Details

sample55.0ms

Algorithm

intervals

Results

28.0ms	289×	body	80	valid
7.0ms	79×	body	80	nan

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	157	37
1	157	37

prune15.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 18.4b

Counts

2 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.7b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite25.0ms

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 → 57

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
9.0ms	(+ (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)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
26.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify41.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5289	908

prune181.0ms

Filtered

58 candidates to 69 candidates (-19.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	66	5	71

Merged error: 6.2b

Counts

71 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
1.7b	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite22.0ms

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 → 57

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
8.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series59.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
16.0ms	(- (sqrt (- (* b b) (* 4.0 (* a c)))) b)
18.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify33.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5552	929

prune151.0ms

Filtered

53 candidates to 69 candidates (-30.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	69	5	74

Merged error: 6.2b

Counts

74 → 5

localize32.0ms

Local error

Found 4 expressions with local error:

21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.1b	(sqrt (- (* b b) (* 4.0 (* a c))))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `sqrt-prod`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-div`
4×	`add-exp-log` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `add-cbrt-cube` `flip--` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

4.0ms	(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)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
17.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify38.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5112	932

prune263.0ms

Filtered

61 candidates to 72 candidates (-18.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	72	5	77

Merged error: 6.2b

Counts

77 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

1.7b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.6b	(* c (/ a b))
4.5b	(/ (- (neg b) (- b (* 2.0 (* c (/ a b))))) (* 2.0 a))
21.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite33.0ms

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-/l*`
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` `flip--` `div-inv` `associate-/l/` `distribute-lft-out` `difference-of-squares` `unswap-sqr`
1×	`+-commutative` `neg-sub0` `associate-+l-` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `neg-log` `clear-num` `associate-/r` `*-commutative` `flip-+`

Counts

4 → 92

Calls

4 calls:

8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(* c (/ a b))
10.0ms	(/ (- (neg b) (- b (* 2.0 (* c (/ a b))))) (* 2.0 a))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series51.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
6.0ms	(* c (/ a b))
13.0ms	(/ (- (neg b) (- b (* 2.0 (* c (/ a b))))) (* 2.0 a))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify38.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4993	1300
1	4993	1300

prune171.0ms

Filtered

77 candidates to 104 candidates (-35.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	2	2
Picked	1	0	1
Done	0	2	2
Total	103	6	109

Merged error: 6.2b

Counts

109 → 6

regimes221.0ms

Accuracy

93% (1.0b remaining)

Error of 6.9b against oracle of 5.9b and baseline of 20.3b

bsearch71.0ms

Steps

Iters	Range		Point
10	1.1487243557305423e+102	3.920821933018458e+112	1.0467953012742888e+112
7	-4.262816151522474e+111	-1.589409284886386e+110	-4.2185216526367483e+111

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	111
1	62	111

end0.0ms

sample1.6s

Algorithm

intervals

Results

841.0ms	8785×	body	80	valid
273.0ms	2992×	body	80	nan

Details

sample55.0ms

simplify4.0ms

prune15.0ms

localize27.0ms

rewrite25.0ms

series73.0ms

simplify41.0ms

prune181.0ms

localize22.0ms

rewrite22.0ms

series59.0ms

simplify33.0ms

prune151.0ms

localize32.0ms

rewrite19.0ms

series65.0ms

simplify38.0ms

prune263.0ms

localize30.0ms

rewrite33.0ms

series51.0ms

simplify38.0ms

prune171.0ms

regimes221.0ms

bsearch71.0ms

simplify1.0ms

end0.0ms

sample1.6s

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