Details

analyze467.0ms

Algorithm: search

sample45.0ms

Algorithm

intervals

Results

12.0ms	40×	body	2560	valid
8.0ms	159×	body	80	valid
7.0ms	28×	body	1280	valid
3.0ms	14×	body	640	valid
2.0ms	6×	body	5120	valid
1.0ms	20×	body	80	nan
1.0ms	6×	body	320	valid
0.0ms	7×	body	80	invalid
0.0ms	3×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	9

prune4.0ms

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: 33.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.7b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.8b	(- (* b b) (* (* 3.0 a) c))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `*-un-lft-identity` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
3×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 60

Calls

4 calls:

7.0ms	(* (* 3.0 a) c)
8.0ms	(+ (neg 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)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(* (* 3.0 a) c)
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(- (* b b) (* (* 3.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	302	469
1	1293	428
2	5002	417

prune147.0ms

Filtered

52 candidates to 72 candidates (-38.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	62	10	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	10	73

Merged error: 11.5b

Counts

73 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 3.0 a) c))
4.3b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
8.6b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite42.0ms

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×	`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` `diff-log` `flip-+`

Counts

4 → 148

Calls

4 calls:

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

series120.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
44.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
54.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	634	2580
1	3161	2341
2	5001	2328

prune317.0ms

Filtered

106 candidates to 160 candidates (-50.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	152	8	160
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	155	15	170

Merged error: 11.0b

Counts

170 → 15

localize21.0ms

Local error

Found 4 expressions with local error:

9.9b	(- (neg b) (* (* (cbrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 3.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log`

Counts

4 → 59

Calls

4 calls:

4.0ms	(- (neg b) (* (* (cbrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 3.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (* (* (cbrt (sqrt (- (* b b) (* (* 3.0 a) c)))) (cbrt (sqrt (- (* b b) (* (* 3.0 a) c))))) (cbrt (sqrt (- (* b b) (* (* 3.0 a) c))))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 3 (104.0ms)

Iter	Nodes	Cost
0	221	891
1	842	706
2	3724	600
3	5002	597

prune232.0ms

Filtered

59 candidates to 71 candidates (-20.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	71	15	86

Merged error: 11.0b

Counts

86 → 15

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* b b) (* (* 3.0 a) c))
4.3b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
8.9b	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac`
19×	`cbrt-undiv` `div-exp`
18×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
17×	`add-cube-cbrt` `*-un-lft-identity`
10×	`associate-*r/` `associate-/r/`
8×	`associate-/l*`
7×	`flip3--` `flip--`
6×	`div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/r*`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 110

Calls

4 calls:

3.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
14.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
45.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
54.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
17.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify122.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (106.0ms)

Iter	Nodes	Cost
0	679	1938
1	4478	1484
2	5001	1443

prune164.0ms

Filtered

81 candidates to 122 candidates (-50.6%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	115	7	122
Fresh	6	6	12
Picked	1	0	1
Done	1	1	2
Total	123	14	137

Merged error: 10.7b

Counts

137 → 14

regimes553.0ms

Accuracy

91.4% (1.9b remaining)

Error of 12.9b against oracle of 11.1b and baseline of 32.8b

bsearch633.0ms

Steps

Iters	Range	Point
8	5.529174115348263e+141	2.4952871312398773e+145	2.5579717161169453e+143
8	-8.735454315335134e-251	-4.1469579703280705e-254	-4.220449130505682e-254
5	-3.4476901083492857e+134	-1.1361128371255774e+134	-3.4009313388987055e+134

Iters

Range

Point

5.529174115348263e+141

2.4952871312398773e+145

2.5579717161169453e+143

-8.735454315335134e-251

-4.1469579703280705e-254

-4.220449130505682e-254

-3.4476901083492857e+134

-1.1361128371255774e+134

-3.4009313388987055e+134

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	49
1	55	49
2	55	49

end0.0ms

analyze457.0ms

Algorithm: search

sample1.3s

Algorithm

intervals

Results

350.0ms	1106×	body	2560	valid
280.0ms	5098×	body	80	valid
232.0ms	894×	body	1280	valid
96.0ms	449×	body	640	valid
37.0ms	97×	body	5120	valid
36.0ms	230×	body	320	valid
32.0ms	630×	body	80	nan
21.0ms	386×	body	80	invalid
13.0ms	126×	body	160	valid

Details

analyze467.0ms

sample45.0ms

simplify10.0ms

prune4.0ms

localize11.0ms

rewrite24.0ms

series41.0ms

simplify42.0ms

prune147.0ms

localize15.0ms

rewrite42.0ms

series120.0ms

simplify114.0ms

prune317.0ms

localize21.0ms

rewrite18.0ms

series57.0ms

simplify112.0ms

prune232.0ms

localize16.0ms

rewrite40.0ms

series124.0ms

simplify122.0ms

prune164.0ms

regimes553.0ms

bsearch633.0ms

simplify2.0ms

end0.0ms

analyze457.0ms

sample1.3s

Profiling