Details

sample43.0ms

Algorithm

intervals

Results

17.0ms	89×	body	1280	valid
7.0ms	59×	body	640	valid
3.0ms	19×	body	2560	valid
2.0ms	63×	body	80	valid
1.0ms	15×	body	320	valid
1.0ms	11×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	5
1	43	5
2	91	5
3	194	5
4	321	5
5	579	5
6	1088	5
7	1305	5
8	1305	5

prune3.0ms

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: 45.9b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x y) z)
9.1b	(- (fma x y z) (+ 1.0 (+ (* x y) z)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-log-exp`
7×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `sum-log`
3×	`diff-log`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `flip--` `flip-+` `distribute-lft-out` `associate--r+` `difference-of-squares`

Counts

2 → 29

Calls

2 calls:

3.0ms	(+ (* x y) z)
7.0ms	(- (fma x y z) (+ 1.0 (+ (* x y) z)))

series15.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(+ (* x y) z)
10.0ms	(- (fma x y z) (+ 1.0 (+ (* x y) z)))

simplify57.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 2 (16.0ms)

Iter	Nodes	Cost
0	178	220
1	602	204
2	2697	203
3	5001	203

prune59.0ms

Filtered

24 candidates to 35 candidates (-45.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	29	6	35
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	30	6	36

Merged error: 45.5b

Counts

36 → 6

localize10.0ms

Local error

Found 1 expressions with local error:

9.1b	(- (fma x y z) (+ z (+ (* x y) 1.0)))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
6×	`*-un-lft-identity`
3×	`add-sqr-sqrt` `diff-log` `sum-log`
2×	`distribute-lft-out--`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out` `associate--r+` `difference-of-squares`

Counts

1 → 18

Calls

1 calls:

8.0ms

(- (fma x y z) (+ z (+ (* x y) 1.0)))

series9.0ms

Counts

1 → 3

Calls

1 calls:

9.0ms

(- (fma x y z) (+ z (+ (* x y) 1.0)))

simplify42.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	106	163
1	340	152
2	1784	152
3	5001	152

prune41.0ms

Filtered

12 candidates to 21 candidates (-75.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	20	1	21
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	21	6	27

Merged error: 32.2b

Counts

27 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (- (fma x y z) z) (+ (* x y) 1.0)) 3)
1.1b	(- (fma x y z) z)
2.7b	(cbrt (pow (- (- (fma x y z) z) (+ (* x y) 1.0)) 3))
8.8b	(- (- (fma x y z) z) (+ (* x y) 1.0))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
18×	`cbrt-prod` `add-log-exp`
16×	`distribute-lft-out--`
12×	`cube-div` `unpow-prod-down` `cube-prod` `frac-sub`
10×	`add-cube-cbrt` `flip3--` `flip--`
7×	`diff-log`
6×	`cbrt-div` `flip3-+` `flip-+` `difference-of-squares`
5×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`sub-neg` `pow-unpow`
2×	`cube-mult` `unpow3` `associate--l+` `sum-log` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `associate--r+` `rem-cube-cbrt`

Counts

4 → 108

Calls

4 calls:

10.0ms	(pow (- (- (fma x y z) z) (+ (* x y) 1.0)) 3)
3.0ms	(- (fma x y z) z)
12.0ms	(cbrt (pow (- (- (fma x y z) z) (+ (* x y) 1.0)) 3))
9.0ms	(- (- (fma x y z) z) (+ (* x y) 1.0))

series73.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(pow (- (- (fma x y z) z) (+ (* x y) 1.0)) 3)
5.0ms	(- (fma x y z) z)
9.0ms	(cbrt (pow (- (- (fma x y z) z) (+ (* x y) 1.0)) 3))
9.0ms	(- (- (fma x y z) z) (+ (* x y) 1.0))

simplify76.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	585	1293
1	2703	1238
2	5002	1229

prune155.0ms

Filtered

67 candidates to 120 candidates (-79.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	118	8	126

Merged error: 12.7b

Counts

126 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (- (- (fma x y z) z) (* x y)) 1.0) 3)
1.1b	(- (fma x y z) z)
2.7b	(cbrt (pow (- (- (- (fma x y z) z) (* x y)) 1.0) 3))
7.8b	(- (- (fma x y z) z) (* x y))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `*-un-lft-identity`
16×	`cbrt-prod`
11×	`add-log-exp`
10×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
5×	`pow1` `add-exp-log` `add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`cube-div` `flip3--` `diff-log` `flip--`
3×	`sub-neg` `pow-unpow`
2×	`cube-mult` `cbrt-div` `unpow3` `associate--l+` `sqr-pow`
1×	`associate--l-` `pow-to-exp` `pow-pow` `pow1/3` `pow-exp` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 86

Calls

4 calls:

9.0ms	(pow (- (- (- (fma x y z) z) (* x y)) 1.0) 3)
3.0ms	(- (fma x y z) z)
10.0ms	(cbrt (pow (- (- (- (fma x y z) z) (* x y)) 1.0) 3))
8.0ms	(- (- (fma x y z) z) (* x y))

series76.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(pow (- (- (- (fma x y z) z) (* x y)) 1.0) 3)
5.0ms	(- (fma x y z) z)
9.0ms	(cbrt (pow (- (- (- (fma x y z) z) (* x y)) 1.0) 3))
8.0ms	(- (- (fma x y z) z) (* x y))

simplify54.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	430	820
1	1762	777
2	5001	771

prune103.0ms

Filtered

54 candidates to 98 candidates (-81.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	6	0	6
Picked	1	0	1
Done	1	0	1
Total	105	1	106

Merged error: 7.0b

Counts

106 → 1

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	7
1	14	7

end0.0ms

sample1.1s

Algorithm

intervals

Results

390.0ms	2587×	body	1280	valid
195.0ms	1637×	body	640	valid
108.0ms	608×	body	2560	valid
70.0ms	2072×	body	80	valid
68.0ms	742×	body	320	valid
22.0ms	354×	body	160	valid

Details

sample43.0ms

simplify26.0ms

prune3.0ms

localize7.0ms

rewrite12.0ms

series15.0ms

simplify57.0ms

prune59.0ms

localize10.0ms

rewrite8.0ms

series9.0ms

simplify42.0ms

prune41.0ms

localize10.0ms

rewrite37.0ms

series73.0ms

simplify76.0ms

prune155.0ms

localize12.0ms

rewrite32.0ms

series76.0ms

simplify54.0ms

prune103.0ms

simplify1.0ms

end0.0ms

sample1.1s

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