Details

analyze457.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample46.0ms

Algorithm

intervals

Results

13.0ms	36×	body	2560	valid
9.0ms	166×	body	80	valid
7.0ms	29×	body	1280	valid
2.0ms	13×	body	640	valid
1.0ms	24×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	14×	body	80	invalid
1.0ms	6×	body	160	valid
0.0ms	3×	body	320	valid

simplify200.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (199.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 33.9b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.4b	(- (* b b) (* (* 4.0 a) c))
1.4b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-sqr-sqrt`
7×	`add-cube-cbrt`
6×	`distribute-lft-out`
5×	`pow1` `times-frac` `associate-/l*`
3×	`distribute-rgt-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` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 69

Calls

4 calls:

11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
6.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify42.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5863	1224

prune155.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	73	8	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	9	82

Merged error: 5.8b

Counts

82 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.8b	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.6b	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
34×	`times-frac`
32×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
11×	`add-cube-cbrt`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r*` `sqrt-prod` `add-log-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `distribute-rgt-neg-in` `flip--`
4×	`div-inv`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 119

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
12.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series138.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
46.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
61.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify71.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4974	2691
1	4974	2691

prune178.0ms

Filtered

84 candidates to 131 candidates (-56.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	133	7	140

Merged error: 5.8b

Counts

140 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.3b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.5b	(sqrt (- (* b b) (* 4.0 (* 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-/r*`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3--` `flip--`
3×	`diff-log` `associate-/l*`
2×	`sub-neg` `sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 88

Calls

4 calls:

9.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series90.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4991	1768
1	4991	1768

prune150.0ms

Filtered

71 candidates to 100 candidates (-40.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	100	7	107

Merged error: 5.6b

Counts

107 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ 1 (* a (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
1.3b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.3b	(* (* (/ 4.0 2.0) (* a c)) (/ 1 (* a (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

166×	`add-exp-log`
95×	`prod-exp`
78×	`add-cbrt-cube`
39×	`cbrt-unprod`
38×	`div-exp`
18×	`cbrt-undiv`
17×	`pow1`
14×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
12×	`rec-exp` `1-exp`
9×	`add-cube-cbrt` `associate-r`
8×	`add-log-exp`
7×	`pow-prod-down`
6×	`times-frac`
5×	`associate-*r/`
4×	`flip3--` `sqrt-prod` `associate-/r/` `flip--`
3×	`associate-l/` `associate-/l`
2×	`pow-flip` `sqrt-div` `diff-log` `div-inv` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-l` `neg-log` `clear-num` `associate-/r` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 137

Calls

4 calls:

11.0ms	(/ 1 (* a (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
18.0ms	(* (* (/ 4.0 2.0) (* a c)) (/ 1 (* a (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series120.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ 1 (* a (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(* (* (/ 4.0 2.0) (* a c)) (/ 1 (* a (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify87.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4945	2542
1	4945	2542

prune130.0ms

Filtered

73 candidates to 149 candidates (-104.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	149	7	156

Merged error: 5.6b

Counts

156 → 7

regimes353.0ms

Accuracy

95.8% (1.0b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 29.8b

bsearch87.0ms

Steps

Iters	Range	Point
7	1.5076119834637862e+100	3.066974460136245e+102	1.3431729974592912e+101
8	-4.723551939164576e-255	-7.853661625213148e-258	-9.33152770776795e-258
8	-3.530573512040272e+132	-1.8658479131162043e+129	-1.66821524347344e+131

Iters

Range

Point

1.5076119834637862e+100

3.066974460136245e+102

1.3431729974592912e+101

-4.723551939164576e-255

-7.853661625213148e-258

-9.33152770776795e-258

-3.530573512040272e+132

-1.8658479131162043e+129

-1.66821524347344e+131

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	146	61
1	146	61

end0.0ms

sample1.3s

Algorithm

intervals

Results

316.0ms	1034×	body	2560	valid
272.0ms	5085×	body	80	valid
234.0ms	943×	body	1280	valid
89.0ms	458×	body	640	valid
51.0ms	138×	body	5120	valid
34.0ms	656×	body	80	nan
32.0ms	202×	body	320	valid
20.0ms	374×	body	80	invalid
14.0ms	140×	body	160	valid

Details

analyze457.0ms

sample46.0ms

simplify200.0ms

prune8.0ms

localize12.0ms

rewrite30.0ms

series65.0ms

simplify42.0ms

prune155.0ms

localize15.0ms

rewrite44.0ms

series138.0ms

simplify71.0ms

prune178.0ms

localize14.0ms

rewrite30.0ms

series90.0ms

simplify46.0ms

prune150.0ms

localize15.0ms

rewrite50.0ms

series120.0ms

simplify87.0ms

prune130.0ms

regimes353.0ms

bsearch87.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling