Details

sample71.0ms

Algorithm

intervals

Results

19.0ms	165×	body	160	valid
14.0ms	520×	pre	80	true
12.0ms	264×	body	80	nan
5.0ms	38×	body	320	valid
2.0ms	53×	body	80	valid

simplify11.0ms

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

prune3.0ms

Filtered

1 candidates to 0 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: 44.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
40.8b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite32.0ms

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:

4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
6.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series313.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
46.0ms	(- (* b b) (* (* 4.0 a) c))
115.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	405	779
1	1563	685
2	5002	674

prune195.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	6	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	6	83

Merged error: 0.2b

Counts

83 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.2b	(- (* b b) (* (* 4.0 a) c))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
82×	`add-sqr-sqrt` `*-un-lft-identity`
38×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
11×	`distribute-rgt-neg-in` `sqrt-prod`
10×	`add-log-exp`
8×	`associate-/r*`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`flip3--` `flip--`
4×	`pow1` `div-inv`
3×	`diff-log` `associate-/l/`
2×	`sub-neg` `frac-2neg` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `flip3-+` `neg-log` `flip-+`

Counts

4 → 151

Calls

4 calls:

9.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
21.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series467.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
189.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
154.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify114.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	642	2664
1	3175	2400
2	5002	2388

prune417.0ms

Filtered

163 candidates to 106 candidates (65.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	154	9	163
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	159	10	169

Merged error: 0b

Counts

169 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
0.4b	(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
0.5b	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

130×	`add-sqr-sqrt` `times-frac`
118×	`pow1`
92×	`*-un-lft-identity`
66×	`pow-prod-down`
56×	`add-exp-log` `add-cbrt-cube`
52×	`add-cube-cbrt`
42×	`difference-of-squares`
39×	`associate-/l*`
29×	`prod-exp` `cbrt-unprod`
20×	`sqrt-prod` `distribute-lft-out--`
12×	`associate-/r*`
10×	`distribute-rgt-neg-in`
9×	`pow-sqr` `pow-prod-up`
8×	`cbrt-undiv` `div-exp` `associate-/r/`
5×	`div-inv` `associate-/l/`
4×	`unpow-prod-down` `flip3--` `flip--` `add-log-exp` `sqr-pow`
3×	`frac-2neg` `pow-plus` `clear-num`
2×	`flip3-+` `flip-+`
1×	`pow2` `div-sub` `swap-sqr` `associate-r` `associate-l` `*-commutative`

Counts

4 → 235

Calls

4 calls:

26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
34.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
11.0ms	(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
11.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series552.0ms

Counts

4 → 12

Calls

4 calls:

229.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
189.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
91.0ms	(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
42.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify75.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	993	5277
1	5001	4702

prune652.0ms

Filtered

247 candidates to 145 candidates (58.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	246	1	247
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	248	9	257

Merged error: 0b

Counts

257 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (/ 1 (+ (* b b) (* (* 4.0 a) c)))))))
0.3b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (/ 1 (+ (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
0.4b	(* (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (/ 1 (+ (* b b) (* (* 4.0 a) c))))
0.5b	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

120×	`pow1`
89×	`times-frac`
84×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
67×	`pow-prod-down`
63×	`add-exp-log`
59×	`add-cbrt-cube`
43×	`add-cube-cbrt`
33×	`prod-exp`
31×	`cbrt-unprod`
27×	`associate-/l*`
20×	`distribute-lft-out--`
16×	`associate-r`
13×	`difference-of-squares`
10×	`distribute-rgt-neg-in`
9×	`div-exp` `pow-sqr` `pow-prod-up`
8×	`cbrt-undiv` `associate-/r/`
7×	`associate-l` `associate-/r*`
5×	`flip3--` `flip--` `div-inv`
4×	`add-log-exp`
3×	`pow-plus` `associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `flip3-+` `associate-l/` `clear-num` `-commutative` `flip-+`
1×	`pow2` `unpow-prod-down` `rec-exp` `1-exp` `associate-*r/` `swap-sqr` `un-div-inv` `sqr-pow`

Counts

4 → 216

Calls

4 calls:

9.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (/ 1 (+ (* b b) (* (* 4.0 a) c)))))))
14.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (/ 1 (+ (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
14.0ms	(* (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (/ 1 (+ (* b b) (* (* 4.0 a) c))))
11.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series551.0ms

Counts

4 → 12

Calls

4 calls:

235.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (/ 1 (+ (* b b) (* (* 4.0 a) c)))))))
188.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (* (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (/ 1 (+ (* b b) (* (* 4.0 a) c))))))) (* 2.0 a))
92.0ms	(* (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (/ 1 (+ (* b b) (* (* 4.0 a) c))))
36.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1012	4607
1	5001	4042

prune567.0ms

Filtered

228 candidates to 129 candidates (56.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	228	0	228
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	228	9	237

Merged error: 0b

Counts

237 → 9

regimes127.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	22
1	38	22
2	38	22

end0.0ms

sample1.9s

Algorithm

intervals

Results

453.0ms	4940×	body	160	valid
439.0ms	15889×	pre	80	true
368.0ms	7889×	body	80	nan
184.0ms	1331×	body	320	valid
88.0ms	1729×	body	80	valid

Details

sample71.0ms

simplify11.0ms

prune3.0ms

localize11.0ms

rewrite32.0ms

series313.0ms

simplify46.0ms

prune195.0ms

localize15.0ms

rewrite53.0ms

series467.0ms

simplify114.0ms

prune417.0ms

localize21.0ms

rewrite94.0ms

series552.0ms

simplify75.0ms

prune652.0ms

localize22.0ms

rewrite63.0ms

series551.0ms

simplify66.0ms

prune567.0ms

regimes127.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.9s

Profiling