Details

sample38.0ms

Algorithm

intervals

Results

11.0ms	75×	body	1280	valid
5.0ms	46×	body	640	valid
3.0ms	20×	body	2560	valid
3.0ms	81×	body	80	valid
2.0ms	25×	body	320	valid
1.0ms	9×	body	160	valid

simplify27.0ms

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

prune4.0ms

Filtered

1 candidates to 0 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: 42.6b

Counts

2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x y) z)
0.0b	(+ 1.0 (+ (* x y) z))
9.8b	(- (fma x y z) (+ 1.0 (+ (* x y) z)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 43

Calls

3 calls:

7.0ms	(+ (* x y) z)
5.0ms	(+ 1.0 (+ (* x y) z))
7.0ms	(- (fma x y z) (+ 1.0 (+ (* x y) z)))

series20.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(+ (* x y) z)
6.0ms	(+ 1.0 (+ (* x y) z))
9.0ms	(- (fma x y z) (+ 1.0 (+ (* x y) z)))

simplify73.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 2 (20.0ms)

Iter	Nodes	Cost
0	223	293
1	768	282
2	3261	281
3	5002	281

prune83.0ms

Filtered

52 candidates to 36 candidates (30.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	45	7	52
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	7	53

Merged error: 42.0b

Counts

53 → 7

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x y) 1.0)
9.8b	(- (fma x y z) (+ z (+ (* x y) 1.0)))

rewrite15.0ms

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:

4.0ms	(+ (* x y) 1.0)
10.0ms	(- (fma x y z) (+ z (+ (* x y) 1.0)))

series13.0ms

Counts

2 → 6

Calls

2 calls:

4.0ms	(+ (* x y) 1.0)
9.0ms	(- (fma x y z) (+ z (+ (* x y) 1.0)))

simplify55.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 2 (15.0ms)

Iter	Nodes	Cost
0	169	220
1	538	204
2	2318	203
3	5003	203

prune68.0ms

Filtered

35 candidates to 22 candidates (37.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	34	1	35
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	35	7	42

Merged error: 29.4b

Counts

42 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (- (fma x y z) z) (+ (* x y) 1.0)) 3)
1.6b	(- (fma x y z) z)
2.4b	(cbrt (pow (- (- (fma x y z) z) (+ (* x y) 1.0)) 3))
9.5b	(- (- (fma x y z) z) (+ (* x y) 1.0))

rewrite36.0ms

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

series75.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(pow (- (- (fma x y z) z) (+ (* x y) 1.0)) 3)
5.0ms	(- (fma x y z) z)
11.0ms	(cbrt (pow (- (- (fma x y z) z) (+ (* x y) 1.0)) 3))
9.0ms	(- (- (fma x y z) z) (+ (* x y) 1.0))

simplify77.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	585	1297
1	2703	1240
2	5001	1229

prune166.0ms

Filtered

120 candidates to 67 candidates (44.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	119	8	127

Merged error: 14.2b

Counts

127 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (- (- (- (fma x y z) z) (* x y)) 1.0) 3)
1.6b	(- (fma x y z) z)
2.4b	(cbrt (pow (- (- (- (fma x y z) z) (* x y)) 1.0) 3))
8.8b	(- (- (fma x y z) z) (* x y))

rewrite29.0ms

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)
9.0ms	(cbrt (pow (- (- (- (fma x y z) z) (* x y)) 1.0) 3))
6.0ms	(- (- (fma x y z) z) (* x y))

series73.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(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))

simplify55.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (45.0ms)

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

prune108.0ms

Filtered

98 candidates to 54 candidates (44.9%)

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: 7.8b

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

380.0ms	2579×	body	1280	valid
188.0ms	1572×	body	640	valid
120.0ms	670×	body	2560	valid
69.0ms	2072×	body	80	valid
68.0ms	742×	body	320	valid
22.0ms	365×	body	160	valid

Details

sample38.0ms

simplify27.0ms

prune4.0ms

localize8.0ms

rewrite20.0ms

series20.0ms

simplify73.0ms

prune83.0ms

localize11.0ms

rewrite15.0ms

series13.0ms

simplify55.0ms

prune68.0ms

localize11.0ms

rewrite36.0ms

series75.0ms

simplify77.0ms

prune166.0ms

localize13.0ms

rewrite29.0ms

series73.0ms

simplify55.0ms

prune108.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling