Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

sample23.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

prune3.0ms

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: 0.2b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
12×	`times-frac`
6×	`distribute-lft-out`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `associate-/r*` `sqrt-prod`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 61

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

series27.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(+ 1.0 (sqrt (+ x 1.0)))
16.0ms	(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify25.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	4963	1021
1	4963	1021

prune125.0ms

Filtered

52 candidates to 70 candidates (-34.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	67	4	71

Merged error: 0b

Counts

71 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.3b	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
0.8b	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

112×	`add-sqr-sqrt`
106×	`times-frac`
101×	`*-un-lft-identity`
71×	`sqrt-prod`
65×	`add-cube-cbrt`
32×	`add-exp-log`
27×	`associate-r` `associate-l`
20×	`add-cbrt-cube`
15×	`distribute-lft-out` `unswap-sqr`
14×	`associate-/r*`
11×	`div-exp`
10×	`sqrt-div`
9×	`pow1`
8×	`prod-exp` `associate-/r/`
6×	`cbrt-undiv` `associate-/l*`
5×	`flip3-+` `flip-+`
4×	`cbrt-unprod` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`frac-times` `rem-sqrt-square` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `inv-pow`

Counts

4 → 205

Calls

4 calls:

5.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
8.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
33.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
8.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ 1.0 (sqrt (+ x 1.0))))
31.0ms	(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
15.0ms	(* (/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))))
19.0ms	(/ 1 (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5035	4229

prune465.0ms

Filtered

131 candidates to 217 candidates (-65.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	217	0	217
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	217	4	221

Merged error: 0b

Counts

221 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
56×	`add-sqr-sqrt`
52×	`times-frac`
39×	`add-cube-cbrt` `sqrt-prod`
30×	`associate-r`
15×	`distribute-lft-out`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`associate-l` `associate-/l*` `add-log-exp` `unswap-sqr`
4×	`flip3-+` `associate-/r*` `associate-/r/` `flip-+`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `cbrt-unprod` `div-inv`
1×	`+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative`

Counts

4 → 132

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
8.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
5.0ms	(+ 1.0 (sqrt (+ x 1.0)))
17.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
27.0ms	(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
7.0ms	(+ 1.0 (sqrt (+ x 1.0)))
15.0ms	(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify65.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4970	2333
1	4970	2333

prune204.0ms

Filtered

92 candidates to 144 candidates (-56.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	145	3	148

Merged error: 0b

Counts

148 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))
0.0b	(sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))
0.1b	(* (* (sqrt x) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))))
0.2b	(* (sqrt x) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

185×	`sqrt-prod`
116×	`*-un-lft-identity`
104×	`times-frac`
98×	`add-sqr-sqrt`
68×	`add-cube-cbrt`
66×	`associate-r`
24×	`distribute-lft-out`
18×	`pow1`
11×	`add-exp-log` `add-cbrt-cube`
10×	`pow-prod-down`
8×	`associate-/r/` `unswap-sqr`
7×	`sqrt-pow1` `pow1/2` `sqrt-div` `associate-l`
6×	`rem-sqrt-square`
4×	`flip3-+` `associate-*r/` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
3×	`sqrt-unprod`
2×	`*-commutative`
1×	`frac-times` `associate-*l/`

Counts

4 → 202

Calls

4 calls:

9.0ms	(sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))
11.0ms	(sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))
25.0ms	(* (* (sqrt x) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))))
18.0ms	(* (sqrt x) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))))

series110.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))
33.0ms	(sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))
15.0ms	(* (* (sqrt x) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))))
33.0ms	(* (sqrt x) (sqrt (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))))

simplify89.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4947	4665
1	4947	4665

prune468.0ms

Filtered

130 candidates to 214 candidates (-64.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	214	3	217

Merged error: 0b

Counts

217 → 3

regimes74.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	8
1	8	8

end0.0ms

sample692.0ms

Algorithm

intervals

Results

216.0ms	7998×	body	80	valid
0.0ms	2×	body	1280	valid

Details

analyze3.0ms

sample23.0ms

simplify3.0ms

prune3.0ms

localize6.0ms

rewrite17.0ms

series27.0ms

simplify25.0ms

prune125.0ms

localize10.0ms

rewrite63.0ms

series76.0ms

simplify54.0ms

prune465.0ms

localize9.0ms

rewrite38.0ms

series52.0ms

simplify65.0ms

prune204.0ms

localize12.0ms

rewrite73.0ms

series110.0ms

simplify89.0ms

prune468.0ms

regimes74.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample692.0ms

Profiling