Details

analyze444.0ms

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

sample44.0ms

Algorithm

intervals

Results

8.0ms	161×	body	80	valid
8.0ms	27×	body	2560	valid
7.0ms	31×	body	1280	valid
7.0ms	22×	body	640	valid
2.0ms	5×	body	5120	valid
1.0ms	7×	body	320	valid
1.0ms	18×	body	80	nan
1.0ms	11×	body	80	invalid
0.0ms	3×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	17
1	30	17

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 36.6b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* a 2.0))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.8b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.1b	(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:

14.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* a 2.0))
3.0ms	(- (* b b) (* 4.0 (* a c)))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series61.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 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))))

simplify35.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5129	1264

prune159.0ms

Filtered

62 candidates to 81 candidates (-30.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	71	10	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	10	82

Merged error: 7.3b

Counts

82 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
3.7b	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
10.6b	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite44.0ms

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)))))
15.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* a 2.0))
12.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series130.0ms

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)))))) (* a 2.0))
58.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5021	2625

prune183.0ms

Filtered

84 candidates to 131 candidates (-56.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	129	2	131
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	133	8	141

Merged error: 7.2b

Counts

141 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (* 4.0 c) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b	(- (* b b) (* 4.0 (* a c)))
0.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

11.0ms	(/ (* 4.0 c) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
3.0ms	(- (* 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))))

series87.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ (* 4.0 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))))

simplify61.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4957	1384
1	4957	1384

prune132.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	2	86
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	85	9	94

Merged error: 7.2b

Counts

94 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
2.0b	(* (/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ a 2.0))
3.8b	(* (/ 4.0 a) (* (/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ a 2.0)))
25.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
57×	`add-exp-log` `add-cbrt-cube`
46×	`*-un-lft-identity`
43×	`times-frac`
40×	`associate-l`
30×	`add-cube-cbrt`
22×	`prod-exp` `cbrt-unprod`
17×	`cbrt-undiv` `div-exp`
14×	`associate-r`
12×	`pow1`
8×	`distribute-lft-out--` `add-log-exp` `difference-of-squares`
7×	`sqrt-prod`
6×	`frac-times` `associate-*r/`
4×	`distribute-rgt-neg-in` `pow-prod-down` `associate-*l/` `unswap-sqr`
3×	`flip3--` `flip--` `div-inv`
2×	`sqrt-div` `diff-log` `associate-/r/` `*-commutative`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `neg-log`

Counts

4 → 147

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
19.0ms	(* (/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ a 2.0))
17.0ms	(* (/ 4.0 a) (* (/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ a 2.0)))
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)))))
56.0ms	(* (/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ a 2.0))
43.0ms	(* (/ 4.0 a) (* (/ c (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (/ a 2.0)))
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify54.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4998	3126
1	4998	3126

prune195.0ms

Filtered

108 candidates to 159 candidates (-47.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	157	2	159
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	160	8	168

Merged error: 7.2b

Counts

168 → 8

regimes243.0ms

Accuracy

92.8% (1.7b remaining)

Error of 7.1b against oracle of 5.4b and baseline of 29.5b

bsearch527.0ms

Steps

Iters	Range		Point
7	1.7708775382058754e+36	1.3639375438100629e+38	1.3430984366882957e+38
10	-1.827838511064216e-303	3.8584104484824506e-299	-4.3571849990037956e-308
3	-9.3022547310091e+44	-6.850425518396183e+44	-9.131152096149943e+44

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	64
1	44	64

end0.0ms

analyze433.0ms

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

sample1.2s

Algorithm

intervals

Results

312.0ms	1047×	body	2560	valid
272.0ms	5184×	body	80	valid
219.0ms	889×	body	1280	valid
84.0ms	427×	body	640	valid
35.0ms	97×	body	5120	valid
34.0ms	224×	body	320	valid
31.0ms	638×	body	80	nan
22.0ms	429×	body	80	invalid
15.0ms	132×	body	160	valid

Details

analyze444.0ms

sample44.0ms

simplify3.0ms

prune8.0ms

localize11.0ms

rewrite30.0ms

series61.0ms

simplify35.0ms

prune159.0ms

localize15.0ms

rewrite44.0ms

series130.0ms

simplify49.0ms

prune183.0ms

localize15.0ms

rewrite28.0ms

series87.0ms

simplify61.0ms

prune132.0ms

localize16.0ms

rewrite55.0ms

series132.0ms

simplify54.0ms

prune195.0ms

regimes243.0ms

bsearch527.0ms

simplify1.0ms

end0.0ms

analyze433.0ms

sample1.2s

Profiling