Details

sample20.0ms

Algorithm

intervals

Results

9.0ms

390×

body

valid

simplify276.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (6.0ms)

Iter	Nodes	Cost
0	16	6
1	33	4
2	56	4
3	76	3
4	88	3
5	131	3
6	236	3
7	328	3
8	343	3
9	443	3
10	797	3
11	3499	3
12	5001	3

prune6.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 0.1b

Counts

2 → 2

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (* x y) (* z z)) (* z z))
0.0b	(+ (* x y) (* z z))
0.1b	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp`
10×	`sum-log`
7×	`fma-def`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
3×	`pow1` `add-exp-log` `+-commutative` `expm1-log1p-u` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
2×	`associate-+l+`

Counts

3 → 51

Calls

3 calls:

6.0ms	(+ (+ (* x y) (* z z)) (* z z))
4.0ms	(+ (* x y) (* z z))
8.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

series132.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(+ (+ (* x y) (* z z)) (* z z))
34.0ms	(+ (* x y) (* z z))
49.0ms	(+ (+ (+ (* x y) (* z z)) (* z z)) (* z z))

simplify131.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	235	373
1	1084	317
2	4667	293
3	5001	292

prune124.0ms

Filtered

60 candidates to 47 candidates (78.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	55	5	60
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	56	6	62

Merged error: 0.0b

Counts

62 → 6

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma 2 (pow z 2) (* x y))
0.1b	(+ (fma 2 (pow z 2) (* x y)) (* z z))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

4×	`add-log-exp`
3×	`add-sqr-sqrt` `add-cube-cbrt` `fma-def` `*-un-lft-identity`
2×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `fma-udef` `log1p-expm1-u`
1×	`+-commutative` `associate-+l+` `flip3-+` `sum-log` `flip-+`

Counts

2 → 27

Calls

2 calls:

1.0ms	(fma 2 (pow z 2) (* x y))
3.0ms	(+ (fma 2 (pow z 2) (* x y)) (* z z))

series86.0ms

Counts

2 → 6

Calls

2 calls:

34.0ms	(fma 2 (pow z 2) (* x y))
51.0ms	(+ (fma 2 (pow z 2) (* x y)) (* z z))

simplify55.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 3 (52.0ms)

Iter	Nodes	Cost
0	106	179
1	456	165
2	1816	162
3	5001	159

prune88.0ms

Filtered

33 candidates to 27 candidates (81.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	33	6	39

Merged error: 0.0b

Counts

39 → 6

localize5.0ms

Local error

Found 1 expressions with local error:

0.1b	(fma 3 (* z z) (* x y))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma 3 (* z z) (* x y))

series34.0ms

Counts

1 → 3

Calls

1 calls:

34.0ms

(fma 3 (* z z) (* x y))

simplify54.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	33	59
1	79	52
2	256	52
3	1025	52
4	5001	52

prune38.0ms

Filtered

13 candidates to 11 candidates (84.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	12	1	13
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	13	6	19

Merged error: 0.0b

Counts

19 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (fma 3 (* z z) (* x y))) (cbrt (fma 3 (* z z) (* x y))))
4.0b	(cbrt (fma 3 (* z z) (* x y)))
4.0b	(cbrt (fma 3 (* z z) (* x y)))
4.0b	(cbrt (fma 3 (* z z) (* x y)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cbrt (fma 3 (* z z) (* x y))) (cbrt (fma 3 (* z z) (* x y))))
1.0ms	(cbrt (fma 3 (* z z) (* x y)))
1.0ms	(cbrt (fma 3 (* z z) (* x y)))
1.0ms	(cbrt (fma 3 (* z z) (* x y)))

series451.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* (cbrt (fma 3 (* z z) (* x y))) (cbrt (fma 3 (* z z) (* x y))))
109.0ms	(cbrt (fma 3 (* z z) (* x y)))
114.0ms	(cbrt (fma 3 (* z z) (* x y)))
109.0ms	(cbrt (fma 3 (* z z) (* x y)))

simplify102.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	207	828
1	675	759
2	3216	701
3	5003	655

prune233.0ms

Filtered

93 candidates to 72 candidates (77.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	91	8	99

Merged error: 0.0b

Counts

99 → 8

regimes179.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample555.0ms

Algorithm

intervals

Results

304.0ms

12142×

body

valid