Details

sample287.0ms

Algorithm

intervals

Results

7.0ms	172×	body	80	valid
6.0ms	30×	body	2560	valid
5.0ms	35×	body	1280	valid
3.0ms	103×	body	80	nan
2.0ms	18×	body	640	valid
1.0ms	6×	body	5120	valid
1.0ms	10×	body	320	valid
0.0ms	7×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite75.0ms

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:

50.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series262.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
37.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms	(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

prune254.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
4.1b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
8.2b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite83.0ms

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))
41.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
27.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
158.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
192.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (81.0ms)

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

prune499.0ms

Filtered

196 candidates to 144 candidates (73.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.5b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
13.2b	(/ a (* a c))
20.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

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:

18.0ms	(- (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)))

series176.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
34.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(/ a (* a c))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify127.0ms

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

prune183.0ms

Filtered

75 candidates to 54 candidates (72.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 4.5b

localize17.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
13.2b	(/ a (* a c))
20.4b	(sqrt (- (* b_2 b_2) (* a c)))
20.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

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

series162.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(/ a (* a c))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify117.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	216	388
1	771	352
2	3614	348
3	5001	346

prune217.0ms

Filtered

75 candidates to 55 candidates (73.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.5b

regimes151.0ms

Accuracy

94.8% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 30.4b

bsearch136.0ms

Steps

Iters	Range	Point
6	2.6216430800597077e+98	1.6496650416179864e+99	1.627530458299668e+99
10	-8.113375868546115e-210	-4.368787621745583e-220	-4.42774749682145e-220
7	-1.3334355299494226e+103	-2.4188752133425037e+101	-8.626773201174524e+102

Iters

Range

Point

2.6216430800597077e+98

1.6496650416179864e+99

1.627530458299668e+99

-8.113375868546115e-210

-4.368787621745583e-220

-4.42774749682145e-220

-1.3334355299494226e+103

-2.4188752133425037e+101

-8.626773201174524e+102

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	31
1	44	31

end0.0ms

sample1.0s

Algorithm

intervals

Results

202.0ms	1041×	body	2560	valid
196.0ms	5848×	body	80	valid
143.0ms	879×	body	1280	valid
90.0ms	2867×	body	80	nan
64.0ms	487×	body	640	valid
30.0ms	118×	body	5120	valid
21.0ms	228×	body	320	valid
7.0ms	110×	body	160	valid