Details

sample82.0ms

Algorithm

intervals

Results

16.0ms	156×	body	160	valid
16.0ms	574×	pre	80	true
16.0ms	318×	body	80	nan
6.0ms	38×	body	320	valid
3.0ms	62×	body	80	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: 43.0b

Counts

2 → 1

localize15.0ms

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))
0.2b	(- (* b b) (* (* 4.0 a) c))
38.1b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite27.0ms

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)))
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))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
8.0ms	(- (* 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 (35.0ms)

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

prune125.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	4	83

Merged error: 0.2b

Counts

83 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

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))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(/ (/ (+ 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)))))

series125.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
43.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
59.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify115.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 2 (90.0ms)

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

prune309.0ms

Filtered

106 candidates to 163 candidates (-53.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	155	8	163
Fresh	1	1	2
Picked	1	0	1
Done	1	0	1
Total	158	9	167

Merged error: 0b

Counts

167 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 117

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
12.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

series126.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(- (* b b) (* (* 4.0 a) c))
55.0ms	(/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
45.0ms	(/ (/ (* 4.0 (* a c)) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))

simplify85.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	647	1861
1	3491	1493
2	5001	1484

prune193.0ms

Filtered

79 candidates to 129 candidates (-63.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	129	9	138

Merged error: 0b

Counts

138 → 9

localize28.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- (pow (neg b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c))
0.4b	(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
0.4b	(* (/ 4.0 (/ (- (pow (neg b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c))) (+ (* (neg b) (neg b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
38.1b	(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

272×	`times-frac`
255×	`add-sqr-sqrt`
150×	`*-un-lft-identity`
128×	`associate-l`
120×	`difference-of-squares`
116×	`unpow-prod-down` `cube-prod`
60×	`add-cube-cbrt`
51×	`sqr-pow`
46×	`sqrt-prod`
45×	`distribute-lft-out--`
42×	`sqrt-div`
37×	`associate-/l*`
24×	`add-exp-log` `add-cbrt-cube`
22×	`flip3--` `associate-*r/` `flip--`
20×	`distribute-rgt-neg-in`
16×	`frac-add`
10×	`frac-times`
8×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`prod-exp` `cbrt-unprod` `add-log-exp`
5×	`difference-cubes` `associate-*l/` `div-inv`
3×	`pow-unpow` `pow-pow` `flip3-+` `associate-r` `flip-+`
2×	`distribute-lft-neg-out` `cube-div` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `distribute-rgt-in` `cube-mult` `pow-to-exp` `distribute-rgt-out` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `unpow3` `div-sub` `unsub-neg` `pow-prod-down` `pow-exp` `clear-num` `associate-/r` `sum-log` `associate-/r/` `-commutative` `sqrt-pow2` `rem-cube-cbrt`

Counts

4 → 313

Calls

4 calls:

35.0ms	(/ (- (pow (neg b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c))
5.0ms	(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
61.0ms	(* (/ 4.0 (/ (- (pow (neg b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c))) (+ (* (neg b) (neg b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
12.0ms	(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series177.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ (- (pow (neg b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c))
10.0ms	(pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)
91.0ms	(* (/ 4.0 (/ (- (pow (neg b) 3) (pow (sqrt (- (* b b) (* (* 4.0 a) c))) 3)) (* a c))) (+ (* (neg b) (neg b)) (+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))))
22.0ms	(+ (* (sqrt (- (* b b) (* (* 4.0 a) c))) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify107.0ms

Algorithm

egg-herbie

Counts

325 → 325

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1740	8256
1	5002	7821

prune979.0ms

Filtered

172 candidates to 325 candidates (-89.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	325	0	325
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	325	9	334

Merged error: 0b

Counts

334 → 9

regimes228.0ms

Accuracy

0% (0.4b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	12
1	22	12

end0.0ms

sample2.4s

Algorithm

intervals

Results

567.0ms	8425×	body	80	nan
507.0ms	4836×	body	160	valid
458.0ms	16425×	pre	80	true
208.0ms	1322×	body	320	valid
97.0ms	1842×	body	80	valid

Details

sample82.0ms

simplify10.0ms

prune4.0ms

localize15.0ms

rewrite27.0ms

series65.0ms

simplify44.0ms

prune125.0ms

localize16.0ms

rewrite47.0ms

series125.0ms

simplify115.0ms

prune309.0ms

localize16.0ms

rewrite42.0ms

series126.0ms

simplify85.0ms

prune193.0ms

localize28.0ms

rewrite135.0ms

series177.0ms

simplify107.0ms

prune979.0ms

regimes228.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

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