Details

analyze333.0ms (18.9%)

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
18.7%	81.1%	0.1%	8
36.7%	60.8%	2.5%	9
43.3%	49.9%	6.8%	10
49.7%	40.8%	9.5%	11
58.2%	30.2%	11.6%	12
61.3%	24.4%	14.3%	13
65%	19.8%	15.3%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample91.0ms (5.2%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	17×	body	128	invalid

Compiler

Compiled 24 to 16 computations (33.3% saved)

simplify24.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

278×	`fma-def_binary64`
251×	`fma-neg_binary64`
71×	`cancel-sign-sub-inv_binary64`
55×	`distribute-rgt-in_binary64`
41×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	11	8
2	24	8
3	46	8
4	81	8
5	139	8
6	212	8
7	345	8
8	487	8
9	601	8
10	661	8
11	668	8
12	625	8

prune10.0ms (0.6%)

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 y (-.f64 z x) x)
	0.0b	(+.f64 x (*.f64 y (-.f64 z x)))

Compiler

Compiled 54 to 29 computations (46.3% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series7.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

7.0ms

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

simplify58.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

694×	`neg-mul-1_binary64`
479×	`distribute-rgt-neg-out_binary64`
433×	`distribute-lft-neg-out_binary64`
343×	`distribute-rgt-in_binary64`
336×	`distribute-lft-in_binary64`

Counts

46 → 21

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	31	472
1	66	374
2	137	374
3	363	374
4	1693	374
5	3955	374
6	5046	374

prune18.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	19	2	21
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	19	4	23

Error

Counts

23 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 y (-.f64 z x) x)
	0.0b	(+.f64 x (*.f64 y (-.f64 z x)))
▶	0.0b	(-.f64 (+.f64 (.f64 y z) x) (.f64 y x))
	1.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (-.f64 z x) x)) (cbrt.f64 (fma.f64 y (-.f64 z x) x))) (cbrt.f64 (fma.f64 y (-.f64 z x) x)))

Compiler

Compiled 284 to 96 computations (66.2% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

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

series12.0ms (0.7%)

Counts

2 → 18

Calls

2 calls:

7.0ms	(-.f64 (+.f64 (.f64 y z) x) (.f64 y x))
5.0ms	(+.f64 (*.f64 y z) x)

rewrite12.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`fma-neg_binary64`

Counts

2 → 36

Calls

2 calls:

6.0ms	(+.f64 (*.f64 y z) x)
5.0ms	(-.f64 (+.f64 (.f64 y z) x) (.f64 y x))

simplify57.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

353×	`fma-def_binary64`
306×	`associate-l_binary64`
262×	`times-frac_binary64`
256×	`associate-r_binary64`
245×	`fma-neg_binary64`

Counts

54 → 68

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	75	629
1	213	515
2	624	493
3	2379	492
4	4147	492
5	5031	492

prune31.0ms (1.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	68	4	72

Error

Counts

72 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 y (-.f64 z x) x)
▶	0.0b	(+.f64 x (*.f64 y (-.f64 z x)))
✓	0.0b	(-.f64 (+.f64 (.f64 y z) x) (.f64 y x))
	1.1b	(-.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 y z x)) (cbrt.f64 (fma.f64 y z x))) (cbrt.f64 (fma.f64 y z x))) (*.f64 y x))

Compiler

Compiled 1099 to 249 computations (77.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series15.0ms (0.9%)

Counts

2 → 60

Calls

2 calls:

9.0ms	(*.f64 y (-.f64 z x))
7.0ms	(+.f64 x (*.f64 y (-.f64 z x)))

rewrite16.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
36×	`prod-diff_binary64`
35×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
26×	`associate-+r+_binary64`

Counts

2 → 92

Calls

2 calls:

5.0ms	(*.f64 y (-.f64 z x))
4.0ms	(+.f64 x (*.f64 y (-.f64 z x)))

simplify104.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

1004×	`fma-neg_binary64`
627×	`fma-def_binary64`
406×	`distribute-rgt-in_binary64`
375×	`distribute-lft-in_binary64`
280×	`*-commutative_binary64`

Counts

152 → 132

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	166	1565
1	291	1349
2	1014	1291
3	3335	1237
4	4283	1237
5	5068	1237

prune66.0ms (3.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	132	4	136

Error

Counts

136 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 y (-.f64 z x) x)
✓	0.0b	(+.f64 x (*.f64 y (-.f64 z x)))
✓	0.0b	(-.f64 (+.f64 (.f64 y z) x) (.f64 y x))
▶	32.8b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (-.f64 z x))) (sqrt.f64 (-.f64 z x))))

Compiler

Compiled 2386 to 586 computations (75.4% saved)

localize9.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (-.f64 z x))) (sqrt.f64 (-.f64 z x))))
✓	0.1b	(*.f64 y (sqrt.f64 (-.f64 z x)))
✓	0.1b	(.f64 (.f64 y (sqrt.f64 (-.f64 z x))) (sqrt.f64 (-.f64 z x)))

series72.0ms (4.1%)

Counts

3 → 72

Calls

3 calls:

33.0ms	(*.f64 y (sqrt.f64 (-.f64 z x)))
23.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (-.f64 z x))) (sqrt.f64 (-.f64 z x))))
16.0ms	(.f64 (.f64 y (sqrt.f64 (-.f64 z x))) (sqrt.f64 (-.f64 z x)))

rewrite21.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`associate-r_binary64`
14×	`sqrt-div_binary64`
13×	`*-un-lft-identity_binary64`
11×	`sqrt-prod_binary64`

Counts

3 → 77

Calls

3 calls:

9.0ms	(.f64 (.f64 y (sqrt.f64 (-.f64 z x))) (sqrt.f64 (-.f64 z x)))
6.0ms	(*.f64 y (sqrt.f64 (-.f64 z x)))
2.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (-.f64 z x))) (sqrt.f64 (-.f64 z x))))

simplify104.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

534×	`fma-def_binary64`
419×	`distribute-rgt-in_binary64`
396×	`distribute-lft-in_binary64`
295×	`fma-neg_binary64`
246×	`times-frac_binary64`

Counts

149 → 126

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	1922
1	479	1749
2	1542	1744
3	4575	1743
4	4975	1743
5	4965	1743

prune47.0ms (2.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	126	4	130

Error

Counts

130 → 4

Alt Table

Status	Error	Program
✓	0.0b	(fma.f64 y (-.f64 z x) x)
✓	0.0b	(+.f64 x (*.f64 y (-.f64 z x)))
✓	0.0b	(-.f64 (+.f64 (.f64 y z) x) (.f64 y x))
✓	32.8b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (-.f64 z x))) (sqrt.f64 (-.f64 z x))))

Compiler

Compiled 2629 to 701 computations (73.3% saved)

regimes60.0ms (3.4%)

Accuracy

Total 0.0b remaining (71%)

Threshold costs 0.0b (71%)

Counts

16 → 1

Compiler

Compiled 764 to 418 computations (45.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	8	8
2	13	8
3	15	8
4	16	8
5	16	8

end0.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

sample569.0ms (32.4%)

Algorithm

1×

intervals

Results

249.0ms	8000×	body	128	valid
18.0ms	573×	body	128	invalid

Compiler

Compiled 70 to 41 computations (41.4% saved)

Iter	Nodes	Cost
0	7	10
1	11	8
2	24	8
3	46	8
4	81	8
5	139	8
6	212	8
7	345	8
8	487	8
9	601	8
10	661	8
11	668	8
12	625	8

Iter	Nodes	Cost
0	7	10
1	11	8
2	24	8
3	46	8
4	81	8
5	139	8
6	212	8
7	345	8
8	487	8
9	601	8
10	661	8
11	668	8
12	625	8

Details

analyze333.0ms (18.9%)

sample91.0ms (5.2%)

simplify24.0ms (1.3%)

prune10.0ms (0.6%)

localize4.0ms (0.2%)

series7.0ms (0.4%)

rewrite1.0ms (0%)

simplify58.0ms (3.3%)

prune18.0ms (1.1%)

localize5.0ms (0.3%)

series12.0ms (0.7%)

rewrite12.0ms (0.7%)

simplify57.0ms (3.3%)

prune31.0ms (1.8%)

localize4.0ms (0.2%)

series15.0ms (0.9%)

rewrite16.0ms (0.9%)

simplify104.0ms (5.9%)

prune66.0ms (3.8%)

localize9.0ms (0.5%)

series72.0ms (4.1%)

rewrite21.0ms (1.2%)

simplify104.0ms (5.9%)

prune47.0ms (2.7%)

regimes60.0ms (3.4%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample569.0ms (32.4%)

Profiling

Iter	Nodes	Cost
0	7	10
1	11	8
2	24	8
3	46	8
4	81	8
5	139	8
6	212	8
7	345	8
8	487	8
9	601	8
10	661	8
11	668	8
12	625	8