Details

sample35.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
6.0ms	180×	body	80	valid
4.0ms	29×	body	1280	valid
3.0ms	88×	body	80	nan
2.0ms	17×	body	640	valid
1.0ms	5×	body	5120	valid
0.0ms	7×	body	160	valid
0.0ms	3×	body	320	valid

simplify9.0ms

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: 33.2b

localize9.0ms

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))
1.7b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite60.0ms

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)
3.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series244.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
32.0ms	(- (* b_2 b_2) (* a c))
69.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	368	966
1	1229	910
2	5002	901

prune235.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.2b

localize11.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.1b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
150×	`add-sqr-sqrt`
115×	`*-un-lft-identity`
81×	`add-cube-cbrt`
34×	`difference-of-squares`
27×	`associate-/l*`
20×	`sqrt-prod`
17×	`distribute-lft-out--`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
9×	`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 → 187

Calls

4 calls:

19.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
43.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
27.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
152.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
184.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
57.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify103.0ms

Algorithm

egg-herbie

Counts

199 → 199

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	730	2960
1	3200	2803
2	5001	2783

prune502.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 5.1b

localize17.0ms

Local error

Found 4 expressions with local error:

5.8b	(* (/ 1 (* (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (/ a (/ (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite302.0ms

Algorithm

rewrite-expression-head

Rules

200×	`times-frac`
163×	`add-sqr-sqrt`
111×	`*-un-lft-identity`
98×	`associate-r`
89×	`add-cube-cbrt`
82×	`add-exp-log`
57×	`cbrt-prod`
33×	`div-exp`
31×	`add-cbrt-cube`
30×	`prod-exp`
18×	`sqrt-prod` `difference-of-squares`
15×	`cbrt-undiv` `associate-l`
12×	`cbrt-div` `cbrt-unprod` `unswap-sqr`
9×	`pow1` `flip3--` `associate-/r/` `flip--` `distribute-lft-out--`
6×	`rec-exp` `sqrt-div` `1-exp`
5×	`frac-times` `div-inv`
4×	`add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `associate-l/`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 212

Calls

4 calls:

276.0ms	(* (/ 1 (* (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (/ a (/ (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series309.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (/ 1 (* (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)))) (/ a (/ (cbrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))
63.0ms	(sqrt (- (* b_2 b_2) (* a c)))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1226	4901
1	5001	4408

prune691.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
4.0b	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
11.1b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

83×	`add-sqr-sqrt`
52×	`times-frac`
51×	`*-un-lft-identity`
33×	`add-cube-cbrt`
28×	`add-exp-log`
24×	`associate-l`
18×	`add-cbrt-cube`
16×	`difference-of-squares`
13×	`associate-r`
11×	`sqrt-prod`
9×	`div-exp`
8×	`prod-exp` `distribute-lft-out--`
7×	`pow1`
6×	`associate-/r*` `add-log-exp` `unswap-sqr`
5×	`cbrt-undiv`
4×	`flip3--` `associate-/r/` `flip--` `cbrt-unprod`
3×	`div-inv` `associate-/l*`
2×	`rec-exp` `sqrt-div` `1-exp` `associate-/l/`
1×	`frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 141

Calls

4 calls:

19.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
63.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
29.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series465.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
148.0ms	(* (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 a))
183.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
62.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	700	1778
1	3208	1574
2	5001	1556

prune366.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.1b

regimes220.0ms

Accuracy

85.4% (4.0b remaining)

Error of 9.4b against oracle of 5.4b and baseline of 32.7b

bsearch139.0ms

Steps

Iters	Range	Point
6	4.706455236749836e+29	5.491842449186372e+30	5.349311795482947e+30
7	-2.782279184329671e-219	-5.296311981150072e-221	-2.7503667729282305e-219
10	-6.255678465194574e+71	-1.2356841275142139e+58	-1.0366436397824178e+68

Iters

Range

Point

4.706455236749836e+29

5.491842449186372e+30

5.349311795482947e+30

-2.782279184329671e-219

-5.296311981150072e-221

-2.7503667729282305e-219

-6.255678465194574e+71

-1.2356841275142139e+58

-1.0366436397824178e+68

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	39
1	45	39

end0.0ms

sample995.0ms

Algorithm

intervals

Results

211.0ms	1094×	body	2560	valid
201.0ms	5857×	body	80	valid
142.0ms	917×	body	1280	valid
88.0ms	2907×	body	80	nan
53.0ms	419×	body	640	valid
24.0ms	102×	body	5120	valid
20.0ms	222×	body	320	valid
7.0ms	108×	body	160	valid