Details

analyze1.2s (29.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
13.2%	86.5%	0.2%	11
16.8%	83%	0.2%	12
22.7%	77.1%	0.2%	13
24.1%	74.7%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample29.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
4.0ms	90×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify67.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

783×	`fma-neg_binary64`
721×	`fma-def_binary64`
244×	`cancel-sign-sub-inv_binary64`
187×	`distribute-rgt-in_binary64`
138×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	17	13
2	39	13
3	98	13
4	258	11
5	542	11
6	1019	11
7	1302	11
8	1414	11
9	1470	11
10	1476	11
11	1481	11
12	1481	11
13	1408	11

prune4.0ms (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	4.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	5.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 46 computations (39.5% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) a)
✓	3.9b	(fma.f64 y (/.f64 (-.f64 t z) a) x)

series35.0ms (0.9%)

Counts

2 → 88

Calls

2 calls:

23.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)
11.0ms	(/.f64 (-.f64 t z) a)

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/l*_binary64`

Counts

2 → 50

Calls

2 calls:

5.0ms	(/.f64 (-.f64 t z) a)
0.0ms	(fma.f64 y (/.f64 (-.f64 t z) a) x)

simplify90.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

696×	`distribute-rgt-in_binary64`
684×	`distribute-lft-in_binary64`
583×	`times-frac_binary64`
453×	`fma-def_binary64`
215×	`div-sub_binary64`

Counts

138 → 78

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	111	1607
1	238	1462
2	525	1460
3	1333	1460
4	4886	1460
5	4983	1460

prune53.0ms (1.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	75	3	78
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	75	5	80

Error

0.0b

Counts

80 → 5

Alt Table

Status	Error	Program
	4.2b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)
▶	2.4b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
✓	4.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	5.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	5.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)))

Compiler

Compiled 1209 to 341 computations (71.8% saved)

localize6.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.3b	(fma.f64 (/.f64 y a) (-.f64 t z) x)

series22.0ms (0.6%)

Counts

1 → 60

Calls

1 calls:

22.0ms

(fma.f64 (/.f64 y a) (-.f64 t z) 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 (/.f64 y a) (-.f64 t z) x)

simplify86.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

426×	`distribute-lft-neg-out_binary64`
425×	`distribute-rgt-neg-out_binary64`
378×	`distribute-rgt-in_binary64`
375×	`distribute-lft-in_binary64`
225×	`distribute-rgt-out_binary64`

Counts

70 → 27

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	40	863
1	76	750
2	164	733
3	450	733
4	2142	733
5	4579	733
6	5069	733

prune15.0ms (0.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	27	5	32

Error

0.0b

Counts

32 → 5

Alt Table

Status	Error	Program
▶	4.2b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)
✓	2.4b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
✓	4.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	5.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	5.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)))

Compiler

Compiled 441 to 136 computations (69.2% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (-.f64 t z))
✓	0.4b	(/.f64 1 (/.f64 a (-.f64 t z)))
✓	3.9b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)

series54.0ms (1.3%)

Counts

3 → 120

Calls

3 calls:

24.0ms	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)
17.0ms	(/.f64 a (-.f64 t z))
13.0ms	(/.f64 1 (/.f64 a (-.f64 t z)))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
103×	`*-un-lft-identity_binary64`
103×	`add-sqr-sqrt_binary64`
71×	`add-cube-cbrt_binary64`
26×	`associate-/r*_binary64`

Counts

3 → 159

Calls

3 calls:

8.0ms	(/.f64 a (-.f64 t z))
7.0ms	(/.f64 1 (/.f64 a (-.f64 t z)))
0.0ms	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)

simplify173.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

382×	`fma-neg_binary64`
340×	`times-frac_binary64`
325×	`associate-/l*_binary64`
268×	`fma-def_binary64`
223×	`associate-/r*_binary64`

Counts

279 → 229

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	204	4381
1	421	3949
2	1210	3759
3	3983	3759
4	4992	3759
5	4962	3759

prune142.0ms (3.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	229	5	234

Error

0.0b

Counts

234 → 5

Alt Table

Status	Error	Program
✓	4.2b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 t z))) x)
✓	2.4b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
✓	4.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
▶	5.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	5.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x))) (cbrt.f64 (fma.f64 y (/.f64 (-.f64 t z) a) x)))

