Details

analyze7.0ms (0.2%)

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)

sample1.2s (40.1%)

Results

1.1s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify115.0ms (3.8%)

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

prune5.0ms (0.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

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

Error

0.0b

Counts

3 → 2

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)))
	1.0b	(/.f64 4 (.f64 (.f64 (.f64 3 (PI.f64)) (-.f64 1 (.f64 v v))) (sqrt.f64 (-.f64 2 (.f64 6 (.f64 v v))))))

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)))

1.0b

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

Compiler

Compiled 113 to 85 computations (24.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series43.0ms (1.4%)

Counts

4 → 48

Calls

4 calls:

24.0ms	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
10.0ms	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
5.0ms	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))
3.0ms	(*.f64 (PI.f64) (fma.f64 v v -1))

rewrite23.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 134

Calls

4 calls:

6.0ms	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
4.0ms	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
3.0ms	(*.f64 (PI.f64) (fma.f64 v v -1))
1.0ms	(sqrt.f64 (fma.f64 v (*.f64 v -6) 2))

simplify158.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

880×	`fma-def_binary64`
306×	`associate-/r*_binary64`
254×	`sub-neg_binary64`
223×	`fma-neg_binary64`
173×	`associate-r_binary64`

Counts

182 → 227

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	386	5649
1	1028	5260
2	3616	5237
3	4798	5236
4	4955	5236

prune212.0ms (6.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	228	1	229

Error

Counts

229 → 1

Alt Table

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

Compiler

Compiled 6613 to 4938 computations (25.3% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series32.0ms (1%)

Counts

3 → 24

Calls

3 calls:

25.0ms	(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
6.0ms	(/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))
0.0ms	(/.f64 -4/3 (PI.f64))

rewrite103.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

804×	`times-frac_binary64`
386×	`*-un-lft-identity_binary64`
386×	`add-sqr-sqrt_binary64`
386×	`add-cube-cbrt_binary64`
132×	`sqrt-prod_binary64`

Counts

3 → 427

Calls

3 calls:

14.0ms	(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
4.0ms	(/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))
2.0ms	(/.f64 -4/3 (PI.f64))

simplify517.0ms (17%)

Algorithm

1×	egg-herbie

Rules

742×	`fma-def_binary64`
505×	`associate-/r*_binary64`
334×	`associate-/l/_binary64`
175×	`*-commutative_binary64`
154×	`fma-neg_binary64`

Counts

451 → 557

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	713	20352
1	1726	20028
2	4222	20011
3	4964	20011
4	4940	20011

prune506.0ms (16.6%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	595	0	595
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	595	1	596

Error

Counts

596 → 1

Alt Table

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

Compiler

Compiled 20606 to 14946 computations (27.5% saved)

regimes40.0ms (1.3%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Counts

10 → 1

Compiler

Compiled 712 to 558 computations (21.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	15	24
2	15	24

end44.0ms (1.4%)

Compiler: Compiled 51 to 39 computations (23.5% saved)

Details

analyze7.0ms (0.2%)

sample1.2s (40.1%)

simplify115.0ms (3.8%)

prune5.0ms (0.2%)

localize9.0ms (0.3%)

series43.0ms (1.4%)

rewrite23.0ms (0.8%)

simplify158.0ms (5.2%)

prune212.0ms (6.9%)

localize11.0ms (0.3%)

series32.0ms (1%)

rewrite103.0ms (3.4%)

simplify517.0ms (17%)

prune506.0ms (16.6%)

regimes40.0ms (1.3%)

simplify2.0ms (0.1%)

end44.0ms (1.4%)

Profiling