Details

sample81.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 93.756105%

Space saved by search: 96.853662%

Guaranteed chance to sample good point: 98.449612%

Results

9.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true
0.0ms	4×	pre	80	false

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	47	7
2	106	7
3	265	7
4	1495	7
5	5001	7

prune7.0ms

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: 13.6b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
13.1b	(/ (- (* a a) (* b b)) (* a a))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 39

Calls

2 calls:

1.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
7.0ms	(/ (- (* a a) (* b b)) (* a a))

series19.0ms

Counts

2 → 6

Calls

2 calls:

11.0ms	(sqrt (fabs (/ (- (* a a) (* b b)) (* a a))))
9.0ms	(/ (- (* a a) (* b b)) (* a a))

simplify141.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 3 (136.0ms)

Iter	Nodes	Cost
0	197	340
1	816	296
2	4110	295
3	5001	292

prune67.0ms

Filtered

34 candidates to 45 candidates (-32.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	2	46

Merged error: 0.0b

Counts

46 → 2

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
0.0b	(/ (+ a b) a)
0.0b	(/ (- a b) a)
0.0b	(* (/ (+ a b) a) (/ (- a b) a))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
68×	`add-sqr-sqrt`
58×	`times-frac`
41×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
16×	`associate-l`
9×	`associate-/l*`
7×	`pow1` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
3×	`sqrt-prod`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+`

Counts

4 → 143

Calls

4 calls:

1.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
5.0ms	(/ (+ a b) a)
7.0ms	(/ (- a b) a)
16.0ms	(* (/ (+ a b) a) (/ (- a b) a))

series27.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(sqrt (fabs (* (/ (+ a b) a) (/ (- a b) a))))
4.0ms	(/ (+ a b) a)
4.0ms	(/ (- a b) a)
9.0ms	(* (/ (+ a b) a) (/ (- a b) a))

simplify64.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	493	951
1	2505	870
2	5002	867

prune161.0ms

Filtered

106 candidates to 155 candidates (-46.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	154	1	155
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	154	3	157

Merged error: 0b

Counts

157 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cbrt (/ (- a b) a)) (cbrt (/ (- a b) a)))
0.1b	(cbrt (/ (- a b) a))
0.1b	(cbrt (/ (- a b) a))
0.1b	(cbrt (/ (- a b) a))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

157×	`cbrt-prod`
141×	`add-sqr-sqrt`
135×	`*-un-lft-identity`
123×	`times-frac`
75×	`add-cube-cbrt`
28×	`swap-sqr`
27×	`distribute-lft-out--`
22×	`associate-r` `associate-l`
21×	`difference-of-squares`
11×	`pow1`
9×	`pow1/3` `unswap-sqr`
7×	`cbrt-div` `div-inv`
6×	`add-exp-log`
4×	`add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `frac-times` `pow-plus` `associate-r/` `associate-l/` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 186

Calls

4 calls:

20.0ms	(* (cbrt (/ (- a b) a)) (cbrt (/ (- a b) a)))
4.0ms	(cbrt (/ (- a b) a))
4.0ms	(cbrt (/ (- a b) a))
4.0ms	(cbrt (/ (- a b) a))

series129.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (cbrt (/ (- a b) a)) (cbrt (/ (- a b) a)))
34.0ms	(cbrt (/ (- a b) a))
31.0ms	(cbrt (/ (- a b) a))
32.0ms	(cbrt (/ (- a b) a))

simplify51.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	292	1818
1	1036	1763
2	5001	1712

prune228.0ms

Filtered

144 candidates to 198 candidates (-37.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	198	3	201

Merged error: 0b

Counts

201 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (fabs (/ (- a (/ (pow b 2) a)) a)))
0.0b	(/ (- a (/ (pow b 2) a)) a)
14.8b	(/ (pow b 2) a)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

84×	`add-sqr-sqrt`
67×	`times-frac`
43×	`*-un-lft-identity`
35×	`add-cube-cbrt`
20×	`difference-of-squares`
17×	`associate-/l*`
16×	`unpow-prod-down`
10×	`add-exp-log`
8×	`unpow2` `sqr-pow`
7×	`add-cbrt-cube`
6×	`associate-/r*`
4×	`pow1` `div-exp` `distribute-lft-out--`
3×	`sqrt-prod` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `clear-num` `div-inv` `associate-/l/`
1×	`pow-to-exp` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `pow-exp` `flip--`

Counts

3 → 116

Calls

3 calls:

1.0ms	(sqrt (fabs (/ (- a (/ (pow b 2) a)) a)))
15.0ms	(/ (- a (/ (pow b 2) a)) a)
5.0ms	(/ (pow b 2) a)

series20.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(sqrt (fabs (/ (- a (/ (pow b 2) a)) a)))
9.0ms	(/ (- a (/ (pow b 2) a)) a)
3.0ms	(/ (pow b 2) a)

simplify42.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	381	856
1	1225	786
2	5001	768

prune170.0ms

Filtered

84 candidates to 125 candidates (-48.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	125	3	128

Merged error: 0b

Counts

128 → 3

regimes80.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	7
1	11	7

end0.0ms

sample700.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 93.756105%

Space saved by search: 96.853662%

Guaranteed chance to sample good point: 98.449612%

Results

275.0ms	8000×	body	80	valid
153.0ms	8000×	pre	80	true
1.0ms	62×	pre	80	false

Details

sample81.0ms

simplify50.0ms

prune7.0ms

localize7.0ms

rewrite9.0ms

series19.0ms

simplify141.0ms

prune67.0ms

localize8.0ms

rewrite34.0ms

series27.0ms

simplify64.0ms

prune161.0ms

localize13.0ms

rewrite45.0ms

series129.0ms

simplify51.0ms

prune228.0ms

localize8.0ms

rewrite26.0ms

series20.0ms

simplify42.0ms

prune170.0ms

regimes80.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample700.0ms

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