Details

sample95.0ms

Algorithm

intervals

Results

24.0ms	121×	body	320	valid
17.0ms	546×	pre	80	true
16.0ms	290×	body	80	nan
11.0ms	97×	body	160	valid
3.0ms	12×	body	640	valid
1.0ms	26×	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

prune2.0ms

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: 53.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.0b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.1b	(- (* b b) (* (* 4.0 a) c))
28.3b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite28.0ms

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)))
11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series314.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
109.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms	(- (* b b) (* (* 4.0 a) c))
81.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

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

prune177.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Merged error: 0.1b

Counts

83 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

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:

4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series452.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (* b b) (* (* 4.0 a) c))
77.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
143.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
184.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify112.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (90.0ms)

Iter	Nodes	Cost
0	642	2665
1	3142	2400
2	5002	2388

prune399.0ms

Filtered

163 candidates to 106 candidates (65.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	158	5	163
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	161	6	167

Merged error: 0b

Counts

167 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* b b) (* (* 4.0 a) c))
0.1b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
0.3b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
0.3b	(* (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt`
61×	`*-un-lft-identity`
51×	`add-exp-log`
46×	`times-frac`
29×	`add-cube-cbrt`
27×	`associate-l` `add-cbrt-cube`
20×	`prod-exp`
16×	`div-exp` `distribute-lft-out--` `difference-of-squares`
10×	`add-log-exp`
8×	`cbrt-undiv` `distribute-rgt-neg-in` `sqrt-prod` `cbrt-unprod`
7×	`associate-r` `associate-/r*`
6×	`pow1`
4×	`rec-exp` `flip3--` `1-exp` `associate-/r/` `flip--`
3×	`diff-log` `div-inv` `associate-/l*`
2×	`sub-neg` `associate-/l/` `unswap-sqr`
1×	`associate--l-` `neg-sub0` `frac-times` `frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `un-div-inv` `*-commutative` `flip-+`

Counts

4 → 146

Calls

4 calls:

4.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
25.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* b b) (* (* 4.0 a) c))
79.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
185.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
154.0ms	(* (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (/ 1 (* 2.0 a)))

simplify145.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (120.0ms)

Iter	Nodes	Cost
0	735	2387
1	3913	2043
2	5003	2036

prune365.0ms

Filtered

158 candidates to 100 candidates (63.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	158	6	164

Merged error: 0b

Counts

164 → 6

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))
0.2b	(/ (/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))) (* 2.0 a))
0.4b	(/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))
0.5b	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

120×	`pow1`
68×	`add-exp-log` `add-cbrt-cube`
67×	`pow-prod-down`
34×	`prod-exp` `cbrt-unprod`
28×	`times-frac`
25×	`flip3--` `flip--`
24×	`associate-/r/`
20×	`associate-/l*`
18×	`add-sqr-sqrt`
16×	`frac-times` `*-un-lft-identity`
12×	`cbrt-undiv` `add-cube-cbrt` `div-exp`
9×	`pow-sqr` `pow-prod-up`
8×	`associate-r/` `associate-l` `associate-l/`
6×	`difference-of-squares`
4×	`associate-r` `div-inv` `add-log-exp`
3×	`pow-plus` `div-sub` `associate-/l/`
2×	`distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `clear-num` `associate-/r` `-commutative` `distribute-lft-out--`
1×	`pow2` `distribute-rgt-neg-in` `sub0-neg` `swap-sqr` `sqrt-prod` `distribute-rgt-neg-out` `unswap-sqr`

Counts

4 → 186

Calls

4 calls:

13.0ms	(* (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))
19.0ms	(/ (/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))) (* 2.0 a))
21.0ms	(/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))
12.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

series507.0ms

Counts

4 → 12

Calls

4 calls:

127.0ms	(* (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))
151.0ms	(/ (/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c))))) (* 2.0 a))
188.0ms	(/ (- (* 0 0) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (* (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (- 0 (* 4.0 (* a c)))))
42.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

198 → 198

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	923	3244
1	5001	2577

prune455.0ms

Filtered

198 candidates to 116 candidates (58.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	198	0	198
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	198	6	204

Merged error: 0b

Counts

204 → 6

regimes93.0ms

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	29	14
1	31	14
2	31	14

end0.0ms

sample2.1s

Algorithm

intervals

Results

485.0ms	3637×	body	320	valid
434.0ms	16253×	pre	80	true
380.0ms	8253×	body	80	nan
269.0ms	2910×	body	160	valid
90.0ms	512×	body	640	valid
44.0ms	941×	body	80	valid

Details

sample95.0ms

simplify11.0ms

prune2.0ms

localize11.0ms

rewrite28.0ms

series314.0ms

simplify47.0ms

prune177.0ms

localize15.0ms

rewrite46.0ms

series452.0ms

simplify112.0ms

prune399.0ms

localize17.0ms

rewrite55.0ms

series464.0ms

simplify145.0ms

prune365.0ms

localize20.0ms

rewrite73.0ms

series507.0ms

simplify55.0ms

prune455.0ms

regimes93.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.1s

Profiling