Details

analyze1.4s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 79.736328%

sample24.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	23×	body	80	invalid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

prune4.0ms

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: 25.1b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* c c) (* d d))
1.0b	(+ (* a c) (* b d))
24.5b	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

rewrite16.0ms

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:

3.0ms	(+ (* c c) (* d d))
3.0ms	(+ (* a c) (* b d))
8.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

series46.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* c c) (* d d))
10.0ms	(+ (* a c) (* b d))
30.0ms	(/ (+ (* a c) (* b d)) (+ (* c c) (* d d)))

simplify131.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	272	527
1	1164	479
2	4437	477
3	5002	477

prune110.0ms

Filtered

49 candidates to 62 candidates (-26.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	55	7	62
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	55	8	63

Merged error: 24.3b

Counts

63 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* a c) (* b d))
14.3b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.1b	(sqrt (+ (* c c) (* d d)))
29.1b	(sqrt (+ (* c c) (* d d)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

3.0ms	(+ (* a c) (* b d))
9.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
3.0ms	(sqrt (+ (* c c) (* d d)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* a c) (* b d))
38.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
6.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

simplify84.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2679	828
3	5002	828

prune120.0ms

Filtered

74 candidates to 96 candidates (-29.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	93	11	104

Merged error: 23.1b

Counts

104 → 11

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(+ (* a c) (* b d))
14.3b	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
29.1b	(sqrt (+ (* c c) (* d d)))
29.1b	(sqrt (+ (* c c) (* d d)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

3.0ms	(+ (* a c) (* b d))
9.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
3.0ms	(sqrt (+ (* c c) (* d d)))
4.0ms	(sqrt (+ (* c c) (* d d)))

series59.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(+ (* a c) (* b d))
35.0ms	(/ (+ (* a c) (* b d)) (sqrt (+ (* c c) (* d d))))
8.0ms	(sqrt (+ (* c c) (* d d)))
6.0ms	(sqrt (+ (* c c) (* d d)))

simplify85.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	273	893
1	868	840
2	2679	828
3	5002	828

prune122.0ms

Filtered

74 candidates to 96 candidates (-29.7%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	95	12	107

Merged error: 23.1b

Counts

107 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* c c) (* d d))
0.6b	(/ 1 (+ (* c c) (* d d)))
1.0b	(+ (* a c) (* b d))
24.5b	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
20×	`add-cube-cbrt` `times-frac`
17×	`add-exp-log`
15×	`associate-r`
11×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
6×	`flip3-+` `flip-+`
4×	`div-exp` `prod-exp` `associate-/r/`
3×	`associate-l` `associate-/r` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `+-commutative` `frac-times` `rec-exp` `1-exp` `associate-*l/` `sum-log` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 97

Calls

4 calls:

4.0ms	(+ (* c c) (* d d))
5.0ms	(/ 1 (+ (* c c) (* d d)))
4.0ms	(+ (* a c) (* b d))
12.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

series51.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* c c) (* d d))
6.0ms	(/ 1 (+ (* c c) (* d d)))
10.0ms	(+ (* a c) (* b d))
29.0ms	(* (+ (* a c) (* b d)) (/ 1 (+ (* c c) (* d d))))

simplify56.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	393	851
1	2037	747
2	5003	718

prune85.0ms

Filtered

68 candidates to 109 candidates (-60.3%)

Pruning

12 alts after pruning (8 fresh and 4 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	109	12	121

Merged error: 23.1b

Counts

121 → 12

regimes511.0ms

Accuracy

0% (2.9b remaining)

Error of 25.9b against oracle of 23.1b and baseline of 25.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	13
1	17	13

end0.0ms

analyze1.2s

Algorithm

sampling

Space saved by range analysis: 0.195169%

Space saved by search: 0.195169%

Guaranteed chance to sample good point: 79.736328%

sample602.0ms

Algorithm

intervals

Results

364.0ms	8000×	body	80	valid
20.0ms	456×	body	80	invalid

Details

analyze1.4s

sample24.0ms

simplify4.0ms

prune4.0ms

localize10.0ms

rewrite16.0ms

series46.0ms

simplify131.0ms

prune110.0ms

localize12.0ms

rewrite22.0ms

series60.0ms

simplify84.0ms

prune120.0ms

localize13.0ms

rewrite22.0ms

series59.0ms

simplify85.0ms

prune122.0ms

localize11.0ms

rewrite27.0ms

series51.0ms

simplify56.0ms

prune85.0ms

regimes511.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.2s

sample602.0ms

Profiling