Details

analyze7.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.8%	0.1%	0.1%	12
99.8%	0%	0.1%	13
99.8%	0%	0.2%	14

Compiler

Compiled 11 to 10 computations (9.1% saved)

sample1.3s (42.9%)

Results

1.2s	8248×	body	128	valid
3.0ms	7×	body	1024	valid
0.0ms	1×	body	256	valid

Compiler

Compiled 32 to 29 computations (9.4% saved)

simplify13.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	16	5
3	14	5

prune4.0ms (0.1%)

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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 841/108 x 4/29)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 841/108 x 4/29)

rewrite64.0ms (2.1%)

Algorithm

2×	batch-egg-rewrite

Rules

407×	`log1p-expm1-u_binary64`
407×	`expm1-log1p-u_binary64`
380×	`add-log-exp_binary64`
365×	`pow1_binary64`
180×	`unpow-prod-down_binary64`

Counts

1 → 37

Calls

1 calls:

62.0ms

(fma.f64 841/108 x 4/29)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	102	5
2	1048	5
3	4864	5
0	0	0
1	0	0

simplify15.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Counts

49 → 40

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	72
1	8	54
2	10	54
3	10	54

prune41.0ms (1.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	39	1	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	39	2	41

Error

0.0b

Counts

41 → 2

Alt Table

Status	Error	Program
▶	15.7b	(pow.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) 2)
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 408 to 350 computations (14.2% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 841/108 x 4/29)
✓	0.1b	(sqrt.f64 (fma.f64 841/108 x 4/29))
✓	0.2b	(pow.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) 2)

series67.0ms (2.2%)

Counts

2 → 8

Calls

2 calls:

53.0ms	(pow.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) 2)
14.0ms	(sqrt.f64 (fma.f64 841/108 x 4/29))

rewrite88.0ms (2.9%)

Algorithm

2×	batch-egg-rewrite

Rules

545×	`log1p-expm1-u_binary64`
545×	`expm1-log1p-u_binary64`
299×	`unpow-prod-down_binary64`
235×	`log-prod_binary64`
159×	`pow2_binary64`

Counts

2 → 87

Calls

2 calls:

85.0ms	(sqrt.f64 (fma.f64 841/108 x 4/29))
85.0ms	(pow.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	148	12
2	1420	12
3	4895	12
0	0	0
1	0	0

simplify96.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-neg_binary64`
542×	`times-frac_binary64`
389×	`associate-/l*_binary64`
326×	`fma-def_binary64`
259×	`associate-/r*_binary64`

Counts

95 → 97

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	29	136
1	79	100
2	203	98
3	733	86
4	3675	86
5	4900	86
6	4971	86
7	4999	86
8	4944	86

prune150.0ms (5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	135	4	139

Error

0.0b

Counts

139 → 4

Alt Table

Status	Error	Program
	29.9b	(fma.f64 (*.f64 841/108 (sqrt.f64 x)) (sqrt.f64 x) 4/29)
✓	15.7b	(pow.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) 2)
▶	11.0b	(.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)) 1/2))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 1825 to 1594 computations (12.7% saved)

localize18.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)) 1/2))
✓	0.6b	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29))
✓	0.8b	(cbrt.f64 (fma.f64 841/108 x 4/29))
✓	9.5b	(pow.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)) 1/2)

series43.0ms (1.4%)

Counts

4 → 48

Calls

4 calls:

19.0ms	(pow.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)) 1/2)
11.0ms	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29))
9.0ms	(cbrt.f64 (fma.f64 841/108 x 4/29))
3.0ms	(.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)) 1/2))

rewrite80.0ms (2.6%)

Algorithm

2×	batch-egg-rewrite

Rules

707×	`log1p-expm1-u_binary64`
707×	`expm1-log1p-u_binary64`
340×	`log-prod_binary64`
140×	`expm1-udef_binary64`
140×	`log1p-udef_binary64`

Counts

4 → 111

Calls

4 calls:

77.0ms	(.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)) 1/2))
77.0ms	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29))
77.0ms	(cbrt.f64 (fma.f64 841/108 x 4/29))
77.0ms	(pow.f64 (*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)) 1/2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	62
1	207	28
2	1828	28
3	5222	28
0	0	0
1	0	0

simplify131.0ms (4.3%)

Algorithm

1×	egg-herbie

Rules

794×	`fma-neg_binary64`
534×	`fma-def_binary64`
385×	`associate-r_binary64`
380×	`associate-l_binary64`
218×	`cancel-sign-sub-inv_binary64`

Counts

159 → 185

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	1683
1	440	1583
2	1242	1233
3	4808	1233
4	5490	1233

prune344.0ms (11.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	243	1	244
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	243	5	248

