Details

sample38.0ms

Algorithm

intervals

Results

6.0ms	33×	body	2560	valid
6.0ms	185×	body	80	valid
5.0ms	30×	body	1280	valid
3.0ms	97×	body	80	nan
2.0ms	18×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	320	valid
0.0ms	2×	body	160	valid

simplify8.0ms

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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.2b	(- (* b_2 b_2) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite106.0ms

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:

61.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
23.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series236.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
61.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
29.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (48.0ms)

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

prune259.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.2b

localize10.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
4.6b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
7.7b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
146×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
81×	`add-cube-cbrt`
32×	`difference-of-squares`
27×	`associate-/l*`
19×	`sqrt-prod`
16×	`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 → 184

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
91.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
58.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series387.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* b_2 b_2) (* a c))
135.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
167.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify105.0ms

Algorithm

egg-herbie

Counts

196 → 196

Iterations

Useful iterations: 2 (77.0ms)

Iter	Nodes	Cost
0	725	2897
1	3210	2743
2	5003	2723

prune450.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.1b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b_2 b_2) (* a c))
2.0b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
4.6b	(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

141×	`times-frac`
119×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
70×	`add-cube-cbrt`
32×	`add-exp-log`
25×	`associate-/r*`
24×	`difference-of-squares`
23×	`add-cbrt-cube`
16×	`div-exp`
15×	`sqrt-prod`
12×	`distribute-lft-out--`
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 → 162

Calls

4 calls:

8.0ms	(- (* b_2 b_2) (* a c))
43.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
35.0ms	(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
152.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
118.0ms	(/ (* 1 (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))) a)
55.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify90.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	773	2158
1	3591	1999
2	5002	1976

prune381.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 4.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
0.9b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
1.2b	(- (* b_2 b_2) (* a c))
22.3b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac`
121×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
68×	`add-cube-cbrt`
26×	`difference-of-squares`
22×	`associate-/r*`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-lft-out--`
9×	`add-cbrt-cube`
8×	`add-log-exp`
7×	`div-exp`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `flip3--` `flip--` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `diff-log` `1-exp`
1×	`rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/r/` `inv-pow`

Counts

4 → 154

Calls

4 calls:

44.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
40.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
8.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ 1 (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
64.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
30.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify69.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	604	1947
1	2473	1778
2	5001	1652

prune242.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.1b

regimes147.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 29.6b

bsearch127.0ms

Steps

Iters	Range	Point
10	8.043557394408689e+68	7.456819745307919e+79	6.930065906216891e+79
6	-4.0354313817188784e-266	-6.878072424672717e-267	-7.260732308007473e-267
8	-5.872364732336956e+155	-1.2603418216603327e+153	-5.127573290098799e+153

Iters

Range

Point

8.043557394408689e+68

7.456819745307919e+79

6.930065906216891e+79

-4.0354313817188784e-266

-6.878072424672717e-267

-7.260732308007473e-267

-5.872364732336956e+155

-1.2603418216603327e+153

-5.127573290098799e+153

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	25
1	51	25
2	51	25

end0.0ms

sample1.1s

Algorithm

intervals

Results

205.0ms	1070×	body	2560	valid
198.0ms	5935×	body	80	valid
138.0ms	860×	body	1280	valid
96.0ms	2988×	body	80	nan
51.0ms	429×	body	640	valid
28.0ms	121×	body	5120	valid
20.0ms	219×	body	320	valid
7.0ms	109×	body	160	valid