Details

sample36.0ms

Algorithm

intervals

Results

7.0ms	35×	body	2560	valid
6.0ms	183×	body	80	valid
4.0ms	25×	body	1280	valid
3.0ms	99×	body	80	nan
1.0ms	11×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	5×	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: 33.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.8b	(- (* b_2 b_2) (* a c))
1.3b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite32.0ms

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:

10.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
34.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

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

prune248.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
3.1b	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
10.9b	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

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:

4.0ms	(- (* b_2 b_2) (* a c))
19.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
11.0ms	(/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series433.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
148.0ms	(/ (/ (+ 0 (* a c)) (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) a)
192.0ms	(/ (+ 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

196 → 196

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	725	2899
1	3204	2743
2	5001	2723

prune485.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b_2 b_2) (* a c))
2.0b	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
3.1b	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac`
545×	`add-sqr-sqrt`
448×	`*-un-lft-identity`
352×	`add-cube-cbrt`
96×	`difference-of-squares`
74×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-lft-out--`
25×	`associate-/r*`
22×	`div-inv`
18×	`add-exp-log` `add-cbrt-cube`
9×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1` `associate-/r/`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 437

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
27.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series395.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
165.0ms	(/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c))
129.0ms	(/ (/ a (/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) c)) a)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify96.0ms

Algorithm

egg-herbie

Counts

449 → 449

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1541	7328
1	5001	6762

prune1.0s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 5.5b

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
0.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
0.8b	(- (* b_2 b_2) (* a c))
21.6b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

789×	`times-frac`
493×	`add-sqr-sqrt`
406×	`*-un-lft-identity`
320×	`add-cube-cbrt`
86×	`difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-lft-out--`
40×	`div-inv`
32×	`div-exp`
29×	`associate-/r/`
24×	`associate-/l*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/r*`
8×	`cbrt-undiv` `rec-exp` `1-exp` `add-log-exp`
5×	`pow1`
2×	`sub-neg` `sqrt-div` `diff-log`
1×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `associate-/l/`

Counts

4 → 423

Calls

4 calls:

21.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

96.0ms	(/ (/ 1 (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) (/ 1 c))
70.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
32.0ms	(- (* b_2 b_2) (* a c))
64.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

435 → 435

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1764	7652
1	5001	6940

prune607.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 5.5b

regimes187.0ms

Accuracy

95.3% (1.1b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 29.7b

bsearch145.0ms

Steps

Iters	Range	Point
9	1.846147638884188e+104	1.7844061428947563e+109	5.431533766856835e+106
7	8.864719785943747e-237	7.298514919297617e-235	1.1073502924772407e-236
9	-3.3506371122085595e+158	-5.17073721832495e+150	-5.503862788874799e+151

Iters

Range

Point

1.846147638884188e+104

1.7844061428947563e+109

5.431533766856835e+106

8.864719785943747e-237

7.298514919297617e-235

1.1073502924772407e-236

-3.3506371122085595e+158

-5.17073721832495e+150

-5.503862788874799e+151

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	23
1	44	23
2	44	23

end0.0ms

sample1.0s

Algorithm

intervals

Results

220.0ms	1089×	body	2560	valid
195.0ms	5824×	body	80	valid
133.0ms	845×	body	1280	valid
93.0ms	2971×	body	80	nan
58.0ms	453×	body	640	valid
28.0ms	113×	body	5120	valid
24.0ms	260×	body	320	valid
8.0ms	129×	body	160	valid