Details

sample52.0ms

Algorithm

intervals

Results

12.0ms	41×	body	2560	valid
9.0ms	172×	body	80	valid
8.0ms	34×	body	1280	valid
5.0ms	98×	body	80	nan
3.0ms	13×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	8×	body	320	valid
0.0ms	3×	body	160	valid

simplify15.0ms

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 32.3b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.1b	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

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

series294.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ (- (- b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
45.0ms	(- (* b b) (* 4.0 (* a c)))
78.0ms	(- (- b) (sqrt (- (* b b) (* 4.0 (* a c)))))
76.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	404	890
1	1481	801
2	5001	796

prune240.0ms

Filtered

89 candidates to 65 candidates (73.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	10	90

Merged error: 3.3b

Counts

90 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

4.3b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
5.8b	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
16.3b	(- (pow b 2) (pow b 2))
18.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite72.0ms

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))
24.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
11.0ms	(- (pow b 2) (pow b 2))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (* 2.0 a))
154.0ms	(/ (+ (- (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))
72.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify181.0ms

Algorithm

egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 2 (156.0ms)

Iter	Nodes	Cost
0	761	2839
1	3905	2393
2	5002	2366

prune441.0ms

Filtered

187 candidates to 124 candidates (66.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	183	4	187
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	188	9	197

Merged error: 3.3b

Counts

197 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
11.9b	(/ (* 4.0 (* a c)) a)
18.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
18.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
6.0ms	(/ (* 4.0 (* a c)) a)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series237.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
10.0ms	(/ (* 4.0 (* a c)) a)
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
73.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	331	546
1	1462	505
2	5002	485

prune256.0ms

Filtered

80 candidates to 59 candidates (73.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	80	9	89

Merged error: 3.2b

Counts

89 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
0.5b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
18.6b	(sqrt (- (* b b) (* 4.0 (* a c))))
18.6b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
8×	`sqrt-prod` `add-log-exp`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `difference-of-squares`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `distribute-lft-out--`

Counts

4 → 60

Calls

4 calls:

7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series316.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
83.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
75.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify88.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (80.0ms)

Iter	Nodes	Cost
0	190	592
1	644	562
2	2456	556
3	5001	550

prune244.0ms

Filtered

72 candidates to 58 candidates (80.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	72	9	81

Merged error: 3.2b

Counts

81 → 9

regimes170.0ms

Accuracy

95.9% (1.0b remaining)

Error of 6.7b against oracle of 5.7b and baseline of 29.8b

bsearch185.0ms

Steps

Iters	Range	Point
9	1.537663903506608e+146	1.524085477896404e+154	1.828434800801383e+151
9	-1.440519304122712e-265	-1.6559327389548765e-274	-1.6894731563618579e-274
4	-6.635354719968133e+153	-4.347244425542823e+153	-4.5617547656451965e+153

Iters

Range

Point

1.537663903506608e+146

1.524085477896404e+154

1.828434800801383e+151

-1.440519304122712e-265

-1.6559327389548765e-274

-1.6894731563618579e-274

-6.635354719968133e+153

-4.347244425542823e+153

-4.5617547656451965e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	35
1	48	35

end0.0ms

sample1.4s

Algorithm

intervals

Results

296.0ms	5861×	body	80	valid
292.0ms	1016×	body	2560	valid
214.0ms	898×	body	1280	valid
144.0ms	2937×	body	80	nan
82.0ms	447×	body	640	valid
42.0ms	119×	body	5120	valid
38.0ms	256×	body	320	valid
12.0ms	127×	body	160	valid