Details

analyze6.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
25%	25%	50%	4
37.5%	12.5%	50%	5
43.7%	6.2%	50%	6
46.9%	3.1%	50%	7
48.4%	1.6%	50%	8
49.2%	0.8%	50%	9
49.6%	0.4%	50%	10
49.8%	0.2%	50%	11
49.9%	0.1%	50%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample192.0ms (10%)

Algorithm

1×

intervals

Results

56.0ms

256×

body

128

valid

Compiler

Compiled 44 to 34 computations (22.7% saved)

simplify122.0ms (6.3%)

Algorithm

1×	egg-herbie

Rules

1332×	`fma-def_binary64`
889×	`associate-/r*_binary64`
605×	`neg-sub0_binary64`
599×	`neg-mul-1_binary64`
576×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	17	31
1	42	28
2	102	26
3	261	26
4	684	26
5	1088	24
6	1801	24
7	3541	24
8	3914	24
9	4002	24
10	4416	24
11	4409	24
12	4415	24
13	5159	24

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 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

Compiler

Compiled 71 to 53 computations (25.4% saved)

localize11.0ms (0.6%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (PI.f64) (fma.f64 v v -1))
✓	0.0b	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
✓	1.0b	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))

series38.0ms (2%)

Counts

3 → 36

Calls

3 calls:

26.0ms	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
6.0ms	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
5.0ms	(*.f64 (PI.f64) (fma.f64 v v -1))

rewrite23.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
39×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
37×	`add-cube-cbrt_binary64`
24×	`sqrt-prod_binary64`

Counts

3 → 119

Calls

3 calls:

7.0ms	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
3.0ms	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
3.0ms	(*.f64 (PI.f64) (fma.f64 v v -1))

simplify143.0ms (7.5%)

Algorithm

1×	egg-herbie

Rules

790×	`fma-def_binary64`
281×	`associate-/r*_binary64`
258×	`cancel-sign-sub-inv_binary64`
201×	`neg-mul-1_binary64`
192×	`fma-neg_binary64`

Counts

155 → 189

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	5140
1	899	4776
2	3213	4751
3	4811	4751
4	5019	4751

prune155.0ms (8%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	188	1	189
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	189	1	190

Error

Counts

190 → 1

Alt Table

Status	Error	Program
▶	0b	(/.f64 (.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

Compiler

Compiled 5651 to 4195 computations (25.8% saved)

localize12.0ms (0.6%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1)))
✓	0.0b	(/.f64 (.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

series35.0ms (1.8%)

Counts

2 → 24

Calls

2 calls:

27.0ms	(/.f64 (.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
8.0ms	(*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1)))

rewrite28.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-exp-log_binary64`
37×	`add-sqr-sqrt_binary64`
32×	`add-cbrt-cube_binary64`
31×	`times-frac_binary64`
25×	`div-exp_binary64`

Counts

2 → 100

Calls

2 calls:

9.0ms	(/.f64 (.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
9.0ms	(*.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1)))

simplify139.0ms (7.2%)

Algorithm

1×	egg-herbie

Rules

723×	`fma-def_binary64`
258×	`cancel-sign-sub-inv_binary64`
197×	`associate-/r*_binary64`
195×	`fma-neg_binary64`
192×	`associate-/l*_binary64`

Counts

124 → 187

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	3898
1	931	3407
2	3361	3386
3	4797	3386
4	4989	3386
5	4924	3386

prune150.0ms (7.8%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	187	1	188

Error

Counts

188 → 1

Alt Table

Status	Error	Program
✓	0b	(/.f64 (.f64 (/.f64 1 (PI.f64)) (/.f64 -4/3 (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

Compiler

Compiled 5689 to 4251 computations (25.3% saved)

regimes87.0ms (4.5%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

14 → 1

Compiler

Compiled 1084 to 846 computations (22% saved)

simplify4.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	27
1	20	27
2	19	27

end1.0ms (0%)

Compiler: Compiled 19 to 15 computations (21.1% saved)

sample775.0ms (40.3%)

Algorithm

1×

intervals

Results

548.0ms	8000×	body	128	valid
0.0ms	3×	body	128	nan

Compiler

Compiled 61 to 48 computations (21.3% saved)

Details

analyze6.0ms (0.3%)

sample192.0ms (10%)

simplify122.0ms (6.3%)

prune4.0ms (0.2%)

localize11.0ms (0.6%)

series38.0ms (2%)

rewrite23.0ms (1.2%)

simplify143.0ms (7.5%)

prune155.0ms (8%)

localize12.0ms (0.6%)

series35.0ms (1.8%)

rewrite28.0ms (1.4%)

simplify139.0ms (7.2%)

prune150.0ms (7.8%)

regimes87.0ms (4.5%)

simplify4.0ms (0.2%)

end1.0ms (0%)

sample775.0ms (40.3%)

Profiling