Details

sample65.0ms

Algorithm

intervals

Results

16.0ms	194×	body	80	valid
14.0ms	36×	body	2560	valid
8.0ms	25×	body	1280	valid
7.0ms	100×	body	80	nan
4.0ms	13×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	7×	body	320	valid
0.0ms	1×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.8b	(- (* b_2 b_2) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite57.0ms

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)
13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series250.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify40.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (31.0ms)

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

prune257.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
0.2b	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.8b	(- (* b_2 b_2) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`*-un-lft-identity`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1` `associate-l`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`prod-exp` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log` `unswap-sqr`
2×	`frac-times` `sub-neg` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `cbrt-unprod`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
54.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series427.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
264.0ms	(* (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
33.0ms	(- (* b_2 b_2) (* a c))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	428	881
1	1823	791
2	5001	771

prune234.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.7b

localize14.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.1b	(* (/ 1 a) (* a c))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
16×	`*-un-lft-identity` `add-cbrt-cube`
13×	`add-sqr-sqrt` `associate-l`
12×	`add-cube-cbrt` `prod-exp`
10×	`pow1` `add-log-exp`
9×	`times-frac`
6×	`cbrt-unprod`
4×	`div-exp`
3×	`pow-prod-down` `sqrt-prod`
2×	`cbrt-undiv` `rec-exp` `flip3--` `sqrt-div` `1-exp` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r` `neg-log` `associate-l/` `-commutative` `flip-+` `div-inv`

Counts

4 → 79

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(* (/ 1 a) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series168.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(* (/ 1 a) (* a c))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	416	490
1	1971	383
2	5002	371

prune225.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (* (/ 1 a) 0) c) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
0.8b	(- (* b_2 b_2) (* a c))
1.4b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite56.0ms

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-/r*`
3×	`flip3-+` `sqrt-prod` `flip-+` `associate-/l*`
2×	`flip3--` `sqrt-div` `sum-log` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 81

Calls

4 calls:

35.0ms	(/ (+ (* (/ 1 a) 0) c) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series313.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (+ (* (/ 1 a) 0) c) (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
32.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	397	953
1	1556	833
2	5002	814

prune226.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 5.7b

regimes180.0ms

Accuracy

96.3% (0.9b remaining)

Error of 6.4b against oracle of 5.5b and baseline of 29.5b

bsearch179.0ms

Steps

Iters	Range	Point
7	6.714891876596302e+121	1.686395921989292e+123	2.8930707274762056e+122
8	3.503395113734112e-306	2.2860026354415495e-302	1.3179246153427595e-303
8	-5.9769678902734345e+158	-1.9689745148643392e+154	-2.0079720992890853e+154

Iters

Range

Point

6.714891876596302e+121

1.686395921989292e+123

2.8930707274762056e+122

3.503395113734112e-306

2.2860026354415495e-302

1.3179246153427595e-303

-5.9769678902734345e+158

-1.9689745148643392e+154

-2.0079720992890853e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	21
1	39	21

end0.0ms

sample1.9s

Algorithm

intervals

Results

489.0ms	5865×	body	80	valid
429.0ms	1094×	body	2560	valid
284.0ms	873×	body	1280	valid
224.0ms	2925×	body	80	nan
119.0ms	452×	body	640	valid
49.0ms	102×	body	5120	valid
48.0ms	239×	body	320	valid
16.0ms	116×	body	160	valid