Details

analyze9.0ms (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)

sample952.0ms (36.4%)

Results

895.0ms

8256×

body

128

valid

Compiler

Compiled 56 to 44 computations (21.4% saved)

simplify26.0ms (1%)

Algorithm

1×	egg-herbie

Rules

1014×	`fma-neg_binary64`
643×	`fma-def_binary64`
397×	`div-sub_binary64`
297×	`cancel-sign-sub-inv_binary64`
168×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	31	19
2	56	19
3	79	19
4	94	19
5	113	19
6	159	19
7	249	19
8	414	19
9	665	19
10	1529	19
11	3538	19

Stop Event

1×	node limit

Counts

1 → 2

prune4.0ms (0.2%)

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)

localize8.0ms (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)
✓	12.7b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series8.0ms (0.3%)

Counts

4 → 48

Calls

4 calls:

3.0ms	(/.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)

rewrite67.0ms (2.6%)

Algorithm

1×	batch-egg-rewrite

Rules

509×	`unpow-prod-down_binary64`
418×	`log-prod_binary64`
268×	`pow2_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	35
1	225	35
2	2518	35

Stop Event

1×	node limit

Counts

4 → 165

Calls

4 calls:

64.0ms	(fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)
64.0ms	(fma.f64 x 4481/100000 99229/100000)
64.0ms	(fma.f64 x 27061/100000 230753/100000)
64.0ms	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

simplify35.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-neg_binary64`
739×	`cancel-sign-sub-inv_binary64`
417×	`times-frac_binary64`
305×	`fma-def_binary64`
185×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	51	459
1	131	417
2	314	389
3	855	369
4	2767	369

Stop Event

1×	node limit

Counts

213 → 197

prune197.0ms (7.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	194	3	197
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	195	3	198

Error

Counts

198 → 3

Alt Table

Status	Error	Program
	0.0b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)) x)
▶	0.0b	(-.f64 (*.f64 (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (fma.f64 x 27061/100000 230753/100000)) x)
	16.8b	(-.f64 (.f64 (sqrt.f64 (fma.f64 x 27061/100000 230753/100000)) (.f64 (sqrt.f64 (fma.f64 x 27061/100000 230753/100000)) (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) x)

Compiler

Compiled 4309 to 3353 computations (22.2% saved)

localize11.0ms (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)
✓	0.3b	(/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
✓	12.4b	(*.f64 (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (fma.f64 x 27061/100000 230753/100000))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(*.f64 (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (fma.f64 x 27061/100000 230753/100000))
3.0ms	(/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

rewrite47.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

454×	`log-prod_binary64`
284×	`pow2_binary64`
201×	`expm1-udef_binary64`
201×	`log1p-udef_binary64`
200×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	246	28
2	2715	28

Stop Event

1×	node limit

Counts

2 → 63

Calls

2 calls:

45.0ms	(/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
45.0ms	(*.f64 (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (fma.f64 x 27061/100000 230753/100000))

simplify29.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

535×	`fma-def_binary64`
344×	`cancel-sign-sub-inv_binary64`
290×	`associate-/r*_binary64`
270×	`fma-neg_binary64`
255×	`associate-l_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	67	398
1	191	390
2	509	382
3	1511	366

Stop Event

1×	node limit

Counts

87 → 92

prune157.0ms (6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	167	3	170

Error

Counts

170 → 3

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)) x)
✓	0.0b	(-.f64 (*.f64 (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (fma.f64 x 27061/100000 230753/100000)) x)
	16.8b	(-.f64 (.f64 (sqrt.f64 (fma.f64 x 27061/100000 230753/100000)) (.f64 (sqrt.f64 (fma.f64 x 27061/100000 230753/100000)) (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) x)

Compiler

Compiled 3481 to 2727 computations (21.7% saved)

localize12.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	0.9b	(pow.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)
	12.7b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
✓	19.6b	(cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3))

series6.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms

(pow.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)

3.0ms

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

rewrite53.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

497×	`log-prod_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
176×	`log-pow_binary64`
126×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	288	35
2	3070	35

