Details

analyze6.0ms (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)

sample1.3s (43%)

Results

1.2s	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 65 to 50 computations (23.1% saved)

simplify116.0ms (3.7%)

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)

localize11.0ms (0.4%)

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)))

series41.0ms (1.3%)

Counts

3 → 36

Calls

3 calls:

30.0ms	(/.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (sqrt.f64 (fma.f64 v (.f64 v -6) 2)))
7.0ms	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))
4.0ms	(*.f64 (PI.f64) (fma.f64 v v -1))

rewrite54.0ms (1.7%)

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:

40.0ms	(/.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))

simplify161.0ms (5.2%)

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

prune203.0ms (6.5%)

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

Status

Error

Program

0.0b

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

▶

0.0b

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

Compiler

Compiled 5689 to 4225 computations (25.7% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

series43.0ms (1.4%)

Counts

3 → 36

Calls

3 calls:

28.0ms

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

8.0ms

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

6.0ms

(/.f64 (/.f64 1 (PI.f64)) (fma.f64 v v -1))

rewrite45.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

152×	`times-frac_binary64`
97×	`add-sqr-sqrt_binary64`
86×	`*-un-lft-identity_binary64`
85×	`add-cube-cbrt_binary64`
49×	`add-exp-log_binary64`

Counts

3 → 180

Calls

3 calls:

11.0ms

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

8.0ms

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

6.0ms

(/.f64 (/.f64 1 (PI.f64)) (fma.f64 v v -1))

simplify168.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

728×	`fma-def_binary64`
256×	`cancel-sign-sub-inv_binary64`
198×	`fma-neg_binary64`
197×	`associate-/r*_binary64`
175×	`sub-neg_binary64`

Counts

216 → 300

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	372	5996
1	1012	5446
2	3325	5406
3	4944	5406
4	4924	5406

prune272.0ms (8.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	300	2	302

Error

Counts

302 → 2

Alt Table

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

Status

Error

Program

▶

0.0b

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

✓

0.0b

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

Compiler

Compiled 9182 to 6685 computations (27.2% saved)

localize13.0ms (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 1 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))
✓	1.0b	(.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (/.f64 1 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
	1.0b	(/.f64 -4/3 (*.f64 (PI.f64) (fma.f64 v v -1)))

series40.0ms (1.3%)

Counts

2 → 24

Calls

2 calls:

29.0ms	(.f64 (/.f64 -4/3 (.f64 (PI.f64) (fma.f64 v v -1))) (/.f64 1 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2))))
11.0ms	(/.f64 1 (sqrt.f64 (fma.f64 v (*.f64 v -6) 2)))

rewrite29.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64`
44×	`add-sqr-sqrt_binary64`
43×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`

Counts

2 → 114

Calls

2 calls:

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

simplify129.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

710×	`fma-def_binary64`
322×	`cancel-sign-sub-inv_binary64`
214×	`associate-/r*_binary64`
204×	`sub-neg_binary64`
172×	`fma-neg_binary64`

Counts

138 → 183

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	322	4573
1	884	4118
2	3187	4095
3	4972	4095
4	4911	4095

prune271.0ms (8.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	259	0	259
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	259	2	261

Error

Counts

261 → 2

Alt Table

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

Status

Error

Program

✓

0.0b

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

✓

0.0b

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

Compiler

Compiled 7939 to 6076 computations (23.5% saved)

regimes97.0ms (3.1%)

Accuracy

Total 0.0b remaining (48.4%)

Threshold costs 0.0b (48.4%)

Counts

23 → 1

Compiler

Compiled 1744 to 1387 computations (20.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	24
1	16	24
2	16	24

end62.0ms (2%)

Compiler: Compiled 72 to 56 computations (22.2% saved)

Details

analyze6.0ms (0.2%)

sample1.3s (43%)

simplify116.0ms (3.7%)

prune5.0ms (0.2%)

localize11.0ms (0.4%)

series41.0ms (1.3%)

rewrite54.0ms (1.7%)

simplify161.0ms (5.2%)

prune203.0ms (6.5%)

localize11.0ms (0.3%)

series43.0ms (1.4%)

rewrite45.0ms (1.4%)

simplify168.0ms (5.4%)

prune272.0ms (8.7%)

localize13.0ms (0.4%)

series40.0ms (1.3%)

rewrite29.0ms (0.9%)

simplify129.0ms (4.1%)

prune271.0ms (8.7%)

regimes97.0ms (3.1%)

simplify2.0ms (0.1%)

end62.0ms (2%)

Profiling