Details

analyze457.0ms

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

sample95.0ms

Algorithm

intervals

Results

10.0ms	35×	body	2560	valid
8.0ms	32×	body	1280	valid
8.0ms	158×	body	80	valid
3.0ms	10×	body	320	valid
3.0ms	14×	body	640	valid
1.0ms	3×	body	5120	valid
0.0ms	4×	body	160	valid

simplify195.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (194.0ms)

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	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

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
4.5b	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
16.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
10.0ms	(/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) (* a 2.0))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify37.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5340	1316

prune169.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	10	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 6.0b

Counts

83 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
4.7b	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
16.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
36.0ms	(* (/ 1 a) (/ (- (sqrt (- (* b b) (* 4.0 (* a c)))) b) 2.0))
14.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify53.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4968	1950
1	4968	1950

prune191.0ms

Filtered

82 candidates to 117 candidates (-42.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	115	12	127

Merged error: 5.9b

Counts

127 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
4.5b	(/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
16.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
24.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
7.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
46.0ms	(/ a (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
17.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify53.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5012	1600

prune164.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	92	13	105

Merged error: 5.7b

Counts

105 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

4.5b	(/ a (/ (* 4.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.9b	(/ (* 4.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))
12.2b	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
24.3b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
40×	`*-un-lft-identity`
27×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
26×	`add-cube-cbrt`
14×	`associate-/r*`
11×	`associate-/r/`
10×	`cbrt-undiv` `div-exp`
7×	`distribute-lft-out`
6×	`flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
4×	`associate-/l*`
3×	`sqrt-prod`
2×	`frac-2neg` `sqrt-div` `clear-num` `distribute-rgt-neg-out`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `distribute-frac-neg` `sum-log` `flip--`

Counts

4 → 117

Calls

4 calls:

13.0ms	(/ a (/ (* 4.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))))
11.0ms	(/ (* 4.0 (* a (neg c))) (+ b (sqrt (- (* 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))))

series110.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ a (/ (* 4.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c)))))))
53.0ms	(/ (* 4.0 (* a (neg c))) (+ b (sqrt (- (* b b) (* 4.0 (* a c))))))
14.0ms	(+ b (sqrt (- (* b b) (* 4.0 (* a c)))))
16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify57.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4960	2874
1	4960	2874

prune190.0ms

Filtered

98 candidates to 129 candidates (-31.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	128	1	129
Fresh	1	9	10
Picked	0	1	1
Done	1	1	2
Total	130	12	142

Merged error: 5.7b

Counts

142 → 12

regimes314.0ms

Accuracy

94.8% (1.3b remaining)

Error of 6.8b against oracle of 5.5b and baseline of 29.6b

bsearch114.0ms

Steps

Iters	Range	Point
6	1.0884356104503121e+95	7.153391658470877e+95	4.2689322255052e+95
9	-1.4442496899584979e-185	-1.96631667940923e-192	-2.631257193759308e-192
10	-1.1251404769851572e+117	-4.787578139113132e+105	-4.769743103503451e+116

Iters

Range

Point

1.0884356104503121e+95

7.153391658470877e+95

4.2689322255052e+95

-1.4442496899584979e-185

-1.96631667940923e-192

-2.631257193759308e-192

-1.1251404769851572e+117

-4.787578139113132e+105

-4.769743103503451e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	104	67
1	104	67

end0.0ms

sample1.9s

Algorithm

intervals

Results

316.0ms	1091×	body	2560	valid
242.0ms	5079×	body	80	valid
211.0ms	897×	body	1280	valid
82.0ms	444×	body	640	valid
47.0ms	130×	body	5120	valid
33.0ms	239×	body	320	valid
12.0ms	120×	body	160	valid

Details

analyze457.0ms

sample95.0ms

simplify195.0ms

prune8.0ms

localize12.0ms

rewrite26.0ms

series63.0ms

simplify37.0ms

prune169.0ms

localize17.0ms

rewrite35.0ms

series72.0ms

simplify53.0ms

prune191.0ms

localize14.0ms

rewrite26.0ms

series86.0ms

simplify53.0ms

prune164.0ms

localize19.0ms

rewrite37.0ms

series110.0ms

simplify57.0ms

prune190.0ms

regimes314.0ms

bsearch114.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling