Details

analyze1.3s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 28.9433%

Guaranteed chance to sample good point: 65.889013%

sample22.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
2.0ms	60×	body	80	invalid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	7
1	55	7
2	101	7
3	182	7
4	335	7
5	731	7
6	1828	7
7	5001	7

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: 26.0b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
4.6b	(- (+ (* x x) (* y y)) (* z z))
24.1b	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`times-frac` `associate-/l*`
3×	`pow1` `difference-of-squares`
2×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `sum-log` `flip--` `associate-/l/`
1×	`+-commutative` `sub-neg` `frac-2neg` `flip3-+` `div-sub` `prod-exp` `associate--l+` `clear-num` `associate-/r*` `cbrt-unprod` `flip-+` `div-inv`

Counts

3 → 52

Calls

3 calls:

4.0ms	(+ (* x x) (* y y))
5.0ms	(- (+ (* x x) (* y y)) (* z z))
9.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

series37.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x x) (* y y))
13.0ms	(- (+ (* x x) (* y y)) (* z z))
19.0ms	(/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0))

simplify37.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	337	520
1	1492	454
2	5001	446

prune82.0ms

Filtered

46 candidates to 61 candidates (-32.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	4	62

Merged error: 10.2b

Counts

62 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
0.2b	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
8.6b	(/ (pow z 2) y)
11.1b	(/ (pow x 2) y)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
56×	`times-frac`
50×	`*-un-lft-identity`
40×	`add-cube-cbrt`
26×	`unpow-prod-down`
16×	`add-exp-log` `associate-/l*`
10×	`associate-r` `add-cbrt-cube` `unpow2` `difference-of-squares` `sqr-pow`
9×	`add-log-exp`
6×	`pow1` `div-exp` `associate-/r*`
4×	`associate-*r/` `frac-sub` `distribute-lft-out--`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `associate--l+`
2×	`cbrt-undiv` `pow-to-exp` `flip3--` `frac-2neg` `flip3-+` `diff-log` `pow-exp` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out`
1×	`pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 156

Calls

4 calls:

19.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
23.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
6.0ms	(/ (pow z 2) y)
5.0ms	(/ (pow x 2) y)

series46.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
23.0ms	(* 0.5 (- (+ y (/ (pow x 2) y)) (/ (pow z 2) y)))
5.0ms	(/ (pow z 2) y)
3.0ms	(/ (pow x 2) y)

simplify59.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	523	1126
1	2010	1020
2	5002	1014

prune253.0ms

Filtered

106 candidates to 168 candidates (-58.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	163	5	168
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Merged error: 2.3b

Counts

172 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ x (/ y x))) (/ (pow z 2) y))
0.2b	(* 0.5 (- (+ y (/ x (/ y x))) (/ (pow z 2) y)))
0.2b	(/ x (/ y x))
8.6b	(/ (pow z 2) y)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

107×	`times-frac`
91×	`add-sqr-sqrt`
75×	`*-un-lft-identity`
65×	`add-cube-cbrt`
16×	`add-exp-log` `associate-/r*`
14×	`unpow-prod-down`
13×	`add-cbrt-cube`
11×	`associate-/l*`
10×	`associate-r` `difference-of-squares`
9×	`add-log-exp`
6×	`pow1` `div-exp` `div-inv` `unpow2` `sqr-pow`
4×	`cbrt-undiv` `associate-*r/` `frac-sub` `distribute-lft-out--`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `associate--l+`
2×	`flip3--` `frac-2neg` `flip3-+` `diff-log` `clear-num` `flip--` `flip-+` `distribute-lft-out`
1×	`pow-to-exp` `pow-prod-down` `pow-exp` `prod-exp` `sum-log` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 177

Calls

4 calls:

26.0ms	(- (+ y (/ x (/ y x))) (/ (pow z 2) y))
27.0ms	(* 0.5 (- (+ y (/ x (/ y x))) (/ (pow z 2) y)))
6.0ms	(/ x (/ y x))
5.0ms	(/ (pow z 2) y)

series34.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (+ y (/ x (/ y x))) (/ (pow z 2) y))
15.0ms	(* 0.5 (- (+ y (/ x (/ y x))) (/ (pow z 2) y)))
3.0ms	(/ x (/ y x))
4.0ms	(/ (pow z 2) y)

simplify89.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	713	1337
1	3285	1218
2	5002	1217

prune217.0ms

Filtered

125 candidates to 189 candidates (-51.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	189	7	196

Merged error: 0.0b

Counts

196 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ x (/ y x))) (/ z (/ y z)))
0.1b	(/ z (/ y z))
0.2b	(* 0.5 (- (+ y (/ x (/ y x))) (/ z (/ y z))))
0.2b	(/ x (/ y x))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
110×	`add-sqr-sqrt`
100×	`*-un-lft-identity`
90×	`add-cube-cbrt`
26×	`associate-/r*`
16×	`add-exp-log` `add-cbrt-cube`
10×	`div-inv`
9×	`add-log-exp`
8×	`associate-r`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/l*` `difference-of-squares`
4×	`associate-*r/` `frac-sub` `distribute-lft-out--`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-l` `associate--l+`
2×	`flip3--` `frac-2neg` `flip3-+` `diff-log` `clear-num` `associate-/r/` `flip--` `flip-+` `distribute-lft-out`
1×	`pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 194

Calls

4 calls:

27.0ms	(- (+ y (/ x (/ y x))) (/ z (/ y z)))
6.0ms	(/ z (/ y z))
33.0ms	(* 0.5 (- (+ y (/ x (/ y x))) (/ z (/ y z))))
6.0ms	(/ x (/ y x))

series35.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(- (+ y (/ x (/ y x))) (/ z (/ y z)))
4.0ms	(/ z (/ y z))
15.0ms	(* 0.5 (- (+ y (/ x (/ y x))) (/ z (/ y z))))
3.0ms	(/ x (/ y x))

simplify109.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	861	1509
1	4341	1391
2	5002	1391

prune342.0ms

Filtered

143 candidates to 206 candidates (-44.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	206	7	213

Merged error: 0b

Counts

213 → 7

regimes221.0ms

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	17	8
1	17	8

end0.0ms

analyze1.3s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 28.9433%

Guaranteed chance to sample good point: 65.889013%

sample602.0ms

Algorithm

intervals

Results

331.0ms	8000×	body	80	valid
72.0ms	1747×	body	80	invalid

Details

analyze1.3s

sample22.0ms

simplify50.0ms

prune3.0ms

localize9.0ms

rewrite19.0ms

series37.0ms

simplify37.0ms

prune82.0ms

localize10.0ms

rewrite59.0ms

series46.0ms

simplify59.0ms

prune253.0ms

localize11.0ms

rewrite70.0ms

series34.0ms

simplify89.0ms

prune217.0ms

localize9.0ms

rewrite83.0ms

series35.0ms

simplify109.0ms

prune342.0ms

regimes221.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.3s

sample602.0ms

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