Details

analyze3.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample802.0ms (42.4%)

Results

770.0ms	8254×	body	128	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	10	12

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize5.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
✓	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.2b	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))

series62.0ms (3.3%)

Counts

3 → 12

Calls

3 calls:

47.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
7.0ms	(sqrt.f64 (+.f64 x 1))

rewrite21.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`*-un-lft-identity_binary64`
30×	`add-sqr-sqrt_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`

Counts

3 → 82

Calls

3 calls:

10.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
4.0ms	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(sqrt.f64 (+.f64 x 1))

simplify104.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

733×	`fma-neg_binary64`
333×	`associate-/r*_binary64`
321×	`associate-/l/_binary64`
303×	`associate-*l/_binary64`
284×	`cancel-sign-sub-inv_binary64`

Counts

94 → 108

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	123	1335
1	263	1239
2	634	1227
3	1878	1212
4	4323	1211
5	4987	1211
6	4875	1211

prune94.0ms (5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	3	109

Error

Counts

109 → 3

Alt Table

Status	Error	Program
	22.5b	(.f64 x (+.f64 1/2 (.f64 x -1/8)))
	38.5b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
▶	0.3b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))

Compiler

Compiled 1598 to 1229 computations (23.1% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (sqrt.f64 (+.f64 x 1)))
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	0.1b	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)
✓	0.2b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))

series61.0ms (3.2%)

Counts

2 → 8

Calls

2 calls:

46.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
15.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)

rewrite36.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`*-un-lft-identity_binary64`
156×	`times-frac_binary64`
108×	`add-sqr-sqrt_binary64`
76×	`add-cube-cbrt_binary64`
64×	`distribute-lft-out_binary64`

Counts

2 → 157

Calls

2 calls:

11.0ms	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))
7.0ms	(/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x)

simplify166.0ms (8.8%)

Algorithm

1×	egg-herbie

Rules

918×	`fma-neg_binary64`
842×	`fma-def_binary64`
286×	`times-frac_binary64`
250×	`*-commutative_binary64`
241×	`distribute-rgt-in_binary64`

Counts

165 → 178

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	134	3593
1	290	3208
2	750	3139
3	2088	3123
4	4240	3123
5	4979	3123
6	4918	3123

prune145.0ms (7.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	235	1	236
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	236	3	239

Error

Counts

239 → 3

Alt Table

Status	Error	Program
▶	22.5b	(*.f64 x (fma.f64 x -1/8 1/2))
	38.5b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.3b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))

Compiler

Compiled 4446 to 3514 computations (21% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (fma.f64 x -1/8 1/2))

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 x (fma.f64 x -1/8 1/2))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64`
3×	`associate-r_binary64`
3×	`associate-l_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-cube-cbrt_binary64`

Counts

1 → 22

Calls

1 calls:

3.0ms

(*.f64 x (fma.f64 x -1/8 1/2))

simplify45.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

684×	`distribute-rgt-in_binary64`
683×	`distribute-lft-in_binary64`
576×	`associate-+r+_binary64`
470×	`associate-+l+_binary64`
258×	`fma-def_binary64`

Counts

34 → 32

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	46	415
1	87	326
2	246	326
3	727	326
4	2466	326
5	5634	326

prune17.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	32	0	32
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	32	3	35

Error

Counts

35 → 3

Alt Table

Status	Error	Program
✓	22.5b	(*.f64 x (fma.f64 x -1/8 1/2))
▶	38.5b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.3b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))

Compiler

Compiled 377 to 264 computations (30% saved)

localize5.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(sqrt.f64 (+.f64 x 1))
✓	3.8b	(-.f64 1 (sqrt.f64 (+.f64 x 1)))

series9.0ms (0.5%)

Counts

1 → 4

Calls

1 calls:

9.0ms

(-.f64 1 (sqrt.f64 (+.f64 x 1)))

rewrite11.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
25×	`add-sqr-sqrt_binary64`
21×	`prod-diff_binary64`
20×	`sqrt-prod_binary64`
17×	`add-cube-cbrt_binary64`

Counts

1 → 51

Calls

1 calls:

7.0ms

(-.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify89.0ms (4.7%)

Algorithm

1×	egg-herbie

Rules

1016×	`fma-neg_binary64`
557×	`unsub-neg_binary64`
351×	`cancel-sign-sub-inv_binary64`
329×	`unswap-sqr_binary64`
299×	`distribute-rgt-in_binary64`

Counts

55 → 52

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	88	978
1	173	803
2	467	629
3	1485	621
4	3213	617
5	4137	617
6	4903	617

prune49.0ms (2.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	81	3	84

Error

Counts

84 → 3

Alt Table

Status	Error	Program
✓	22.5b	(*.f64 x (fma.f64 x -1/8 1/2))
✓	38.5b	(*.f64 -1 (-.f64 1 (sqrt.f64 (+.f64 x 1))))
✓	0.3b	(/.f64 1 (/.f64 (+.f64 1 (sqrt.f64 (+.f64 x 1))) x))

Compiler

Compiled 1604 to 1384 computations (13.7% saved)

regimes91.0ms (4.8%)

Accuracy

Total 0.2b remaining (94.1%)

Threshold costs 0.2b (94.1%)

Counts

35 → 1

Compiler

Compiled 1114 to 872 computations (21.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	11	12
2	10	12

end51.0ms (2.7%)

Compiler: Compiled 45 to 36 computations (20% saved)

Details

analyze3.0ms (0.2%)

sample802.0ms (42.4%)

simplify7.0ms (0.4%)

prune2.0ms (0.1%)

localize5.0ms (0.3%)

series62.0ms (3.3%)

rewrite21.0ms (1.1%)

simplify104.0ms (5.5%)

prune94.0ms (5%)

localize6.0ms (0.3%)

series61.0ms (3.2%)

rewrite36.0ms (1.9%)

simplify166.0ms (8.8%)

prune145.0ms (7.7%)

localize4.0ms (0.2%)

series3.0ms (0.2%)

rewrite4.0ms (0.2%)

simplify45.0ms (2.4%)

prune17.0ms (0.9%)

localize5.0ms (0.3%)

series9.0ms (0.5%)

rewrite11.0ms (0.6%)

simplify89.0ms (4.7%)

prune49.0ms (2.6%)

regimes91.0ms (4.8%)

simplify3.0ms (0.1%)

end51.0ms (2.7%)

Profiling