Details

sample295.0ms

Algorithm

intervals

Results

13.0ms	42×	body	2560	valid
12.0ms	186×	body	80	valid
6.0ms	23×	body	1280	valid
5.0ms	79×	body	80	nan
3.0ms	8×	body	160	valid
3.0ms	14×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	1×	body	5120	valid

simplify11.0ms

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: 34.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.4b	(- (* b_2 b_2) (* a c))
2.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

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:

42.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
66.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
71.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

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

prune247.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
4.9b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.0b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
20.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite84.0ms

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

series425.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
149.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
183.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (80.0ms)

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

prune472.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
2.6b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.9b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
20.4b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite115.0ms

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))
23.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
49.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series382.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* 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)
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify91.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1541	7328
1	5001	6762

prune984.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b_2 b_2) (* a c))
4.9b	(/ (/ (+ 0 (* a c)) (- (sqrt (pow (- (* b_2 b_2) (* a c)) 1)) b_2)) a)
10.0b	(/ (+ 0 (* a c)) (- (sqrt (pow (- (* b_2 b_2) (* a c)) 1)) b_2))
20.4b	(sqrt (pow (- (* b_2 b_2) (* a c)) 1))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

212×	`add-sqr-sqrt`
210×	`times-frac`
130×	`*-un-lft-identity`
98×	`add-cube-cbrt`
64×	`difference-of-squares`
55×	`sqrt-prod`
33×	`associate-/l*`
20×	`unpow-prod-down`
18×	`sqr-pow`
16×	`distribute-lft-out--`
11×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
10×	`associate-/r/`
6×	`flip3--` `flip--` `div-inv` `add-log-exp`
4×	`pow1` `cbrt-undiv` `div-exp`
3×	`rem-sqrt-square` `associate-/l/`
2×	`frac-2neg` `clear-num`
1×	`sub-neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip-+`

Counts

4 → 220

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (pow (- (* b_2 b_2) (* a c)) 1)) b_2)) a)
44.0ms	(/ (+ 0 (* a c)) (- (sqrt (pow (- (* b_2 b_2) (* a c)) 1)) b_2))
8.0ms	(sqrt (pow (- (* b_2 b_2) (* a c)) 1))

series426.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
150.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (pow (- (* b_2 b_2) (* a c)) 1)) b_2)) a)
183.0ms	(/ (+ 0 (* a c)) (- (sqrt (pow (- (* b_2 b_2) (* a c)) 1)) b_2))
61.0ms	(sqrt (pow (- (* b_2 b_2) (* a c)) 1))

simplify115.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	883	3786
1	3783	3589
2	5002	3557

prune545.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.3b

regimes185.0ms

Accuracy

90.3% (2.6b remaining)

Error of 8.2b against oracle of 5.6b and baseline of 32.1b

bsearch166.0ms

Steps

Iters	Range		Point
9	1.0966316111626227e+109	8.247031634266059e+117	4.065778967411843e+116
9	9.46352497816692e-234	1.1833547256545857e-226	9.57911224209111e-234
7	-1.5320971041566743e+27	-3.280360895118841e+25	-9.20386152989908e+25

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	23
1	41	23

end0.0ms

sample1.6s

Algorithm

intervals

Results

384.0ms	5878×	body	80	valid
346.0ms	1067×	body	2560	valid
244.0ms	893×	body	1280	valid
174.0ms	2986×	body	80	nan
93.0ms	445×	body	640	valid
44.0ms	116×	body	5120	valid
36.0ms	223×	body	320	valid
15.0ms	114×	body	160	valid