Details

analyze673.0ms

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

sample48.0ms

Algorithm

intervals

Results

12.0ms	171×	body	80	valid
11.0ms	35×	body	2560	valid
7.0ms	27×	body	1280	valid
2.0ms	8×	body	640	valid
1.0ms	25×	body	80	nan
1.0ms	2×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	15×	body	80	invalid
1.0ms	6×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	9
1	64	9
2	114	9
3	135	9
4	144	9
5	148	9
6	148	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: 32.1b

Counts

2 → 1

localize19.0ms

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)))
1.5b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 77

Calls

4 calls:

12.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
3.0ms	(- (* 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))))

series66.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
10.0ms	(- (* b b) (* 4.0 (* a c)))
20.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	398	888
1	1466	803
2	5001	798

prune176.0ms

Filtered

65 candidates to 89 candidates (-36.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	80	9	89
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	10	90

Merged error: 6.0b

Counts

90 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.5b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

67×	`times-frac`
48×	`add-sqr-sqrt`
47×	`*-un-lft-identity`
27×	`add-cube-cbrt`
25×	`add-exp-log`
13×	`associate-/r*` `add-cbrt-cube`
12×	`div-exp`
10×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
9×	`associate-/r/`
8×	`sqrt-prod`
7×	`flip3--` `flip--`
6×	`pow1`
5×	`cbrt-undiv` `distribute-rgt-neg-in` `div-inv`
3×	`rec-exp` `diff-log` `1-exp` `prod-exp` `associate-/l*`
2×	`sub-neg` `sqrt-div`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `pow-flip` `frac-2neg` `sqrt-pow1` `pow1/2` `neg-log` `clear-num` `cbrt-unprod` `inv-pow`

Counts

4 → 125

Calls

4 calls:

14.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
11.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(/ 1 (/ (* 2.0 a) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify75.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	538	1801
1	2573	1602
2	5002	1528

prune160.0ms

Filtered

73 candidates to 137 candidates (-87.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	134	3	137
Fresh	4	4	8
Picked	0	1	1
Done	1	0	1
Total	139	8	147

Merged error: 5.9b

Counts

147 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.6b	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
16.3b	(- (pow b 2) (pow b 2))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt`
23×	`*-un-lft-identity`
22×	`unpow-prod-down`
19×	`add-exp-log`
16×	`difference-of-squares`
15×	`add-cube-cbrt`
13×	`add-cbrt-cube`
12×	`unpow2` `sqr-pow`
10×	`distribute-rgt-out--` `add-log-exp`
8×	`distribute-lft-out--`
7×	`div-exp`
5×	`pow1` `associate-/l/`
4×	`cbrt-undiv` `prod-exp`
3×	`flip3-+` `times-frac` `associate-/r*` `sqrt-prod` `flip-+`
2×	`frac-times` `flip3--` `sqrt-div` `associate-*r/` `sum-log` `flip--` `cbrt-unprod` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `rec-exp` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `+-inverses` `diff-log` `1-exp` `neg-log` `associate-l/` `clear-num` `div-inv` `associate-/l`

Counts

4 → 107

Calls

4 calls:

8.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
22.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
8.0ms	(- (pow b 2) (pow b 2))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series36.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(/ (* (/ 1 2.0) (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c)))) a)
1.0ms	(- (pow b 2) (pow b 2))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify206.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (196.0ms)

Iter	Nodes	Cost
0	590	777
1	3981	571
2	5002	555

prune204.0ms

Filtered

79 candidates to 119 candidates (-50.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	119	8	127

Merged error: 5.9b

Counts

127 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.2b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
21.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

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-/r*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 69

Calls

4 calls:

11.0ms	(/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms	(- (* 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))))

series100.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
10.0ms	(- (* b b) (* 4.0 (* a c)))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify63.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	374	757
1	1550	658
2	5002	645

prune143.0ms

Filtered

60 candidates to 81 candidates (-35.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	81	8	89

Merged error: 5.9b

Counts

89 → 8

regimes293.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 29.3b

bsearch889.0ms

Steps

Iters	Range	Point
8	4.529000382666176e+128	3.8663659387801394e+132	5.797243682937961e+131
10	3.567398194928607e-193	1.9570420447905172e-177	3.623429539767513e-193
10	-1.458015329704561e+157	-4.7426666837828205e+144	-4.766412713580042e+146

Iters

Range

Point

4.529000382666176e+128

3.8663659387801394e+132

5.797243682937961e+131

3.567398194928607e-193

1.9570420447905172e-177

3.623429539767513e-193

-1.458015329704561e+157

-4.7426666837828205e+144

-4.766412713580042e+146

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	25
1	44	25

end0.0ms

analyze450.0ms

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

sample1.2s

Algorithm

intervals

Results

334.0ms	1106×	body	2560	valid
275.0ms	5119×	body	80	valid
223.0ms	913×	body	1280	valid
78.0ms	409×	body	640	valid
38.0ms	106×	body	5120	valid
36.0ms	675×	body	80	nan
35.0ms	243×	body	320	valid
22.0ms	374×	body	80	invalid
10.0ms	104×	body	160	valid

Details

analyze673.0ms

sample48.0ms

simplify13.0ms

prune4.0ms

localize19.0ms

rewrite29.0ms

series66.0ms

simplify49.0ms

prune176.0ms

localize13.0ms

rewrite36.0ms

series77.0ms

simplify75.0ms

prune160.0ms

localize18.0ms

rewrite44.0ms

series36.0ms

simplify206.0ms

prune204.0ms

localize11.0ms

rewrite27.0ms

series100.0ms

simplify63.0ms

prune143.0ms

regimes293.0ms

bsearch889.0ms

simplify2.0ms

end0.0ms

analyze450.0ms

sample1.2s

Profiling