Details

sample300.0ms

Algorithm

intervals

Results

11.0ms	40×	body	2560	valid
10.0ms	183×	body	80	valid
6.0ms	27×	body	1280	valid
4.0ms	25×	body	640	valid
4.0ms	93×	body	80	nan
1.0ms	5×	body	320	valid
0.0ms	5×	body	160	valid
0.0ms	1×	body	5120	valid

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	7
1	23	7
2	30	7
3	32	7
4	34	7
5	34	7

prune4.0ms

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: 35.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.6b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.6b	(- (* b_2 b_2) (* a c))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

23.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series281.0ms

Counts

4 → 12

Calls

4 calls:

94.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
75.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
40.0ms	(- (* b_2 b_2) (* a c))
72.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	389	850
1	1366	779
2	5001	753

prune292.0ms

Filtered

112 candidates to 88 candidates (78.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	104	8	112
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	105	8	113

Merged error: 3.4b

Counts

113 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
4.7b	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
9.1b	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite49.0ms

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` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `prod-diff` `flip-+`

Counts

4 → 210

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
15.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
141.0ms	(/ (/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
172.0ms	(/ (+ 0 (* a c)) (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))))
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify118.0ms

Algorithm

egg-herbie

Counts

222 → 222

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	761	3434
1	3490	3258
2	5002	3250

prune490.0ms

Filtered

222 candidates to 152 candidates (68.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	219	3	222
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	221	9	230

Merged error: 3.4b

Counts

230 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
2.9b	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
4.7b	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

951×	`times-frac`
585×	`add-sqr-sqrt`
584×	`*-un-lft-identity`
392×	`add-cube-cbrt`
96×	`distribute-lft-out--` `difference-of-squares`
83×	`associate-/l*`
51×	`sqrt-prod`
48×	`distribute-rgt-neg-in`
28×	`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/`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `associate-/l/`

Counts

4 → 495

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
29.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series438.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* b_2 b_2) (* a c))
184.0ms	(/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c))
157.0ms	(/ (/ a (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) c)) a)
60.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify108.0ms

Algorithm

egg-herbie

Counts

507 → 507

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1561	8690
1	5001	8042

prune986.0ms

Filtered

507 candidates to 308 candidates (60.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	506	1	507
Fresh	1	6	7
Picked	0	1	1
Done	1	0	1
Total	508	8	516

Merged error: 3.4b

Counts

516 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (* b_2 b_2) (* a c))
1.8b	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
4.7b	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite221.0ms

Algorithm

rewrite-expression-head

Rules

3489×	`times-frac`
1827×	`add-sqr-sqrt`
1826×	`*-un-lft-identity`
1346×	`add-cube-cbrt`
267×	`associate-/l*`
240×	`distribute-lft-out--` `difference-of-squares`
123×	`sqrt-prod`
120×	`distribute-rgt-neg-in`
58×	`div-inv`
41×	`add-exp-log`
28×	`div-exp`
23×	`add-cbrt-cube`
13×	`cbrt-undiv`
6×	`associate-/r*` `add-log-exp`
5×	`pow1`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`rec-exp` `1-exp`
2×	`flip3--` `frac-2neg` `sqrt-div` `div-sub` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 1152

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
20.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
61.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* b_2 b_2) (* a c))
93.0ms	(/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)
110.0ms	(/ (/ 1 (/ (/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a) c)) a)
65.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify274.0ms

Algorithm

egg-herbie

Counts

1164 → 1164

Iterations

Useful iterations: 1 (72.0ms)

Iter	Nodes	Cost
0	4276	24795
1	5001	24124

prune2.2s

Filtered

1164 candidates to 583 candidates (50.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	1164	0	1164
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	1164	8	1172

Merged error: 3.4b

Counts

1172 → 8

regimes209.0ms

Accuracy

90% (2.7b remaining)

Error of 8.2b against oracle of 5.5b and baseline of 32.5b

bsearch186.0ms

Steps

Iters	Range		Point
10	1.100420074551047e-18	0.0163835844060345	6.948103979107274e-08
9	1.1405585128681756e-186	1.2232775426196791e-178	1.164566682148749e-186
11	-3.334524116472281e+99	-2.3662890435539516e+79	-1.599359189869806e+99

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	40	23
1	40	23

end0.0ms

sample1.3s

Algorithm

intervals

Results

284.0ms	1089×	body	2560	valid
260.0ms	5799×	body	80	valid
185.0ms	879×	body	1280	valid
122.0ms	2960×	body	80	nan
74.0ms	446×	body	640	valid
36.0ms	118×	body	5120	valid
29.0ms	239×	body	320	valid
11.0ms	133×	body	160	valid