Details

sample283.0ms

Algorithm

intervals

Results

8.0ms	189×	body	80	valid
7.0ms	35×	body	2560	valid
4.0ms	25×	body	1280	valid
3.0ms	87×	body	80	nan
1.0ms	12×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 34.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.3b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite65.0ms

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:

41.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
69.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune228.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.3b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.5b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite97.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 206

Calls

4 calls:

12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
28.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
139.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
167.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify115.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	741	3477
1	3329	3295
2	5001	3269

prune491.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.3b	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
32×	`add-exp-log`
28×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
23×	`add-cbrt-cube`
16×	`div-exp` `sqrt-prod`
13×	`distribute-rgt-neg-in`
10×	`cbrt-undiv`
8×	`add-log-exp`
6×	`prod-exp` `div-inv`
5×	`pow1`
4×	`associate-/l*`
3×	`1-exp` `cbrt-unprod`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `clear-num` `flip--`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `neg-log` `associate-/r/` `associate-/l/`

Counts

4 → 180

Calls

4 calls:

12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
26.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
23.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
179.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
152.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify98.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	814	2587
1	3756	2402
2	5002	2379

prune418.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
1.0b	(- (* b_2 b_2) (* a c))
1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
23.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

144×	`times-frac`
123×	`add-sqr-sqrt`
96×	`*-un-lft-identity`
70×	`add-cube-cbrt`
26×	`difference-of-squares`
24×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`associate-/r/` `add-cbrt-cube`
8×	`add-log-exp`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `inv-pow`

Counts

4 → 162

Calls

4 calls:

29.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
3.0ms	(- (* b_2 b_2) (* a c))
18.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series286.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ 1 (/ a (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
37.0ms	(- (* b_2 b_2) (* a c))
65.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	569	2101
1	2555	1900
2	5001	1763

prune250.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

regimes215.0ms

Accuracy

90.2% (2.6b remaining)

Error of 7.9b against oracle of 5.3b and baseline of 32.1b

bsearch126.0ms

Steps

Iters	Range	Point
6	4.706455236749836e+29	5.491842449186372e+30	1.5921386900724074e+30
10	-5.493255184560768e-264	-2.235079772666708e-277	-2.2625897093650334e-277
7	-2.963931757502914e+119	-3.3757792073266624e+117	-5.955152059551362e+118

Iters

Range

Point

4.706455236749836e+29

5.491842449186372e+30

1.5921386900724074e+30

-5.493255184560768e-264

-2.235079772666708e-277

-2.2625897093650334e-277

-2.963931757502914e+119

-3.3757792073266624e+117

-5.955152059551362e+118

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	44	24
2	44	24

end0.0ms

sample996.0ms

Algorithm

intervals

Results

210.0ms	1079×	body	2560	valid
190.0ms	5758×	body	80	valid
149.0ms	915×	body	1280	valid
92.0ms	2894×	body	80	nan
55.0ms	449×	body	640	valid
24.0ms	100×	body	5120	valid
23.0ms	223×	body	320	valid
8.0ms	133×	body	160	valid