Details

analyze31.0ms (0.9%)

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
48.4%	1.6%	50%	9
48.4%	1.6%	50%	10
48.4%	1.6%	50%	11
48.5%	1.5%	50%	12
48.6%	1.4%	50.1%	13
48.6%	1.3%	50.1%	14

Compiler

Compiled 22 to 17 computations (22.7% saved)

sample1.3s (37.8%)

Results

1.2s	8256×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 43 to 33 computations (23.3% saved)

simplify121.0ms (3.4%)

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 (0.1%)

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

Status

Error

Program

1.0b

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

▶

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 113 to 85 computations (24.8% saved)

localize10.0ms (0.3%)

Local error

Found 3 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	(*.f64 (PI.f64) (fma.f64 v v -1))
✓	1.0b	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))

series42.0ms (1.2%)

Counts

3 → 36

Calls

3 calls:

28.0ms	(/.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)))
3.0ms	(*.f64 (PI.f64) (fma.f64 v v -1))

rewrite27.0ms (0.8%)

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)))
5.0ms	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
4.0ms	(*.f64 (PI.f64) (fma.f64 v v -1))

simplify159.0ms (4.5%)

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

prune202.0ms (5.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	187	2	189
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	189	2	191

Error

Counts

191 → 2

Alt Table

Status	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	(/.f64 (log1p.f64 (expm1.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

Status

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

(/.f64 (log1p.f64 (expm1.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

Compiler

Compiled 5685 to 4221 computations (25.8% saved)

localize11.0ms (0.3%)

Local error

Found 3 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	(/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))
✓	1.0b	(/.f64 -4/3 (PI.f64))

series36.0ms (1%)

Counts

3 → 24

Calls

3 calls:

29.0ms	(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
7.0ms	(/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))
0.0ms	(/.f64 -4/3 (PI.f64))

rewrite109.0ms (3.1%)

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:

15.0ms	(/.f64 (/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1)) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
7.0ms	(/.f64 (/.f64 -4/3 (PI.f64)) (fma.f64 v v -1))
3.0ms	(/.f64 -4/3 (PI.f64))

simplify517.0ms (14.6%)

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

prune534.0ms (15.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	557	0	557
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	557	2	559

Error

Counts

559 → 2

Alt Table

Status	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	(/.f64 (log1p.f64 (expm1.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

Status

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

(/.f64 (log1p.f64 (expm1.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

Compiler

Compiled 19680 to 14231 computations (27.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (PI.f64) (fma.f64 v v -1))
	1.0b	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
✓	1.0b	(log1p.f64 (expm1.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))))
✓	1.0b	(expm1.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))))

series28.0ms (0.8%)

Counts

2 → 24

Calls

2 calls:

21.0ms	(expm1.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))))
7.0ms	(log1p.f64 (expm1.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

2.0ms	(log1p.f64 (expm1.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))))
1.0ms	(expm1.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))))

simplify75.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

690×	`fma-neg_binary64`
451×	`fma-def_binary64`
421×	`associate-/r*_binary64`
264×	`associate-l_binary64`
252×	`associate--r+_binary64`

Counts

46 → 59

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	146	1541
1	415	1471
2	1361	1423
3	4921	1423
4	5508	1423

prune136.0ms (3.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	135	2	137

Error

Counts

137 → 2

Alt Table

Status	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	(/.f64 (log1p.f64 (expm1.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))

Status

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

(/.f64 (log1p.f64 (expm1.f64 (/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1))))) (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

Compiler

Compiled 3771 to 2760 computations (26.8% saved)

regimes69.0ms (2%)

Accuracy

Total 0.0b remaining (31.5%)

Threshold costs 0.0b (31.5%)

Counts

16 → 1

Compiler

Compiled 1156 to 914 computations (20.9% 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

end60.0ms (1.7%)

Compiler: Compiled 70 to 54 computations (22.9% saved)

Details

analyze31.0ms (0.9%)

sample1.3s (37.8%)

simplify121.0ms (3.4%)

prune5.0ms (0.1%)

localize10.0ms (0.3%)

series42.0ms (1.2%)

rewrite27.0ms (0.8%)

simplify159.0ms (4.5%)

prune202.0ms (5.7%)

localize11.0ms (0.3%)

series36.0ms (1%)

rewrite109.0ms (3.1%)

simplify517.0ms (14.6%)

prune534.0ms (15.1%)

localize14.0ms (0.4%)

series28.0ms (0.8%)

rewrite4.0ms (0.1%)

simplify75.0ms (2.1%)

prune136.0ms (3.8%)

regimes69.0ms (2%)

simplify2.0ms (0.1%)

end60.0ms (1.7%)

Profiling