Details

analyze462.0ms

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample89.0ms

Algorithm

intervals

Results

8.0ms	168×	body	80	valid
7.0ms	32×	body	1280	valid
7.0ms	26×	body	2560	valid
4.0ms	21×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify177.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (176.0ms)

Iter	Nodes	Cost
0	1784	16
1	1784	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: 31.9b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* (* 3.0 a) c))
4.5b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
14.8b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite29.0ms

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:

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

series63.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
27.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5899	1226

prune168.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	70	11	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	11	82

Merged error: 5.6b

Counts

82 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
10.3b	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
12.7b	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
21.1b	(sqrt (- (* b b) (* 3.0 (* a c))))

rewrite48.0ms

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:

16.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
13.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
10.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series128.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(/ (/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))) (* 3.0 a))
55.0ms	(/ (* 3.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify72.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4973	2553
1	4973	2553

prune185.0ms

Filtered

84 candidates to 131 candidates (-56.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	128	3	131
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	133	9	142

Merged error: 5.5b

Counts

142 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* b b) (* 3.0 (* a c)))
2.2b	(/ c (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
12.7b	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
21.1b	(sqrt (- (* b b) (* 3.0 (* 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:

4.0ms	(- (* b b) (* 3.0 (* a c)))
10.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
9.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 3.0 (* a c)))
48.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* 3.0 (* a c))))))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 3.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 3.0 (* a c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4991	1768
1	4991	1768

prune154.0ms

Filtered

71 candidates to 100 candidates (-40.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	99	10	109

Merged error: 5.5b

Counts

109 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

2.2b	(/ c (- (neg b) (* (fabs (cbrt (- (* b b) (* 3.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 3.0 (* a c))))))))
12.7b	(- (neg b) (* (fabs (cbrt (- (* b b) (* 3.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 3.0 (* a c)))))))
21.9b	(cbrt (- (* b b) (* 3.0 (* a c))))
21.9b	(cbrt (- (* b b) (* 3.0 (* a c))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `cbrt-prod` `add-cbrt-cube`
4×	`pow1` `cbrt-div` `flip3--` `flip--`
3×	`associate-/r` `associate-/l`
2×	`pow1/3` `diff-log` `associate-/r/`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `sub-neg` `frac-2neg` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 68

Calls

4 calls:

6.0ms	(/ c (- (neg b) (* (fabs (cbrt (- (* b b) (* 3.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 3.0 (* a c))))))))
4.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* 3.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 3.0 (* a c)))))))
4.0ms	(cbrt (- (* b b) (* 3.0 (* a c))))
4.0ms	(cbrt (- (* b b) (* 3.0 (* a c))))

series348.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(/ c (- (neg b) (* (fabs (cbrt (- (* b b) (* 3.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 3.0 (* a c))))))))
35.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* 3.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 3.0 (* a c)))))))
24.0ms	(cbrt (- (* b b) (* 3.0 (* a c))))
24.0ms	(cbrt (- (* b b) (* 3.0 (* a c))))

simplify65.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4945	2389
1	4945	2389

prune212.0ms

Filtered

70 candidates to 80 candidates (-14.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	80	10	90

Merged error: 5.5b

Counts

90 → 10

regimes291.0ms

Accuracy

93.9% (1.5b remaining)

Error of 7.0b against oracle of 5.6b and baseline of 29.6b

bsearch99.0ms

Steps

Iters	Range		Point
6	1.0884356104503121e+95	7.153391658470877e+95	6.588320973147626e+95
7	-4.992175761170256e-178	-1.1107609119088008e-179	-1.1275433833610337e-179
7	-9.6824112406062e+64	-8.919446196083717e+62	-9.543475095388701e+64

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	132	59
1	132	59

end0.0ms

sample1.9s

Algorithm

intervals

Results

309.0ms	1068×	body	2560	valid
246.0ms	5121×	body	80	valid
206.0ms	879×	body	1280	valid
88.0ms	470×	body	640	valid
45.0ms	129×	body	5120	valid
32.0ms	231×	body	320	valid
9.0ms	102×	body	160	valid

Details

analyze462.0ms

sample89.0ms

simplify177.0ms

prune8.0ms

localize14.0ms

rewrite29.0ms

series63.0ms

simplify41.0ms

prune168.0ms

localize15.0ms

rewrite48.0ms

series128.0ms

simplify72.0ms

prune185.0ms

localize14.0ms

rewrite30.0ms

series85.0ms

simplify46.0ms

prune154.0ms

localize21.0ms

rewrite20.0ms

series348.0ms

simplify65.0ms

prune212.0ms

regimes291.0ms

bsearch99.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling