Details

sample79.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 99.998264%

Space saved by search: 99.998264%

Guaranteed chance to sample good point: 0%

Results

17.0ms	298×	body	80	nan
16.0ms	554×	pre	80	true
15.0ms	156×	body	160	valid
7.0ms	47×	body	320	valid
3.0ms	53×	body	80	valid

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

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.2b	(* (* 3.0 a) c)
0.3b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
40.3b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite33.0ms

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)
14.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))

series53.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(* (* 3.0 a) c)
26.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
15.0ms	(+ (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	5001	602

prune126.0ms

Filtered

59 candidates to 85 candidates (-44.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	80	5	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	5	86

Merged error: 0.3b

Counts

86 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 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))
0.3b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

rewrite47.0ms

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)
13.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
5.0ms	(* 3.0 (* a c))
17.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series112.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* (* 3.0 a) c)
58.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
3.0ms	(* 3.0 (* a c))
47.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify114.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (93.0ms)

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

prune294.0ms

Filtered

104 candidates to 169 candidates (-62.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	159	10	169
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	163	11	174

Merged error: 0b

Counts

174 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 3.0 (/ 3.0 (* a c)))
0.2b	(* (* 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))

rewrite113.0ms

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)
62.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

series93.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/ 3.0 (/ 3.0 (* a c)))
3.0ms	(* (* 3.0 a) c)
36.0ms	(/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
50.0ms	(* (/ 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 (32.0ms)

Iter	Nodes	Cost
0	1526	5405
1	5001	4609

prune834.0ms

Filtered

212 candidates to 369 candidates (-74.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	367	2	369
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	371	9	380

Merged error: 0b

Counts

380 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* (* 3.0 a) c))
0.2b	(* (* 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`
53×	`add-sqr-sqrt` `*-un-lft-identity`
29×	`add-cube-cbrt`
23×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/l*`
12×	`distribute-lft-out--` `difference-of-squares`
10×	`associate-/r*` `associate-/r/`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`flip3--` `distribute-rgt-neg-in` `sqrt-prod` `flip--` `div-inv` `add-log-exp`
5×	`prod-exp` `cbrt-unprod`
3×	`associate-r` `pow-prod-down`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `diff-log` `associate-l` `*-commutative` `associate-/l/`

Counts

4 → 133

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
7.0ms	(* (* 3.0 a) c)
14.0ms	(/ (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
11.0ms	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

series112.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(* (* 3.0 a) c)
45.0ms	(/ (/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a)
54.0ms	(/ (* a c) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))

simplify83.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	612	1894
1	3156	1677
2	5001	1661

prune188.0ms

Filtered

95 candidates to 145 candidates (-52.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	145	9	154

Merged error: 0b

Counts

154 → 9

regimes211.0ms

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	17	10
1	17	10

end0.0ms

sample2.1s

Algorithm

intervals

sampling

Space saved by range analysis: 99.998264%

Space saved by search: 99.998264%

Guaranteed chance to sample good point: 0%

Results

481.0ms	4936×	body	160	valid
471.0ms	16253×	pre	80	true
396.0ms	8253×	body	80	nan
200.0ms	1367×	body	320	valid
86.0ms	1697×	body	80	valid

Details

sample79.0ms

simplify9.0ms

prune3.0ms

localize11.0ms

rewrite33.0ms

series53.0ms

simplify53.0ms

prune126.0ms

localize15.0ms

rewrite47.0ms

series112.0ms

simplify114.0ms

prune294.0ms

localize18.0ms

rewrite113.0ms

series93.0ms

simplify80.0ms

prune834.0ms

localize13.0ms

rewrite41.0ms

series112.0ms

simplify83.0ms

prune188.0ms

regimes211.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.1s

Profiling