Details

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 99.998264%

Space saved by search: 99.999091%

Guaranteed chance to sample good point: 88.065532%

Results

16.0ms	168×	body	160	valid
8.0ms	273×	pre	80	true
5.0ms	37×	body	320	valid
3.0ms	51×	body	80	valid
1.0ms	17×	body	80	nan

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

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: 44.7b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.3b	(* (* 3.0 a) c)
0.3b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
39.6b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
14×	`add-exp-log` `add-cbrt-cube`
10×	`add-log-exp`
9×	`pow1`
7×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`distribute-lft-out`
5×	`times-frac` `associate-/l*`
4×	`prod-exp` `cbrt-unprod`
3×	`distribute-rgt-neg-in` `associate-r` `pow-prod-down`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3-+` `div-exp` `sum-log` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-sub` `associate-l` `neg-log` `clear-num` `associate-/r` `-commutative` `flip--` `div-inv`

Counts

4 → 73

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(* (* 3.0 a) c)
11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (* b b) (* (* 3.0 a) c))
3.0ms	(* (* 3.0 a) c)
24.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify52.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	417	711
1	1922	611
2	5001	602

prune113.0ms

Filtered

59 candidates to 85 candidates (-44.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	3	86

Merged error: 0.2b

Counts

86 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
0.3b	(* 3.0 (* a c))
0.3b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.4b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt` `*-un-lft-identity`
40×	`add-cube-cbrt`
30×	`associate-/l*`
28×	`add-exp-log` `add-cbrt-cube`
20×	`distribute-lft-out--` `difference-of-squares`
14×	`pow1`
10×	`distribute-rgt-neg-in` `sqrt-prod`
8×	`prod-exp` `associate-/r*` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
6×	`pow-prod-down` `associate-/r/`
4×	`associate-r` `associate-l` `div-inv` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 157

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
5.0ms	(* 3.0 (* a c))
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
16.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series104.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 3.0 a) c)
3.0ms	(* 3.0 (* a c))
56.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
42.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify115.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	628	2481
1	3322	2152
2	5002	2149

prune298.0ms

Filtered

104 candidates to 169 candidates (-62.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	163	6	169
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Merged error: 0.0b

Counts

172 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 3.0 (/ 3.0 (* a c)))
0.3b	(* (* 3.0 a) c)
0.3b	(/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
0.3b	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

386×	`times-frac`
280×	`add-sqr-sqrt`
254×	`*-un-lft-identity`
168×	`add-cube-cbrt`
117×	`add-exp-log`
88×	`associate-r`
77×	`add-cbrt-cube`
60×	`div-exp`
42×	`distribute-lft-out--` `difference-of-squares`
35×	`cbrt-undiv`
30×	`associate-/l*`
29×	`prod-exp`
27×	`associate-l`
21×	`distribute-rgt-neg-in` `sqrt-prod`
19×	`cbrt-unprod`
18×	`div-inv`
16×	`associate-/r/`
11×	`pow1`
10×	`associate-/r*`
8×	`unswap-sqr`
7×	`flip3--` `flip--`
5×	`rec-exp` `1-exp`
4×	`pow-prod-down` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `associate-r/` `associate-l/` `associate-/l/`

Counts

4 → 357

Calls

4 calls:

6.0ms	(/ 3.0 (/ 3.0 (* a c)))
5.0ms	(* (* 3.0 a) c)
16.0ms	(/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
51.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

series87.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 3.0 (/ 3.0 (* a c)))
3.0ms	(* (* 3.0 a) c)
33.0ms	(/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
47.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

simplify80.0ms

Algorithm

egg-herbie

Counts

369 → 369

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1526	5405
1	5001	4609

prune660.0ms

Filtered

212 candidates to 369 candidates (-74.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	367	2	369
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	368	8	376

Merged error: 0b

Counts

376 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.3b	(* (* 3.0 a) c)
0.3b	(/ (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
0.3b	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
57×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
23×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
10×	`associate-/r*` `associate-/r/`
9×	`pow1`
8×	`add-log-exp`
7×	`cbrt-undiv` `distribute-rgt-neg-in` `div-exp` `sqrt-prod`
6×	`flip3--` `flip--` `div-inv`
5×	`prod-exp` `cbrt-unprod`
3×	`associate-r` `pow-prod-down`
2×	`frac-2neg` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `associate-l` `neg-log` `*-commutative` `associate-/l/`

Counts

4 → 139

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.0ms	(* (* 3.0 a) c)
13.0ms	(/ (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
10.0ms	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series113.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(* (* 3.0 a) c)
39.0ms	(/ (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
55.0ms	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify79.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	601	2012
1	2963	1782
2	5002	1766

prune188.0ms

Filtered

101 candidates to 151 candidates (-49.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	1	5	6
Picked	0	1	1
Done	1	0	1
Total	152	7	159

Merged error: 0b

Counts

159 → 7

regimes166.0ms

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	20	11
1	22	11
2	22	11

end0.0ms

sample3.2s

Algorithm

intervals

sampling

Space saved by range analysis: 99.998264%

Space saved by search: 99.999091%

Guaranteed chance to sample good point: 88.065532%

Results

484.0ms	4838×	body	160	valid
250.0ms	8473×	pre	80	true
198.0ms	1349×	body	320	valid
94.0ms	1813×	body	80	valid
25.0ms	473×	body	80	nan

Details

sample1.8s

simplify9.0ms

prune3.0ms

localize12.0ms

rewrite28.0ms

series53.0ms

simplify52.0ms

prune113.0ms

localize14.0ms

rewrite45.0ms

series104.0ms

simplify115.0ms

prune298.0ms

localize19.0ms

rewrite99.0ms

series87.0ms

simplify80.0ms

prune660.0ms

localize14.0ms

rewrite41.0ms

series113.0ms

simplify79.0ms

prune188.0ms

regimes166.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.2s

Profiling