Details

sample79.0ms

Algorithm

intervals

Results

40.0ms

499×

body

valid

simplify69.0ms

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

prune16.0ms

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

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 18.0) y)
0.5b	(* (* j 27.0) k)
1.9b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
6.1b	(* (* (* x 18.0) y) z)

rewrite19.0ms

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)

series2.8s

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (* x 18.0) y)
17.0ms	(* (* j 27.0) k)
2.7s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
25.0ms	(* (* (* x 18.0) y) z)

simplify51.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (10.0ms)

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

prune297.0ms

Filtered

85 candidates to 54 candidates (63.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	77	8	85
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	79	8	87

Merged error: 1.3b

Counts

87 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k)))
0.5b	(* (* j 27.0) k)
1.9b	(fma t (- (* (* x 18.0) (* y z)) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
4.1b	(* (* x 18.0) (* y z))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`prod-diff`
2×	`associate-l` `*-commutative` `fma-udef`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--` `associate--r+`

Counts

4 → 73

Calls

4 calls:

4.0ms	(- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k)))
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))))
10.0ms	(* (* x 18.0) (* y z))

series2.9s

Counts

4 → 12

Calls

4 calls:

99.0ms	(- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k)))
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))))
26.0ms	(* (* x 18.0) (* y z))

simplify55.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	405	628
1	1656	489
2	5001	489

prune264.0ms

Filtered

85 candidates to 51 candidates (60.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	1	85
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 1.3b

Counts

93 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x (* 4.0 i) (* (* j 27.0) k))
0.5b	(* (* j 27.0) k)
1.9b	(fma t (- (* (* x 18.0) (* y z)) (* a 4.0)) (fma b c (- (fma x (* 4.0 i) (* (* j 27.0) k)))))
4.1b	(* (* x 18.0) (* y z))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u` `add-log-exp`
2×	`associate-l` `*-commutative` `fma-udef`

Counts

4 → 64

Calls

4 calls:

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

series3.1s

Counts

4 → 12

Calls

4 calls:

59.0ms	(fma x (* 4.0 i) (* (* j 27.0) k))
17.0ms	(* (* j 27.0) k)
3.0s	(fma t (- (* (* x 18.0) (* y z)) (* a 4.0)) (fma b c (- (fma x (* 4.0 i) (* (* j 27.0) k)))))
25.0ms	(* (* x 18.0) (* y z))

simplify44.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	305	448
1	1289	364
2	5001	364

prune258.0ms

Filtered

76 candidates to 48 candidates (63.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 1.3b

Counts

83 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* i x))
0.2b	(fma 27.0 (* k j) (* 4.0 (* i x)))
1.9b	(fma t (- (* (* x 18.0) (* y z)) (* a 4.0)) (fma b c (- (fma 27.0 (* k j) (* 4.0 (* i x))))))
4.1b	(* (* x 18.0) (* y z))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u` `add-log-exp`
2×	`associate-r` `*-commutative` `fma-udef`

Counts

4 → 64

Calls

4 calls:

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

series2.9s

Counts

4 → 12

Calls

4 calls:

20.0ms	(* 4.0 (* i x))
65.0ms	(fma 27.0 (* k j) (* 4.0 (* i x)))
2.8s	(fma t (- (* (* x 18.0) (* y z)) (* a 4.0)) (fma b c (- (fma 27.0 (* k j) (* 4.0 (* i x))))))
25.0ms	(* (* x 18.0) (* y z))

simplify46.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	287	447
1	1167	363
2	5002	363

prune238.0ms

Filtered

76 candidates to 50 candidates (65.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 1.3b

Counts

83 → 8

regimes821.0ms

Accuracy

44.4% (2.3b remaining)

Error of 4.3b against oracle of 2.0b and baseline of 6.2b

bsearch246.0ms

Steps

Iters	Range		Point
9	7.953671895441392e-38	2.807060798620796e-32	1.0687522878389014e-36
6	-1.0332884915054241e+189	-6.634506351794128e+187	-6.741904871473899e+187

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	24
1	57	24

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.4s

16033×

body

valid

Details

sample79.0ms

simplify69.0ms

prune16.0ms

localize20.0ms

rewrite19.0ms

series2.8s

simplify51.0ms

prune297.0ms

localize20.0ms

rewrite22.0ms

series2.9s

simplify55.0ms

prune264.0ms

localize21.0ms

rewrite14.0ms

series3.1s

simplify44.0ms

prune258.0ms

localize21.0ms

rewrite14.0ms

series2.9s

simplify46.0ms

prune238.0ms

regimes821.0ms

bsearch246.0ms

simplify2.0ms

end0.0ms

sample2.3s

Profiling