Details

sample78.0ms

Algorithm

intervals

Results

19.0ms	194×	body	80	valid
16.0ms	33×	body	2560	valid
8.0ms	23×	body	1280	valid
7.0ms	96×	body	80	nan
5.0ms	18×	body	640	valid
2.0ms	3×	body	5120	valid
2.0ms	9×	body	320	valid
1.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 35.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-rgt-neg-in` `distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `neg-mul-1` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 90

Calls

4 calls:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series307.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
48.0ms	(- (* b b) (* (* 3.0 a) c))
72.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify51.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	433	855
1	1670	751
2	5001	736

prune266.0ms

Filtered

102 candidates to 82 candidates (80.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	92	10	102
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	10	103

Merged error: 7.1b

Counts

103 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.2b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.6b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
80×	`add-sqr-sqrt`
79×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
20×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
10×	`distribute-rgt-neg-in`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/` `add-log-exp`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 158

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
16.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series448.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
150.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
181.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify125.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 2 (102.0ms)

Iter	Nodes	Cost
0	669	2663
1	3431	2412
2	5001	2406

prune414.0ms

Filtered

170 candidates to 117 candidates (68.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	167	3	170
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	170	10	180

Merged error: 7.0b

Counts

180 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.2b	(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
9.4b	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-exp-log`
54×	`add-cbrt-cube`
40×	`div-exp`
30×	`prod-exp`
22×	`cbrt-undiv`
16×	`add-sqr-sqrt` `cbrt-unprod`
15×	`*-un-lft-identity`
8×	`times-frac` `1-exp` `associate-/l*`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `sqrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--` `associate-/l/`
2×	`distribute-rgt-neg-in` `frac-2neg` `sqrt-div` `clear-num` `associate-/r*` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `associate-*r/` `prod-diff`

Counts

4 → 111

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
16.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series353.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 3.0 a) c))
131.0ms	(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
104.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify102.0ms

Algorithm

egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	776	1633
1	4091	1284
2	5001	1266

prune241.0ms

Filtered

123 candidates to 73 candidates (59.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	123	10	133

Merged error: 7.0b

Counts

133 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
2.9b	(/ (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
9.4b	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

337×	`times-frac`
175×	`add-sqr-sqrt`
174×	`*-un-lft-identity`
118×	`add-cube-cbrt`
45×	`associate-/l*`
28×	`distribute-lft-out--` `difference-of-squares`
23×	`add-exp-log` `add-cbrt-cube`
18×	`div-inv`
17×	`sqrt-prod`
14×	`distribute-rgt-neg-in`
11×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r*` `associate-/r/` `log1p-expm1-u`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `div-sub` `prod-diff`

Counts

4 → 243

Calls

4 calls:

6.0ms	(- (* b b) (* (* 3.0 a) c))
33.0ms	(/ (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
27.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series359.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 3.0 a) c))
128.0ms	(/ (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
101.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
86.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1170	4250
1	5001	4007

prune640.0ms

Filtered

255 candidates to 185 candidates (72.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	252	3	255
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	254	11	265

Merged error: 7.0b

Counts

265 → 11

regimes378.0ms

Accuracy

92% (1.9b remaining)

Error of 7.4b against oracle of 5.5b and baseline of 29.4b

bsearch177.0ms

Steps

Iters	Range		Point
7	0.008549975533169097	1.4731263457460937	1.4443031837246074
8	-1.7832961101597004e-170	-3.712432627983841e-174	-3.760762857445126e-174
9	-2.075239967640102e+144	-1.1758805254835388e+137	-8.06152635231149e+142

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	30
1	50	30

end0.0ms

sample1.4s

Algorithm

intervals

Results

306.0ms	1094×	body	2560	valid
290.0ms	5847×	body	80	valid
202.0ms	871×	body	1280	valid
134.0ms	2881×	body	80	nan
80.0ms	454×	body	640	valid
38.0ms	110×	body	5120	valid
32.0ms	235×	body	320	valid
10.0ms	115×	body	160	valid