Details

analyze269.0ms

Algorithm: search

sample42.0ms

Algorithm

intervals

Results

13.0ms	137×	body	160	valid
8.0ms	290×	pre	80	true
8.0ms	119×	body	80	valid
2.0ms	34×	body	80	nan

simplify9.0ms

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: 29.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
29.0b	(+ (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:

3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
12.0ms	(/ (+ (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))))

series67.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
28.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
9.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5001	673

prune146.0ms

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: 0.3b

Counts

83 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (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))))) (* 2.0 a))
0.3b	(- (* b b) (* (* 4.0 a) c))
0.4b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite48.0ms

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:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
3.0ms	(- (* b b) (* (* 4.0 a) c))
13.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series131.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* 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))
9.0ms	(- (* b b) (* (* 4.0 a) c))
61.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify114.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	643	2666
1	3210	2408
2	5001	2396

prune341.0ms

Filtered

106 candidates to 163 candidates (-53.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	150	13	163
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	157	13	170

Merged error: 0.0b

Counts

170 → 13

localize23.0ms

Local error

Found 4 expressions with local error:

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

34.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg 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)))
26.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (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)))

series165.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))) (* 2.0 a))
21.0ms	(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
76.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c))))))
8.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify70.0ms

Algorithm

egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	991	5279
1	5001	4708

prune633.0ms

Filtered

144 candidates to 247 candidates (-71.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	244	3	247
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	250	10	260

Merged error: 0b

Counts

260 → 10

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))
0.3b	(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
0.4b	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (/ (- (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)))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

118×	`pow1`
66×	`pow-prod-down`
63×	`add-exp-log` `add-cbrt-cube`
36×	`prod-exp` `cbrt-unprod`
30×	`add-sqr-sqrt`
20×	`times-frac`
19×	`*-un-lft-identity`
15×	`add-cube-cbrt` `difference-of-squares`
9×	`pow-sqr` `pow-prod-up`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp` `associate-/l*`
4×	`unpow-prod-down` `associate-/r*` `associate-/r/` `sqr-pow`
3×	`flip3--` `pow-plus` `flip--`
2×	`frac-2neg` `diff-log` `associate-*r/` `clear-num` `sqrt-prod` `div-inv` `associate-/l/` `distribute-lft-out--`
1×	`associate--l-` `pow2` `neg-sub0` `sub-neg` `distribute-rgt-neg-in` `flip3-+` `div-sub` `swap-sqr` `associate-r` `associate-l` `neg-log` `*-commutative` `flip-+`

Counts

4 → 150

Calls

4 calls:

22.0ms	(- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))
11.0ms	(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
30.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (/ (- (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)))

series121.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))
22.0ms	(/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))
62.0ms	(/ (* 4.0 (* a c)) (* a (- (neg b) (sqrt (/ (- (pow b 4) (* (* 4.0 (* a c)) (* 4.0 (* a c)))) (+ (* b b) (* (* 4.0 a) c)))))))
8.0ms	(* (* 4.0 (* a c)) (* 4.0 (* a c)))

simplify135.0ms

Algorithm

egg-herbie

Counts

162 → 162

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	783	2455
1	4947	1919
2	5001	1919

prune257.0ms

Filtered

87 candidates to 162 candidates (-86.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	162	10	172

Merged error: 0b

Counts

172 → 10

regimes260.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	21
1	33	21

end0.0ms

analyze265.0ms

Algorithm: search

sample1.3s

Algorithm

intervals

Results

435.0ms	4470×	body	160	valid
401.0ms	8829×	pre	80	true
180.0ms	3530×	body	80	valid
43.0ms	829×	body	80	nan

Details

analyze269.0ms

sample42.0ms

simplify9.0ms

prune4.0ms

localize11.0ms

rewrite28.0ms

series67.0ms

simplify44.0ms

prune146.0ms

localize16.0ms

rewrite48.0ms

series131.0ms

simplify114.0ms

prune341.0ms

localize23.0ms

rewrite94.0ms

series165.0ms

simplify70.0ms

prune633.0ms

localize21.0ms

rewrite81.0ms

series121.0ms

simplify135.0ms

prune257.0ms

regimes260.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze265.0ms

sample1.3s

Profiling