Details

analyze388.0ms (20.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
12.5%	71.8%	15.7%	8
25%	56.2%	18.9%	9
31.2%	43.7%	25.1%	10
39%	34.7%	26.3%	11
44.9%	27.9%	27.3%	12
47.8%	22%	30.2%	13
52.6%	16.8%	30.7%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample922.0ms (48.2%)

Symmetry

(sort y z)

Results

809.0ms	8256×	body	128	valid
47.0ms	489×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify20.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

335×	`fma-def_binary64`
126×	`fma-neg_binary64`
60×	`cancel-sign-sub-inv_binary64`
40×	`distribute-rgt-neg-in_binary64`
28×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	19	11
2	45	11
3	91	11
4	120	11
5	179	11
6	240	11
7	294	11
8	377	11
9	396	11
10	450	11
11	462	11
12	413	11

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) z))

Compiler

Compiled 44 to 27 computations (38.6% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) z))

series13.0ms (0.7%)

Counts

1 → 36

Calls

1 calls:

13.0ms

(-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) z))

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64`
1×	`cancel-sign-sub-inv_binary64`
1×	`flip--_binary64`
1×	`sub-neg_binary64`
1×	`*-un-lft-identity_binary64`

Counts

1 → 16

Calls

1 calls:

3.0ms

(-.f64 (*.f64 x x) (*.f64 (*.f64 y 4) z))

simplify57.0ms (3%)

Algorithm

1×	egg-herbie

Rules

974×	`fma-def_binary64`
507×	`associate-l_binary64`
406×	`associate-r_binary64`
356×	`distribute-rgt-neg-in_binary64`
346×	`distribute-lft-neg-in_binary64`

Counts

52 → 33

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	47	649
1	128	606
2	473	595
3	2020	593
4	4542	593
5	4918	593

prune29.0ms (1.5%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	33	1	34

Error

Counts

34 → 1

Alt Table

Status	Error	Program
▶	0b	(+.f64 (fma.f64 x x (neg.f64 (.f64 z (.f64 y 4)))) (fma.f64 (neg.f64 z) (.f64 y 4) (.f64 z (*.f64 y 4))))

Compiler

Compiled 537 to 274 computations (49% saved)

localize10.0ms (0.5%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (neg.f64 (.f64 z (.f64 y 4))))
✓	50.6b	(fma.f64 (neg.f64 z) (.f64 y 4) (.f64 z (*.f64 y 4)))

series21.0ms (1.1%)

Counts

2 → 60

Calls

2 calls:

11.0ms	(fma.f64 (neg.f64 z) (.f64 y 4) (.f64 z (*.f64 y 4)))
9.0ms	(fma.f64 x x (neg.f64 (.f64 z (.f64 y 4))))

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`
2×	`add-exp-log_binary64`

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 (neg.f64 z) (.f64 y 4) (.f64 z (*.f64 y 4)))
0.0ms	(fma.f64 x x (neg.f64 (.f64 z (.f64 y 4))))

simplify65.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

511×	`associate-l_binary64`
401×	`associate-r_binary64`
367×	`neg-mul-1_binary64`
252×	`distribute-rgt-out_binary64`
231×	`distribute-rgt-neg-out_binary64`

Counts

80 → 41

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	782
1	66	627
2	152	544
3	552	544
4	2008	544
5	4307	544
6	4899	544

prune42.0ms (2.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	1	42

Error

Counts

42 → 1

Alt Table

Status	Error	Program
✓	0b	(+.f64 (fma.f64 x x (neg.f64 (.f64 z (.f64 y 4)))) (fma.f64 (neg.f64 z) (.f64 y 4) (.f64 z (*.f64 y 4))))

Compiler

Compiled 994 to 585 computations (41.1% saved)

regimes274.0ms (14.3%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

37 → 1

Compiler

Compiled 4486 to 3149 computations (29.8% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
4×	`distribute-lft-neg-in_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`sub-neg_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	31
1	24	29
2	39	29
3	45	29
4	48	29
5	49	29
6	48	29

end54.0ms (2.8%)

Remove: (sort y z)
Compiler: Compiled 116 to 76 computations (34.5% saved)

Iter	Nodes	Cost
0	9	13
1	19	11
2	45	11
3	91	11
4	120	11
5	179	11
6	240	11
7	294	11
8	377	11
9	396	11
10	450	11
11	462	11
12	413	11

Iter	Nodes	Cost
0	9	13
1	19	11
2	45	11
3	91	11
4	120	11
5	179	11
6	240	11
7	294	11
8	377	11
9	396	11
10	450	11
11	462	11
12	413	11

Details

analyze388.0ms (20.3%)

sample922.0ms (48.2%)

simplify20.0ms (1.1%)

prune3.0ms (0.1%)

localize6.0ms (0.3%)

series13.0ms (0.7%)

rewrite3.0ms (0.2%)

simplify57.0ms (3%)

prune29.0ms (1.5%)

localize10.0ms (0.5%)

series21.0ms (1.1%)

rewrite1.0ms (0.1%)

simplify65.0ms (3.4%)

prune42.0ms (2.2%)

regimes274.0ms (14.3%)

simplify3.0ms (0.2%)

end54.0ms (2.8%)

Profiling

Iter	Nodes	Cost
0	9	13
1	19	11
2	45	11
3	91	11
4	120	11
5	179	11
6	240	11
7	294	11
8	377	11
9	396	11
10	450	11
11	462	11
12	413	11