Details

sample60.0ms

Algorithm

intervals

Results

14.0ms	260×	body	80	nan
12.0ms	164×	body	160	valid
10.0ms	516×	pre	80	true
5.0ms	44×	body	320	valid
2.0ms	48×	body	80	valid

simplify12.0ms

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: 45.0b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
0.2b	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.2b	(- (* b b) (* (* 4.0 a) c))
39.2b	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

139×	`add-sqr-sqrt`
116×	`*-un-lft-identity`
60×	`times-frac`
42×	`unswap-sqr`
36×	`add-cube-cbrt` `associate-l`
30×	`difference-of-squares`
28×	`distribute-lft-out`
24×	`sqrt-prod`
18×	`associate-r`
14×	`distribute-rgt-neg-in`
12×	`associate-/r` `-commutative` `distribute-lft-out--`
10×	`add-log-exp`
9×	`add-exp-log` `add-cbrt-cube`
6×	`swap-sqr`
5×	`pow1` `associate-/l*`
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` `cbrt-unprod` `div-inv`

Counts

4 → 178

Calls

4 calls:

22.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
42.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
22.0ms	(- (* b b) (* (* 4.0 a) c))
36.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

series312.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
108.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
49.0ms	(- (* b b) (* (* 4.0 a) c))
82.0ms	(+ (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))

simplify77.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	628	2253
1	2517	2157
2	5001	2140

prune501.0ms

Filtered

190 candidates to 109 candidates (57.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	184	6	190
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	6	191

Merged error: 0.2b

Counts

191 → 6

localize19.0ms

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	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
0.3b	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

1801×	`*-un-lft-identity`
1346×	`times-frac`
946×	`add-sqr-sqrt`
408×	`distribute-lft-out--`
400×	`distribute-lft-out`
385×	`add-cube-cbrt`
377×	`associate-l`
217×	`difference-of-squares`
168×	`associate-r`
101×	`distribute-rgt-neg-in` `sqrt-prod`
74×	`unswap-sqr`
69×	`associate-/l*`
59×	`*-commutative`
28×	`associate-/r/`
26×	`associate-/r*`
23×	`associate-/l/`
18×	`add-exp-log` `add-cbrt-cube`
16×	`flip3--` `flip--`
15×	`div-inv`
10×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `diff-log` `div-sub` `swap-sqr` `clear-num`
2×	`associate-+l-` `sub-neg` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+`
1×	`associate--l-` `neg-sub0` `neg-log`

Counts

4 → 896

Calls

4 calls:

37.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
21.0ms	(- (* b b) (* (* 4.0 a) c))
109.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
84.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

series416.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(- (* b b) (* (* 4.0 a) c))
125.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
170.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 4.0 a) c)))))

simplify234.0ms

Algorithm

egg-herbie

Counts

908 → 908

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1740	24064
1	5002	22948

prune1.3s

Filtered

908 candidates to 283 candidates (31.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	901	7	908
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	906	8	914

Merged error: 0.0b

Counts

914 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* (* 4.0 a) c))
0.1b	(- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c))))))
0.3b	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c))))))) (* 2.0 a))
0.3b	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c)))))))

rewrite347.0ms

Algorithm

rewrite-expression-head

Rules

1969×	`*-un-lft-identity`
1528×	`times-frac`
1271×	`add-sqr-sqrt`
456×	`distribute-lft-out`
432×	`associate-l`
430×	`distribute-lft-out--`
425×	`add-cube-cbrt`
303×	`difference-of-squares`
224×	`sqrt-prod`
195×	`associate-r`
171×	`unswap-sqr`
101×	`distribute-rgt-neg-in`
76×	`associate-/l*`
65×	`*-commutative`
28×	`associate-/r*` `associate-/r/`
24×	`associate-/l/`
18×	`add-exp-log` `add-cbrt-cube`
15×	`flip3--` `flip--` `div-inv`
10×	`pow1`
8×	`add-log-exp`
7×	`cbrt-undiv` `div-exp`
3×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `div-sub` `pow-prod-down` `clear-num`
2×	`associate-+l-` `flip3-+` `diff-log` `prod-exp` `cbrt-unprod` `flip-+`
1×	`associate--l-` `neg-sub0` `sub-neg` `pow1/2` `neg-log`

Counts

4 → 1000

Calls

4 calls:

8.0ms	(sqrt (* (* 4.0 a) c))
42.0ms	(- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c))))))
114.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c))))))) (* 2.0 a))
87.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c)))))))

series1.7s

Counts

4 → 12

Calls

4 calls:

123.0ms	(sqrt (* (* 4.0 a) c))
306.0ms	(- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c))))))
591.0ms	(/ (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c))))))) (* 2.0 a))
649.0ms	(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c)))))))

simplify315.0ms

Algorithm

egg-herbie

Counts

1012 → 1012

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	2028	35570
1	5001	34803

prune1.8s

Filtered

1012 candidates to 340 candidates (33.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	1008	4	1012
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	1012	8	1020

Merged error: 0b

Counts

1020 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (* (* 4.0 a) c))
0.1b	(/ 1 (- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c)))))))
0.1b	(- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c))))))
0.3b	(* (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (/ (/ 1 (- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c))))))) 2.0))

rewrite348.0ms

Algorithm

rewrite-expression-head

Rules

1298×	`*-un-lft-identity`
1029×	`add-sqr-sqrt`
891×	`associate-/l*`
750×	`frac-times`
605×	`times-frac`
442×	`add-cube-cbrt`
337×	`associate-/r*`
329×	`associate-/l/`
264×	`distribute-lft-out--`
234×	`difference-of-squares`
216×	`distribute-lft-out`
178×	`sqrt-prod`
148×	`associate-l`
100×	`associate-r`
93×	`unswap-sqr`
86×	`clear-num`
84×	`frac-2neg`
78×	`distribute-rgt-neg-in`
51×	`flip3-+` `flip-+`
50×	`associate-*r/`
43×	`add-exp-log`
40×	`associate-/r/`
27×	`add-cbrt-cube`
23×	`div-inv`
21×	`flip3--` `flip--`
19×	`div-exp`
15×	`associate-*l/`
13×	`pow1`
10×	`cbrt-undiv` `prod-exp`
8×	`add-log-exp`
6×	`un-div-inv` `cbrt-unprod`
4×	`pow-prod-down`
3×	`rem-sqrt-square` `rec-exp` `sqrt-pow1` `1-exp` `*-commutative`
2×	`diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `pow-flip` `pow1/2` `neg-log` `inv-pow`

Counts

4 → 1081

Calls

4 calls:

8.0ms	(sqrt (* (* 4.0 a) c))
43.0ms	(/ 1 (- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c)))))))
38.0ms	(- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c))))))
158.0ms	(* (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (/ (/ 1 (- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c))))))) 2.0))

series1.5s

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt (* (* 4.0 a) c))
487.0ms	(/ 1 (- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c)))))))
288.0ms	(- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c))))))
599.0ms	(* (/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) a) (/ (/ 1 (- (- b) (sqrt (* (+ (sqrt (* (* 4.0 a) c)) b) (- b (sqrt (* (* 4.0 a) c))))))) 2.0))

simplify347.0ms

Algorithm

egg-herbie

Counts

1093 → 1093

Iterations

Useful iterations: 1 (67.0ms)

Iter	Nodes	Cost
0	3608	33914
1	5001	32195

prune2.2s

Filtered

1093 candidates to 427 candidates (39.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	1090	3	1093
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	1094	7	1101

Merged error: 0b

Counts

1101 → 7

regimes135.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	22
1	35	22

end0.0ms

sample1.6s

Algorithm

intervals

Results

380.0ms	4911×	body	160	valid
313.0ms	8410×	body	80	nan
309.0ms	16410×	pre	80	true
153.0ms	1345×	body	320	valid
72.0ms	1744×	body	80	valid