Details

sample639.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 99.999783%

Space saved by search: 99.999887%

Guaranteed chance to sample good point: 88.012896%

Results

17.0ms	156×	body	160	valid
8.0ms	275×	pre	80	true
5.0ms	100×	body	80	valid
1.0ms	19×	body	80	nan

simplify10.0ms

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

prune4.0ms

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: 30.1b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* 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))
30.0b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite32.0ms

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:

4.0ms	(- (* b b) (* (* 3.0 a) c))
5.0ms	(* (* 3.0 a) c)
13.0ms	(/ (+ (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)
25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify55.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (45.0ms)

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

prune133.0ms

Filtered

59 candidates to 85 candidates (-44.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	79	6	85
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	7	86

Merged error: 0.4b

Counts

86 → 7

localize16.0ms

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

rewrite48.0ms

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)
15.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
17.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

series109.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
3.0ms	(* (* 3.0 a) c)
58.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
44.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))

simplify118.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (96.0ms)

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

prune319.0ms

Filtered

104 candidates to 169 candidates (-62.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	156	13	169
Fresh	5	0	5
Picked	1	0	1
Done	1	0	1
Total	163	13	176

Merged error: 0.0b

Counts

176 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log` `add-cbrt-cube`
31×	`prod-exp` `cbrt-unprod`
16×	`pow1`
14×	`add-sqr-sqrt`
12×	`cbrt-undiv` `*-un-lft-identity` `div-exp`
11×	`associate-r`
9×	`associate-l`
8×	`add-cube-cbrt`
7×	`pow-prod-down`
4×	`add-log-exp`
3×	`*-commutative`
2×	`distribute-rgt-in` `frac-times` `sub-neg` `flip3--` `distribute-lft-in` `times-frac` `associate-*r/` `flip--` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`distribute-rgt-neg-in` `frac-2neg` `associate-l/` `clear-num` `associate-/r` `sqrt-prod` `associate-/l*` `unswap-sqr`

Counts

4 → 106

Calls

4 calls:

5.0ms	(* 3.0 (* a c))
5.0ms	(* (* 3.0 a) c)
20.0ms	(* (/ (* 3.0 a) (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
7.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))

series35.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* 3.0 (* a c))
3.0ms	(* (* 3.0 a) c)
26.0ms	(* (/ (* 3.0 a) (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
2.0ms	(/ (* 3.0 a) (* 3.0 (* a c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (103.0ms)

Iter	Nodes	Cost
0	554	1160
1	4000	791
2	5002	699

prune171.0ms

Filtered

65 candidates to 118 candidates (-81.5%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	3	9	12
Picked	0	1	1
Done	0	0	0
Total	119	12	131

Merged error: 0b

Counts

131 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

192×	`times-frac`
163×	`add-sqr-sqrt` `*-un-lft-identity`
100×	`unpow-prod-down`
95×	`add-cube-cbrt`
34×	`distribute-lft-out--` `difference-of-squares`
32×	`associate-/r*`
27×	`add-exp-log`
17×	`distribute-rgt-neg-in` `sqrt-prod`
13×	`add-cbrt-cube`
12×	`div-exp`
10×	`associate-/l*`
9×	`pow1`
8×	`add-log-exp`
6×	`pow-exp` `div-inv`
4×	`rec-exp` `1-exp` `sqr-pow`
3×	`pow-to-exp` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `diff-log` `clear-num` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `sub-neg` `pow-flip` `div-sub` `associate-l` `neg-log` `*-commutative` `inv-pow`

Counts

4 → 226

Calls

4 calls:

10.0ms	(/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
17.0ms	(/ 1 (pow (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c) 1))
5.0ms	(* (* 3.0 a) c)

series74.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c)
15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
37.0ms	(/ 1 (pow (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) c) 1))
4.0ms	(* (* 3.0 a) c)

simplify100.0ms

Algorithm

egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	720	3519
1	3340	3048
2	5003	2914

prune236.0ms

Filtered

107 candidates to 238 candidates (-122.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	235	3	238
Fresh	3	7	10
Picked	1	0	1
Done	0	1	1
Total	239	11	250

Merged error: 0b

Counts

250 → 11

regimes337.0ms

Accuracy

0% (0.3b 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	22	11
1	22	11

end0.0ms

sample1.8s

Algorithm

intervals

sampling

Space saved by range analysis: 99.999783%

Space saved by search: 99.999887%

Guaranteed chance to sample good point: 88.012896%

Results

475.0ms	4556×	body	160	valid
260.0ms	8565×	pre	80	true
195.0ms	3444×	body	80	valid
29.0ms	565×	body	80	nan

Details

sample639.0ms

simplify10.0ms

prune4.0ms

localize14.0ms

rewrite32.0ms

series53.0ms

simplify55.0ms

prune133.0ms

localize16.0ms

rewrite48.0ms

series109.0ms

simplify118.0ms

prune319.0ms

localize15.0ms

rewrite41.0ms

series35.0ms

simplify114.0ms

prune171.0ms

localize16.0ms

rewrite53.0ms

series74.0ms

simplify100.0ms

prune236.0ms

regimes337.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.8s

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