Details

analyze476.0ms

Algorithm: search

sample50.0ms

Algorithm

intervals

Results

12.0ms	37×	body	2560	valid
9.0ms	32×	body	1280	valid
9.0ms	151×	body	80	valid
4.0ms	18×	body	640	valid
2.0ms	15×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	18×	body	80	nan
1.0ms	14×	body	80	invalid

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

prune6.0ms

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: 32.8b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.6b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.6b	(- (* b b) (* (* 3.0 a) c))
18.9b	(sqrt (- (* b b) (* (* 3.0 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:

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

series70.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
16.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	391	774
1	1518	684
2	5001	674

prune169.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	70	12	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	12	83

Merged error: 3.6b

Counts

83 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.1b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
7.4b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
18.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
18.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series135.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
44.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
61.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	644	2693
1	3143	2447
2	5001	2434

prune297.0ms

Filtered

111 candidates to 166 candidates (-49.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	161	5	166
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	167	11	178

Merged error: 3.5b

Counts

178 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.1b	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
7.4b	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
18.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log` `add-cbrt-cube`
26×	`times-frac`
22×	`add-sqr-sqrt`
21×	`*-un-lft-identity`
19×	`cbrt-undiv` `div-exp`
18×	`prod-exp` `cbrt-unprod`
17×	`add-cube-cbrt`
10×	`associate-*r/` `associate-/r/`
8×	`associate-/l*` `add-log-exp`
7×	`flip3--` `flip--`
6×	`div-inv`
5×	`pow1`
4×	`associate-/r*` `sqrt-prod`
2×	`frac-2neg` `sqrt-div` `diff-log` `clear-num` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `neg-log` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
18.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
14.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series138.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
46.0ms	(/ (/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))) a)
60.0ms	(/ (* 3.0 (* a c)) (* 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify127.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	697	2051
1	4478	1590
2	5002	1549

prune194.0ms

Filtered

86 candidates to 128 candidates (-48.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	128	11	139

Merged error: 3.5b

Counts

139 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
0.7b	(/ 3.0 (/ 3.0 (* a c)))
12.8b	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
18.9b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

221×	`times-frac`
165×	`add-sqr-sqrt`
138×	`*-un-lft-identity`
103×	`add-exp-log`
96×	`add-cube-cbrt`
85×	`associate-r`
67×	`add-cbrt-cube`
54×	`div-exp`
32×	`cbrt-undiv`
26×	`associate-l` `prod-exp`
20×	`distribute-lft-out--` `difference-of-squares`
16×	`cbrt-unprod`
13×	`sqrt-prod` `div-inv`
10×	`distribute-rgt-neg-in`
8×	`associate-/r/` `add-log-exp` `unswap-sqr`
7×	`pow1` `associate-/r*`
5×	`flip3--` `flip--`
4×	`rec-exp` `1-exp`
3×	`associate-/l*`
2×	`sqrt-div` `diff-log`
1×	`associate--l-` `neg-sub0` `frac-times` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `associate-r/` `pow-prod-down` `neg-log` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 244

Calls

4 calls:

11.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
6.0ms	(/ 3.0 (/ 3.0 (* a c)))
58.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series83.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
7.0ms	(/ 3.0 (/ 3.0 (* a c)))
45.0ms	(* (/ 3.0 (/ 3.0 (* a c))) (/ (/ 1 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) a))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 1 (30.0ms)

Iter	Nodes	Cost
0	1389	3350
1	5002	2680

prune386.0ms

Filtered

163 candidates to 256 candidates (-57.1%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	256	11	267

Merged error: 3.5b

Counts

267 → 11

regimes476.0ms

Accuracy

83.1% (4.6b remaining)

Error of 10.1b against oracle of 5.5b and baseline of 32.7b

bsearch508.0ms

Steps

Iters	Range		Point
6	1.87420319089864e-40	1.0648719733408399e-39	5.8608602365427546e-40
10	-4.8908751238470227e+154	-7.181262992992344e+144	-1.0259403690672002e+146

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	16
1	34	16

end0.0ms

analyze472.0ms

Algorithm: search

sample1.3s

Algorithm

intervals

Results

362.0ms	1099×	body	2560	valid
291.0ms	5125×	body	80	valid
236.0ms	887×	body	1280	valid
95.0ms	457×	body	640	valid
46.0ms	110×	body	5120	valid
36.0ms	218×	body	320	valid
35.0ms	658×	body	80	nan
21.0ms	370×	body	80	invalid
11.0ms	104×	body	160	valid

Details

analyze476.0ms

sample50.0ms

simplify11.0ms

prune6.0ms

localize11.0ms

rewrite28.0ms

series70.0ms

simplify49.0ms

prune169.0ms

localize15.0ms

rewrite49.0ms

series135.0ms

simplify116.0ms

prune297.0ms

localize16.0ms

rewrite49.0ms

series138.0ms

simplify127.0ms

prune194.0ms

localize17.0ms

rewrite95.0ms

series83.0ms

simplify59.0ms

prune386.0ms

regimes476.0ms

bsearch508.0ms

simplify1.0ms

end0.0ms

analyze472.0ms

sample1.3s

Profiling