Details

sample19.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
3.0ms	115×	body	80	overflowed

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	5
1	7	5

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: 0.8b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (exp a) (exp b))
0.7b	(/ (exp a) (+ (exp a) (exp b)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
12×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
5×	`distribute-lft-out`
4×	`associate-/r*` `add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `fma-def` `associate-/l*`
2×	`pow1` `expm1-log1p-u` `flip3-+` `associate-/r/` `flip-+` `log1p-expm1-u`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 52

Calls

2 calls:

4.0ms	(+ (exp a) (exp b))
7.0ms	(/ (exp a) (+ (exp a) (exp b)))

series51.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(+ (exp a) (exp b))
32.0ms	(/ (exp a) (+ (exp a) (exp b)))

simplify90.0ms

Algorithm

egg-herbie

Counts

58 → 58

Iterations

Useful iterations: 3 (32.0ms)

Iter	Nodes	Cost
0	171	405
1	513	376
2	1324	374
3	4489	373
4	5001	373

prune107.0ms

Filtered

58 candidates to 44 candidates (75.9%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	54	4	58
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	4	59

Merged error: 0.5b

Counts

59 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp a) (exp b))
0.0b	(exp (- a (log (+ (exp a) (exp b)))))
1.6b	(- a (log (+ (exp a) (exp b))))
4.3b	(log (+ (exp a) (exp b)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
24×	`prod-diff`
23×	`add-cube-cbrt`
16×	`exp-sum`
13×	`pow1`
9×	`log-pow` `add-log-exp`
8×	`log-prod`
6×	`log-div` `exp-prod`
5×	`add-exp-log`
4×	`expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u` `associate--r+` `distribute-lft-out--` `associate--r-`
3×	`fma-def` `fma-neg` `distribute-lft-out`
2×	`sub-neg` `diff-log` `rem-exp-log` `difference-of-squares`
1×	`+-commutative` `flip3--` `exp-diff` `rem-log-exp` `sum-log` `flip--`

Counts

4 → 106

Calls

4 calls:

7.0ms	(+ (exp a) (exp b))
6.0ms	(exp (- a (log (+ (exp a) (exp b)))))
8.0ms	(- a (log (+ (exp a) (exp b))))
4.0ms	(log (+ (exp a) (exp b)))

series138.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (exp a) (exp b))
53.0ms	(exp (- a (log (+ (exp a) (exp b)))))
33.0ms	(- a (log (+ (exp a) (exp b))))
33.0ms	(log (+ (exp a) (exp b)))

simplify84.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	308	1330
1	791	946
2	2960	789
3	5001	691

prune191.0ms

Filtered

118 candidates to 71 candidates (60.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Merged error: 0.5b

Counts

122 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (exp a))
0.0b	(sqrt (exp a))
0.0b	(fma (sqrt (exp a)) (sqrt (exp a)) (exp b))
0.7b	(/ (exp a) (fma (sqrt (exp a)) (sqrt (exp a)) (exp b)))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
16×	`add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
8×	`sqrt-pow1`
6×	`pow1` `exp-prod` `sqrt-prod` `add-cbrt-cube`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`rem-sqrt-square` `pow1/2`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

4 → 75

Calls

4 calls:

2.0ms	(sqrt (exp a))
2.0ms	(sqrt (exp a))
1.0ms	(fma (sqrt (exp a)) (sqrt (exp a)) (exp b))
4.0ms	(/ (exp a) (fma (sqrt (exp a)) (sqrt (exp a)) (exp b)))

series117.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt (exp a))
14.0ms	(sqrt (exp a))
37.0ms	(fma (sqrt (exp a)) (sqrt (exp a)) (exp b))
54.0ms	(/ (exp a) (fma (sqrt (exp a)) (sqrt (exp a)) (exp b)))

simplify66.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (60.0ms)

Iter	Nodes	Cost
0	155	617
1	469	536
2	2140	526
3	5001	522

prune168.0ms

Filtered

87 candidates to 69 candidates (79.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	87	4	91

Merged error: 0.5b

Counts

91 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp a) (exp b))
0.0b	(cbrt (pow (+ (exp a) (exp b)) 3))
0.1b	(pow (+ (exp a) (exp b)) 3)
0.7b	(/ (exp a) (cbrt (pow (+ (exp a) (exp b)) 3)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`cbrt-prod`
51×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt`
24×	`unpow-prod-down` `cube-prod`
17×	`associate-/r*`
13×	`distribute-lft-out`
6×	`add-exp-log` `cube-div` `cube-mult` `unpow3` `add-cbrt-cube` `add-log-exp` `sqr-pow`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-div` `flip3-+` `flip-+` `log1p-expm1-u`
3×	`pow-unpow` `fma-def` `associate-/l*`
2×	`associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `pow-pow` `frac-2neg` `pow1/3` `div-exp` `pow-exp` `clear-num` `sum-log` `rem-cbrt-cube` `div-inv` `rem-cube-cbrt`

Counts

4 → 160

Calls

4 calls:

4.0ms	(+ (exp a) (exp b))
6.0ms	(cbrt (pow (+ (exp a) (exp b)) 3))
5.0ms	(pow (+ (exp a) (exp b)) 3)
11.0ms	(/ (exp a) (cbrt (pow (+ (exp a) (exp b)) 3)))

series116.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(+ (exp a) (exp b))
22.0ms	(cbrt (pow (+ (exp a) (exp b)) 3))
36.0ms	(pow (+ (exp a) (exp b)) 3)
33.0ms	(/ (exp a) (cbrt (pow (+ (exp a) (exp b)) 3)))

simplify49.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	356	1491
1	1354	1394
2	5002	1365

prune244.0ms

Filtered

172 candidates to 89 candidates (51.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	172	0	172
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	172	4	176

Merged error: 0.5b

Counts

176 → 4

regimes82.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	6
1	9	6

end0.0ms

sample511.0ms

Algorithm

intervals

Results

221.0ms	8000×	body	80	valid
97.0ms	3516×	body	80	overflowed