Details

analyze3.4s (47.3%)

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 (16.7%)

Results

1.0s	8255×	body	128	valid
92.0ms	750×	body	128	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify116.0ms (1.6%)

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%)

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
▶	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	10.9b	(+.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))
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series64.0ms (0.9%)

Counts

2 → 96

Calls

2 calls:

41.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
22.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite12.0ms (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:

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

simplify112.0ms (1.6%)

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

prune100.0ms (1.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

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

Error

0.0b

Counts

140 → 5

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
▶	1.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
	28.5b	(*.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)))
	3.2b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	10.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))

Compiler

Compiled 3381 to 1128 computations (66.6% 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)))
✓	1.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

series71.0ms (1%)

Counts

3 → 120

Calls

3 calls:

42.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
20.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
8.0ms	(/.f64 1 (-.f64 a t))

rewrite22.0ms (0.3%)

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:

12.0ms	(*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t)))
4.0ms	(/.f64 1 (-.f64 a t))
0.0ms	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)

simplify136.0ms (1.9%)

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

prune147.0ms (2.1%)

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

0.0b

Counts

232 → 5

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	1.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
	28.5b	(*.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)))
▶	3.2b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
	10.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))

Compiler

Compiled 5310 to 1956 computations (63.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 a t))
✓	0.0b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	10.0b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series99.0ms (1.4%)

Counts

3 → 132

Calls

3 calls:

46.0ms	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
36.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
16.0ms	(/.f64 y (-.f64 a t))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`add-sqr-sqrt_binary64`
68×	`*-un-lft-identity_binary64`
52×	`add-cube-cbrt_binary64`
36×	`prod-diff_binary64`
31×	`times-frac_binary64`

Counts

3 → 155

Calls

3 calls:

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

simplify198.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

422×	`sub-neg_binary64`
404×	`fma-neg_binary64`
222×	`associate--l+_binary64`
218×	`+-commutative_binary64`
182×	`associate-l_binary64`

Counts

287 → 308

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	443	6869
1	1078	6148
2	3977	6052
3	4707	6051
4	4994	6051
5	4942	6051

prune217.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	306	2	308
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	308	5	313

Error

0.0b

Counts

313 → 5

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	1.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
▶	3.2b	(+.f64 (fma.f64 z (/.f64 y (-.f64 a t)) x) (*.f64 (neg.f64 t) (/.f64 y (-.f64 a t))))
	33.2b	(+.f64 x (*.f64 (/.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (sqrt.f64 (-.f64 a t))) (-.f64 z t)))
	10.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))

Compiler

Compiled 8052 to 2073 computations (74.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(/.f64 y (-.f64 a t))
✓	2.8b	(fma.f64 z (/.f64 y (-.f64 a t)) x)
✓	8.3b	(*.f64 (neg.f64 t) (/.f64 y (-.f64 a t)))

series48.0ms (0.7%)

Counts

2 → 96

Calls

2 calls:

27.0ms	(fma.f64 z (/.f64 y (-.f64 a t)) x)
21.0ms	(*.f64 (neg.f64 t) (/.f64 y (-.f64 a t)))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
21×	`associate-r_binary64`
20×	`*-un-lft-identity_binary64`
16×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`

Counts

2 → 60

Calls

2 calls:

11.0ms	(*.f64 (neg.f64 t) (/.f64 y (-.f64 a t)))
0.0ms	(fma.f64 z (/.f64 y (-.f64 a t)) x)

simplify89.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

506×	`fma-def_binary64`
292×	`div-sub_binary64`
195×	`cancel-sign-sub-inv_binary64`
188×	`associate-/r/_binary64`
176×	`distribute-lft-neg-out_binary64`

Counts

156 → 126

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	211	2651
1	553	2565
2	1993	2298
3	4653	2298
4	5288	2298

prune172.0ms (2.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	256	0	256
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	256	5	261

Error

0.0b

Counts

261 → 5

Alt Table

Status	Error	Program
✓	1.3b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
✓	1.3b	(fma.f64 y (*.f64 (-.f64 z t) (/.f64 1 (-.f64 a t))) x)
✓	3.2b	(+.f64 (fma.f64 z (/.f64 y (-.f64 a t)) x) (*.f64 (neg.f64 t) (/.f64 y (-.f64 a t))))
	33.2b	(+.f64 x (*.f64 (/.f64 (/.f64 y (sqrt.f64 (-.f64 a t))) (sqrt.f64 (-.f64 a t))) (-.f64 z t)))
	10.9b	(-.f64 (+.f64 (/.f64 (.f64 y z) (-.f64 a t)) x) (/.f64 (.f64 y t) (-.f64 a t)))

Compiler

Compiled 6768 to 1498 computations (77.9% saved)

regimes782.0ms (11%)

Accuracy

Total 0.7b remaining (98.1%)

Threshold costs 0.7b (98.1%)

Counts

104 → 3

Compiler

Compiled 13246 to 8115 computations (38.7% saved)

bsearch7.0ms (0.1%)

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

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
1×	`*-lft-identity_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	83
1	33	83
2	38	83
3	40	83
4	41	83
5	40	83

end73.0ms (1%)

Compiler: Compiled 222 to 99 computations (55.4% saved)

Details

analyze3.4s (47.3%)

sample1.2s (16.7%)

simplify116.0ms (1.6%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series64.0ms (0.9%)

rewrite12.0ms (0.2%)

simplify112.0ms (1.6%)

prune100.0ms (1.4%)

localize8.0ms (0.1%)

series71.0ms (1%)

rewrite22.0ms (0.3%)

simplify136.0ms (1.9%)

prune147.0ms (2.1%)

localize7.0ms (0.1%)

series99.0ms (1.4%)

rewrite31.0ms (0.4%)

simplify198.0ms (2.8%)

prune217.0ms (3.1%)

localize9.0ms (0.1%)

series48.0ms (0.7%)

rewrite15.0ms (0.2%)

simplify89.0ms (1.3%)

prune172.0ms (2.4%)

regimes782.0ms (11%)

bsearch7.0ms (0.1%)

simplify4.0ms (0.1%)

end73.0ms (1%)

Profiling