms

analyze1.0ms

sample1.1s

Profiling