Details

sample42.0ms

Algorithm

intervals

Results

9.0ms	278×	body	80	nan
9.0ms	63×	body	640	valid
7.0ms	42×	body	1280	valid
5.0ms	125×	body	80	valid
2.0ms	17×	body	320	valid
1.0ms	9×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	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: 20.0b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.9b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 117

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
5.0ms	(/ 1.0 (sqrt x))
35.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series591.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms	(/ 1.0 (sqrt (+ x 1.0)))
194.0ms	(/ 1.0 (sqrt x))
270.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify59.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	541	1048
1	2015	1014
2	5002	983

prune271.0ms

Filtered

126 candidates to 85 candidates (67.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	112	14	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	14	127

Merged error: 19.5b

Counts

127 → 14

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`sqrt-prod`
17×	`add-exp-log` `add-cbrt-cube`
16×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt` `associate-r`
6×	`associate-r/` `associate-l*`
5×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`pow-prod-down` `distribute-lft-out--`
2×	`flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`sub-neg` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

3 → 77

Calls

3 calls:

21.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series1.0s

Counts

3 → 9

Calls

3 calls:

707.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
120.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
191.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify95.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	785	930
1	4068	833
2	5002	827

prune211.0ms

Filtered

86 candidates to 61 candidates (70.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	88	12	100

Merged error: 18.9b

Counts

100 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
2.2b	(+ x (- 1.0 x))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

105×	`*-un-lft-identity`
41×	`distribute-lft-out`
35×	`sqrt-prod`
31×	`times-frac`
29×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
21×	`add-cube-cbrt`
9×	`cbrt-undiv` `div-exp` `add-log-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `associate-/l*`
5×	`flip3-+` `associate-*r/` `flip-+`
4×	`sqrt-div` `associate-/r/` `unswap-sqr`
3×	`pow-prod-down` `associate-/l/`
2×	`associate-+r-` `associate-+r+` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log` `div-inv`
1×	`+-commutative` `sub-neg` `sqrt-unprod` `diff-log` `div-sub` `*-commutative`

Counts

4 → 136

Calls

4 calls:

15.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
23.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
12.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
6.0ms	(+ x (- 1.0 x))

series1.2s

Counts

4 → 12

Calls

4 calls:

219.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
851.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
124.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify42.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	938	1674
1	5002	1471

prune308.0ms

Filtered

148 candidates to 91 candidates (61.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	150	10	160

Merged error: 0.3b

Counts

160 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
31×	`sqrt-prod`
29×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
21×	`distribute-lft-out`
19×	`add-cube-cbrt` `times-frac`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`associate-*r/`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `associate-/l*` `unswap-sqr`
3×	`pow-prod-down`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series1.3s

Counts

4 → 12

Calls

4 calls:

106.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
208.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
859.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
120.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify38.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	935	1360
1	5002	1197

prune280.0ms

Filtered

128 candidates to 89 candidates (69.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	120	8	128
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	126	12	138

Merged error: 0.0b

Counts

138 → 12

regimes45.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	11
1	13	11

end0.0ms

sample1.2s

Algorithm

intervals

Results

280.0ms	8174×	body	80	nan
271.0ms	1873×	body	640	valid
208.0ms	1142×	body	1280	valid
151.0ms	4001×	body	80	valid
68.0ms	650×	body	320	valid
26.0ms	334×	body	160	valid

Details

sample42.0ms

simplify6.0ms

prune2.0ms

localize7.0ms

rewrite51.0ms

series591.0ms

simplify59.0ms

prune271.0ms

localize8.0ms

rewrite41.0ms

series1.0s

simplify95.0ms

prune211.0ms

localize12.0ms

rewrite60.0ms

series1.2s

simplify42.0ms

prune308.0ms

localize10.0ms

rewrite53.0ms

series1.3s

simplify38.0ms

prune280.0ms

regimes45.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling