Details

analyze443.0ms

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

13.0ms	45×	body	2560	valid
9.0ms	168×	body	80	valid
5.0ms	20×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	16×	body	80	nan
1.0ms	13×	body	80	invalid
1.0ms	6×	body	160	valid
1.0ms	4×	body	320	valid
0.0ms	1×	body	5120	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	17
1	50	17

prune7.0ms

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: 33.3b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
1.4b	(- (* b b) (* 4.0 (* a c)))
1.5b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

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-/l*`
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-/l/`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `neg-log` `prod-exp` `clear-num` `associate-/r*` `cbrt-unprod` `div-inv`

Counts

4 → 75

Calls

4 calls:

12.0ms	(/ (- (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)))))
3.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5664	1454

prune153.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	80	7	87
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	8	88

Merged error: 5.5b

Counts

88 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* 4.0 (* a c)))
4.3b	(/ (/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))) (* 2.0 a))
11.1b	(/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log` `add-cbrt-cube`
27×	`*-un-lft-identity`
26×	`times-frac`
17×	`cbrt-undiv` `div-exp`
13×	`prod-exp` `cbrt-unprod`
12×	`add-sqr-sqrt` `associate-/l*`
11×	`add-cube-cbrt`
8×	`distribute-lft-out`
6×	`associate-/r*` `associate-/r/` `add-log-exp`
5×	`pow1`
4×	`distribute-rgt-neg-in` `div-inv`
3×	`flip3-+` `sqrt-prod` `flip-+`
2×	`flip3--` `frac-2neg` `sqrt-div` `clear-num` `flip--`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `associate-/l/`

Counts

4 → 105

Calls

4 calls:

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

series134.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
48.0ms	(/ (/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))) (* 2.0 a))
63.0ms	(/ (* 4.0 (* a c)) (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify70.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4969	2323
1	4969	2323

prune159.0ms

Filtered

77 candidates to 117 candidates (-51.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	118	7	125

Merged error: 5.4b

Counts

125 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
1.1b	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
1.4b	(- (* b b) (* 4.0 (* a c)))
23.4b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `sum-log` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+r-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `unsub-neg` `neg-log` `clear-num` `div-inv`

Counts

4 → 79

Calls

4 calls:

11.0ms	(/ c (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
8.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series92.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(/ c (+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b)))
15.0ms	(+ (sqrt (- (* b b) (* 4.0 (* a c)))) (neg b))
9.0ms	(- (* b b) (* 4.0 (* a c)))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify49.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4970	1398
1	4970	1398

prune141.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	89	9	98

Merged error: 5.4b

Counts

98 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (* b b) (* 4.0 (* a c)))
8.1b	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
24.1b	(cbrt (- (* b b) (* 4.0 (* a c))))
24.1b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
6×	`cbrt-prod` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `cbrt-div` `flip3--` `add-cbrt-cube` `flip--`
3×	`diff-log`
2×	`sub-neg` `pow1/3`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 50

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
5.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

series97.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
38.0ms	(- (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
25.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
25.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify55.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5027	1191

prune141.0ms

Filtered

54 candidates to 62 candidates (-14.8%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	62	9	71

Merged error: 5.4b

Counts

71 → 9

regimes342.0ms

Accuracy

92.5% (1.8b remaining)

Error of 7.6b against oracle of 5.8b and baseline of 30.0b

bsearch585.0ms

Steps

Iters	Range		Point
7	7.200572495685986e+23	1.3280225432795167e+25	1.3122237402844517e+25
5	-1.3594521996163033e-306	-4.857635311348578e-307	-4.94356880916646e-307
8	-3.002904259416049e+39	-8.633966939698405e+36	-2.957820971125819e+39

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	62
1	45	62

end0.0ms

analyze439.0ms

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

318.0ms	1067×	body	2560	valid
269.0ms	5204×	body	80	valid
210.0ms	866×	body	1280	valid
85.0ms	446×	body	640	valid
41.0ms	113×	body	5120	valid
38.0ms	670×	body	80	nan
28.0ms	196×	body	320	valid
19.0ms	383×	body	80	invalid
10.0ms	108×	body	160	valid

Details

analyze443.0ms

sample42.0ms

simplify3.0ms

prune7.0ms

localize13.0ms

rewrite29.0ms

series62.0ms

simplify45.0ms

prune153.0ms

localize13.0ms

rewrite41.0ms

series134.0ms

simplify70.0ms

prune159.0ms

localize13.0ms

rewrite29.0ms

series92.0ms

simplify49.0ms

prune141.0ms

localize15.0ms

rewrite18.0ms

series97.0ms

simplify55.0ms

prune141.0ms

regimes342.0ms

bsearch585.0ms

simplify1.0ms

end0.0ms

analyze439.0ms

sample1.2s

Profiling