Details

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 99.986886%

Space saved by search: 99.993135%

Guaranteed chance to sample good point: 88.065532%

Results

19.0ms	130×	body	320	valid
9.0ms	90×	body	160	valid
8.0ms	262×	pre	80	true
2.0ms	11×	body	640	valid
1.0ms	25×	body	80	valid
0.0ms	6×	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: 54.3b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 3.0 a) c))
0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.3b	(* (* 3.0 a) c)
24.8b	(+ (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))
11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
5.0ms	(* (* 3.0 a) c)
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series54.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (* b b) (* (* 3.0 a) c))
24.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms	(* (* 3.0 a) c)
16.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify53.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	417	711
1	1922	611
2	5002	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: 0.1b

Counts

86 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (* 3.0 a) c)
0.3b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.3b	(* 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)
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(* 3.0 (* a c))
16.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series103.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 3.0 a) c)
54.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
3.0ms	(* 3.0 (* a c))
42.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify117.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (96.0ms)

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

prune256.0ms

Filtered

104 candidates to 169 candidates (-62.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	166	6	172

Merged error: 0b

Counts

172 → 6

localize12.0ms

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×	`associate-r` `pow-prod-down` `associate-/r/`
4×	`div-inv` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `associate-l` `clear-num` `*-commutative`
1×	`flip3-+` `flip-+`

Counts

4 → 157

Calls

4 calls:

4.0ms	(* (* 3.0 a) c)
5.0ms	(* (* 3.0 a) c)
14.0ms	(/ (+ 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)
55.0ms	(/ (+ 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))

simplify103.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	571	2482
1	3060	2153
2	5003	2150

prune246.0ms

Filtered

103 candidates to 169 candidates (-64.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	169	6	175

Merged error: 0b

Counts

175 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

224×	`times-frac`
162×	`add-sqr-sqrt`
136×	`*-un-lft-identity`
113×	`add-exp-log`
98×	`add-cube-cbrt`
88×	`associate-r`
77×	`add-cbrt-cube`
56×	`div-exp`
34×	`cbrt-undiv`
30×	`prod-exp`
27×	`associate-l`
20×	`cbrt-unprod`
18×	`distribute-lft-out--` `difference-of-squares`
14×	`div-inv`
11×	`pow1`
9×	`distribute-rgt-neg-in` `sqrt-prod`
8×	`associate-/r*` `associate-/r/` `unswap-sqr`
6×	`associate-/l*`
4×	`rec-exp` `1-exp` `pow-prod-down` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`frac-times` `associate-r/` `associate-l/`

Counts

4 → 250

Calls

4 calls:

4.0ms	(/ 3.0 (* a c))
6.0ms	(/ 3.0 (/ 3.0 (* a c)))
5.0ms	(* (* 3.0 a) c)
54.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

series52.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 3.0 (* a c))
3.0ms	(/ 3.0 (/ 3.0 (* a c)))
3.0ms	(* (* 3.0 a) c)
42.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

simplify57.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1335	3162
1	5001	2477

prune364.0ms

Filtered

162 candidates to 262 candidates (-61.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	261	1	262
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	262	6	268

Merged error: 0b

Counts

268 → 6

regimes212.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	13
1	20	13
2	20	13

end0.0ms

sample3.4s

Algorithm

intervals

sampling

Space saved by range analysis: 99.986886%

Space saved by search: 99.993135%

Guaranteed chance to sample good point: 88.065532%

Results

523.0ms	3549×	body	320	valid
298.0ms	2971×	body	160	valid
255.0ms	8419×	pre	80	true
102.0ms	521×	body	640	valid
53.0ms	959×	body	80	valid
21.0ms	419×	body	80	nan

Details

sample1.8s

simplify9.0ms

prune3.0ms

localize13.0ms

rewrite28.0ms

series54.0ms

simplify53.0ms

prune113.0ms

localize14.0ms

rewrite45.0ms

series103.0ms

simplify117.0ms

prune256.0ms

localize12.0ms

rewrite45.0ms

series104.0ms

simplify103.0ms

prune246.0ms

localize15.0ms

rewrite86.0ms

series52.0ms

simplify57.0ms

prune364.0ms

regimes212.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.4s

Profiling