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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.7b

localize10.0ms

Local error

Found 3 expressions with local error:

1.0b	(+ (* x y) (* x z))
2.0b	(+ (+ (* x y) (* x z)) (* y z))
19.6b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite20.0ms

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:

5.0ms	(+ (* x y) (* x z))
7.0ms	(+ (+ (* x y) (* x z)) (* y z))
7.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

series199.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(+ (* x y) (* x z))
30.0ms	(+ (+ (* x y) (* x z)) (* y z))
130.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify143.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (136.0ms)

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

prune203.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.6b

localize19.0ms

Local error

Found 4 expressions with local error:

16.2b	(cbrt (+ (* x y) (* x z)))
16.2b	(cbrt (+ (* x y) (* x z)))
16.2b	(cbrt (+ (* x y) (* x z)))
19.6b	(sqrt (fma (* (cbrt (+ (* x y) (* x z))) (cbrt (+ (* x y) (* x z)))) (cbrt (+ (* x y) (* x z))) (* y z)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 63

Calls

4 calls:

4.0ms	(cbrt (+ (* x y) (* x z)))
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)))

series868.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(cbrt (+ (* x y) (* x z)))
139.0ms	(cbrt (+ (* x y) (* x z)))
138.0ms	(cbrt (+ (* x y) (* x z)))
451.0ms	(sqrt (fma (* (cbrt (+ (* x y) (* x z))) (cbrt (+ (* x y) (* x z)))) (cbrt (+ (* x y) (* x z))) (* y z)))

simplify151.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	361	841
1	1141	788
2	4842	741
3	5001	741

prune375.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.6b

localize20.0ms

Local error

Found 4 expressions with local error:

1.5b	(fma (* (cbrt (+ (* x y) (* x z))) (cbrt (+ (* x y) (* x z)))) (* (cbrt x) (cbrt (+ y z))) (* y z))
16.2b	(cbrt (+ (* x y) (* x z)))
16.2b	(cbrt (+ (* x y) (* x z)))
19.6b	(sqrt (fma (* (cbrt (+ (* x y) (* x z))) (cbrt (+ (* x y) (* x z)))) (* (cbrt x) (cbrt (+ y z))) (* y z)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

1.0ms	(fma (* (cbrt (+ (* x y) (* x z))) (cbrt (+ (* x y) (* x z)))) (* (cbrt x) (cbrt (+ y z))) (* y z))
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) (cbrt (+ y z))) (* y z)))

series1.0s

Counts

4 → 12

Calls

4 calls:

239.0ms	(fma (* (cbrt (+ (* x y) (* x z))) (cbrt (+ (* x y) (* x z)))) (* (cbrt x) (cbrt (+ y z))) (* y z))
142.0ms	(cbrt (+ (* x y) (* x z)))
141.0ms	(cbrt (+ (* x y) (* x z)))
512.0ms	(sqrt (fma (* (cbrt (+ (* x y) (* x z))) (cbrt (+ (* x y) (* x z)))) (* (cbrt x) (cbrt (+ y z))) (* y z)))

simplify56.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	409	1003
1	1345	923
2	5002	888

prune401.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 20.5b

localize245.0ms

Local error

Found 4 expressions with local error:

2.0b	(+ (+ (* x y) (* x z)) (* y z))
2.0b	(+ (+ (* x y) (* x z)) (* y z))
19.6b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))
19.6b	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

rewrite30.0ms

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

series321.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(+ (+ (* x y) (* x z)) (* y z))
26.0ms	(+ (+ (* x y) (* x z)) (* y z))
131.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))
131.0ms	(sqrt (+ (+ (* x y) (* x z)) (* y z)))

simplify124.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 3 (116.0ms)

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

prune336.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 20.5b

regimes237.0ms

Accuracy

0% (0.2b remaining)

Error of 19.6b against oracle of 19.4b and baseline of 19.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	7
1	17	7

end0.0ms

sample820.0ms

Algorithm

intervals

Results

252.0ms	8000×	body	80	valid
249.0ms	8137×	body	80	nan