Details

sample324.0ms

Algorithm

intervals

Results

15.0ms	188×	body	80	valid
12.0ms	31×	body	2560	valid
10.0ms	30×	body	1280	valid
9.0ms	91×	body	80	nan
4.0ms	15×	body	640	valid
2.0ms	4×	body	5120	valid
1.0ms	5×	body	320	valid
1.0ms	6×	body	160	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: 33.7b

localize13.0ms

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))
1.5b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite68.0ms

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:

35.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series266.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
73.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

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

prune247.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.2b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.9b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
20.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite102.0ms

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:

13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
44.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
29.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series434.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(- (- 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)))))
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (85.0ms)

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

prune527.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 6.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
3.2b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
20.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
589×	`add-sqr-sqrt`
588×	`*-un-lft-identity`
392×	`add-cube-cbrt`
98×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
52×	`sqrt-prod`
49×	`distribute-rgt-neg-in`
28×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
8×	`add-log-exp`
5×	`pow1` `associate-/r/`
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` `neg-log` `associate-/l/`

Counts

4 → 491

Calls

4 calls:

13.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
29.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
55.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
178.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
152.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
59.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

503 → 503

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1582	8734
1	5001	8085

prune1.1s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 6.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
0.4b	(- (* b_2 b_2) (* a c))
0.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
20.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
528×	`add-sqr-sqrt`
527×	`*-un-lft-identity`
355×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-rgt-neg-in` `div-inv`
32×	`div-exp`
29×	`associate-/r/`
27×	`associate-/l*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/r*`
10×	`add-log-exp`
8×	`cbrt-undiv` `rec-exp` `1-exp`
5×	`pow1`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 468

Calls

4 calls:

47.0ms	(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (/ 1 (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) (/ 1 c))
32.0ms	(- (* b_2 b_2) (* a c))
70.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify107.0ms

Algorithm

egg-herbie

Counts

480 → 480

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1780	8961
1	5001	8170

prune638.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 6.0b

regimes211.0ms

Accuracy

94.9% (1.3b remaining)

Error of 6.8b against oracle of 5.6b and baseline of 30.0b

bsearch160.0ms

Steps

Iters	Range	Point
8	5.408584085660923e+89	6.673576309669011e+92	4.122987415476214e+92
6	-4.407080684076564e-271	-3.922245627457753e-272	-4.003960444831885e-272
7	-1.2511146020293208e+129	-2.5570389401985865e+127	-4.032376794487168e+127

Iters

Range

Point

5.408584085660923e+89

6.673576309669011e+92

4.122987415476214e+92

-4.407080684076564e-271

-3.922245627457753e-272

-4.003960444831885e-272

-1.2511146020293208e+129

-2.5570389401985865e+127

-4.032376794487168e+127

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	24
1	42	24

end0.0ms

sample1.9s

Algorithm

intervals

Results

492.0ms	5911×	body	80	valid
413.0ms	1058×	body	2560	valid
280.0ms	848×	body	1280	valid
218.0ms	2843×	body	80	nan
119.0ms	460×	body	640	valid
44.0ms	222×	body	320	valid
43.0ms	93×	body	5120	valid
20.0ms	131×	body	160	valid