Details

sample72.0ms

Algorithm

intervals

Results

34.0ms

522×

body

valid

simplify76.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

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

prune18.0ms

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: 4.8b

Counts

2 → 2

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 18.0) y)
0.4b	(* (* j 27.0) k)
2.7b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
3.7b	(* (* (* x 18.0) y) z)

rewrite21.0ms

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	(* (* x 18.0) y)
5.0ms	(* (* j 27.0) k)
1.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
7.0ms	(* (* (* x 18.0) y) z)

series2.9s

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* x 18.0) y)
18.0ms	(* (* j 27.0) k)
2.8s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
29.0ms	(* (* (* x 18.0) y) z)

simplify56.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	326	447
1	1657	364
2	5001	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	77	8	85
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	78	9	87

Merged error: 1.8b

Counts

87 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 18.0) y)
0.2b	(* j (* 27.0 k))
2.7b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
3.7b	(* (* (* x 18.0) y) z)

rewrite20.0ms

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	(* (* x 18.0) y)
5.0ms	(* j (* 27.0 k))
1.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
7.0ms	(* (* (* x 18.0) y) z)

series2.9s

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* x 18.0) y)
32.0ms	(* j (* 27.0 k))
2.9s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
31.0ms	(* (* (* x 18.0) y) z)

simplify54.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	318	446
1	1546	363
2	5002	363

prune562.0ms

Filtered

85 candidates to 52 candidates (61.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	81	4	85
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Merged error: 1.8b

Counts

94 → 8

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 18.0) y)
0.2b	(* j (* 27.0 k))
2.7b	(* t (- (* (* (* x 18.0) y) z) (* a 4.0)))
3.7b	(* (* (* x 18.0) y) z)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

25×	`pow1` `add-exp-log` `add-cbrt-cube`
13×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
10×	`associate-r`
9×	`add-cube-cbrt` `*-un-lft-identity`
8×	`associate-l`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `associate-*r/` `prod-diff`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 91

Calls

4 calls:

8.0ms	(* (* x 18.0) y)
5.0ms	(* j (* 27.0 k))
9.0ms	(* t (- (* (* (* x 18.0) y) z) (* a 4.0)))
7.0ms	(* (* (* x 18.0) y) z)

series182.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* x 18.0) y)
18.0ms	(* j (* 27.0 k))
114.0ms	(* t (- (* (* (* x 18.0) y) z) (* a 4.0)))
27.0ms	(* (* (* x 18.0) y) z)

simplify71.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	420	525
1	2107	445
2	5002	445

prune412.0ms

Filtered

103 candidates to 65 candidates (63.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	102	9	111

Merged error: 1.8b

Counts

111 → 9

localize30.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
2.7b	(* t (- (* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z) (* a 4.0)))
3.7b	(* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z)

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

31×	`pow1` `add-exp-log`
22×	`add-cbrt-cube`
20×	`pow-prod-down` `prod-exp` `cbrt-unprod`
11×	`add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod` `associate-r`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `pow1/3` `associate-r/` `prod-diff` `-commutative`
1×	`flip3--` `flip--` `unswap-sqr`

Counts

4 → 86

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
16.0ms	(* t (- (* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z) (* a 4.0)))
15.0ms	(* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z)

series561.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt y)
183.0ms	(cbrt y)
143.0ms	(* t (- (* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z) (* a 4.0)))
53.0ms	(* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z)

simplify78.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	441	851
1	2149	689
2	5002	597

prune463.0ms

Filtered

98 candidates to 67 candidates (68.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	1	6	7
Picked	0	1	1
Done	0	1	1
Total	97	10	107

Merged error: 1.5b

Counts

107 → 10

regimes1.1s

Accuracy

50.7% (1.9b remaining)

Error of 3.7b against oracle of 1.8b and baseline of 5.6b

bsearch224.0ms

Steps

Iters	Range		Point
8	1.9015896051648368e-70	4.0775050088721686e-67	7.910406446147375e-70
5	-8.307141717812166e-51	-2.5987841252092732e-51	-6.021952827580205e-51

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	66	28
1	72	28
2	73	28
3	73	28

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s

16112×

body

valid