Details

analyze1.3s (24.4%)

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
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
22.4%	77.4%	0.2%	13
23.5%	76.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.2s (22.5%)

Results

1.0s	8252×	body	128	valid
86.0ms	729×	body	128	invalid
1.0ms	2×	body	2048	valid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify118.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

1894×	`fma-neg_binary64`
843×	`div-sub_binary64`
750×	`fma-def_binary64`
582×	`times-frac_binary64`
397×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	37	14
3	78	14
4	163	14
5	295	14
6	645	14
7	1554	14
8	3040	14
9	3228	14
10	3469	14
11	3370	14
12	3363	14
13	3398	14
14	4949	14

prune3.0ms (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
▶	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	9.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	0.8b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series70.0ms (1.3%)

Counts

2 → 96

Calls

2 calls:

46.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
23.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite10.0ms (0.2%)

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:

6.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify116.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

690×	`cancel-sign-sub-inv_binary64`
647×	`times-frac_binary64`
542×	`fma-neg_binary64`
354×	`sub-neg_binary64`
188×	`neg-mul-1_binary64`

Counts

160 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4118
1	740	4035
2	2434	3427
3	4231	3410
4	4964	3410

prune110.0ms (2.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	134	4	138
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	135	5	140

Error

Counts

140 → 5

Alt Table

Status	Error	Program
	9.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
▶	0.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
	18.1b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)
	30.0b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))

Compiler

Compiled 3406 to 1139 computations (66.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
✓	0.4b	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
✓	0.8b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)

series85.0ms (1.6%)

Counts

3 → 132

Calls

3 calls:

41.0ms	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
23.0ms	(/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t)))
20.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

rewrite39.0ms (0.7%)

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:

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

simplify168.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

927×	`cancel-sign-sub-inv_binary64`
524×	`sub-neg_binary64`
249×	`associate--l+_binary64`
234×	`+-commutative_binary64`
217×	`fma-neg_binary64`

Counts

346 → 337

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	8735
1	1041	8263
2	3678	8083
3	5565	8083

prune223.0ms (4.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	337	0	337
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	337	5	342

Error

Counts

342 → 5

Alt Table

Status	Error	Program
	9.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
▶	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
	18.1b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)
	30.0b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))

Compiler

Compiled 8683 to 2777 computations (68% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a t))
✓	0.2b	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
✓	0.8b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

series713.0ms (13.5%)

Counts

3 → 120

Calls

3 calls:

650.0ms	(/.f64 1 (-.f64 a t))
41.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
21.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 105

Calls

3 calls:

10.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
6.0ms	(/.f64 1 (-.f64 a t))
0.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

simplify134.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

700×	`cancel-sign-sub-inv_binary64`
675×	`times-frac_binary64`
380×	`fma-neg_binary64`
354×	`sub-neg_binary64`
192×	`+-commutative_binary64`

Counts

225 → 227

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	298	4903
1	792	4646
2	2764	4604
3	4923	4603
4	5113	4603

prune143.0ms (2.7%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	227	0	227
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	227	5	232

Error

Counts

232 → 5

Alt Table

Status	Error	Program
▶	9.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
	18.1b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)
	30.0b	(*.f64 (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (sqrt.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))

Compiler

Compiled 5318 to 1956 computations (63.2% 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)) (-.f64 a t)))
✓	0.0b	(*.f64 y (-.f64 z t))
✓	10.0b	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

series89.0ms (1.7%)

Counts

3 → 144

Calls

3 calls:

46.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
34.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
9.0ms	(*.f64 y (-.f64 z t))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 98

Calls

3 calls:

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

simplify138.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

426×	`sub-neg_binary64`
348×	`div-sub_binary64`
330×	`fma-neg_binary64`
239×	`associate-/l*_binary64`
225×	`associate--l+_binary64`

Counts

242 → 216

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	349	5059
1	885	4624
2	3750	4528
3	4597	4524
4	5233	4524

prune142.0ms (2.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	216	5	221

Error

Counts

221 → 5

Alt Table

Status	Error	Program
✓	9.8b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	0.9b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	0.9b	(fma.f64 y (/.f64 1 (/.f64 (-.f64 a t) (-.f64 z t))) x)
	18.1b	(fma.f64 y (*.f64 (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) x)
	1.9b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))))

Compiler

Compiled 5338 to 1540 computations (71.2% saved)

regimes358.0ms (6.8%)

Accuracy

Total 1.4b remaining (98%)

Threshold costs 0b (0%)

Counts

60 → 1

Compiler

Compiled 7002 to 4223 computations (39.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`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	10	14
1	13	14
2	19	14
3	21	14
4	22	14
5	22	14

end67.0ms (1.3%)

Compiler: Compiled 132 to 74 computations (43.9% saved)

Details

analyze1.3s (24.4%)

sample1.2s (22.5%)

simplify118.0ms (2.2%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series70.0ms (1.3%)

rewrite10.0ms (0.2%)

simplify116.0ms (2.2%)

prune110.0ms (2.1%)

localize8.0ms (0.2%)

series85.0ms (1.6%)

rewrite39.0ms (0.7%)

simplify168.0ms (3.2%)

prune223.0ms (4.2%)

localize8.0ms (0.1%)

series713.0ms (13.5%)

rewrite22.0ms (0.4%)

simplify134.0ms (2.5%)

prune143.0ms (2.7%)

localize8.0ms (0.2%)

series89.0ms (1.7%)

rewrite27.0ms (0.5%)

simplify138.0ms (2.6%)

prune142.0ms (2.7%)

regimes358.0ms (6.8%)

simplify2.0ms (0%)

end67.0ms (1.3%)

Profiling