Details

sample29.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
7.0ms	239×	body	80	nan

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	7
1	44	7
2	63	7
3	70	7
4	71	7
5	71	7

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 18.6b

localize18.0ms

Local error

Found 3 expressions with local error:

1.0b	(+ (* x y) (* x z))
1.4b	(+ (+ (* x y) (* x z)) (* y z))
17.5b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `fma-def` `*-un-lft-identity`
4×	`pow1` `sum-log`
3×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-prod` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `sqrt-div` `distribute-lft-out`
1×	`rem-sqrt-square` `associate-+l+` `sqrt-pow1` `pow1/2`

Counts

3 → 51

Calls

3 calls:

4.0ms	(+ (* x y) (* x z))
7.0ms	(+ (+ (* x y) (* x z)) (* y z))
6.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series194.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(+ (* x y) (* x z))
24.0ms	(+ (+ (* x y) (* x z)) (* y z))
127.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify146.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (140.0ms)

Iter	Nodes	Cost
0	270	383
1	1009	344
2	4339	335
3	5001	334

prune201.0ms

Filtered

60 candidates to 48 candidates (80.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.5b

localize9.0ms

Local error

Found 2 expressions with local error:

1.3b	(fma x (+ y z) (* y z))
17.5b	(sqrt (fma x (+ y z) (* y z)))

rewrite3.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-sqr-sqrt`
3×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
2×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-udef`

Counts

2 → 25

Calls

2 calls:

1.0ms	(fma x (+ y z) (* y z))
2.0ms	(sqrt (fma x (+ y z) (* y z)))

series152.0ms

Counts

2 → 6

Calls

2 calls:

24.0ms	(fma x (+ y z) (* y z))
128.0ms	(sqrt (fma x (+ y z) (* y z)))

simplify110.0ms

Algorithm

egg-herbie

Counts

31 → 31

Iterations

Useful iterations: 3 (36.0ms)

Iter	Nodes	Cost
0	106	164
1	261	147
2	833	144
3	4087	141
4	5001	141

prune111.0ms

Filtered

31 candidates to 26 candidates (83.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.5b

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(+ (+ (* x y) (* x z)) (* y z))
1.4b	(+ (+ (* x y) (* x z)) (* y z))
17.5b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))
17.5b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-log-exp`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `fma-def` `*-un-lft-identity`
6×	`pow1` `sum-log` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`+-commutative` `rem-sqrt-square` `associate-+l+` `sqrt-pow1` `pow1/2` `distribute-lft-out`

Counts

4 → 72

Calls

4 calls:

7.0ms	(+ (+ (* x y) (* x z)) (* y z))
12.0ms	(+ (+ (* x y) (* x z)) (* y z))
6.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))
6.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series310.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (+ (* x y) (* x z)) (* y z))
23.0ms	(+ (+ (* x y) (* x z)) (* y z))
127.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))
130.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify115.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (107.0ms)

Iter	Nodes	Cost
0	200	618
1	734	550
2	3300	534
3	5001	532

prune351.0ms

Filtered

84 candidates to 68 candidates (81.0%)

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 18.5b

localize21.0ms

Local error

Found 4 expressions with local error:

14.8b	(cbrt (+ (* x y) (* x z)))
14.8b	(cbrt (+ (* x y) (* x z)))
17.5b	(sqrt (fma (* (cbrt (+ (* x y) (* x z))) (cbrt (+ (* x y) (* x z)))) (cbrt (+ (* x y) (* x z))) (* y z)))
17.5b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `cbrt-div` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3` `sqrt-div` `distribute-lft-out`

Counts

4 → 64

Calls

4 calls:

4.0ms	(cbrt (+ (* x y) (* x z)))
4.0ms	(cbrt (+ (* x y) (* x z)))
2.0ms	(sqrt (fma (* (cbrt (+ (* x y) (* x z))) (cbrt (+ (* x y) (* x z)))) (cbrt (+ (* x y) (* x z))) (* y z)))
6.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series905.0ms

Counts

4 → 12

Calls

4 calls:

150.0ms	(cbrt (+ (* x y) (* x z)))
153.0ms	(cbrt (+ (* x y) (* x z)))
470.0ms	(sqrt (fma (* (cbrt (+ (* x y) (* x z))) (cbrt (+ (* x y) (* x z)))) (cbrt (+ (* x y) (* x z))) (* y z)))
132.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify69.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	480	880
1	1595	822
2	5002	640

prune445.0ms

Filtered

76 candidates to 71 candidates (93.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 18.5b

regimes231.0ms

Accuracy

0% (0.1b remaining)

Error of 19.9b against oracle of 19.8b and baseline of 19.9b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	12	5

end0.0ms

sample799.0ms

Algorithm

intervals

Results

257.0ms	8000×	body	80	valid
237.0ms	7832×	body	80	nan