Details

analyze839.0ms (26.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
25%	75%	0%	4
37.5%	62.5%	0%	5
43.7%	56.2%	0%	6
46.9%	53.1%	0%	7
46.9%	53.1%	0%	8
46.9%	53.1%	0%	9
47.2%	52.7%	0%	10
47.2%	52.7%	0%	11
47.3%	52.7%	0%	12
47.3%	52.6%	0%	13
47.4%	52.6%	0%	14

Compiler

Compiled 19 to 15 computations (21.1% saved)

sample1.1s (34.3%)

Results

958.0ms

8256×

body

128

valid

Compiler

Compiled 37 to 29 computations (21.6% saved)

simplify115.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

1041×	`fma-neg_binary64`
807×	`times-frac_binary64`
600×	`associate-/r/_binary64`
564×	`sub-neg_binary64`
392×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	25	19
2	45	19
3	72	19
4	115	19
5	188	19
6	308	19
7	491	19
8	989	19
9	1283	19
10	3056	19
11	4408	19
12	4532	19
13	4794	19
14	4959	19
15	4564	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 x (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))

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)
✓	16.0b	(/.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:

3.0ms	(fma.f64 x 27061/100000 230753/100000)
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)
2.0ms	(fma.f64 x 4481/100000 99229/100000)

rewrite5.0ms (0.2%)

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

simplify89.0ms (2.8%)

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

prune94.0ms (3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	2	101

Error

Counts

101 → 2

Alt Table

Status	Error	Program
	0.0b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
▶	0.0b	(-.f64 x (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Status

Error

Program

0.0b

(-.f64 x (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

▶

0.0b

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

Compiler

Compiled 1987 to 1497 computations (24.7% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))))
✓	0.2b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))
	0.2b	(fma.f64 x 27061/100000 230753/100000)
✓	15.9b	(sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

series20.0ms (0.6%)

Counts

3 → 36

Calls

3 calls:

10.0ms

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

6.0ms

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

3.0ms

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

rewrite34.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

92×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
51×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
44×	`sqrt-prod_binary64`

Counts

3 → 141

Calls

3 calls:

15.0ms

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

3.0ms

(/.f64 (fma.f64 x 27061/100000 230753/100000) (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))

simplify166.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

464×	`fma-def_binary64`
340×	`fma-neg_binary64`
339×	`times-frac_binary64`
249×	`cancel-sign-sub-inv_binary64`
226×	`distribute-rgt-in_binary64`

Counts

177 → 232

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	275	6185
1	738	5177
2	2413	5161
3	4875	5150
4	4965	5150

prune359.0ms (11.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	286	0	286
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	286	2	288

Error

Counts

288 → 2

Alt Table

Status	Error	Program
▶	0.0b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
✓	0.0b	(-.f64 x (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Status

Error

Program

▶

0.0b

(-.f64 x (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

✓

0.0b

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

Compiler

Compiled 10609 to 8473 computations (20.1% saved)

localize14.0ms (0.4%)

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)
	16.0b	(/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))

prune101.0ms (3.2%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	100	0	100
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	100	2	102

Error

Counts

102 → 2

Alt Table

Status	Error	Program
✓	0.0b	(-.f64 x (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))
✓	0.0b	(-.f64 x (*.f64 (/.f64 1 (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1))) (/.f64 (fma.f64 x 27061/100000 230753/100000) (sqrt.f64 (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

Status

Error

Program

✓

0.0b

(-.f64 x (expm1.f64 (log1p.f64 (/.f64 (fma.f64 x 27061/100000 230753/100000) (fma.f64 x (fma.f64 x 4481/100000 99229/100000) 1)))))

✓

0.0b

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

Compiler

Compiled 2143 to 1663 computations (22.4% saved)

regimes124.0ms (3.9%)

Accuracy

Total 0.1b remaining (76.3%)

Threshold costs 0.1b (76.3%)

Counts

57 → 1

Compiler

Compiled 1860 to 1418 computations (23.8% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	37
1	23	37
2	34	37
3	42	37
4	48	37
5	51	37
6	52	37
7	50	37

end82.0ms (2.6%)

Compiler: Compiled 98 to 76 computations (22.4% saved)

Details

analyze839.0ms (26.5%)

sample1.1s (34.3%)

simplify115.0ms (3.6%)

prune3.0ms (0.1%)

localize9.0ms (0.3%)

series11.0ms (0.3%)

rewrite5.0ms (0.2%)

simplify89.0ms (2.8%)

prune94.0ms (3%)

localize12.0ms (0.4%)

series20.0ms (0.6%)

rewrite34.0ms (1.1%)

simplify166.0ms (5.2%)

prune359.0ms (11.3%)

localize14.0ms (0.4%)

prune101.0ms (3.2%)

regimes124.0ms (3.9%)

simplify4.0ms (0.1%)

end82.0ms (2.6%)

Profiling