Details

sample89.0ms

Algorithm

intervals

Results

50.0ms

539×

body

valid

simplify83.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (13.0ms)

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

prune12.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 4.1b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* j 27.0) k)
0.4b	(* (* x 18.0) y)
2.4b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
4.6b	(* (* (* 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	(* (* j 27.0) k)
5.0ms	(* (* x 18.0) y)
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)

series2.8s

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (* j 27.0) k)
21.0ms	(* (* x 18.0) y)
2.8s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
33.0ms	(* (* (* x 18.0) y) z)

simplify64.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	326	447
1	1657	364
2	5001	364

prune335.0ms

Filtered

85 candidates to 54 candidates (63.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	78	7	85
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	7	86

Merged error: 1.5b

Counts

86 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (* 18.0 y))
0.2b	(* (* j 27.0) k)
2.4b	(fma t (- (* (* x (* 18.0 y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
4.6b	(* (* 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`
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:

21.0ms	(* x (* 18.0 y))
19.0ms	(* (* 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)

simplify62.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	324	447
1	1471	364
2	5001	364

prune476.0ms

Filtered

85 candidates to 49 candidates (57.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	85	7	92

Merged error: 1.5b

Counts

92 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* j (* 27.0 k))
0.4b	(* (* x 18.0) y)
2.4b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
4.6b	(* (* (* 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`
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))
5.0ms	(* (* x 18.0) y)
1.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
8.0ms	(* (* (* x 18.0) y) z)

series2.9s

Counts

4 → 12

Calls

4 calls:

33.0ms	(* j (* 27.0 k))
22.0ms	(* (* x 18.0) y)
2.8s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
33.0ms	(* (* (* x 18.0) y) z)

simplify68.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (15.0ms)

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

prune310.0ms

Filtered

85 candidates to 52 candidates (61.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	82	3	85
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	84	8	92

Merged error: 1.4b

Counts

92 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(cbrt y)
2.4b	(fma t (- (* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
4.6b	(* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1` `add-exp-log`
20×	`add-cbrt-cube`
19×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r`
2×	`pow1/3`
1×	`associate-l` `*-commutative` `fma-udef`

Counts

4 → 68

Calls

4 calls:

2.0ms	(cbrt y)
2.0ms	(cbrt y)
1.0ms	(fma t (- (* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
16.0ms	(* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z)

series3.4s

Counts

4 → 12

Calls

4 calls:

207.0ms	(cbrt y)
201.0ms	(cbrt y)
2.9s	(fma t (- (* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
60.0ms	(* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z)

simplify73.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	349	677
1	1623	524
2	5002	471

prune340.0ms

Filtered

80 candidates to 55 candidates (68.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	80	8	88

Merged error: 1.4b

Counts

88 → 8

regimes839.0ms

Accuracy

46.9% (1.8b remaining)

Error of 4.2b against oracle of 2.4b and baseline of 5.8b

bsearch313.0ms

Steps

Iters	Range		Point
10	45510.75291281057	2221768967065238.5	52122827.05018439
6	-1.3815410543181663e+138	-9.328162386240646e+136	-1.0168436787936453e+137

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	50	24
1	50	24

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.4s

16150×

body

valid