Details

sample61.0ms

Algorithm

intervals

Results

11.0ms	37×	body	2560	valid
9.0ms	171×	body	80	valid
8.0ms	33×	body	1280	valid
4.0ms	85×	body	80	nan
3.0ms	15×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	4×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	9

prune7.0ms

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: 37.2b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.7b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.2b	(- (* b b) (* 4.0 (* a c)))
26.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	398	888
1	1466	803
2	5001	798

prune165.0ms

Filtered

89 candidates to 65 candidates (27.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	8	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	8	90

Merged error: 7.5b

Counts

90 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

2.1b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
11.7b	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
20.3b	(- (pow b 2) (pow b 2))
26.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

101×	`add-sqr-sqrt`
78×	`times-frac`
68×	`*-un-lft-identity`
44×	`add-cube-cbrt`
36×	`difference-of-squares`
27×	`associate-/l*`
22×	`unpow-prod-down`
18×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out--`
13×	`sqrt-prod`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`div-sub` `associate-/l/`
2×	`associate-+l-` `frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `+-inverses` `diff-log` `flip-+`

Counts

4 → 175

Calls

4 calls:

26.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
25.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
8.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
35.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
1.0ms	(- (pow b 2) (pow b 2))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify180.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (156.0ms)

Iter	Nodes	Cost
0	760	2835
1	3914	2397
2	5002	2370

prune376.0ms

Filtered

187 candidates to 124 candidates (33.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	184	3	187
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	188	7	195

Merged error: 7.5b

Counts

195 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
2.1b	(/ (/ 1 (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 4.0 (* a c)))) (* 2.0 a))
11.5b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 4.0 (* a c)))
26.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

137×	`times-frac`
122×	`add-exp-log`
74×	`add-sqr-sqrt`
63×	`div-exp`
58×	`add-cbrt-cube`
57×	`*-un-lft-identity`
41×	`add-cube-cbrt` `associate-/l*`
34×	`prod-exp`
27×	`cbrt-undiv`
16×	`difference-of-squares`
14×	`cbrt-unprod`
11×	`sqrt-prod`
10×	`div-inv`
8×	`rec-exp` `1-exp` `distribute-lft-out--`
6×	`add-log-exp`
5×	`pow1`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r*` `associate-/r/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-sub`

Counts

4 → 177

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(/ (/ 1 (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 4.0 (* a c)))) (* 2.0 a))
12.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
28.0ms	(/ (/ 1 (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 4.0 (* a c)))) (* 2.0 a))
24.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1025	2771
1	5001	2368

prune248.0ms

Filtered

189 candidates to 105 candidates (44.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	188	8	196

Merged error: 7.4b

Counts

196 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* 4.0 (* a c)))
2.8b	(* (* 2.0 a) (/ (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a))
26.0b	(sqrt (- (* b b) (* 4.0 (* a c))))
26.0b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
31×	`associate-r`
28×	`*-un-lft-identity`
27×	`times-frac` `sqrt-prod`
22×	`add-cube-cbrt`
16×	`add-exp-log` `add-cbrt-cube`
11×	`pow1`
6×	`prod-exp` `cbrt-unprod` `add-log-exp` `difference-of-squares`
4×	`sqrt-div`
3×	`flip3--` `pow-prod-down` `flip--` `distribute-lft-out--`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp`
1×	`sub-neg` `diff-log` `associate-r/` `associate-l` `-commutative` `div-inv`

Counts

4 → 93

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(* (* 2.0 a) (/ (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series73.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
35.0ms	(* (* 2.0 a) (/ (sqrt (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) a))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify65.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	501	1024
1	2437	919
2	5002	905

prune193.0ms

Filtered

105 candidates to 70 candidates (33.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	105	8	113

Merged error: 7.4b

Counts

113 → 8

regimes220.0ms

Accuracy

94.4% (1.2b remaining)

Error of 7.2b against oracle of 6.0b and baseline of 28.0b

bsearch108.0ms

Steps

Iters	Range		Point
7	1.5733488064158731e+78	9.799352262304037e+79	9.661456755605028e+79
9	4.4115275333905e-304	6.739992957276137e-299	1.9472897126842423e-302
9	-1.7589271863164288e+111	-7.097887949638186e+104	-2.1911797219824148e+108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	37
1	49	37

end0.0ms

sample1.7s

Algorithm

intervals

Results

324.0ms	1061×	body	2560	valid
300.0ms	1151×	body	1280	valid
293.0ms	5301×	body	80	valid
143.0ms	2609×	body	80	nan
115.0ms	549×	body	640	valid
41.0ms	272×	body	320	valid
41.0ms	105×	body	5120	valid
13.0ms	114×	body	160	valid

Details

sample61.0ms

simplify16.0ms

prune7.0ms

localize12.0ms

rewrite29.0ms

series59.0ms

simplify46.0ms

prune165.0ms

localize16.0ms

rewrite70.0ms

series75.0ms

simplify180.0ms

prune376.0ms

localize13.0ms

rewrite49.0ms

series74.0ms

simplify46.0ms

prune248.0ms

localize18.0ms

rewrite29.0ms

series73.0ms

simplify65.0ms

prune193.0ms

regimes220.0ms

bsearch108.0ms

simplify2.0ms

end0.0ms

sample1.7s

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