Details

sample268.0ms

Algorithm

intervals

Results

7.0ms	39×	body	2560	valid
5.0ms	171×	body	80	valid
4.0ms	26×	body	1280	valid
4.0ms	74×	body	80	nan
2.0ms	9×	body	5120	valid
2.0ms	13×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	2×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	7
1	32	7
2	41	7
3	44	7
4	44	7

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
25.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 91

Calls

4 calls:

41.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
68.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	368	965
1	1241	910
2	5001	901

prune246.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 6.3b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
3.6b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.7b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
25.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`associate-/r*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `div-exp`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 184

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
40.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
26.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series428.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
152.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
182.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	725	2897
1	3210	2743
2	5003	2723

prune473.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.0b	(- (* b_2 b_2) (* a c))
15.5b	(/ a (* a c))
25.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

17.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
2.0ms	(- (* b_2 b_2) (* a c))
3.0ms	(/ a (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(/ a (* a c))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify128.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (122.0ms)

Iter	Nodes	Cost
0	277	415
1	944	374
2	4178	369
3	5002	368

prune167.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 6.2b

localize15.0ms

Local error

Found 4 expressions with local error:

15.5b	(/ a (* a c))
25.6b	(sqrt (- (* b_2 b_2) (* a c)))
25.6b	(sqrt (- (* b_2 b_2) (* a c)))
25.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod` `add-cbrt-cube`
7×	`pow1`
6×	`sqrt-div`
4×	`add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `times-frac` `pow1/2` `flip--` `associate-/l*`
2×	`cbrt-undiv` `div-exp`
1×	`frac-2neg` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 66

Calls

4 calls:

3.0ms	(/ a (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
3.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series179.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ a (* a c))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify104.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	202	421
1	720	389
2	3365	384
3	5002	381

prune227.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 6.2b

regimes243.0ms

Accuracy

88.1% (3.2b remaining)

Error of 8.5b against oracle of 5.3b and baseline of 32.5b

bsearch114.0ms

Steps

Iters	Range	Point
8	1.9559514031553493e+101	2.0413668072230428e+104	7.9196559434345e+101
6	-1.0297975893808616e-282	-2.1519527073941584e-283	-4.357184784472192e-283
8	-2.334183243992744e+54	-5.015218154388399e+51	-3.987052893645674e+52

Iters

Range

Point

1.9559514031553493e+101

2.0413668072230428e+104

7.9196559434345e+101

-1.0297975893808616e-282

-2.1519527073941584e-283

-4.357184784472192e-283

-2.334183243992744e+54

-5.015218154388399e+51

-3.987052893645674e+52

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

sample952.0ms

Algorithm

intervals

Results

205.0ms	1069×	body	2560	valid
184.0ms	5806×	body	80	valid
129.0ms	855×	body	1280	valid
85.0ms	2840×	body	80	nan
57.0ms	469×	body	640	valid
25.0ms	110×	body	5120	valid
22.0ms	244×	body	320	valid
9.0ms	144×	body	160	valid