Details

analyze467.0ms

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

sample44.0ms

Algorithm

intervals

Results

10.0ms	27×	body	2560	valid
9.0ms	167×	body	80	valid
9.0ms	35×	body	1280	valid
4.0ms	18×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	16×	body	80	nan
1.0ms	14×	body	80	invalid
1.0ms	2×	body	5120	valid
0.0ms	1×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	17
1	50	17

prune6.0ms

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: 35.7b

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))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.2b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite27.0ms

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 → 75

Calls

4 calls:

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

series59.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
8.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5664	1454

prune154.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	78	9	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	9	88

Merged error: 6.8b

Counts

88 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* b b) (* 4.0 (* a c)))
0.2b	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* a 2.0)))
0.2b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

3.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* a 2.0)))
7.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series58.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
19.0ms	(* (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (/ 1 (* a 2.0)))
15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5193	1531

prune128.0ms

Filtered

64 candidates to 95 candidates (-48.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	93	2	95
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	96	8	104

Merged error: 6.8b

Counts

104 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
5.1b	(/ (/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))) (* 2.0 a))
11.6b	(/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
31×	`*-un-lft-identity`
26×	`times-frac`
17×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt` `associate-/l*`
11×	`add-cube-cbrt`
10×	`distribute-lft-out`
8×	`add-log-exp`
6×	`associate-/r*` `associate-/r/`
5×	`pow1` `distribute-rgt-neg-in`
4×	`flip3-+` `flip-+` `div-inv`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num` `sum-log`
1×	`+-commutative` `neg-sub0` `associate-+r-` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `unsub-neg` `neg-log` `flip--` `associate-/l/`

Counts

4 → 110

Calls

4 calls:

8.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
15.0ms	(/ (/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))) (* 2.0 a))
13.0ms	(/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series135.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
47.0ms	(/ (/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))) (* 2.0 a))
57.0ms	(/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5030	2415

prune162.0ms

Filtered

80 candidates to 122 candidates (-52.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	120	10	130

Merged error: 6.7b

Counts

130 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
0.2b	(- (* b b) (* 4.0 (* a c)))
0.6b	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
24.2b	(sqrt (- (* b b) (* 4.0 (* 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-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+r-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `unsub-neg` `neg-log` `clear-num` `div-inv`

Counts

4 → 79

Calls

4 calls:

11.0ms	(/ c (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
3.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ c (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify48.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4970	1398
1	4970	1398

prune118.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	1	6	7
Picked	1	0	1
Done	0	2	2
Total	92	9	101

Merged error: 6.7b

Counts

101 → 9

regimes302.0ms

Accuracy

84.3% (4.5b remaining)

Error of 9.9b against oracle of 5.4b and baseline of 34.2b

bsearch352.0ms

Steps

Iters	Range		Point
4	1.3385522824099182e+107	2.5817609460188806e+107	1.8526227140702638e+107
8	-5.998972135711252e-68	-1.1319009519835325e-70	-3.600616946333796e-70

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	37
1	34	37

end0.0ms

analyze459.0ms

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

sample1.3s

Algorithm

intervals

Results

342.0ms	1093×	body	2560	valid
273.0ms	5098×	body	80	valid
226.0ms	886×	body	1280	valid
97.0ms	470×	body	640	valid
43.0ms	116×	body	5120	valid
33.0ms	220×	body	320	valid
32.0ms	595×	body	80	nan
19.0ms	365×	body	80	invalid
12.0ms	117×	body	160	valid

Details

analyze467.0ms

sample44.0ms

simplify3.0ms

prune6.0ms

localize12.0ms

rewrite27.0ms

series59.0ms

simplify45.0ms

prune154.0ms

localize12.0ms

rewrite31.0ms

series58.0ms

simplify47.0ms

prune128.0ms

localize13.0ms

rewrite43.0ms

series135.0ms

simplify49.0ms

prune162.0ms

localize14.0ms

rewrite30.0ms

series86.0ms

simplify48.0ms

prune118.0ms

regimes302.0ms

bsearch352.0ms

simplify1.0ms

end0.0ms

analyze459.0ms

sample1.3s

Profiling