Details

analyze1.5s (32.5%)

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)

sample130.0ms (2.7%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
3.0ms	73×	body	128	invalid

Compiler

Compiled 34 to 24 computations (29.4% saved)

simplify68.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

946×	`fma-def_binary64`
719×	`fma-neg_binary64`
235×	`cancel-sign-sub-inv_binary64`
163×	`distribute-rgt-in_binary64`
116×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	16	13
2	31	11
3	62	11
4	130	11
5	231	11
6	390	11
7	639	11
8	955	11
9	1272	11
10	1381	11
11	1449	11
12	1474	11
13	1471	11
14	1471	11
15	1398	11

prune5.0ms (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
▶	5.4b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	7.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) a)
✓	5.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)

series42.0ms (0.9%)

Counts

2 → 88

Calls

2 calls:

32.0ms	(fma.f64 y (/.f64 (-.f64 z t) a) x)
9.0ms	(/.f64 (-.f64 z t) a)

rewrite15.0ms (0.3%)

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:

12.0ms	(/.f64 (-.f64 z t) a)
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) a) x)

simplify107.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

699×	`distribute-rgt-in_binary64`
686×	`distribute-lft-in_binary64`
589×	`times-frac_binary64`
434×	`fma-def_binary64`
215×	`div-sub_binary64`

Counts

138 → 77

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	109	1877
1	238	1462
2	529	1460
3	1344	1460
4	4947	1460
5	5050	1460

prune58.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	72	5	77
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	73	6	79

Error

0.0b

Counts

79 → 6

Alt Table

Status	Error	Program
	7.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	34.7b	(*.f64 (-.f64 (/.f64 z a) (/.f64 t a)) y)
▶	3.3b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	33.4b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
	35.8b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 a)) (sqrt.f64 a)) x)
	5.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)

Compiler

Compiled 1225 to 367 computations (70% saved)

localize12.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	3.2b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

series25.0ms (0.5%)

Counts

1 → 60

Calls

1 calls:

25.0ms

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

simplify80.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

429×	`distribute-lft-neg-out_binary64`
429×	`distribute-rgt-neg-out_binary64`
368×	`distribute-rgt-in_binary64`
367×	`distribute-lft-in_binary64`
237×	`distribute-rgt-out_binary64`

Counts

70 → 26

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	1133
1	75	750
2	165	733
3	447	733
4	2165	733
5	4627	733
6	4940	733

prune20.0ms (0.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	26	6	32

Error

0.0b

Counts

32 → 6

Alt Table

Status	Error	Program
	7.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	34.7b	(*.f64 (-.f64 (/.f64 z a) (/.f64 t a)) y)
✓	3.3b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	33.4b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
	35.8b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 a)) (sqrt.f64 a)) x)
▶	5.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)

Compiler

Compiled 457 to 162 computations (64.6% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 a (-.f64 z t))
✓	0.3b	(/.f64 1 (/.f64 a (-.f64 z t)))
✓	5.1b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)

series79.0ms (1.7%)

Counts

3 → 120

Calls

3 calls:

36.0ms	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)
26.0ms	(/.f64 a (-.f64 z t))
17.0ms	(/.f64 1 (/.f64 a (-.f64 z t)))

rewrite34.0ms (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:

7.0ms	(/.f64 1 (/.f64 a (-.f64 z t)))
4.0ms	(/.f64 a (-.f64 z t))
1.0ms	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)

simplify165.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

727×	`fma-neg_binary64`
346×	`times-frac_binary64`
328×	`associate-/l*_binary64`
274×	`fma-def_binary64`
229×	`associate-/r*_binary64`

Counts

279 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	4651
1	421	3949
2	1216	3759
3	4143	3759
4	4963	3759

prune165.0ms (3.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	228	0	228
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	228	6	234

Error

0.0b

Counts

234 → 6

Alt Table

Status	Error	Program
▶	7.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	34.7b	(*.f64 (-.f64 (/.f64 z a) (/.f64 t a)) y)
✓	3.3b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	33.4b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) a) x)))
	35.8b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 a)) (sqrt.f64 a)) x)
✓	5.4b	(fma.f64 y (/.f64 1 (/.f64 a (-.f64 z t))) x)

Compiler

Compiled 4337 to 1518 computations (65% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	0.0b	(*.f64 y (-.f64 z t))
✓	8.1b	(/.f64 (*.f64 y (-.f64 z t)) a)

series76.0ms (1.6%)

Counts

3 → 144

Calls

3 calls:

42.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
28.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
7.0ms	(*.f64 y (-.f64 z t))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 92

Calls

3 calls:

10.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
5.0ms	(*.f64 y (-.f64 z t))
4.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

simplify85.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

599×	`times-frac_binary64`
517×	`distribute-rgt-in_binary64`
492×	`distribute-lft-in_binary64`
448×	`fma-def_binary64`
124×	`associate-l_binary64`

Counts

236 → 148

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	2898
1	425	2525
2	1558	2355
3	5186	2355

prune102.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	1	2	3
Picked	0	1	1
Done	1	1	2
Total	148	6	154

Error

0.0b

Counts

154 → 6

Alt Table

Status	Error	Program
✓	7.4b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
	34.7b	(*.f64 (-.f64 (/.f64 z a) (/.f64 t a)) y)
✓	3.3b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	5.0b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
	7.5b	(+.f64 x (/.f64 1 (/.f64 a (*.f64 y (-.f64 z t)))))
	35.8b	(fma.f64 y (/.f64 (/.f64 (-.f64 z t) (sqrt.f64 a)) (sqrt.f64 a)) x)

Compiler

Compiled 2523 to 703 computations (72.1% saved)

regimes651.0ms (13.7%)

Accuracy

Total 0.7b remaining (98.2%)

Threshold costs 0.7b (98.2%)

Counts

36 → 3

Compiler

Compiled 5432 to 3221 computations (40.7% saved)

bsearch29.0ms (0.6%)

Steps

Iters	Range		Point
4	6.508541667459229e-9	2.2417936783500166e-7	4.871718399021154e-8
8	-3.491311910968596e-51	-1.8247790748704565e-54	-7.468413263144839e-53

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	49
1	27	49
2	32	49
3	34	49
4	35	49
5	35	49

end1.0ms (0%)

Compiler: Compiled 39 to 20 computations (48.7% saved)

sample1.2s (25.5%)

Algorithm

1×

intervals

Results

521.0ms	8000×	body	128	valid
103.0ms	2561×	body	128	invalid

Compiler

Compiled 147 to 91 computations (38.1% saved)

Details

analyze1.5s (32.5%)

sample130.0ms (2.7%)

simplify68.0ms (1.4%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

series42.0ms (0.9%)

rewrite15.0ms (0.3%)

simplify107.0ms (2.2%)

prune58.0ms (1.2%)

localize12.0ms (0.2%)

series25.0ms (0.5%)

rewrite1.0ms (0%)

simplify80.0ms (1.7%)

prune20.0ms (0.4%)

localize7.0ms (0.2%)

series79.0ms (1.7%)

rewrite34.0ms (0.7%)

simplify165.0ms (3.5%)

prune165.0ms (3.5%)

localize8.0ms (0.2%)

series76.0ms (1.6%)

rewrite24.0ms (0.5%)

simplify85.0ms (1.8%)

prune102.0ms (2.1%)

regimes651.0ms (13.7%)

bsearch29.0ms (0.6%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.2s (25.5%)

Profiling