Details

sample46.0ms

Algorithm

intervals

Results

9.0ms	194×	body	80	valid
9.0ms	33×	body	2560	valid
5.0ms	23×	body	1280	valid
4.0ms	96×	body	80	nan
3.0ms	18×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
0.0ms	3×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	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: 35.2b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.9b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite29.0ms

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:

12.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(- (* b b) (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series290.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ (+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
76.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
43.0ms	(- (* b b) (* (* 3.0 a) c))
68.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	400	780
1	1529	686
2	5002	675

prune204.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	10	83

Merged error: 7.1b

Counts

83 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.2b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
9.6b	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
13.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series436.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- (* b b) (* (* 3.0 a) c))
145.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
177.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
66.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	635	2579
1	3125	2333
2	5001	2320

prune365.0ms

Filtered

160 candidates to 106 candidates (66.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	157	3	160
Fresh	1	7	8
Picked	1	0	1
Done	1	0	1
Total	160	10	170

Merged error: 7.0b

Counts

170 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
3.2b	(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
9.4b	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-exp-log`
54×	`add-cbrt-cube`
40×	`div-exp`
30×	`prod-exp`
22×	`cbrt-undiv`
16×	`add-sqr-sqrt` `cbrt-unprod`
15×	`*-un-lft-identity`
8×	`times-frac` `1-exp` `associate-/l*`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `sqrt-prod`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--` `associate-/l/`
2×	`distribute-rgt-neg-in` `frac-2neg` `sqrt-div` `clear-num` `associate-/r*` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-*r/`

Counts

4 → 101

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
19.0ms	(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
13.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series344.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* b b) (* (* 3.0 a) c))
123.0ms	(/ (* 1 (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
97.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
81.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify88.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (75.0ms)

Iter	Nodes	Cost
0	744	1553
1	3960	1209
2	5002	1197

prune206.0ms

Filtered

113 candidates to 63 candidates (55.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	113	10	123

Merged error: 7.0b

Counts

123 → 10

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
2.9b	(/ (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
9.4b	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
25.3b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

337×	`times-frac`
175×	`add-sqr-sqrt`
174×	`*-un-lft-identity`
118×	`add-cube-cbrt`
45×	`associate-/l*`
28×	`distribute-lft-out--` `difference-of-squares`
23×	`add-exp-log` `add-cbrt-cube`
18×	`div-inv`
17×	`sqrt-prod`
14×	`distribute-rgt-neg-in`
11×	`cbrt-undiv` `div-exp`
6×	`add-log-exp`
5×	`pow1`
4×	`associate-/r*` `associate-/r/`
3×	`flip3--` `flip--` `associate-/l/`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `cbrt-unprod`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-sub`

Counts

4 → 233

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
21.0ms	(/ (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
13.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* b b) (* (* 3.0 a) c))
120.0ms	(/ (/ 3.0 (/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))) a)
98.0ms	(/ (- (- b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify64.0ms

Algorithm

egg-herbie

Counts

245 → 245

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1138	4174
1	5001	3940

prune599.0ms

Filtered

245 candidates to 175 candidates (71.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	243	2	245
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	243	12	255

Merged error: 7.0b

Counts

255 → 12

regimes385.0ms

Accuracy

83.2% (4.5b remaining)

Error of 10.0b against oracle of 5.5b and baseline of 32.5b

bsearch108.0ms

Steps

Iters	Range		Point
6	3.6571079890251755e-55	4.166047552770363e-54	1.9353511252618917e-54
9	-2.075239967640102e+144	-1.1758805254835388e+137	-8.06152635231149e+142

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	18
1	39	18

end0.0ms

sample1.4s

Algorithm

intervals

Results

309.0ms	1094×	body	2560	valid
284.0ms	5847×	body	80	valid
205.0ms	871×	body	1280	valid
135.0ms	2881×	body	80	nan
83.0ms	454×	body	640	valid
42.0ms	110×	body	5120	valid
32.0ms	235×	body	320	valid
10.0ms	115×	body	160	valid