Details

sample256.0ms

Algorithm

intervals

Results

194.0ms	23×	body	1280	valid
10.0ms	212×	body	80	valid
5.0ms	20×	body	2560	valid
4.0ms	87×	body	80	nan
2.0ms	14×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify267.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune5.0ms

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: 31.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

9.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
22.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify140.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	338	783
1	1216	724
2	4971	703
3	5001	703

prune128.0ms

Filtered

92 candidates to 69 candidates (25.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	8	93

Merged error: 7.2b

Counts

93 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt a) (cbrt a))
0.8b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt`
17×	`*-un-lft-identity`
16×	`cbrt-prod`
13×	`add-cube-cbrt`
12×	`pow1`
10×	`add-log-exp`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `unswap-sqr`
3×	`sqrt-prod`
2×	`flip3--` `sqrt-div` `pow-prod-down` `sum-log` `pow-sqr` `pow-prod-up` `flip--` `distribute-lft-out`
1×	`+-commutative` `pow2` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow-plus` `pow1/2` `diff-log` `neg-log` `prod-exp` `*-commutative` `cbrt-unprod` `flip-+`

Counts

4 → 82

Calls

4 calls:

5.0ms	(* (cbrt a) (cbrt a))
9.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cbrt a) (cbrt a))
12.0ms	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	337	535
1	1231	494
2	5002	459

prune100.0ms

Filtered

94 candidates to 64 candidates (31.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	94	8	102

Merged error: 7.2b

Counts

102 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
9.3b	(+ (neg b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `flip3-+` `diff-log` `neg-log` `flip-+`

Counts

4 → 55

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(+ (neg b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(+ (neg b_2) (* (sqrt (sqrt (- (* b_2 b_2) (* a c)))) (sqrt (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify98.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	237	549
1	897	455
2	3523	443
3	5002	440

prune88.0ms

Filtered

67 candidates to 53 candidates (20.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	66	1	67
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	67	8	75

Merged error: 7.2b

Counts

75 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
2.0b	(/ (/ (* a c) (neg (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
12.1b	(/ (* a c) (neg (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
72×	`*-un-lft-identity`
47×	`add-sqr-sqrt`
46×	`add-cube-cbrt`
24×	`distribute-lft-neg-in` `distribute-rgt-neg-in`
19×	`associate-/l*`
18×	`add-exp-log` `add-cbrt-cube`
15×	`associate-/r*`
13×	`distribute-lft-out`
10×	`associate-/r/` `distribute-neg-frac`
7×	`cbrt-undiv` `div-exp`
6×	`neg-mul-1` `flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `sum-log` `flip--` `associate-/l/`

Counts

4 → 160

Calls

4 calls:

5.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(/ (/ (* a c) (neg (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
9.0ms	(/ (* a c) (neg (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series118.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(/ (/ (* a c) (neg (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))) a)
53.0ms	(/ (* a c) (neg (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify87.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	724	2110
1	3322	1942
2	5003	1942

prune138.0ms

Filtered

172 candidates to 127 candidates (26.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	169	3	172
Fresh	1	3	4
Picked	1	0	1
Done	0	3	3
Total	171	9	180

Merged error: 7.1b

Counts

180 → 9

regimes346.0ms

Accuracy

92.2% (2.1b remaining)

Error of 8.0b against oracle of 6.0b and baseline of 32.6b

bsearch92.0ms

Steps

Iters	Range	Point
10	5.5981910563155256e+85	9.646889156889423e+104	8.843372296946954e+91
7	4.7985447999292916e-278	1.0764593068146029e-275	1.0544880027489772e-275
5	-4.3562246007774435e+118	-1.8745594453170666e+118	-3.926021394052593e+118

Iters

Range

Point

5.5981910563155256e+85

9.646889156889423e+104

8.843372296946954e+91

4.7985447999292916e-278

1.0764593068146029e-275

1.0544880027489772e-275

-4.3562246007774435e+118

-1.8745594453170666e+118

-3.926021394052593e+118

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	49	43
1	49	43

end0.0ms

sample1.3s

Algorithm

intervals

Results

286.0ms	6321×	body	80	valid
220.0ms	840×	body	2560	valid
156.0ms	755×	body	1280	valid
106.0ms	2489×	body	80	nan
64.0ms	369×	body	640	valid
24.0ms	76×	body	5120	valid
22.0ms	165×	body	320	valid
10.0ms	99×	body	160	valid

Details

sample256.0ms

simplify267.0ms

prune5.0ms

localize13.0ms

rewrite29.0ms

series69.0ms

simplify140.0ms

prune128.0ms

localize14.0ms

rewrite24.0ms

series56.0ms

simplify42.0ms

prune100.0ms

localize12.0ms

rewrite17.0ms

series46.0ms

simplify98.0ms

prune88.0ms

localize11.0ms

rewrite36.0ms

series118.0ms

simplify87.0ms

prune138.0ms

regimes346.0ms

bsearch92.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling