Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
100%	0%	0%	2

Compiler

Compiled 10 to 8 computations (20% saved)

sample826.0ms (38.4%)

Results

718.0ms

8256×

body

128

valid

Compiler

Compiled 29 to 23 computations (20.7% saved)

simplify84.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

638×	`fma-def_binary64`
434×	`unswap-sqr_binary64`
366×	`fma-neg_binary64`
277×	`*-commutative_binary64`
262×	`exp-prod_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	13
1	15	13
2	20	13
3	27	13
4	46	13
5	78	13
6	146	13
7	274	13
8	670	13
9	1896	13
10	2692	13
11	3535	13
12	4713	13
13	4865	13
14	4794	13

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

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

Compiler

Compiled 27 to 21 computations (22.2% saved)

localize6.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

series14.0ms (0.7%)

Counts

2 → 16

Calls

2 calls:

12.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
2.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

rewrite12.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

2 → 57

Calls

2 calls:

6.0ms	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))
3.0ms	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))

simplify77.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-neg_binary64`
684×	`fma-def_binary64`
548×	`associate-l_binary64`
292×	`times-frac_binary64`
257×	`distribute-rgt-in_binary64`

Counts

73 → 105

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	115	1210
1	248	1114
2	549	1101
3	1241	1099
4	4205	1099
5	4980	1099

prune78.0ms (3.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	3	106

Error

Counts

106 → 3

Alt Table

Status	Error	Program
	0.0b	(/.f64 2 (fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (exp.f64 (neg.f64 x))))
	28.6b	(fma.f64 x (*.f64 x -1/2) 1)
▶	0.0b	(*.f64 (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))

Compiler

Compiled 1652 to 690 computations (58.2% saved)

localize7.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
	0.0b	(+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))
✓	0.0b	(*.f64 (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
	0.0b	(/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))

series39.0ms (1.8%)

Counts

2 → 24

Calls

2 calls:

21.0ms	(sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))
18.0ms	(*.f64 (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))

rewrite52.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

131×	`sqrt-prod_binary64`
104×	`add-sqr-sqrt_binary64`
103×	`*-un-lft-identity_binary64`
100×	`times-frac_binary64`
55×	`add-cube-cbrt_binary64`

Counts

2 → 160

Calls

2 calls:

23.0ms	(*.f64 (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))
5.0ms	(sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x)))))

simplify140.0ms (6.5%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-neg_binary64`
376×	`associate-/l*_binary64`
301×	`times-frac_binary64`
223×	`associate-/r*_binary64`
223×	`fma-def_binary64`

Counts

184 → 209

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	250	4718
1	481	4394
2	1630	4275
3	4718	4271
4	5268	4271

prune354.0ms (16.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	469	0	469
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	469	3	472

Error

Counts

472 → 3

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 2 (fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (exp.f64 (neg.f64 x))))
	28.6b	(fma.f64 x (*.f64 x -1/2) 1)
✓	0.0b	(*.f64 (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))

Compiler

Compiled 12889 to 5806 computations (55% saved)

localize8.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (exp.f64 (neg.f64 x)))
✓	0.0b	(sqrt.f64 (exp.f64 x))
✓	0.0b	(/.f64 2 (fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (exp.f64 (neg.f64 x))))

series23.0ms (1.1%)

Counts

3 → 28

Calls

3 calls:

15.0ms	(/.f64 2 (fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (exp.f64 (neg.f64 x))))
5.0ms	(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (exp.f64 (neg.f64 x)))
3.0ms	(sqrt.f64 (exp.f64 x))

rewrite7.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 57

Calls

3 calls:

3.0ms	(/.f64 2 (fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (exp.f64 (neg.f64 x))))
1.0ms	(sqrt.f64 (exp.f64 x))
0.0ms	(fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (exp.f64 (neg.f64 x)))

simplify85.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

817×	`fma-neg_binary64`
743×	`fma-def_binary64`
692×	`cancel-sign-sub-inv_binary64`
308×	`unswap-sqr_binary64`
250×	`*-commutative_binary64`

Counts

85 → 112

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	127	1263
1	227	1180
2	486	1170
3	1169	1161
4	2892	1161
5	4759	1161
6	4949	1161

prune88.0ms (4.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	137	3	140

Error

Counts

140 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 2 (fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (exp.f64 (neg.f64 x))))
▶	28.6b	(fma.f64 x (*.f64 x -1/2) 1)
✓	0.0b	(*.f64 (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))

Compiler

Compiled 2426 to 869 computations (64.2% saved)

localize4.0ms (0.2%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

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

Error

Counts

3 → 3

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 2 (fma.f64 (sqrt.f64 (exp.f64 x)) (sqrt.f64 (exp.f64 x)) (exp.f64 (neg.f64 x))))
✓	28.6b	(fma.f64 x (*.f64 x -1/2) 1)
✓	0.0b	(*.f64 (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))) (sqrt.f64 (/.f64 2 (+.f64 (exp.f64 x) (exp.f64 (neg.f64 x))))))

Compiler

Compiled 40 to 25 computations (37.5% saved)

regimes174.0ms (8.1%)

Accuracy

Total 0.0b remaining (72.3%)

Threshold costs 0.0b (72.3%)

Counts

71 → 1

Compiler

Compiled 3550 to 2715 computations (23.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	24
1	15	24
2	17	24
3	18	24
4	18	24

end63.0ms (2.9%)

Compiler: Compiled 70 to 45 computations (35.7% saved)

Details

analyze1.0ms (0%)

sample826.0ms (38.4%)

simplify84.0ms (3.9%)

prune2.0ms (0.1%)

localize6.0ms (0.3%)

series14.0ms (0.7%)

rewrite12.0ms (0.6%)

simplify77.0ms (3.6%)

prune78.0ms (3.6%)

localize7.0ms (0.3%)

series39.0ms (1.8%)

rewrite52.0ms (2.4%)

simplify140.0ms (6.5%)

prune354.0ms (16.5%)

localize8.0ms (0.4%)

series23.0ms (1.1%)

rewrite7.0ms (0.3%)

simplify85.0ms (3.9%)

prune88.0ms (4.1%)

localize4.0ms (0.2%)

prune2.0ms (0.1%)

regimes174.0ms (8.1%)

simplify2.0ms (0.1%)

end63.0ms (2.9%)

Profiling