Details

analyze531.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample23.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	14×	body	80	invalid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15

prune6.0ms

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: 24.0b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.0b	(+ (* a c) (* b d))
23.5b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
7×	`add-log-exp`
5×	`add-exp-log` `add-cbrt-cube`
4×	`flip3-+` `flip-+`
3×	`pow1` `associate-/r` `associate-/l`
2×	`+-commutative` `sum-log` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

3 → 53

Calls

3 calls:

4.0ms	(+ (* c c) (* d d))
4.0ms	(+ (* a c) (* b d))
8.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series42.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* c c) (* d d))
10.0ms	(+ (* a c) (* b d))
27.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify44.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5334	951

prune103.0ms

Filtered

48 candidates to 62 candidates (-29.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	55	7	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	56	7	63

Merged error: 23.3b

Counts

63 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
15.1b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
26.7b	(sqrt (+ (* c c) (* d d)))
26.7b	(sqrt (+ (* c c) (* d d)))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

288×	`times-frac`
164×	`add-sqr-sqrt`
162×	`add-cube-cbrt` `*-un-lft-identity`
156×	`sqrt-prod`
27×	`associate-/l*`
22×	`sqrt-div`
18×	`associate-/r/`
12×	`flip3-+` `associate-/r*` `flip-+`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
6×	`pow1`
4×	`cbrt-undiv` `div-exp` `add-log-exp`
3×	`associate-/l/`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`

Counts

4 → 264

Calls

4 calls:

18.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
11.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series77.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d)))) (sqrt (+ (* c c) (* d d))))
35.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

simplify94.0ms

Algorithm

egg-herbie

Counts

276 → 276

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4969	8788
1	4969	8788

prune211.0ms

Filtered

150 candidates to 276 candidates (-84.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	272	4	276
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	274	9	283

Merged error: 20.3b

Counts

283 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* a c) (* b d))
0.0b	(+ (* c c) (* d d))
0.4b	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
23.3b	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`flip3-+` `div-exp` `flip-+` `add-log-exp`
6×	`div-inv` `associate-/l*`
5×	`pow1`
4×	`cbrt-undiv`
2×	`+-commutative` `rec-exp` `frac-2neg` `1-exp` `clear-num` `sum-log` `associate-/l/`
1×	`pow-flip` `inv-pow`

Counts

4 → 137

Calls

4 calls:

4.0ms	(+ (* a c) (* b d))
4.0ms	(+ (* c c) (* d d))
10.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
9.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

series64.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* a c) (* b d))
5.0ms	(+ (* c c) (* d d))
28.0ms	(/ 1 (/ (+ (* c c) (* d d)) (+ (* a c) (* b d))))
21.0ms	(/ (+ (* c c) (* d d)) (+ (* a c) (* b d)))

simplify65.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4991	3201
1	4991	3201

prune153.0ms

Filtered

103 candidates to 149 candidates (-44.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	149	9	158

Merged error: 20.3b

Counts

158 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

7.1b	(/ (+ (* c a) (* d b)) (sqrt (sqrt (+ (* c c) (* d d)))))
15.5b	(* (/ (+ (* c a) (* d b)) (sqrt (sqrt (+ (* c c) (* d d))))) (/ 1 (pow (sqrt (sqrt (+ (* c c) (* d d)))) 3)))
26.7b	(sqrt (+ (* c c) (* d d)))
26.7b	(sqrt (+ (* c c) (* d d)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

306×	`add-sqr-sqrt`
241×	`times-frac`
222×	`sqrt-prod`
125×	`*-un-lft-identity`
93×	`add-cube-cbrt`
78×	`associate-r`
68×	`unswap-sqr`
56×	`add-exp-log`
51×	`unpow-prod-down` `cube-prod`
33×	`associate-l`
23×	`div-exp`
20×	`prod-exp`
18×	`add-cbrt-cube`
16×	`sqrt-div`
11×	`sqr-pow`
9×	`associate-/r*`
8×	`pow1`
6×	`pow-to-exp` `rec-exp` `flip3-+` `1-exp` `pow-exp` `associate-/r/` `flip-+`
5×	`cbrt-undiv`
4×	`cbrt-unprod` `add-log-exp`
3×	`cube-mult` `unpow3` `div-inv` `associate-/l*`
2×	`cube-div` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/l/`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative`

Counts

4 → 301

Calls

4 calls:

10.0ms	(/ (+ (* c a) (* d b)) (sqrt (sqrt (+ (* c c) (* d d)))))
62.0ms	(* (/ (+ (* c a) (* d b)) (sqrt (sqrt (+ (* c c) (* d d))))) (/ 1 (pow (sqrt (sqrt (+ (* c c) (* d d)))) 3)))
4.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series126.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (+ (* c a) (* d b)) (sqrt (sqrt (+ (* c c) (* d d)))))
21.0ms	(* (/ (+ (* c a) (* d b)) (sqrt (sqrt (+ (* c c) (* d d))))) (/ 1 (pow (sqrt (sqrt (+ (* c c) (* d d)))) 3)))
6.0ms	(sqrt (+ (* c c) (* d d)))
10.0ms	(sqrt (+ (* c c) (* d d)))

simplify127.0ms

Algorithm

egg-herbie

Counts

313 → 313

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	4982	9425
1	4982	9425

prune236.0ms

Filtered

146 candidates to 313 candidates (-114.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	312	1	313
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	313	9	322

Merged error: 20.3b

Counts

322 → 9

regimes316.0ms

Accuracy

-4% (3.2b remaining)

Error of 26.1b against oracle of 22.9b and baseline of 26.0b

bsearch20.0ms

Steps

Iters	Range		Point
9	4.26328807029034e+47	2.4518150383389165e+56	1.7331516180898825e+56

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	39
1	21	39

end0.0ms

sample591.0ms

Algorithm

intervals

Results

351.0ms	8000×	body	80	valid
20.0ms	487×	body	80	invalid

Details

analyze531.0ms

sample23.0ms

simplify3.0ms

prune6.0ms

localize11.0ms

rewrite17.0ms

series42.0ms

simplify44.0ms

prune103.0ms

localize12.0ms

rewrite50.0ms

series77.0ms

simplify94.0ms

prune211.0ms

localize11.0ms

rewrite32.0ms

series64.0ms

simplify65.0ms

prune153.0ms

localize17.0ms

rewrite98.0ms

series126.0ms

simplify127.0ms

prune236.0ms

regimes316.0ms

bsearch20.0ms

simplify1.0ms

end0.0ms

sample591.0ms

Profiling