Details

sample100.0ms

Algorithm

intervals

Results

17.0ms	119×	body	320	valid
9.0ms	312×	pre	80	true
9.0ms	92×	body	160	valid
4.0ms	23×	body	640	valid
3.0ms	56×	body	80	nan
1.0ms	22×	body	80	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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

localize15.0ms

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))
0.4b	(* (* 3.0 a) c)
25.4b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))

rewrite30.0ms

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)
8.0ms	(+ (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))
25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
3.0ms	(* (* 3.0 a) c)
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))

simplify58.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	417	711
1	1922	611
2	5002	602

prune116.0ms

Filtered

85 candidates to 59 candidates (30.6%)

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

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.3b	(* 3.0 (* a c))
0.4b	(* (* 3.0 a) c)
0.4b	(/ (/ (+ 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:

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

series105.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify118.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	628	2482
1	3326	2152
2	5003	2149

prune259.0ms

Filtered

169 candidates to 104 candidates (38.5%)

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

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 3.0 (* a c))
0.3b	(/ 3.0 (/ 3.0 (* a c)))
0.4b	(* (* 3.0 a) c)
0.4b	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

rewrite92.0ms

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)
58.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

series53.0ms

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)
43.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))

simplify62.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1335	3162
1	5001	2477

prune392.0ms

Filtered

262 candidates to 162 candidates (38.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	260	2	262
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	262	6	268

Merged error: 0b

Counts

268 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* a (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
0.1b	(- (* b b) (* (* 3.0 a) c))
0.3b	(/ (* a c) (* a (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
0.4b	(* (* 3.0 a) c)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

11.0ms	(* a (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
13.0ms	(/ (* a c) (* a (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
5.0ms	(* (* 3.0 a) c)

series82.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* a (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
8.0ms	(- (* b b) (* (* 3.0 a) c))
44.0ms	(/ (* a c) (* a (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
3.0ms	(* (* 3.0 a) c)

simplify76.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	442	827
1	2571	641
2	5001	631

prune115.0ms

Filtered

93 candidates to 59 candidates (36.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	95	4	99

Merged error: 0b

Counts

99 → 4

regimes193.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	8
1	22	8
2	22	8

end0.0ms

sample1.6s

Algorithm

intervals

Results

506.0ms	3619×	body	320	valid
288.0ms	2993×	body	160	valid
274.0ms	9479×	pre	80	true
93.0ms	503×	body	640	valid
74.0ms	1479×	body	80	nan
46.0ms	885×	body	80	valid

Details

sample100.0ms

simplify13.0ms

prune4.0ms

localize15.0ms

rewrite30.0ms

series54.0ms

simplify58.0ms

prune116.0ms

localize15.0ms

rewrite47.0ms

series105.0ms

simplify118.0ms

prune259.0ms

localize16.0ms

rewrite92.0ms

series53.0ms

simplify62.0ms

prune392.0ms

localize16.0ms

rewrite34.0ms

series82.0ms

simplify76.0ms

prune115.0ms

regimes193.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.6s

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