Stop Event

1×	node limit

Counts

2 → 89

Calls

2 calls:

51.0ms

(pow.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)

51.0ms

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

simplify31.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

536×	`fma-def_binary64`
454×	`associate-/r*_binary64`
343×	`associate-l_binary64`
336×	`cancel-sign-sub-inv_binary64`
273×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	71	398
1	196	390
2	523	382
3	1558	366

Stop Event

1×	node limit

Counts

113 → 117

prune325.0ms (12.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	234	3	237

Error

Counts

237 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)) x)
✓	0.0b	(-.f64 (*.f64 (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (fma.f64 x 27061/100000 230753/100000)) x)
▶	16.8b	(-.f64 (.f64 (sqrt.f64 (fma.f64 x 27061/100000 230753/100000)) (.f64 (sqrt.f64 (fma.f64 x 27061/100000 230753/100000)) (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) x)

Compiler

Compiled 5678 to 4512 computations (20.5% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(fma.f64 x 27061/100000 230753/100000)
	0.3b	(/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))
✓	1.9b	(*.f64 (sqrt.f64 (fma.f64 x 27061/100000 230753/100000)) (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
✓	5.3b	(.f64 (sqrt.f64 (fma.f64 x 27061/100000 230753/100000)) (.f64 (sqrt.f64 (fma.f64 x 27061/100000 230753/100000)) (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))

series13.0ms (0.5%)

Counts

2 → 16

Calls

2 calls:

11.0ms

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

3.0ms

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

rewrite52.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

572×	`log-prod_binary64`
232×	`expm1-udef_binary64`
232×	`log1p-udef_binary64`
198×	`log-pow_binary64`
135×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	37
1	289	34
2	3243	34

Stop Event

1×	node limit

Counts

2 → 50

Calls

2 calls:

51.0ms

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

51.0ms

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

simplify36.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

679×	`fma-neg_binary64`
675×	`times-frac_binary64`
324×	`fma-def_binary64`
223×	`associate-+l+_binary64`
193×	`associate--l+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	86	397
1	251	382
2	850	350
3	3614	346

Stop Event

1×	node limit

Counts

66 → 71

prune167.0ms (6.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	186	0	186
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	186	3	189

Error

Counts

189 → 3

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) 3)) x)
✓	0.0b	(-.f64 (*.f64 (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)) (fma.f64 x 27061/100000 230753/100000)) x)
✓	16.8b	(-.f64 (.f64 (sqrt.f64 (fma.f64 x 27061/100000 230753/100000)) (.f64 (sqrt.f64 (fma.f64 x 27061/100000 230753/100000)) (/.f64 1 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))) x)

Compiler

Compiled 4995 to 4001 computations (19.9% saved)

regimes272.0ms (10.4%)

Accuracy

Total 0.1b remaining (89.4%)

Threshold costs 0.1b (89.4%)

Counts

130 → 1

Compiler

Compiled 4610 to 3602 computations (21.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	24
1	29	24
2	39	24
3	42	24
4	43	24

Stop Event

1×

saturated

end80.0ms (3%)

Compiler: Compiled 93 to 72 computations (22.6% saved)

Details

analyze9.0ms (0.3%)

sample952.0ms (36.4%)

simplify26.0ms (1%)

prune4.0ms (0.2%)

localize8.0ms (0.3%)

series8.0ms (0.3%)

rewrite67.0ms (2.6%)

simplify35.0ms (1.3%)

prune197.0ms (7.5%)

localize11.0ms (0.4%)

series6.0ms (0.2%)

rewrite47.0ms (1.8%)

simplify29.0ms (1.1%)

prune157.0ms (6%)

localize12.0ms (0.5%)

series6.0ms (0.2%)

rewrite53.0ms (2%)

simplify31.0ms (1.2%)

prune325.0ms (12.4%)

localize13.0ms (0.5%)

series13.0ms (0.5%)

rewrite52.0ms (2%)

simplify36.0ms (1.4%)

prune167.0ms (6.4%)

regimes272.0ms (10.4%)

simplify3.0ms (0.1%)

end80.0ms (3%)

Profiling