Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample20.0ms

Algorithm

intervals

Results

14.0ms

256×

body

valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4970	14
1	4970	14

prune8.0ms

Filtered

1 candidates to 1 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: 0.0b

Counts

2 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
0.0b	(+ x (+ 1.0 (* 4.0 (sqrt x))))
0.0b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
41×	`times-frac`
26×	`associate-r`
25×	`add-cube-cbrt`
12×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
5×	`pow1` `associate-/l*`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `associate-l` `sum-log` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`

Counts

3 → 105

Calls

3 calls:

14.0ms	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
5.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
9.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

series23.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
4.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

simplify34.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5591	1958

prune173.0ms

Filtered

82 candidates to 114 candidates (-39.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	109	5	114
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	111	5	116

Merged error: 0.0b

Counts

116 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 6.0 (/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))))
0.0b	(+ x (+ 1.0 (* 4.0 (sqrt x))))
0.0b	(/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))
0.0b	(/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

322×	`times-frac`
292×	`*-un-lft-identity`
220×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
83×	`associate-r`
42×	`distribute-lft-out`
36×	`add-exp-log`
33×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-/r*`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
10×	`div-inv`
9×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`pow1` `cbrt-undiv` `prod-exp` `associate-/l*`
5×	`unswap-sqr`
4×	`rec-exp` `1-exp`
3×	`associate-l` `sum-log` `cbrt-unprod`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+r+` `pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 299

Calls

4 calls:

30.0ms	(* 6.0 (/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))))
5.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
9.0ms	(/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))
15.0ms	(/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0)))

series30.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* 6.0 (/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))))
4.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
6.0ms	(/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))
12.0ms	(/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0)))

simplify100.0ms

Algorithm

egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4954	5899
1	4954	5899

prune441.0ms

Filtered

180 candidates to 311 candidates (-72.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	311	0	311
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	311	5	316

Merged error: 0.0b

Counts

316 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ 1.0 (* 4.0 (sqrt x))))
0.0b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
0.0b	(cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3))
0.1b	(pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

153×	`*-un-lft-identity`
100×	`times-frac`
99×	`add-sqr-sqrt`
58×	`cbrt-prod`
57×	`add-cube-cbrt`
52×	`unpow-prod-down` `cube-prod`
27×	`distribute-lft-out`
21×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r/`
9×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
6×	`flip3-+` `flip-+`
5×	`pow1` `div-inv` `associate-/l*`
4×	`associate-/r*`
3×	`pow-unpow` `sum-log`
2×	`cbrt-undiv` `cube-div` `cube-mult` `unpow3` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `cbrt-div` `associate-+r+` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `clear-num` `flip--` `rem-cbrt-cube`

Counts

4 → 200

Calls

4 calls:

5.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
9.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
12.0ms	(cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3))
11.0ms	(pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)

series35.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
10.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
10.0ms	(cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3))
11.0ms	(pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)

simplify70.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5213	4440

prune234.0ms

Filtered

103 candidates to 212 candidates (-105.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	212	0	212
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	212	5	217

Merged error: 0.0b

Counts

217 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
0.0b	(cbrt (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
0.0b	(cbrt (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
0.0b	(cbrt (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

121×	`*-un-lft-identity`
80×	`times-frac`
79×	`add-sqr-sqrt`
78×	`cbrt-prod`
45×	`add-cube-cbrt`
21×	`distribute-lft-out`
17×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r/`
6×	`add-exp-log` `add-cbrt-cube`
5×	`associate-/l*`
4×	`pow1` `flip3-+` `associate-/r*` `flip-+` `div-inv` `add-log-exp`
3×	`cbrt-div` `pow1/3`
2×	`associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `div-sub` `div-exp` `clear-num` `flip--`

Counts

4 → 151

Calls

4 calls:

9.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
8.0ms	(cbrt (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
8.0ms	(cbrt (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
10.0ms	(cbrt (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
22.0ms	(cbrt (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
19.0ms	(cbrt (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
19.0ms	(cbrt (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))

simplify44.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5098	4028

prune475.0ms

Filtered

115 candidates to 163 candidates (-41.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	162	1	163
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	163	5	168

Merged error: 0b

Counts

168 → 5

regimes37.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	16
1	27	16

end0.0ms

sample394.0ms

Algorithm

intervals

Results

305.0ms	8000×	body	80	valid
0.0ms	4×	body	80	nan

Details

analyze3.0ms

sample20.0ms

simplify64.0ms

prune8.0ms

localize9.0ms

rewrite31.0ms

series23.0ms

simplify34.0ms

prune173.0ms

localize10.0ms

rewrite76.0ms

series30.0ms

simplify100.0ms

prune441.0ms

localize14.0ms

rewrite46.0ms

series35.0ms

simplify70.0ms

prune234.0ms

localize12.0ms

rewrite41.0ms

series66.0ms

simplify44.0ms

prune475.0ms

regimes37.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample394.0ms

Profiling