Details

sample303.0ms

Algorithm

intervals

Results

13.0ms	40×	body	2560	valid
12.0ms	184×	body	80	valid
7.0ms	25×	body	1280	valid
6.0ms	72×	body	80	nan
5.0ms	22×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	5×	body	160	valid
0.0ms	3×	body	320	valid

simplify12.0ms

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: 35.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.2b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite65.0ms

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

series267.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
35.0ms	(- (* b_2 b_2) (* a c))
68.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
74.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (33.0ms)

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

prune234.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
5.6b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.3b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

186×	`times-frac`
154×	`add-sqr-sqrt`
153×	`*-un-lft-identity`
89×	`add-cube-cbrt`
32×	`distribute-lft-out--` `difference-of-squares`
30×	`associate-/l*`
19×	`sqrt-prod`
16×	`distribute-rgt-neg-in`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*` `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 → 200

Calls

4 calls:

3.0ms	(- (* b_2 b_2) (* a c))
41.0ms	(/ (/ (+ 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)))

series393.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
139.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
164.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify111.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	729	3368
1	3320	3193
2	5001	3167

prune472.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.1b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
5.6b	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
126×	`add-sqr-sqrt`
125×	`*-un-lft-identity`
77×	`add-cube-cbrt`
32×	`add-exp-log`
28×	`associate-/r*`
24×	`distribute-lft-out--` `difference-of-squares`
23×	`add-cbrt-cube`
16×	`div-exp`
15×	`sqrt-prod`
12×	`distribute-rgt-neg-in`
10×	`cbrt-undiv`
6×	`prod-exp` `div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/l*`
3×	`1-exp` `cbrt-unprod`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-*r/` `associate-/r/` `associate-/l/`

Counts

4 → 174

Calls

4 calls:

2.0ms	(- (* b_2 b_2) (* a c))
24.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
20.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
176.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
152.0ms	(/ (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) a)
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify94.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	768	2481
1	3552	2301
2	5003	2278

prune392.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 6.6b

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.1b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
5.6b	(* (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) (/ 1 a))
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
131×	`add-sqr-sqrt`
130×	`*-un-lft-identity`
108×	`add-exp-log`
82×	`add-cube-cbrt`
52×	`prod-exp`
41×	`div-exp` `add-cbrt-cube`
25×	`associate-/r*`
24×	`distribute-lft-out--` `difference-of-squares`
19×	`1-exp`
15×	`sqrt-prod`
14×	`cbrt-unprod`
13×	`cbrt-undiv` `associate-r`
12×	`distribute-rgt-neg-in`
10×	`pow1`
7×	`rec-exp`
6×	`div-inv` `add-log-exp`
3×	`associate-r/` `pow-prod-down` `associate-/l`
2×	`flip3--` `sqrt-div` `flip--`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-l` `associate-l/` `clear-num` `associate-/r/` `un-div-inv` `-commutative`

Counts

4 → 209

Calls

4 calls:

2.0ms	(- (* b_2 b_2) (* a c))
25.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
76.0ms	(* (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) (/ 1 a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series413.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* b_2 b_2) (* a c))
173.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
148.0ms	(* (* 1 (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))) (/ 1 a))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify109.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	981	2944
1	4175	2632
2	5003	2580

prune406.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 6.6b

regimes155.0ms

Accuracy

89.8% (2.7b remaining)

Error of 8.3b against oracle of 5.5b and baseline of 32.2b

bsearch132.0ms

Steps

Iters	Range	Point
5	6.012009925983545e+34	1.951400559087758e+35	1.2011474830795371e+35
8	-4.266024305910705e-225	-6.994418685499569e-228	-8.615626397712376e-228
8	-1.0362695438716464e+73	-8.682929093782064e+69	-2.9644058459680186e+71

Iters

Range

Point

6.012009925983545e+34

1.951400559087758e+35

1.2011474830795371e+35

-4.266024305910705e-225

-6.994418685499569e-228

-8.615626397712376e-228

-1.0362695438716464e+73

-8.682929093782064e+69

-2.9644058459680186e+71

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	26
1	47	26
2	47	26

end0.0ms

sample1.6s

Algorithm

intervals

Results

379.0ms	5896×	body	80	valid
360.0ms	1096×	body	2560	valid
224.0ms	835×	body	1280	valid
168.0ms	2913×	body	80	nan
98.0ms	463×	body	640	valid
41.0ms	107×	body	5120	valid
37.0ms	234×	body	320	valid
12.0ms	105×	body	160	valid