Compiler

Compiled 4321 to 1491 computations (65.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (-.f64 z t))
✓	5.5b	(/.f64 (*.f64 y (-.f64 z t)) a)

series28.0ms (0.7%)

Counts

2 → 84

Calls

2 calls:

21.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
7.0ms	(*.f64 y (-.f64 z t))

rewrite17.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 75

Calls

2 calls:

7.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
5.0ms	(*.f64 y (-.f64 z t))

simplify85.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

667×	`associate-/l*_binary64`
508×	`times-frac_binary64`
338×	`fma-def_binary64`
275×	`distribute-rgt-in_binary64`
261×	`distribute-lft-in_binary64`

Counts

159 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	167	1706
1	335	1575
2	1241	1521
3	4826	1521
4	4942	1521

prune71.0ms (1.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	1	0	1
Picked	0	1	1
Done	1	2	3
Total	113	5	118

Error

Counts

118 → 5

Alt Table

Status	Error	Program
	29.8b	(-.f64 x (/.f64 (*.f64 (/.f64 y (sqrt.f64 a)) (-.f64 z t)) (sqrt.f64 a)))
✓	5.1b	(-.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	2.4b	(fma.f64 (/.f64 y a) (-.f64 t z) x)
✓	4.1b	(fma.f64 y (/.f64 (-.f64 t z) a) x)
	3.9b	(-.f64 x (/.f64 y (/.f64 a (-.f64 z t))))

Compiler

Compiled 1988 to 604 computations (69.6% saved)

regimes758.0ms (18.8%)

Accuracy

Total 0.7b remaining (98.3%)

Threshold costs 0.7b (98.3%)

Counts

40 → 3

Compiler

Compiled 6767 to 4189 computations (38.1% saved)

bsearch39.0ms (1%)

Steps

Iters	Range		Point
7	8.907524735097039e+52	2.5649169579830777e+54	9.357780273859336e+52
9	-1.545512374344709e+23	-245080292437357060.0	-280431850242306000.0

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	49
1	32	49
2	50	49
3	67	49
4	80	49
5	93	49
6	100	49
7	102	49
8	104	49
9	105	49
10	101	49

end1.0ms (0%)

Compiler: Compiled 39 to 21 computations (46.2% saved)

sample1.0s (25.3%)

Algorithm

1×

intervals

Results

353.0ms	8000×	body	128	valid
121.0ms	2656×	body	128	invalid

Compiler

Compiled 131 to 81 computations (38.2% saved)

Iter	Nodes	Cost
0	23	49
1	32	49
2	50	49
3	67	49
4	80	49
5	93	49
6	100	49
7	102	49
8	104	49
9	105	49
10	101	49

Iter	Nodes	Cost
0	23	49
1	32	49
2	50	49
3	67	49
4	80	49
5	93	49
6	100	49
7	102	49
8	104	49
9	105	49
10	101	49

Details

analyze1.2s (29.2%)

sample29.0ms (0.7%)

simplify67.0ms (1.6%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series35.0ms (0.9%)

rewrite7.0ms (0.2%)

simplify90.0ms (2.2%)

prune53.0ms (1.3%)

localize6.0ms (0.2%)

series22.0ms (0.6%)

rewrite1.0ms (0%)

simplify86.0ms (2.1%)

prune15.0ms (0.4%)

localize11.0ms (0.3%)

series54.0ms (1.3%)

rewrite29.0ms (0.7%)

simplify173.0ms (4.3%)

prune142.0ms (3.5%)

localize6.0ms (0.2%)

series28.0ms (0.7%)

rewrite17.0ms (0.4%)

simplify85.0ms (2.1%)

prune71.0ms (1.7%)

regimes758.0ms (18.8%)

bsearch39.0ms (1%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.0s (25.3%)

Profiling

Iter	Nodes	Cost
0	23	49
1	32	49
2	50	49
3	67	49
4	80	49
5	93	49
6	100	49
7	102	49
8	104	49
9	105	49
10	101	49