Error

0.0b

Counts

248 → 5

Alt Table

Status	Error	Program
	29.9b	(fma.f64 (*.f64 841/108 (sqrt.f64 x)) (sqrt.f64 x) 4/29)
▶	17.4b	(fma.f64 (.f64 841/108 (cbrt.f64 (.f64 x x))) (cbrt.f64 x) 4/29)
✓	15.7b	(pow.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) 2)
✓	11.0b	(.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)) 1/2))
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 6248 to 5347 computations (14.4% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (.f64 841/108 (cbrt.f64 (.f64 x x))) (cbrt.f64 x) 4/29)
✓	0.3b	(.f64 841/108 (cbrt.f64 (.f64 x x)))
✓	0.6b	(cbrt.f64 x)
✓	32.5b	(cbrt.f64 (*.f64 x x))

series202.0ms (6.7%)

Counts

4 → 48

Calls

4 calls:

67.0ms	(fma.f64 (.f64 841/108 (cbrt.f64 (.f64 x x))) (cbrt.f64 x) 4/29)
63.0ms	(cbrt.f64 x)
41.0ms	(cbrt.f64 (*.f64 x x))
30.0ms	(.f64 841/108 (cbrt.f64 (.f64 x x)))

rewrite54.0ms (1.8%)

Algorithm

2×	batch-egg-rewrite

Rules

675×	`log1p-expm1-u_binary64`
675×	`expm1-log1p-u_binary64`
338×	`log-prod_binary64`
139×	`expm1-udef_binary64`
139×	`log1p-udef_binary64`

Counts

4 → 97

Calls

4 calls:

53.0ms	(fma.f64 (.f64 841/108 (cbrt.f64 (.f64 x x))) (cbrt.f64 x) 4/29)
52.0ms	(.f64 841/108 (cbrt.f64 (.f64 x x)))
52.0ms	(cbrt.f64 x)
52.0ms	(cbrt.f64 (*.f64 x x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	33
1	175	21
2	1779	19
3	5166	19
0	0	0
1	0	0

simplify98.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

866×	`unswap-sqr_binary64`
765×	`fma-def_binary64`
461×	`associate-l_binary64`
330×	`sqr-pow_binary64`
312×	`*-commutative_binary64`

Counts

145 → 107

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	348
1	52	332
2	95	324
3	209	324
4	469	324
5	1173	324
6	1716	324
7	3327	324
8	3968	324
9	4548	324
10	4860	324
11	4766	324

prune57.0ms (1.9%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	106	6	112

Error

0.0b

Counts

112 → 6

Alt Table

Status	Error	Program
	29.9b	(fma.f64 (*.f64 841/108 (sqrt.f64 x)) (sqrt.f64 x) 4/29)
✓	17.4b	(fma.f64 (.f64 841/108 (cbrt.f64 (.f64 x x))) (cbrt.f64 x) 4/29)
✓	15.7b	(pow.f64 (sqrt.f64 (fma.f64 841/108 x 4/29)) 2)
✓	11.0b	(.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (fma.f64 841/108 x 4/29)) 1/2))
	17.5b	(fma.f64 (.f64 841/108 (cbrt.f64 (.f64 x x))) (pow.f64 (cbrt.f64 (cbrt.f64 x)) 3) 4/29)
✓	0.1b	(fma.f64 841/108 x 4/29)

Compiler

Compiled 1366 to 915 computations (33% saved)

regimes54.0ms (1.8%)

Accuracy

Total 0.0b remaining (50.7%)

Threshold costs 0.0b (50.7%)

Counts

17 → 1

Compiler

Compiled 582 to 486 computations (16.5% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	7
1	14	7
2	12	7

end74.0ms (2.4%)

Compiler: Compiled 78 to 62 computations (20.5% saved)

Details

analyze7.0ms (0.2%)

sample1.3s (42.9%)

simplify13.0ms (0.4%)

prune4.0ms (0.1%)

localize4.0ms (0.1%)

series3.0ms (0.1%)

rewrite64.0ms (2.1%)

simplify15.0ms (0.5%)

prune41.0ms (1.4%)

localize8.0ms (0.3%)

series67.0ms (2.2%)

rewrite88.0ms (2.9%)

simplify96.0ms (3.2%)

prune150.0ms (5%)

localize18.0ms (0.6%)

series43.0ms (1.4%)

rewrite80.0ms (2.6%)

simplify131.0ms (4.3%)

prune344.0ms (11.3%)

localize13.0ms (0.4%)

series202.0ms (6.7%)

rewrite54.0ms (1.8%)

simplify98.0ms (3.2%)

prune57.0ms (1.9%)

regimes54.0ms (1.8%)

simplify2.0ms (0.1%)

end74.0ms (2.4%)

Profiling