Details

analyze716.0ms

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

sample71.0ms

Algorithm

intervals

Results

22.0ms

256×

body

valid

simplify659.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (215.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune13.0ms

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: 16.0b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.3b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `sum-log` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
1×	`+-commutative` `associate--l-` `associate-+l-` `sub-neg` `flip3-+` `flip-+`

Counts

4 → 62

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series72.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
19.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify56.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4900	1063
1	4900	1063

prune186.0ms

Filtered

63 candidates to 74 candidates (-17.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	69	5	74
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	5	75

Merged error: 5.5b

Counts

75 → 5

localize34.0ms

Local error

Found 4 expressions with local error:

6.6b	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
20.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.8b	(cbrt (- (* b b) (* 4.0 (* a c))))
20.8b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
7×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
5×	`pow1`
4×	`add-exp-log` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
3×	`sqrt-prod`
2×	`pow1/3` `sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 54

Calls

4 calls:

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

series99.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
26.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify66.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4903	1193
1	4903	1193

prune194.0ms

Filtered

55 candidates to 66 candidates (-20.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	66	5	71

Merged error: 5.5b

Counts

71 → 5

localize32.0ms

Local error

Found 4 expressions with local error:

20.0b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.0b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.0b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4955	932
1	4955	932

prune255.0ms

Filtered

61 candidates to 72 candidates (-18.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	71	6	77

Merged error: 5.5b

Counts

77 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.5b	(* c (/ a b))
4.5b	(/ (+ (* 2.0 (* c (/ a b))) (* b -2)) (* 2.0 a))
20.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

9.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(* c (/ a b))
10.0ms	(/ (+ (* 2.0 (* c (/ a b))) (* b -2)) (* 2.0 a))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(* c (/ a b))
16.0ms	(/ (+ (* 2.0 (* c (/ a b))) (* b -2)) (* 2.0 a))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify27.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5079	1250

prune164.0ms

Filtered

75 candidates to 99 candidates (-32.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	97	2	99
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	98	7	105

Merged error: 5.4b

Counts

105 → 7

regimes258.0ms

Accuracy

91.5% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 19.6b

bsearch70.0ms

Steps

Iters	Range		Point
9	1.796391671969355e+95	7.055120248280938e+103	4.430506721371134e+95
6	-5.069941376543122e+67	-8.77243028957601e+66	-3.2773817389906695e+67

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	191	123
1	191	123

end0.0ms

sample2.1s

Algorithm

intervals

Results

627.0ms

8000×

body

valid

Details

analyze716.0ms

sample71.0ms

simplify659.0ms

prune13.0ms

localize24.0ms

rewrite42.0ms

series72.0ms

simplify56.0ms

prune186.0ms

localize34.0ms

rewrite17.0ms

series99.0ms

simplify66.0ms

prune194.0ms

localize32.0ms

rewrite18.0ms

series57.0ms

simplify47.0ms

prune255.0ms

localize26.0ms

rewrite32.0ms

series51.0ms

simplify27.0ms

prune164.0ms

regimes258.0ms

bsearch70.0ms

simplify3.0ms

end0.0ms

sample2.1s

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