Details

analyze769.0ms

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

sample45.0ms

Algorithm

intervals

Results

25.0ms	256×	body	80	valid
3.0ms	31×	body	80	nan
1.0ms	7×	body	80	invalid

simplify630.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (215.0ms)

Iter	Nodes	Cost
0	3270	37
1	3270	37

prune14.0ms

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: 19.6b

Counts

2 → 1

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* c (* 4.0 a)))
1.3b	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
23.9b	(sqrt (- (* b b) (* c (* 4.0 a))))
23.9b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `add-log-exp`
7×	`sqrt-prod`
6×	`pow1` `add-cube-cbrt`
4×	`add-exp-log` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `difference-of-squares`
1×	`distribute-lft-out--`

Counts

4 → 55

Calls

4 calls:

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

series63.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* c (* 4.0 a)))
15.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
15.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
23.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify49.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4994	921
1	4994	921

prune208.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	60	7	67
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	7	68

Merged error: 6.6b

Counts

68 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
2.3b	(* c (/ a b))
5.5b	(/ c (- (neg b) (- b (* 2.0 (* c (/ a b))))))
23.9b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt` `*-un-lft-identity`
28×	`times-frac`
24×	`add-cube-cbrt`
13×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-out--`
7×	`pow1`
6×	`associate-/r*` `add-log-exp` `difference-of-squares`
4×	`distribute-rgt-neg-in` `sqrt-prod`
3×	`flip3--` `associate-l` `flip--` `associate-/l*`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 102

Calls

4 calls:

7.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
7.0ms	(* c (/ a b))
8.0ms	(/ c (- (neg b) (- b (* 2.0 (* c (/ a b))))))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (sqrt (- (* b b) (* c (* 4.0 a)))) b)
5.0ms	(* c (/ a b))
26.0ms	(/ c (- (neg b) (- b (* 2.0 (* c (/ a b))))))
15.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify47.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5107	1546

prune288.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	113	8	121

Merged error: 6.6b

Counts

121 → 8

localize35.0ms

Local error

Found 4 expressions with local error:

5.5b	(/ c (- (neg b) (- b (* 2.0 (* c (/ a b))))))
12.1b	(- (* (fabs (cbrt (- (* b b) (* c (* 4.0 a))))) (sqrt (cbrt (- (* b b) (* c (* 4.0 a)))))) b)
24.7b	(cbrt (- (* b b) (* c (* 4.0 a))))
24.7b	(cbrt (- (* b b) (* c (* 4.0 a))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
18×	`times-frac`
17×	`add-cube-cbrt`
8×	`distribute-lft-out--`
6×	`add-exp-log` `cbrt-prod` `associate-/r*` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `cbrt-div` `flip3--` `distribute-rgt-neg-in` `flip--` `difference-of-squares`
3×	`associate-/l*`
2×	`pow1/3` `associate-/r/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

4 → 78

Calls

4 calls:

8.0ms	(/ c (- (neg b) (- b (* 2.0 (* c (/ a b))))))
8.0ms	(- (* (fabs (cbrt (- (* b b) (* c (* 4.0 a))))) (sqrt (cbrt (- (* b b) (* c (* 4.0 a)))))) b)
4.0ms	(cbrt (- (* b b) (* c (* 4.0 a))))
4.0ms	(cbrt (- (* b b) (* c (* 4.0 a))))

series110.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ c (- (neg b) (- b (* 2.0 (* c (/ a b))))))
32.0ms	(- (* (fabs (cbrt (- (* b b) (* c (* 4.0 a))))) (sqrt (cbrt (- (* b b) (* c (* 4.0 a)))))) b)
28.0ms	(cbrt (- (* b b) (* c (* 4.0 a))))
27.0ms	(cbrt (- (* b b) (* c (* 4.0 a))))

simplify59.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4930	1724
1	4930	1724

prune320.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	90	8	98

Merged error: 6.6b

Counts

98 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

8.8b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* c (* 4.0 a))))) (sqrt (sqrt (- (* b b) (* c (* 4.0 a)))))))
23.9b	(sqrt (- (* b b) (* c (* 4.0 a))))
23.9b	(sqrt (- (* b b) (* c (* 4.0 a))))
23.9b	(sqrt (- (* b b) (* c (* 4.0 a))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `flip3--` `add-cbrt-cube` `flip--`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 59

Calls

4 calls:

4.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* c (* 4.0 a))))) (sqrt (sqrt (- (* b b) (* c (* 4.0 a)))))))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
6.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
4.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (* (sqrt (sqrt (- (* b b) (* c (* 4.0 a))))) (sqrt (sqrt (- (* b b) (* c (* 4.0 a)))))))
15.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))
14.0ms	(sqrt (- (* b b) (* c (* 4.0 a))))

simplify53.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5629	983

prune224.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	71	8	79

Merged error: 6.6b

Counts

79 → 8

regimes312.0ms

Accuracy

92.2% (1.2b remaining)

Error of 7.3b against oracle of 6.1b and baseline of 21.7b

bsearch58.0ms

Steps

Iters	Range		Point
7	8.257715293948687e+43	2.7435207047165594e+45	4.877750719758907e+44
8	-2.7921892159152142e+150	-6.710560792818507e+147	-9.653956009291089e+148

simplify14.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	669	93
1	669	93

end0.0ms

sample1.1s

Algorithm

intervals

Results

757.0ms	8000×	body	80	valid
60.0ms	662×	body	80	nan
39.0ms	431×	body	80	invalid

Details

analyze769.0ms

sample45.0ms

simplify630.0ms

prune14.0ms

localize32.0ms

rewrite24.0ms

series63.0ms

simplify49.0ms

prune208.0ms

localize28.0ms

rewrite30.0ms

series62.0ms

simplify47.0ms

prune288.0ms

localize35.0ms

rewrite27.0ms

series110.0ms

simplify59.0ms

prune320.0ms

localize26.0ms

rewrite19.0ms

series60.0ms

simplify53.0ms

prune224.0ms

regimes312.0ms

bsearch58.0ms

simplify14.0ms

end0.0ms

sample1.1s

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