Details

analyze558.0ms (7.1%)

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
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
74.8%	24.9%	0.2%	11
74.8%	24.9%	0.2%	12
74.8%	24.9%	0.2%	13
74.8%	24.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.5s (19.2%)

Results

1.4s	8255×	body	128	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify175.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1691×	`fma-neg_binary64`
841×	`div-sub_binary64`
807×	`distribute-rgt-in_binary64`
769×	`fma-def_binary64`
504×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	19	16
2	40	14
3	82	14
4	166	14
5	297	14
6	643	14
7	1551	14
8	3111	14
9	3064	14
10	3153	14
11	3152	14
12	3170	14
13	3201	14
14	5494	14

prune7.0ms (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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	10.7b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize14.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

series118.0ms (1.5%)

Counts

2 → 96

Calls

2 calls:

77.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
40.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

rewrite26.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

16.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
1.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)

simplify179.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

878×	`fma-def_binary64`
685×	`times-frac_binary64`
505×	`cancel-sign-sub-inv_binary64`
356×	`sub-neg_binary64`
161×	`+-commutative_binary64`

Counts

160 → 135

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	271	4135
1	699	4064
2	2396	3758
3	5075	3758

prune176.0ms (2.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	131	4	135
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	132	5	137

Error

0.0b

Counts

137 → 5

Alt Table

Status	Error	Program
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
	7.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
▶	1.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
	28.2b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	38.6b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x) 3))

Compiler

Compiled 3360 to 1095 computations (67.4% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
✓	0.3b	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
✓	1.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

series140.0ms (1.8%)

Counts

3 → 132

Calls

3 calls:

65.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
42.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
33.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))

rewrite92.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
195×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

3 → 214

Calls

3 calls:

21.0ms	(/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t)))
14.0ms	(/.f64 (-.f64 z a) (-.f64 z t))
1.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)

simplify361.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

709×	`cancel-sign-sub-inv_binary64`
528×	`sub-neg_binary64`
232×	`fma-neg_binary64`
224×	`associate--l+_binary64`
221×	`+-commutative_binary64`

Counts

346 → 336

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	403	8765
1	1010	8314
2	3667	8134
3	5378	8134

prune311.0ms (3.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	336	0	336
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	336	5	341

Error

0.0b

Counts

341 → 5

Alt Table

Status	Error	Program
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
▶	7.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	1.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 z a) (-.f64 z t))) x)
	28.2b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)))
	38.6b	(cbrt.f64 (pow.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x) 3))

Compiler

Compiled 8580 to 2755 computations (67.9% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 z a))
✓	0.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	3.5b	(fma.f64 (/.f64 y (-.f64 z a)) z x)
✓	5.3b	(/.f64 (*.f64 y t) (-.f64 z a))

series236.0ms (3%)

Counts

4 → 156

Calls

4 calls:

83.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
71.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
51.0ms	(fma.f64 (/.f64 y (-.f64 z a)) z x)
29.0ms	(/.f64 y (-.f64 z a))

rewrite55.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64`
33×	`prod-diff_binary64`

Counts

4 → 141

Calls

4 calls:

17.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
10.0ms	(/.f64 (*.f64 y t) (-.f64 z a))
8.0ms	(/.f64 y (-.f64 z a))
1.0ms	(fma.f64 (/.f64 y (-.f64 z a)) z x)

simplify405.0ms (5.1%)

Algorithm

1×	egg-herbie

Rules

540×	`cancel-sign-sub-inv_binary64`
307×	`fma-neg_binary64`
252×	`sub-neg_binary64`
206×	`associate-/l*_binary64`
189×	`times-frac_binary64`

Counts

297 → 265

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	398	7851
1	956	7082
2	3439	6648
3	4776	6648
4	4997	6648
5	4858	6648

prune453.0ms (5.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	263	2	265
Fresh	2	0	2
Picked	0	1	1
Done	1	1	2
Total	266	4	270

Error

Counts

270 → 4

Alt Table

Status	Error	Program
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	7.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
▶	3.4b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 y (/.f64 (-.f64 z a) t)))
	7.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 1 (/.f64 (-.f64 z a) (*.f64 y t))))

Compiler

Compiled 8512 to 1739 computations (79.6% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 y (/.f64 (-.f64 z a) t)))
✓	0.0b	(/.f64 (-.f64 z a) t)
	3.5b	(fma.f64 (/.f64 y (-.f64 z a)) z x)
✓	6.7b	(/.f64 y (/.f64 (-.f64 z a) t))

series172.0ms (2.2%)

Counts

3 → 136

Calls

3 calls:

77.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 y (/.f64 (-.f64 z a) t)))
66.0ms	(/.f64 y (/.f64 (-.f64 z a) t))
28.0ms	(/.f64 (-.f64 z a) t)

rewrite207.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

543×	`times-frac_binary64`
433×	`add-sqr-sqrt_binary64`
426×	`*-un-lft-identity_binary64`
320×	`add-cube-cbrt_binary64`
186×	`prod-diff_binary64`

Counts

3 → 405

Calls

3 calls:

46.0ms	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 y (/.f64 (-.f64 z a) t)))
11.0ms	(/.f64 y (/.f64 (-.f64 z a) t))
9.0ms	(/.f64 (-.f64 z a) t)

simplify742.0ms (9.4%)

Algorithm

1×	egg-herbie

Rules

390×	`associate-/r/_binary64`
330×	`associate-/l*_binary64`
217×	`distribute-neg-frac_binary64`
210×	`sub-neg_binary64`
203×	`associate-/l/_binary64`

Counts

541 → 563

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	807	31264
1	2248	21128
2	5047	21128

prune714.0ms (9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	599	0	599
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	599	4	603

Error

Counts

603 → 4

Alt Table

Status	Error	Program
✓	1.9b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 z a)) x)
✓	7.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 (*.f64 y t) (-.f64 z a)))
✓	3.4b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 y (/.f64 (-.f64 z a) t)))
	7.5b	(-.f64 (fma.f64 (/.f64 y (-.f64 z a)) z x) (/.f64 1 (/.f64 (-.f64 z a) (*.f64 y t))))

Compiler

Compiled 26699 to 3897 computations (85.4% saved)

regimes1.0s (13%)

Accuracy

Total 0.2b remaining (92.3%)

Threshold costs 0.2b (92.3%)

Counts

61 → 3

Compiler

Compiled 7303 to 4377 computations (40.1% saved)

bsearch3.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	83
1	32	83
2	39	83
3	43	83
4	45	83
5	44	83

end143.0ms (1.8%)

Compiler: Compiled 204 to 88 computations (56.9% saved)

Details

analyze558.0ms (7.1%)

sample1.5s (19.2%)

simplify175.0ms (2.2%)

prune7.0ms (0.1%)

localize14.0ms (0.2%)

series118.0ms (1.5%)

rewrite26.0ms (0.3%)

simplify179.0ms (2.3%)

prune176.0ms (2.2%)

localize15.0ms (0.2%)

series140.0ms (1.8%)

rewrite92.0ms (1.2%)

simplify361.0ms (4.6%)

prune311.0ms (3.9%)

localize21.0ms (0.3%)

series236.0ms (3%)

rewrite55.0ms (0.7%)

simplify405.0ms (5.1%)

prune453.0ms (5.7%)

localize21.0ms (0.3%)

series172.0ms (2.2%)

rewrite207.0ms (2.6%)

simplify742.0ms (9.4%)

prune714.0ms (9%)

regimes1.0s (13%)

bsearch3.0ms (0%)

simplify8.0ms (0.1%)

end143.0ms (1.8%)

Profiling