Details

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

sample42.0ms

Algorithm

intervals

Results

10.0ms	176×	body	80	valid
8.0ms	27×	body	2560	valid
7.0ms	26×	body	1280	valid
3.0ms	13×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	25×	body	80	nan
1.0ms	2×	body	5120	valid
1.0ms	11×	body	80	invalid
0.0ms	3×	body	160	valid

simplify205.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (203.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune10.0ms

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: 34.9b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.8b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.8b	(- (* b b) (* (* 4.0 a) c))
24.5b	(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-/l*`
3×	`distribute-rgt-neg-in` `sqrt-prod`
2×	`cbrt-undiv` `neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `div-exp` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 69

Calls

4 calls:

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5863	1224

prune149.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	74	7	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	8	82

Merged error: 8.2b

Counts

82 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.4b	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
11.8b	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
34×	`times-frac`
32×	`add-sqr-sqrt`
31×	`*-un-lft-identity`
17×	`cbrt-undiv` `div-exp`
14×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
11×	`add-cube-cbrt`
10×	`distribute-lft-out--` `difference-of-squares`
8×	`associate-/r*` `sqrt-prod` `add-log-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `distribute-rgt-neg-in` `flip--`
4×	`div-inv`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 119

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
13.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series129.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
44.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
56.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify71.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4974	2691
1	4974	2691

prune172.0ms

Filtered

84 candidates to 131 candidates (-56.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	131	8	139

Merged error: 8.1b

Counts

139 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 88

Calls

4 calls:

10.0ms	(/ 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))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms	(- (* 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))))

simplify49.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4991	1768
1	4991	1768

prune150.0ms

Filtered

71 candidates to 100 candidates (-40.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	1	4	5
Picked	1	0	1
Done	0	2	2
Total	99	9	108

Merged error: 8.1b

Counts

108 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c (/ -1 (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))))
0.8b	(- (* b b) (* 4.0 (* a c)))
1.6b	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
24.5b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
20×	`add-sqr-sqrt`
18×	`associate-r`
14×	`add-cube-cbrt`
13×	`times-frac`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
7×	`pow1`
4×	`distribute-lft-out`
3×	`associate-l` `sqrt-prod`
2×	`flip3--` `flip3-+` `sqrt-div` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `div-exp` `pow-prod-down` `sum-log` `-commutative` `div-inv`

Counts

4 → 75

Calls

4 calls:

12.0ms	(* c (/ -1 (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
6.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series84.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* c (/ -1 (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))))
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify36.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5103	1238

prune129.0ms

Filtered

68 candidates to 87 candidates (-27.9%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	85	11	96

Merged error: 8.1b

Counts

96 → 11

regimes378.0ms

Accuracy

94.1% (1.4b remaining)

Error of 7.2b against oracle of 5.8b and baseline of 29.8b

bsearch85.0ms

Steps

Iters	Range	Point
8	4.695729674754504e+68	2.483542536808759e+71	2.0926984773604138e+71
7	-4.792304454331811e-277	-1.2327606543262558e-278	-5.437168469057273e-278
9	-1.0749833233155278e+75	-1.0334900432915288e+69	-1.0573233580703993e+75

Iters

Range

Point

4.695729674754504e+68

2.483542536808759e+71

2.0926984773604138e+71

-4.792304454331811e-277

-1.2327606543262558e-278

-5.437168469057273e-278

-1.0749833233155278e+75

-1.0334900432915288e+69

-1.0573233580703993e+75

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	132	62
1	132	62

end0.0ms

sample1.3s

Algorithm

intervals

Results

310.0ms	994×	body	2560	valid
293.0ms	5219×	body	80	valid
229.0ms	880×	body	1280	valid
94.0ms	465×	body	640	valid
39.0ms	235×	body	320	valid
39.0ms	103×	body	5120	valid
37.0ms	679×	body	80	nan
22.0ms	378×	body	80	invalid
11.0ms	104×	body	160	valid

Details

analyze459.0ms

sample42.0ms

simplify205.0ms

prune10.0ms

localize11.0ms

rewrite30.0ms

series64.0ms

simplify39.0ms

prune149.0ms

localize13.0ms

rewrite47.0ms

series129.0ms

simplify71.0ms

prune172.0ms

localize16.0ms

rewrite29.0ms

series86.0ms

simplify49.0ms

prune150.0ms

localize14.0ms

rewrite30.0ms

series84.0ms

simplify36.0ms

prune129.0ms

regimes378.0ms

bsearch85.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling