Details

analyze458.0ms (22.9%)

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)

sample25.0ms (1.3%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 28 to 20 computations (28.6% saved)

simplify24.0ms (1.2%)

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 (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 -4 (.f64 y z) (.f64 x x))
	0.3b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) z))

Compiler

Compiled 66 to 41 computations (37.9% saved)

localize6.0ms (0.3%)

Local error

Found 1 expressions with local error:

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

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

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

series29.0ms (1.5%)

Counts

1 → 36

Calls

1 calls:

29.0ms

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

simplify81.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

490×	`*-commutative_binary64`
334×	`neg-sub0_binary64`
314×	`neg-mul-1_binary64`
290×	`times-frac_binary64`
288×	`associate-l_binary64`

Counts

46 → 90

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	565
1	40	488
2	87	488
3	294	488
4	1369	488
5	2959	488
6	4609	488
7	5240	488

prune17.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	89	3	92

Error

Counts

92 → 3

Alt Table

Status	Error	Program
▶	0.0b	(fma.f64 x x (.f64 (.f64 y z) -4))
	0.3b	(-.f64 (.f64 x x) (.f64 (*.f64 y 4) z))
	37.1b	(cbrt.f64 (pow.f64 (fma.f64 x x (.f64 (.f64 y z) -4)) 3))

Compiler

Compiled 362 to 175 computations (51.7% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
3×	`associate-r_binary64`
3×	`*-un-lft-identity_binary64`

Counts

2 → 30

Calls

2 calls:

4.0ms	(.f64 (.f64 y z) -4)
0.0ms	(fma.f64 x x (.f64 (.f64 y z) -4))

series88.0ms (4.4%)

Counts

2 → 60

Calls

2 calls:

64.0ms	(fma.f64 x x (.f64 (.f64 y z) -4))
24.0ms	(.f64 (.f64 y z) -4)

simplify88.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

692×	`neg-mul-1_binary64`
552×	`associate-l_binary64`
501×	`distribute-rgt-neg-in_binary64`
483×	`neg-sub0_binary64`
388×	`associate-r_binary64`

Counts

90 → 143

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	61	888
1	124	829
2	407	829
3	1391	829
4	3156	829
5	4399	829
6	4915	829

prune26.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	142	1	143
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	143	3	146

Error

Counts

146 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x x (.f64 (.f64 y z) -4))
▶	0.3b	(fma.f64 x x (.f64 y (.f64 z -4)))
	37.1b	(cbrt.f64 (pow.f64 (fma.f64 x x (.f64 (.f64 y z) -4)) 3))

Compiler

Compiled 689 to 348 computations (49.5% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 y (.f64 z -4)))
✓	0.2b	(.f64 y (.f64 z -4))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`

Counts

2 → 30

Calls

2 calls:

3.0ms	(.f64 y (.f64 z -4))
0.0ms	(fma.f64 x x (.f64 y (.f64 z -4)))

series56.0ms (2.8%)

Counts

2 → 60

Calls

2 calls:

34.0ms	(fma.f64 x x (.f64 y (.f64 z -4)))
21.0ms	(.f64 y (.f64 z -4))

simplify80.0ms (4%)

Algorithm

1×	egg-herbie

Rules

726×	`neg-sub0_binary64`
712×	`neg-mul-1_binary64`
518×	`associate-l_binary64`
476×	`distribute-rgt-neg-in_binary64`
379×	`associate-r_binary64`

Counts

90 → 144

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	58	886
1	118	827
2	368	827
3	1318	827
4	3101	827
5	4372	827
6	5000	827

prune26.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	144	3	147

Error

Counts

147 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x x (.f64 (.f64 y z) -4))
✓	0.3b	(fma.f64 x x (.f64 y (.f64 z -4)))
▶	37.1b	(cbrt.f64 (pow.f64 (fma.f64 x x (.f64 (.f64 y z) -4)) 3))

Compiler

Compiled 697 to 373 computations (46.5% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(fma.f64 x x (.f64 (.f64 y z) -4))
	0.0b	(.f64 (.f64 y z) -4)
✓	0.3b	(pow.f64 (fma.f64 x x (.f64 (.f64 y z) -4)) 3)
✓	35.5b	(cbrt.f64 (pow.f64 (fma.f64 x x (.f64 (.f64 y z) -4)) 3))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cube-prod_binary64`

Counts

2 → 48

Calls

2 calls:

2.0ms	(cbrt.f64 (pow.f64 (fma.f64 x x (.f64 (.f64 y z) -4)) 3))
1.0ms	(pow.f64 (fma.f64 x x (.f64 (.f64 y z) -4)) 3)

series61.0ms (3.1%)

Counts

2 → 72

Calls

2 calls:

32.0ms	(cbrt.f64 (pow.f64 (fma.f64 x x (.f64 (.f64 y z) -4)) 3))
29.0ms	(pow.f64 (fma.f64 x x (.f64 (.f64 y z) -4)) 3)

simplify122.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

660×	`associate-l_binary64`
644×	`fma-neg_binary64`
571×	`associate-r_binary64`
374×	`exp-prod_binary64`
326×	`log-prod_binary64`

Counts

120 → 219

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	89	2499
1	199	2340
2	605	2293
3	3099	2261
4	4834	2261
5	4983	2261

prune63.0ms (3.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	362	0	362
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	362	3	365

Error

Counts

365 → 3

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 x x (.f64 (.f64 y z) -4))
✓	0.3b	(fma.f64 x x (.f64 y (.f64 z -4)))
✓	37.1b	(cbrt.f64 (pow.f64 (fma.f64 x x (.f64 (.f64 y z) -4)) 3))

Compiler

Compiled 2205 to 1278 computations (42% saved)

regimes113.0ms (5.7%)

Accuracy

Total 0.0b remaining (55.3%)

Threshold costs 0.0b (55.3%)

Compiler

Compiled 1304 to 887 computations (32% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	10	11

end6.0ms (0.3%)

Remove: (sort y z)
Compiler: Compiled 33 to 21 computations (36.4% saved)

sample590.0ms (29.5%)

Algorithm

1×

intervals

Results

279.0ms	8000×	body	128	valid
15.0ms	471×	body	128	invalid

Compiler

Compiled 63 to 43 computations (31.7% 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

analyze458.0ms (22.9%)

sample25.0ms (1.3%)

simplify24.0ms (1.2%)

prune3.0ms (0.2%)

localize6.0ms (0.3%)

rewrite1.0ms (0%)

series29.0ms (1.5%)

simplify81.0ms (4.1%)

prune17.0ms (0.8%)

localize5.0ms (0.3%)

rewrite5.0ms (0.2%)

series88.0ms (4.4%)

simplify88.0ms (4.4%)

prune26.0ms (1.3%)

localize5.0ms (0.3%)

rewrite5.0ms (0.2%)

series56.0ms (2.8%)

simplify80.0ms (4%)

prune26.0ms (1.3%)

localize8.0ms (0.4%)

rewrite5.0ms (0.2%)

series61.0ms (3.1%)

simplify122.0ms (6.1%)

prune63.0ms (3.1%)

regimes113.0ms (5.7%)

simplify3.0ms (0.1%)

end6.0ms (0.3%)

sample590.0ms (29.5%)

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