Details

sample80.0ms

Algorithm

intervals

Results

43.0ms

506×

body

valid

simplify73.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	67	15
1	225	13
2	823	12
3	3028	12
4	5001	12

prune15.0ms

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: 4.6b

Counts

2 → 2

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* j 27.0) k)
0.5b	(* (* x 18.0) y)
2.7b	(* (* (* x 18.0) y) z)
3.8b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-r`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `*-commutative`
1×	`fma-udef`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* (* j 27.0) k)
6.0ms	(* (* x 18.0) y)
8.0ms	(* (* (* x 18.0) y) z)
1.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))

series3.1s

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* j 27.0) k)
23.0ms	(* (* x 18.0) y)
45.0ms	(* (* (* x 18.0) y) z)
3.0s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))

simplify61.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	326	447
1	1657	364
2	5002	364

prune350.0ms

Filtered

85 candidates to 54 candidates (63.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	76	9	85
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	78	9	87

Merged error: 2.4b

Counts

87 → 9

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* j (* 27.0 k))
0.5b	(* (* x 18.0) y)
2.7b	(* (* (* x 18.0) y) z)
3.8b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`fma-udef`

Counts

4 → 73

Calls

4 calls:

5.0ms	(* j (* 27.0 k))
6.0ms	(* (* x 18.0) y)
8.0ms	(* (* (* x 18.0) y) z)
1.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))

series3.1s

Counts

4 → 12

Calls

4 calls:

20.0ms	(* j (* 27.0 k))
23.0ms	(* (* x 18.0) y)
31.0ms	(* (* (* x 18.0) y) z)
3.0s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))

simplify64.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	318	446
1	1546	363
2	5001	363

prune318.0ms

Filtered

85 candidates to 53 candidates (62.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	85	9	94

Merged error: 2.4b

Counts

94 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* (cbrt (* (* j 27.0) k)) (cbrt (* (* j 27.0) k))) (cbrt (* (* j 27.0) k))))))
8.4b	(cbrt (* (* j 27.0) k))
8.4b	(cbrt (* (* j 27.0) k))
8.4b	(cbrt (* (* j 27.0) k))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 43

Calls

4 calls:

1.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* (cbrt (* (* j 27.0) k)) (cbrt (* (* j 27.0) k))) (cbrt (* (* j 27.0) k))))))
4.0ms	(cbrt (* (* j 27.0) k))
4.0ms	(cbrt (* (* j 27.0) k))
5.0ms	(cbrt (* (* j 27.0) k))

series3.5s

Counts

4 → 12

Calls

4 calls:

3.1s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* (cbrt (* (* j 27.0) k)) (cbrt (* (* j 27.0) k))) (cbrt (* (* j 27.0) k))))))
108.0ms	(cbrt (* (* j 27.0) k))
108.0ms	(cbrt (* (* j 27.0) k))
107.0ms	(cbrt (* (* j 27.0) k))

simplify127.0ms

Algorithm

egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 3 (34.0ms)

Iter	Nodes	Cost
0	155	506
1	346	442
2	1017	412
3	4024	403
4	5001	403

prune376.0ms

Filtered

55 candidates to 50 candidates (90.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	54	1	55
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	54	10	64

Merged error: 2.4b

Counts

64 → 10

localize31.0ms

Local error

Found 4 expressions with local error:

8.4b	(cbrt (* (* j 27.0) k))
8.4b	(cbrt (* (* j 27.0) k))
8.4b	(cbrt (* (* j 27.0) k))
8.4b	(cbrt (* (* j 27.0) k))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1` `add-exp-log` `cbrt-prod` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `pow1/3` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`

Counts

4 → 44

Calls

4 calls:

4.0ms	(cbrt (* (* j 27.0) k))
4.0ms	(cbrt (* (* j 27.0) k))
4.0ms	(cbrt (* (* j 27.0) k))
5.0ms	(cbrt (* (* j 27.0) k))

series427.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(cbrt (* (* j 27.0) k))
110.0ms	(cbrt (* (* j 27.0) k))
106.0ms	(cbrt (* (* j 27.0) k))
106.0ms	(cbrt (* (* j 27.0) k))

simplify116.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 4 (36.0ms)

Iter	Nodes	Cost
0	91	304
1	177	276
2	423	244
3	1037	244
4	3361	220
5	5001	220

prune344.0ms

Filtered

56 candidates to 48 candidates (85.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	56	10	66

Merged error: 2.4b

Counts

66 → 10

regimes1.4s

Accuracy

29% (2.5b remaining)

Error of 4.8b against oracle of 2.3b and baseline of 5.8b

bsearch215.0ms

Steps

Iters	Range		Point
8	3.5535986133383242e-43	4.6871535454932795e-39	8.380273989308787e-41
6	-1.7231856411834927e-105	-2.1389120799988593e-106	-2.3544036538359494e-106

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	21
1	58	21
2	58	21

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s

16263×

body

valid