Details

analyze457.0ms

Algorithm: search

sample47.0ms

Algorithm

intervals

Results

14.0ms	47×	body	2560	valid
10.0ms	157×	body	80	valid
5.0ms	22×	body	1280	valid
2.0ms	11×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	18×	body	80	nan
1.0ms	14×	body	80	invalid
0.0ms	4×	body	160	valid

simplify10.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune4.0ms

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: 36.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(- (* b b) (* 4.0 (* a c)))
1.4b	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
24.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

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

series69.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
9.0ms	(- (* b b) (* 4.0 (* a c)))
18.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	394	773
1	1501	683
2	5002	673

prune163.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 7.1b

Counts

83 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* b b) (* 4.0 (* a c)))
3.2b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
10.7b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
24.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
21.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
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)))
46.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))) (* 2.0 a))
64.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
15.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify101.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	626	2580
1	2991	2341
2	5003	2328

prune294.0ms

Filtered

106 candidates to 160 candidates (-50.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	155	5	160
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	157	10	167

Merged error: 7.0b

Counts

167 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b	(- (* b b) (* 4.0 (* a c)))
15.2b	(/ (* 2.0 a) (* 4.0 (* a c)))
24.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

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

series42.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify55.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	410	626
1	2230	543
2	5001	535

prune129.0ms

Filtered

55 candidates to 82 candidates (-49.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Merged error: 7.0b

Counts

92 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
0.4b	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
0.4b	(- (* b b) (* 4.0 (* a c)))
24.1b	(sqrt (- (* b b) (* 4.0 (* a c))))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
13×	`add-cube-cbrt` `associate-l`
10×	`times-frac` `add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
7×	`pow1` `associate-r`
5×	`flip3--` `sqrt-prod` `flip--`
4×	`sub-neg` `distribute-lft-out--` `difference-of-squares`
3×	`diff-log`
2×	`distribute-rgt-in` `frac-times` `distribute-rgt-neg-in` `distribute-lft-in` `sqrt-div` `associate-*r/` `prod-exp` `cbrt-unprod` `unswap-sqr`
1×	`cbrt-undiv` `associate--l-` `neg-sub0` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `pow-prod-down` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 89

Calls

4 calls:

14.0ms	(* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
8.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))))
17.0ms	(- (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
9.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	444	994
1	1831	905
2	5001	895

prune140.0ms

Filtered

74 candidates to 101 candidates (-36.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	99	2	101
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	99	10	109

Merged error: 7.0b

Counts

109 → 10

regimes285.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.6b against oracle of 5.4b and baseline of 29.6b

bsearch725.0ms

Steps

Iters	Range	Point
7	6.456597936901001e+108	1.4212766687140906e+111	6.334342461162187e+110
8	-2.260557668595697e-279	-3.789249006808309e-282	-1.2557731009466896e-280
8	-7.400135821921412e+97	-2.0353633612918009e+93	-3.9716980978113024e+95

Iters

Range

Point

6.456597936901001e+108

1.4212766687140906e+111

6.334342461162187e+110

-2.260557668595697e-279

-3.789249006808309e-282

-1.2557731009466896e-280

-7.400135821921412e+97

-2.0353633612918009e+93

-3.9716980978113024e+95

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	26
1	46	26

end0.0ms

analyze453.0ms

Algorithm: search

sample1.3s

Algorithm

intervals

Results

347.0ms	1104×	body	2560	valid
279.0ms	5158×	body	80	valid
226.0ms	875×	body	1280	valid
86.0ms	434×	body	640	valid
43.0ms	109×	body	5120	valid
34.0ms	660×	body	80	nan
32.0ms	202×	body	320	valid
20.0ms	368×	body	80	invalid
12.0ms	118×	body	160	valid

Details

analyze457.0ms

sample47.0ms

simplify10.0ms

prune4.0ms

localize11.0ms

rewrite30.0ms

series69.0ms

simplify45.0ms

prune163.0ms

localize14.0ms

rewrite49.0ms

series134.0ms

simplify101.0ms

prune294.0ms

localize16.0ms

rewrite25.0ms

series42.0ms

simplify55.0ms

prune129.0ms

localize12.0ms

rewrite32.0ms

series75.0ms

simplify47.0ms

prune140.0ms

regimes285.0ms

bsearch725.0ms

simplify2.0ms

end0.0ms

analyze453.0ms

sample1.3s

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