Details

analyze12.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 19 to 15 computations (21.1% saved)

sample1.1s (30.1%)

Results

932.0ms

8256×

body

128

valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify111.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1572×	`fma-neg_binary64`
1419×	`fma-def_binary64`
565×	`sub-neg_binary64`
397×	`div-sub_binary64`
395×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	31	19
2	50	19
3	71	19
4	84	19
5	103	19
6	137	19
7	208	19
8	304	19
9	493	19
10	931	19
11	1441	19
12	2503	19
13	3175	19
14	3604	19
15	4118	19
16	4302	19
17	4751	19

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x)

Compiler

Compiled 62 to 46 computations (25.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
✓	0.2b	(fma.f64 x 4481/100000 99229/100000)
✓	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	15.7b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series11.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

6.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
2.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
1.0ms	(fma.f64 x 27061/100000 230753/100000)
1.0ms	(fma.f64 x 4481/100000 99229/100000)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
12×	`add-sqr-sqrt_binary64`
12×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
6×	`add-cbrt-cube_binary64`

Counts

4 → 59

Calls

4 calls:

2.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
0.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
0.0ms	(fma.f64 x 27061/100000 230753/100000)
0.0ms	(fma.f64 x 4481/100000 99229/100000)

simplify88.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

496×	`fma-def_binary64`
477×	`associate-l_binary64`
447×	`fma-neg_binary64`
424×	`distribute-rgt-in_binary64`
411×	`distribute-lft-in_binary64`

Counts

107 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	120	1537
1	235	1385
2	582	1380
3	1485	1370
4	4572	1370
5	4900	1370

prune118.0ms (3.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	97	3	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	3	101

Error

Counts

101 → 3

Alt Table

Status	Error	Program
	21.3b	(-.f64 (/.f64 (cbrt.f64 (pow.f64 (fma.f64 x 27061/100000 230753/100000) 3)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x)
	0.0b	(-.f64 (/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) x)
▶	0.0b	(-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 3))) x)

Compiler

Compiled 2021 to 1523 computations (24.6% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 x 4481/100000 99229/100000)
	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	10.1b	(cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 3))
✓	15.7b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 3)))

series5.0ms (0.1%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 3)))
2.0ms	(cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 3))

rewrite14.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`cbrt-prod_binary64`
45×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64`
37×	`add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`

Counts

2 → 100

Calls

2 calls:

4.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 3)))
1.0ms	(cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 3))

simplify174.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

619×	`fma-def_binary64`
588×	`associate-/r/_binary64`
265×	`fma-neg_binary64`
239×	`cancel-sign-sub-inv_binary64`
197×	`associate-/r*_binary64`

Counts

124 → 147

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	159	3214
1	264	2917
2	736	2912
3	2654	2902
4	4695	2844
5	4990	2844
6	5000	2844
7	4901	2844

prune211.0ms (6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	178	3	181

Error

Counts

181 → 3

Alt Table

Status	Error	Program
	21.3b	(-.f64 (/.f64 (cbrt.f64 (pow.f64 (fma.f64 x 27061/100000 230753/100000) 3)) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) x)
▶	0.0b	(-.f64 (/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) x)
✓	0.0b	(-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 3))) x)

Compiler

Compiled 4692 to 3695 computations (21.2% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 x 4481/100000 99229/100000)
	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	0.2b	(/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	15.6b	(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series7.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

5.0ms

(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

3.0ms

(/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

rewrite42.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

258×	`times-frac_binary64`
141×	`add-sqr-sqrt_binary64`
140×	`*-un-lft-identity_binary64`
140×	`add-cube-cbrt_binary64`
135×	`sqrt-prod_binary64`

Counts

2 → 192

Calls

2 calls:

8.0ms

(/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

1.0ms

(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

simplify269.0ms (7.6%)

Algorithm

1×	egg-herbie

Rules

512×	`associate-/l/_binary64`
483×	`fma-neg_binary64`
391×	`associate-/r*_binary64`
348×	`sub-neg_binary64`
337×	`times-frac_binary64`

Counts

216 → 253

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	291	10912
1	689	10058
2	1567	9360
3	4164	9143
4	4907	9143

prune489.0ms (13.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	338	1	339
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	339	3	342

Error

Counts

342 → 3

Alt Table

Status	Error	Program
▶	0.9b	(-.f64 (/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (fma.f64 99229/200000 x 1)) x)
✓	0.0b	(-.f64 (/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) x)
✓	0.0b	(-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 3))) x)

Compiler

Compiled 13047 to 10266 computations (21.3% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 x 4481/100000 99229/100000)
	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	0.2b	(/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (fma.f64 99229/200000 x 1))
	15.6b	(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series9.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

9.0ms

(/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (fma.f64 99229/200000 x 1))

rewrite22.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
76×	`*-un-lft-identity_binary64`
76×	`add-sqr-sqrt_binary64`
76×	`add-cube-cbrt_binary64`
36×	`sqrt-prod_binary64`

Counts

1 → 108

Calls

1 calls:

6.0ms

(/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (fma.f64 99229/200000 x 1))

simplify201.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

578×	`associate-/r*_binary64`
465×	`associate-/l/_binary64`
407×	`fma-neg_binary64`
339×	`times-frac_binary64`
282×	`associate-/l*_binary64`

Counts

120 → 193

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	270	5636
1	648	5469
2	1851	5429
3	4545	5421
4	4978	5421
5	5083	5421

prune331.0ms (9.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	263	0	263
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	263	3	266

Error

Counts

266 → 3

Alt Table

Status	Error	Program
✓	0.9b	(-.f64 (/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (fma.f64 99229/200000 x 1)) x)
✓	0.0b	(-.f64 (/.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) x)
✓	0.0b	(-.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (cbrt.f64 (pow.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1) 3))) x)

Compiler

Compiled 9603 to 7655 computations (20.3% saved)

regimes216.0ms (6.1%)

Accuracy

Total 0.0b remaining (43.3%)

Threshold costs 0.0b (43.3%)

Counts

105 → 1

Compiler

Compiled 3814 to 2920 computations (23.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
2×	`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	16	27
1	20	27
2	24	27
3	26	27
4	27	27
5	26	27

end80.0ms (2.3%)

Compiler: Compiled 104 to 81 computations (22.1% saved)

Details

analyze12.0ms (0.3%)

sample1.1s (30.1%)

simplify111.0ms (3.1%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series11.0ms (0.3%)

rewrite5.0ms (0.1%)

simplify88.0ms (2.5%)

prune118.0ms (3.3%)

localize13.0ms (0.4%)

series5.0ms (0.1%)

rewrite14.0ms (0.4%)

simplify174.0ms (4.9%)

prune211.0ms (6%)

localize14.0ms (0.4%)

series7.0ms (0.2%)

rewrite42.0ms (1.2%)

simplify269.0ms (7.6%)

prune489.0ms (13.8%)

localize16.0ms (0.4%)

series9.0ms (0.2%)

rewrite22.0ms (0.6%)

simplify201.0ms (5.7%)

prune331.0ms (9.3%)

regimes216.0ms (6.1%)

simplify2.0ms (0.1%)

end80.0ms (2.3%)

Profiling