Details

analyze595.0ms

Algorithm: search

sample43.0ms

Algorithm

intervals

Results

10.0ms	36×	body	2560	valid
8.0ms	172×	body	80	valid
5.0ms	22×	body	1280	valid
3.0ms	15×	body	640	valid
1.0ms	29×	body	80	nan
1.0ms	8×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	6×	body	80	invalid

simplify382.0ms

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

prune5.0ms

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: 33.0b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.2b	(- (* b_2 b_2) (* a c))
0.3b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

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	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
3.0ms	(- (* b_2 b_2) (* a c))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(/ (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
36.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify43.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	360	964
1	1233	910
2	5002	901

prune144.0ms

Filtered

72 candidates to 103 candidates (-43.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	93	10	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	10	104

Merged error: 5.4b

Counts

104 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.2b	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.3b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

165×	`times-frac`
130×	`add-sqr-sqrt`
129×	`*-un-lft-identity`
77×	`add-cube-cbrt`
27×	`associate-/r*`
26×	`distribute-lft-out--` `difference-of-squares`
16×	`sqrt-prod`
15×	`add-exp-log`
13×	`distribute-rgt-neg-in`
10×	`add-log-exp`
9×	`associate-/r/` `add-cbrt-cube`
7×	`flip3--` `div-exp` `flip--`
6×	`pow1`
5×	`div-inv`
3×	`cbrt-undiv` `diff-log` `associate-/l*`
2×	`sub-neg` `rec-exp` `sqrt-div` `1-exp`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `inv-pow`

Counts

4 → 177

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(/ 1 (/ a (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
16.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify73.0ms

Algorithm

egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	587	2454
1	2706	2223
2	5001	2068

prune131.0ms

Filtered

87 candidates to 189 candidates (-117.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	5	4	9
Picked	0	1	1
Done	0	0	0
Total	191	8	199

Merged error: 5.3b

Counts

199 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b_2 b_2) (* a c))
0.2b	(/ (/ 1 a) (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
0.3b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

897×	`times-frac`
528×	`add-sqr-sqrt`
527×	`*-un-lft-identity`
355×	`add-cube-cbrt`
86×	`distribute-lft-out--` `difference-of-squares`
46×	`sqrt-prod`
44×	`add-exp-log`
43×	`distribute-rgt-neg-in` `div-inv`
32×	`div-exp`
29×	`associate-/r/`
27×	`associate-/r*`
17×	`flip3--` `flip--`
16×	`add-cbrt-cube`
13×	`associate-/l*`
10×	`add-log-exp`
8×	`cbrt-undiv` `rec-exp` `1-exp`
5×	`pow1`
3×	`diff-log`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 468

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
23.0ms	(/ (/ 1 a) (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
8.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(- (* b_2 b_2) (* a c))
29.0ms	(/ (/ 1 a) (/ 1 (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
13.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify110.0ms

Algorithm

egg-herbie

Counts

480 → 480

Iterations

Useful iterations: 1 (35.0ms)

Iter	Nodes	Cost
0	1704	8879
1	5001	7992

prune311.0ms

Filtered

173 candidates to 480 candidates (-177.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	478	2	480
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	479	9	488

Merged error: 5.3b

Counts

488 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
0.2b	(- (* b_2 b_2) (* a c))
6.0b	(- (/ (neg b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
22.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

44×	`add-sqr-sqrt`
38×	`*-un-lft-identity`
37×	`times-frac`
24×	`add-cube-cbrt`
17×	`sqrt-prod`
8×	`add-log-exp`
7×	`distribute-lft-out--`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `difference-of-squares`
5×	`pow1`
4×	`flip3--` `sqrt-div` `flip--`
3×	`distribute-rgt-neg-in` `associate-/r*` `div-inv`
2×	`sub-neg` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-out--` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `frac-sub` `sub-div`

Counts

4 → 97

Calls

4 calls:

6.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
3.0ms	(- (* b_2 b_2) (* a c))
34.0ms	(- (/ (neg b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (sqrt (- (* b_2 b_2) (* a c))) a)
7.0ms	(- (* b_2 b_2) (* a c))
16.0ms	(- (/ (neg b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify141.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	388	1005
1	1221	965
2	4837	951
3	5001	951

prune93.0ms

Filtered

80 candidates to 109 candidates (-36.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	108	10	118

Merged error: 5.3b

Counts

118 → 10

regimes349.0ms

Accuracy

88.7% (3.3b remaining)

Error of 8.5b against oracle of 5.1b and baseline of 34.4b

bsearch578.0ms

Steps

Iters	Range	Point
8	9.325215425799226e+119	1.1948726877763068e+123	2.0225082120326953e+121
7	-4.3580765900694236e-119	-3.5555997616746505e-121	-6.694125078168422e-121
6	-2.0990360732308106e+54	-2.5281299580505936e+53	-7.750663243330526e+53

Iters

Range

Point

9.325215425799226e+119

1.1948726877763068e+123

2.0225082120326953e+121

-4.3580765900694236e-119

-3.5555997616746505e-121

-6.694125078168422e-121

-2.0990360732308106e+54

-2.5281299580505936e+53

-7.750663243330526e+53

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	26
1	46	26
2	46	26

end0.0ms

analyze400.0ms

Algorithm: search

sample1.1s

Algorithm

intervals

Results

274.0ms	1077×	body	2560	valid
238.0ms	5064×	body	80	valid
185.0ms	886×	body	1280	valid
77.0ms	465×	body	640	valid
34.0ms	109×	body	5120	valid
33.0ms	785×	body	80	nan
32.0ms	257×	body	320	valid
12.0ms	142×	body	160	valid
11.0ms	246×	body	80	invalid

Details

analyze595.0ms

sample43.0ms

simplify382.0ms

prune5.0ms

localize13.0ms

rewrite30.0ms

series73.0ms

simplify43.0ms

prune144.0ms

localize10.0ms

rewrite37.0ms

series63.0ms

simplify73.0ms

prune131.0ms

localize14.0ms

rewrite76.0ms

series66.0ms

simplify110.0ms

prune311.0ms

localize11.0ms

rewrite52.0ms

series63.0ms

simplify141.0ms

prune93.0ms

regimes349.0ms

bsearch578.0ms

simplify5.0ms

end0.0ms

analyze400.0ms

sample1.1s

Profiling