Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	34×	body	2560	valid
6.0ms	186×	body	80	valid
5.0ms	88×	body	80	nan
4.0ms	25×	body	1280	valid
2.0ms	14×	body	640	valid
1.0ms	13×	body	320	valid
0.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify8.0ms

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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.2b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.4b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite55.0ms

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:

34.0ms	(/ (- (- 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))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series241.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms	(- (* b_2 b_2) (* a c))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

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

prune235.0ms

Filtered

103 candidates to 72 candidates (69.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.8b

localize10.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
4.4b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.1b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite82.0ms

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))
42.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
24.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series426.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
150.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
181.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify101.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (77.0ms)

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

prune478.0ms

Filtered

196 candidates to 144 candidates (73.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.7b

localize11.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
1.9b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.4b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
44.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series394.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
162.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
131.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
66.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify93.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1541	7328
1	5001	6762

prune1.0s

Filtered

449 candidates to 297 candidates (66.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.7b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b_2 b_2) (* a c))
1.4b	(- (* b_2 b_2) (* a c))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))
24.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

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

series189.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
32.0ms	(- (* b_2 b_2) (* a c))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (47.0ms)

Iter	Nodes	Cost
0	140	390
1	455	366
2	1490	364
3	5002	360

prune217.0ms

Filtered

66 candidates to 50 candidates (75.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.7b

regimes218.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.9b

bsearch132.0ms

Steps

Iters	Range	Point
5	1.1874868645648804e+84	3.824179182553312e+84	3.771181145902542e+84
9	-2.2055828438389438e-285	-3.294617881327087e-290	-3.4150755057481537e-290
9	-2.2987999557012895e+125	-2.547655572124114e+119	-1.1991509811871915e+121

Iters

Range

Point

1.1874868645648804e+84

3.824179182553312e+84

3.771181145902542e+84

-2.2055828438389438e-285

-3.294617881327087e-290

-3.4150755057481537e-290

-2.2987999557012895e+125

-2.547655572124114e+119

-1.1991509811871915e+121

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	31
1	43	31

end0.0ms

sample997.0ms

Algorithm

intervals

Results

218.0ms	1092×	body	2560	valid
196.0ms	5868×	body	80	valid
141.0ms	894×	body	1280	valid
87.0ms	2861×	body	80	nan
61.0ms	439×	body	640	valid
26.0ms	106×	body	5120	valid
20.0ms	213×	body	320	valid
7.0ms	114×	body	160	valid