Details

sample264.0ms

Algorithm

intervals

Results

207.0ms	27×	body	1280	valid
13.0ms	35×	body	2560	valid
12.0ms	189×	body	80	valid
6.0ms	101×	body	80	nan
6.0ms	17×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	4×	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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.8b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite64.0ms

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

series65.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
14.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

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

prune633.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 5.6b

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.8b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.7b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite98.0ms

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)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
42.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
51.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
14.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 2 (83.0ms)

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

prune1.6s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 5.5b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.1b	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
4.8b	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite303.0ms

Algorithm

rewrite-expression-head

Rules

3489×	`times-frac`
1831×	`add-sqr-sqrt`
1830×	`*-un-lft-identity`
1346×	`add-cube-cbrt`
267×	`associate-/l*`
242×	`distribute-lft-out--` `difference-of-squares`
124×	`sqrt-prod`
121×	`distribute-rgt-neg-in`
58×	`div-inv`
41×	`add-exp-log`
28×	`div-exp`
23×	`add-cbrt-cube`
13×	`cbrt-undiv`
8×	`add-log-exp`
6×	`associate-/r*`
5×	`pow1`
4×	`associate-/r/`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `diff-log` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 1148

Calls

4 calls:

15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
39.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
106.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series82.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
24.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
30.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify254.0ms

Algorithm

egg-herbie

Counts

1160 → 1160

Iterations

Useful iterations: 1 (65.0ms)

Iter	Nodes	Cost
0	4287	24836
1	5001	24170

prune8.4s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 5.5b

localize18.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
1.0b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.3b	(/ (/ (cbrt 1) (/ (/ 1 a) c)) a)
24.2b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite217.0ms

Algorithm

rewrite-expression-head

Rules

3405×	`times-frac`
1462×	`add-sqr-sqrt`
1461×	`*-un-lft-identity`
1457×	`add-cube-cbrt`
516×	`cbrt-prod`
263×	`associate-/l*`
101×	`div-inv`
26×	`add-exp-log`
17×	`div-exp`
15×	`add-cbrt-cube`
10×	`cbrt-undiv` `add-log-exp`
5×	`pow1`
4×	`sqrt-prod` `associate-/r/`
3×	`flip3--` `diff-log` `associate-/r*` `flip--`
2×	`sub-neg` `sqrt-div` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `rec-exp` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `1-exp` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 1121

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
12.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
72.0ms	(/ (/ (cbrt 1) (/ (/ 1 a) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
2.0ms	(/ (/ (cbrt 1) (/ (/ 1 a) c)) a)
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify210.0ms

Algorithm

egg-herbie

Counts

1133 → 1133

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	4799	16402
1	5001	15606

prune11.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 5.5b

regimes322.0ms

Accuracy

88.8% (3.0b remaining)

Error of 8.7b against oracle of 5.8b and baseline of 32.1b

bsearch109.0ms

Steps

Iters	Range		Point
8	1.239611320374306e+48	5.283842533261271e+50	1.7889848425355323e+48
9	-2.26016353878232e-246	-2.0825697103975006e-253	-8.141064449292044e-250
8	-6.30521239297407e+53	-2.0681333037085905e+50	-4.837192574744688e+53

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	25
1	43	25

end0.0ms

sample1.6s

Algorithm

intervals

Results

370.0ms	1042×	body	2560	valid
361.0ms	5874×	body	80	valid
266.0ms	910×	body	1280	valid
166.0ms	2868×	body	80	nan
110.0ms	461×	body	640	valid
50.0ms	112×	body	5120	valid
40.0ms	230×	body	320	valid
14.0ms	104×	body	160	valid