Details

analyze501.0ms

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

sample37.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
1.0ms	16×	body	80	nan
1.0ms	12×	body	80	invalid

simplify224.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (223.0ms)

Iter	Nodes	Cost
0	3532	37
1	3532	37

prune12.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 20.0b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.5b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite26.0ms

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))))
8.0ms	(+ (neg b) (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)))

series63.0ms

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))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
18.0ms	(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

prune184.0ms

Filtered

63 candidates to 74 candidates (-17.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	69	7	76

Merged error: 6.1b

Counts

76 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

1.5b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.1b	(* c (/ a b))
7.4b	(/ (+ (* 2.0 (* c (/ a b))) (* b -2)) (* 2.0 a))
24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

21×	`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`
3×	`cbrt-undiv` `div-exp` `associate-l` `prod-exp` `sqrt-prod` `cbrt-unprod` `associate-/l*`
2×	`flip3-+` `sqrt-div` `sum-log` `flip-+` `div-inv` `associate-/l/` `distribute-lft-out` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `flip3--` `distribute-rgt-neg-in` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `*-commutative` `flip--`

Counts

4 → 85

Calls

4 calls:

8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(* c (/ a b))
12.0ms	(/ (+ (* 2.0 (* c (/ a b))) (* b -2)) (* 2.0 a))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series52.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (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))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify27.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5103	1167

prune200.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	90	7	97
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	94	10	104

Merged error: 6.0b

Counts

104 → 10

localize22.0ms

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))
1.5b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 4.0 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-/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 → 68

Calls

4 calls:

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

series93.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (* 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))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5665	1168

prune167.0ms

Filtered

64 candidates to 80 candidates (-25.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	76	4	80
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	80	10	90

Merged error: 6.0b

Counts

90 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

24.4b	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.6b	(cbrt (* c (/ a b)))
25.6b	(cbrt (* c (/ a b)))
25.6b	(cbrt (* c (/ a b)))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`cbrt-prod` `cbrt-div` `pow1/3` `associate-*r/` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 45

Calls

4 calls:

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

series95.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
27.0ms	(cbrt (* c (/ a b)))
32.0ms	(cbrt (* c (/ a b)))
21.0ms	(cbrt (* c (/ a b)))

simplify37.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5057	527

prune96.0ms

Filtered

49 candidates to 57 candidates (-16.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	56	1	57
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	57	10	67

Merged error: 6.0b

Counts

67 → 10

regimes272.0ms

Accuracy

91.6% (1.3b remaining)

Error of 7.0b against oracle of 5.7b and baseline of 20.9b

bsearch40.0ms

Steps

Iters	Range		Point
6	1.0672592596569214e+96	1.3516021862208058e+97	1.279846718371356e+97
5	-7.10397709953434e+89	-2.8750983083054284e+89	-6.197456258693133e+89

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	135	74
1	135	74

end0.0ms

sample1.0s

Algorithm

intervals

Results

727.0ms	8000×	body	80	valid
60.0ms	683×	body	80	nan
36.0ms	412×	body	80	invalid

Details

analyze501.0ms

sample37.0ms

simplify224.0ms

prune12.0ms

localize21.0ms

rewrite26.0ms

series63.0ms

simplify56.0ms

prune184.0ms

localize26.0ms

rewrite33.0ms

series52.0ms

simplify27.0ms

prune200.0ms

localize22.0ms

rewrite29.0ms

series93.0ms

simplify39.0ms

prune167.0ms

localize29.0ms

rewrite16.0ms

series95.0ms

simplify37.0ms

prune96.0ms

regimes272.0ms

bsearch40.0ms

simplify2.0ms

end0.0ms

sample1.0s

Profiling