Details

analyze525.0ms

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

23.0ms	256×	body	80	valid
2.0ms	17×	body	80	nan
1.0ms	6×	body	80	invalid

simplify216.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (215.0ms)

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: 17.3b

Counts

2 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
20.7b	(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))))
9.0ms	(- (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)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (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)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify58.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4900	1063
1	4900	1063

prune190.0ms

Filtered

63 candidates to 74 candidates (-17.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	68	6	74
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	70	6	76

Merged error: 4.6b

Counts

76 → 6

localize30.0ms

Local error

Found 4 expressions with local error:

7.6b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
20.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.7b	(sqrt (- (* b b) (* 4.0 (* a c))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

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

series58.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify49.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4959	931
1	4959	931

prune188.0ms

Filtered

58 candidates to 70 candidates (-20.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	70	6	76

Merged error: 4.6b

Counts

76 → 6

localize25.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b	(* c (/ a b))
3.4b	(/ (+ (* 2.0 (* c (/ a b))) (* b -2)) (* 2.0 a))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

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

series50.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(* c (/ a b))
17.0ms	(/ (+ (* 2.0 (* c (/ a b))) (* b -2)) (* 2.0 a))
14.0ms	(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

prune195.0ms

Filtered

74 candidates to 97 candidates (-31.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	0	4	4
Picked	1	0	1
Done	0	1	1
Total	94	9	103

Merged error: 4.5b

Counts

103 → 9

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))
0.8b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

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)))))
5.0ms	(- (* 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)))

series88.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(/ (* 2.0 c) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(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

prune133.0ms

Filtered

64 candidates to 80 candidates (-25.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	7	7
Picked	1	0	1
Done	1	0	1
Total	79	10	89

Merged error: 4.5b

Counts

89 → 10

regimes328.0ms

Accuracy

93.5% (1.0b remaining)

Error of 6.6b against oracle of 5.6b and baseline of 21.1b

bsearch108.0ms

Steps

Iters	Range	Point
9	4.5822900966867137e+145	9.979557504900018e+150	2.745617712906307e+146
8	1.899056070754716e-303	2.1904377506738937e-300	4.6451347271489274e-303
10	-8.86880988964721e+112	-6.91697785679341e+100	-6.999030654439093e+112

Iters

Range

Point

4.5822900966867137e+145

9.979557504900018e+150

2.745617712906307e+146

1.899056070754716e-303

2.1904377506738937e-300

4.6451347271489274e-303

-8.86880988964721e+112

-6.91697785679341e+100

-6.999030654439093e+112

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	163	172
1	163	172

end0.0ms

sample1.0s

Algorithm

intervals

Results

742.0ms	8000×	body	80	valid
56.0ms	656×	body	80	nan
32.0ms	368×	body	80	invalid

Details

analyze525.0ms

sample37.0ms

simplify216.0ms

prune12.0ms

localize25.0ms

rewrite26.0ms

series61.0ms

simplify58.0ms

prune190.0ms

localize30.0ms

rewrite18.0ms

series58.0ms

simplify49.0ms

prune188.0ms

localize25.0ms

rewrite30.0ms

series50.0ms

simplify27.0ms

prune195.0ms

localize22.0ms

rewrite30.0ms

series88.0ms

simplify39.0ms

prune133.0ms

regimes328.0ms

bsearch108.0ms

simplify3.0ms

end0.0ms

sample1.0s

Profiling