Details

sample76.0ms

Algorithm

intervals

Results

40.0ms

657×

body

valid

simplify84.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	47	14
1	110	13
2	335	13
3	1059	13
4	3442	13
5	5001	13

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: 11.1b

Counts

2 → 1

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
4.0b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
5.4b	(* b (- (* c z) (* i a)))
5.9b	(* x (- (* y z) (* t a)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-commutative`
36×	`prod-diff`
24×	`distribute-rgt-in` `distribute-lft-in`
12×	`associate-*r/` `associate--l+` `associate--r+`
9×	`sub-neg`
7×	`flip3--` `flip--`
4×	`frac-sub`
2×	`fma-neg`
1×	`fma-udef`

Counts

4 → 69

Calls

4 calls:

13.0ms	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
1.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
5.0ms	(* b (- (* c z) (* i a)))
5.0ms	(* x (- (* y z) (* t a)))

series915.0ms

Counts

4 → 12

Calls

4 calls:

214.0ms	(- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a))))
564.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
68.0ms	(* b (- (* c z) (* i a)))
69.0ms	(* x (- (* y z) (* t a)))

simplify55.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	496	769
1	1882	737
2	5003	733

prune279.0ms

Filtered

81 candidates to 43 candidates (53.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	70	11	81
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	71	11	82

Merged error: 4.8b

Counts

82 → 11

localize29.0ms

Local error

Found 4 expressions with local error:

4.0b	(fma (- (* c t) (* i y)) j (+ (* (fma y z (- (* t a))) x) (- (* (fma (- t) a (* t a)) x) (* b (- (* c z) (* i a))))))
5.4b	(* b (- (* c z) (* i a)))
5.9b	(* (fma y z (- (* t a))) x)
48.9b	(fma (- t) a (* t a))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-commutative`
8×	`prod-diff`
6×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `associate-*r/` `fma-udef`
1×	`flip3--` `flip--`

Counts

4 → 18

Calls

4 calls:

1.0ms	(fma (- (* c t) (* i y)) j (+ (* (fma y z (- (* t a))) x) (- (* (fma (- t) a (* t a)) x) (* b (- (* c z) (* i a))))))
5.0ms	(* b (- (* c z) (* i a)))
2.0ms	(* (fma y z (- (* t a))) x)
1.0ms	(fma (- t) a (* t a))

series3.5s

Counts

4 → 12

Calls

4 calls:

3.4s	(fma (- (* c t) (* i y)) j (+ (* (fma y z (- (* t a))) x) (- (* (fma (- t) a (* t a)) x) (* b (- (* c z) (* i a))))))
63.0ms	(* b (- (* c z) (* i a)))
68.0ms	(* (fma y z (- (* t a))) x)
26.0ms	(fma (- t) a (* t a))

simplify82.0ms

Algorithm

egg-herbie

Counts

30 → 30

Iterations

Useful iterations: 4 (79.0ms)

Iter	Nodes	Cost
0	151	138
1	381	135
2	995	133
3	2513	133
4	5001	101

prune124.0ms

Filtered

30 candidates to 13 candidates (43.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	29	1	30
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	30	11	41

Merged error: 4.8b

Counts

41 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

2.4b	(fma z (* b c) (* a (* x t)))
3.0b	(fma a (* i b) (- (fma z (* b c) (* a (* x t)))))
4.0b	(fma (- (* c t) (* i y)) j (fma a (* i b) (- (fma z (* b c) (* a (* x t))))))
5.8b	(* a (* x t))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

3×	`fma-udef`
2×	`associate-r` `*-commutative`

Counts

4 → 6

Calls

4 calls:

1.0ms	(fma z (* b c) (* a (* x t)))
1.0ms	(fma a (* i b) (- (fma z (* b c) (* a (* x t)))))
1.0ms	(fma (- (* c t) (* i y)) j (fma a (* i b) (- (fma z (* b c) (* a (* x t))))))
3.0ms	(* a (* x t))

series824.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(fma z (* b c) (* a (* x t)))
135.0ms	(fma a (* i b) (- (fma z (* b c) (* a (* x t)))))
546.0ms	(fma (- (* c t) (* i y)) j (fma a (* i b) (- (fma z (* b c) (* a (* x t))))))
29.0ms	(* a (* x t))

simplify120.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	61	50
1	112	50
2	225	50
3	412	50
4	534	50
5	713	50
6	1236	50
7	1693	50
8	1942	50
9	2031	50
10	2166	50
11	2197	50
12	2197	50

prune103.0ms

Filtered

18 candidates to 10 candidates (55.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	15	3	18
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	17	12	29

Merged error: 4.7b

Counts

29 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

2.4b	(fma z (* b c) (* (* a x) t))
3.0b	(fma a (* i b) (- (fma z (* b c) (* (* a x) t))))
4.0b	(fma (- (* c t) (* i y)) j (fma a (* i b) (- (fma z (* b c) (* (* a x) t)))))
6.6b	(* (* a x) t)

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

3×	`fma-udef`
2×	`associate-l` `*-commutative`

Counts

4 → 6

Calls

4 calls:

1.0ms	(fma z (* b c) (* (* a x) t))
1.0ms	(fma a (* i b) (- (fma z (* b c) (* (* a x) t))))
1.0ms	(fma (- (* c t) (* i y)) j (fma a (* i b) (- (fma z (* b c) (* (* a x) t)))))
4.0ms	(* (* a x) t)

series966.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(fma z (* b c) (* (* a x) t))
129.0ms	(fma a (* i b) (- (fma z (* b c) (* (* a x) t))))
703.0ms	(fma (- (* c t) (* i y)) j (fma a (* i b) (- (fma z (* b c) (* (* a x) t)))))
26.0ms	(* (* a x) t)

simplify119.0ms

Algorithm

egg-herbie

Counts

18 → 18

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	61	50
1	111	50
2	224	50
3	411	50
4	533	50
5	712	50
6	1235	50
7	1692	50
8	1941	50
9	2030	50
10	2165	50
11	2196	50
12	2196	50

prune43.0ms

Filtered

18 candidates to 9 candidates (50.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	18	0	18
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	18	12	30

Merged error: 4.7b

Counts

30 → 12

regimes750.0ms

Accuracy

12.7% (6.1b remaining)

Error of 10.9b against oracle of 4.8b and baseline of 11.8b

bsearch236.0ms

Steps

Iters	Range		Point
9	3.015824262888155e-177	3.636382238941645e-168	9.751634481264663e-175
10	-2.010206062777737e-51	-3.5169477567309204e-70	-1.4891416355699024e-67

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	29
1	61	29
2	61	29

end0.0ms

sample2.1s

Algorithm

intervals

Results

1.2s

19182×

body

valid