Details

analyze729.0ms

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

sample39.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
2.0ms	22×	body	80	nan
1.0ms	10×	body	80	invalid

simplify407.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	57	38
1	57	38

prune23.0ms

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: 21.8b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
2.1b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
8×	`add-sqr-sqrt`
6×	`pow1` `add-cube-cbrt` `sqrt-prod`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `distribute-rgt-neg-in` `flip3-+` `diff-log` `neg-log` `flip-+`

Counts

4 → 56

Calls

4 calls:

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

series66.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
19.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify36.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4963	913
1	4963	913

prune185.0ms

Filtered

58 candidates to 68 candidates (-17.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	8	69

Merged error: 7.2b

Counts

69 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

2.1b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b	(* c (/ a b))
3.5b	(/ (* 2.0 c) (- (neg b) (- b (* 2.0 (* c (/ a b))))))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

27×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
16×	`times-frac`
15×	`add-cube-cbrt`
14×	`add-exp-log` `add-cbrt-cube`
13×	`associate-r`
8×	`add-log-exp`
7×	`pow1`
6×	`associate-/r*`
4×	`distribute-lft-out--`
3×	`cbrt-undiv` `distribute-rgt-neg-in` `div-exp` `associate-l` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `associate-/r/` `flip--` `div-inv` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `clear-num` `-commutative` `flip-+` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
7.0ms	(* c (/ a b))
9.0ms	(/ (* 2.0 c) (- (neg b) (- b (* 2.0 (* c (/ a b))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series62.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
5.0ms	(* c (/ a b))
27.0ms	(/ (* 2.0 c) (- (neg b) (- b (* 2.0 (* c (/ a b))))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify39.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5381	1278

prune211.0ms

Filtered

77 candidates to 103 candidates (-33.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	101	10	111

Merged error: 7.1b

Counts

111 → 10

localize33.0ms

Local error

Found 4 expressions with local error:

3.5b	(/ (* 2.0 c) (- (neg b) (- b (* 2.0 (* c (/ a b))))))
12.1b	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
14×	`add-sqr-sqrt`
9×	`add-exp-log` `add-cbrt-cube`
8×	`add-cube-cbrt` `add-log-exp`
6×	`pow1` `times-frac` `associate-/r*` `sqrt-prod`
4×	`sqrt-div` `distribute-lft-out--`
3×	`flip3--` `flip--`
2×	`cbrt-undiv` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `div-exp` `sum-log` `associate-/r/` `difference-of-squares`
1×	`+-commutative` `neg-sub0` `associate-+l-` `frac-2neg` `flip3-+` `neg-log` `prod-exp` `clear-num` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*`

Counts

4 → 72

Calls

4 calls:

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

series71.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (* 2.0 c) (- (neg b) (- b (* 2.0 (* c (/ a b))))))
15.0ms	(+ (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify37.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4946	1251
1	4946	1251

prune220.0ms

Filtered

64 candidates to 84 candidates (-31.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Merged error: 7.1b

Counts

94 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

7.3b	(- (neg b) (* (sqrt (sqrt (- (* b b) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.2b	(sqrt (- (* b b) (* 4.0 (* a c))))
24.2b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

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) (* 4.0 (* a c))))) (sqrt (sqrt (- (* b b) (* 4.0 (* a c)))))))
5.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify48.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5080	983

prune176.0ms

Filtered

61 candidates to 71 candidates (-16.4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	71	10	81

Merged error: 7.1b

Counts

81 → 10

regimes326.0ms

Accuracy

93% (1.0b remaining)

Error of 6.5b against oracle of 5.5b and baseline of 19.7b

bsearch575.0ms

Steps

Iters	Range		Point
8	1.4510983022418856e+94	8.522349741829671e+97	3.921780894513456e+97
9	-9.227781755529824e+134	-5.174829238339161e+129	-9.42133325574221e+131

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	133
1	63	133

end0.0ms

analyze499.0ms

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

sample976.0ms

Algorithm

intervals

Results

695.0ms	8000×	body	80	valid
53.0ms	665×	body	80	nan
38.0ms	406×	body	80	invalid

Details

analyze729.0ms

sample39.0ms

simplify407.0ms

prune23.0ms

localize25.0ms

rewrite23.0ms

series66.0ms

simplify36.0ms

prune185.0ms

localize28.0ms

rewrite30.0ms

series62.0ms

simplify39.0ms

prune211.0ms

localize33.0ms

rewrite23.0ms

series71.0ms

simplify37.0ms

prune220.0ms

localize30.0ms

rewrite18.0ms

series60.0ms

simplify48.0ms

prune176.0ms

regimes326.0ms

bsearch575.0ms

simplify2.0ms

end0.0ms

analyze499.0ms

sample976.0ms

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