Details

analyze475.0ms

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

sample40.0ms

Algorithm

intervals

Results

10.0ms	189×	body	80	valid
6.0ms	25×	body	1280	valid
5.0ms	16×	body	2560	valid
3.0ms	23×	body	80	nan
3.0ms	15×	body	640	valid
1.0ms	3×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	12×	body	80	invalid
0.0ms	1×	body	160	valid

simplify202.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (201.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune8.0ms

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: 28.3b

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))
0.4b	(- (* b b) (* (* 4.0 a) c))
0.7b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.3b	(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-/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:

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(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

prune151.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	72	9	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	9	82

Merged error: 4.5b

Counts

82 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* a 2.0)))
0.4b	(- (* b b) (* (* 4.0 a) c))
0.7b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
20.3b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(* (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (/ 1 (* a 2.0)))
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)))

simplify44.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4969	1369
1	4969	1369

prune138.0ms

Filtered

66 candidates to 91 candidates (-37.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	91	9	100

Merged error: 4.4b

Counts

100 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* a (/ 2.0 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
20.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

14.0ms	(* a (/ 2.0 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
6.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* a (/ 2.0 (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)))
8.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify50.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5227	1437

prune156.0ms

Filtered

70 candidates to 95 candidates (-35.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	94	10	104

Merged error: 4.4b

Counts

104 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
1.4b	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
8.6b	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
20.3b	(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:

9.0ms	(- (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))))

series132.0ms

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))
57.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify72.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4974	2691
1	4974	2691

prune153.0ms

Filtered

84 candidates to 131 candidates (-56.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	1	6	7
Picked	0	1	1
Done	0	2	2
Total	131	10	141

Merged error: 4.4b

Counts

141 → 10

regimes296.0ms

Accuracy

96.1% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 34.0b

bsearch86.0ms

Steps

Iters	Range	Point
9	2.1493534443249127e+106	2.2092326298850077e+111	5.9089157297044016e+110
8	-5.04152782348078e-188	-1.2071086576418101e-190	-1.4544105329255394e-190
5	-1.0967546375658848e+142	-3.3216190050040345e+141	-4.705720954619456e+141

Iters

Range

Point

2.1493534443249127e+106

2.2092326298850077e+111

5.9089157297044016e+110

-5.04152782348078e-188

-1.2071086576418101e-190

-1.4544105329255394e-190

-1.0967546375658848e+142

-3.3216190050040345e+141

-4.705720954619456e+141

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	148	63
1	148	63

end0.0ms

sample1.3s

Algorithm

intervals

Results

333.0ms	1065×	body	2560	valid
273.0ms	5149×	body	80	valid
230.0ms	899×	body	1280	valid
92.0ms	447×	body	640	valid
37.0ms	99×	body	5120	valid
35.0ms	709×	body	80	nan
35.0ms	235×	body	320	valid
20.0ms	341×	body	80	invalid
11.0ms	106×	body	160	valid

Details

analyze475.0ms

sample40.0ms

simplify202.0ms

prune8.0ms

localize12.0ms

rewrite29.0ms

series64.0ms

simplify39.0ms

prune151.0ms

localize13.0ms

rewrite34.0ms

series64.0ms

simplify44.0ms

prune138.0ms

localize13.0ms

rewrite35.0ms

series89.0ms

simplify50.0ms

prune156.0ms

localize13.0ms

rewrite47.0ms

series132.0ms

simplify72.0ms

prune153.0ms

regimes296.0ms

bsearch86.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling