Details

sample291.0ms

Algorithm

intervals

Results

8.0ms	187×	body	80	valid
7.0ms	35×	body	2560	valid
5.0ms	31×	body	1280	valid
3.0ms	94×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	8×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 36.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.6b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite40.0ms

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:

10.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series258.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (- (- 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))))
68.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

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

prune261.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.6b	(- (* b_2 b_2) (* a c))
1.6b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 177

Calls

4 calls:

14.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ 1 (/ a (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))))
33.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify74.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	591	2458
1	2706	2226
2	5001	2071

prune294.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b_2 b_2) (* a c))
5.6b	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
23.1b	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`add-cube-cbrt` `log-prod` `exp-sum`
7×	`pow1` `sqrt-prod`
6×	`exp-prod`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
3×	`diff-log` `log-pow` `difference-of-squares`
2×	`sub-neg` `log-div` `sqrt-pow1` `pow1/2` `exp-diff` `distribute-lft-out--`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `neg-log` `rem-exp-log`

Counts

4 → 68

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
10.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series223.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* b_2 b_2) (* a c))
57.0ms	(exp (log (sqrt (- (* b_2 b_2) (* a c)))))
70.0ms	(- (- b_2) (exp (log (sqrt (- (* b_2 b_2) (* a c))))))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	269	613
1	835	560
2	2865	536
3	5001	523

prune216.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 7.0b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.8b	(/ a (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
11.8b	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
23.9b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac`
57×	`add-sqr-sqrt`
42×	`*-un-lft-identity`
28×	`add-cube-cbrt`
18×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
14×	`difference-of-squares`
11×	`associate-/r/`
10×	`sqrt-prod`
7×	`cbrt-undiv` `flip3--` `div-exp` `flip--` `distribute-lft-out--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/l*`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 127

Calls

4 calls:

7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
15.0ms	(/ a (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
10.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
70.0ms	(/ a (/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))
191.0ms	(/ (* a c) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	551	1604
1	2542	1427
2	5001	1413

prune330.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 7.0b

regimes202.0ms

Accuracy

88% (3.4b remaining)

Error of 9.1b against oracle of 5.7b and baseline of 34.3b

bsearch110.0ms

Steps

Iters	Range		Point
3	5.062782482725967e+112	6.853081242536654e+112	6.293612880095814e+112
7	-2.1605152142522817e-113	-1.8017938791730603e-115	-2.125553485370055e-113
5	-1.1619433740097673e-94	-3.191731313316827e-95	-6.180620892104376e-95
4	-2.1402528215307472e+20	-1.2933083028149787e+20	-1.8507408941501855e+20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	32
1	53	32
2	53	32

end0.0ms

sample1.0s

Algorithm

intervals

Results

223.0ms	1073×	body	2560	valid
203.0ms	5855×	body	80	valid
150.0ms	904×	body	1280	valid
98.0ms	2905×	body	80	nan
65.0ms	469×	body	640	valid
24.0ms	95×	body	5120	valid
24.0ms	243×	body	320	valid
8.0ms	116×	body	160	valid