Details

analyze624.0ms

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample43.0ms

Algorithm

intervals

Results

8.0ms	166×	body	80	valid
8.0ms	28×	body	2560	valid
6.0ms	28×	body	1280	valid
4.0ms	17×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	24×	body	80	nan
1.0ms	6×	body	320	valid
1.0ms	6×	body	160	valid
0.0ms	5×	body	80	invalid

simplify450.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	13
1	12	13

prune6.0ms

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: 34.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
1.0b	(- (* b_2 b_2) (* a c))
1.5b	(+ (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 79

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)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (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))))
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify45.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5018	1301

prune139.0ms

Filtered

69 candidates to 91 candidates (-31.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	82	9	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	9	92

Merged error: 7.6b

Counts

92 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.4b	(/ (/ (* a c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
11.2b	(/ (* a c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

74×	`times-frac`
58×	`add-sqr-sqrt`
57×	`*-un-lft-identity`
29×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
14×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
10×	`associate-/r*` `sqrt-prod` `associate-/r/`
8×	`add-log-exp`
7×	`cbrt-undiv` `flip3--` `distribute-rgt-neg-in` `div-exp` `flip--`
6×	`div-inv`
5×	`pow1`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 135

Calls

4 calls:

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

series119.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
41.0ms	(/ (/ (* a c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))) a)
52.0ms	(/ (* a c) (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify65.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4939	2825
1	4939	2825

prune148.0ms

Filtered

105 candidates to 147 candidates (-40.0%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	147	9	156

Merged error: 7.5b

Counts

156 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
1.0b	(- (* b_2 b_2) (* a c))
1.0b	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

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:

10.0ms	(/ c (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(- (* 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)))

series80.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ c (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms	(- (* b_2 b_2) (* a c))
15.0ms	(- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4952	1531
1	4952	1531

prune110.0ms

Filtered

71 candidates to 100 candidates (-40.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	99	10	109

Merged error: 7.4b

Counts

109 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

6.7b	(cbrt (/ c (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))
23.5b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
27×	`cbrt-prod`
21×	`times-frac`
18×	`add-cube-cbrt`
12×	`sqrt-prod`
7×	`pow1`
6×	`sqrt-div` `distribute-lft-out--` `difference-of-squares`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--` `add-log-exp`
3×	`rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2`
2×	`associate-/r/`
1×	`cbrt-div` `pow1/3` `div-inv`

Counts

4 → 81

Calls

4 calls:

10.0ms	(cbrt (/ c (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series414.0ms

Counts

4 → 12

Calls

4 calls:

378.0ms	(cbrt (/ c (- (neg b_2) (sqrt (- (* b_2 b_2) (* a c))))))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4965	1508
1	4965	1508

prune101.0ms

Filtered

72 candidates to 93 candidates (-29.2%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	92	11	103

Merged error: 7.4b

Counts

103 → 11

regimes344.0ms

Accuracy

93.2% (1.6b remaining)

Error of 6.8b against oracle of 5.2b and baseline of 29.0b

bsearch730.0ms

Steps

Iters	Range		Point
8	1.501023588850394e+71	4.069369628469616e+73	5.8169366956900916e+72
8	-8.462785971166471e-196	-9.835079688879864e-199	-2.375397364334649e-198
10	-1.011339686245993e+43	-7.078127003988134e+31	-1.0012485150414439e+43

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	64
1	48	64

end0.0ms

analyze423.0ms

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample1.1s

Algorithm

intervals

Results

283.0ms	1053×	body	2560	valid
244.0ms	5164×	body	80	valid
197.0ms	888×	body	1280	valid
78.0ms	444×	body	640	valid
36.0ms	106×	body	5120	valid
32.0ms	735×	body	80	nan
31.0ms	242×	body	320	valid
12.0ms	253×	body	80	invalid
9.0ms	103×	body	160	valid

Details

analyze624.0ms

sample43.0ms

simplify450.0ms

prune6.0ms

localize12.0ms

rewrite30.0ms

series69.0ms

simplify45.0ms

prune139.0ms

localize11.0ms

rewrite44.0ms

series119.0ms

simplify65.0ms

prune148.0ms

localize11.0ms

rewrite29.0ms

series80.0ms

simplify67.0ms

prune110.0ms

localize17.0ms

rewrite24.0ms

series414.0ms

simplify67.0ms

prune101.0ms

regimes344.0ms

bsearch730.0ms

simplify2.0ms

end0.0ms

analyze423.0ms

sample1.1s

Profiling