Details

analyze4.0ms (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)

sample776.0ms (44.1%)

Results

723.0ms	8253×	body	128	valid
0.0ms	2×	body	1024	valid
0.0ms	1×	body	512	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 32 to 29 computations (9.4% saved)

simplify6.0ms (0.3%)

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

prune3.0ms (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

0.1b

Counts

3 → 2

Alt Table

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

Compiler

Compiled 44 to 38 computations (13.6% saved)

localize2.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series2.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

1.0ms

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

rewrite35.0ms (2%)

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 → 38

Calls

1 calls:

35.0ms

(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

simplify7.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

50 → 40

Iterations

Useful iterations: 1 (0.0ms)

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

prune39.0ms (2.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	35	5	40
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	36	6	42

Error

0.0b

Counts

42 → 6

Alt Table

Status	Error	Program
	19.1b	(pow.f64 (E.f64) (log.f64 (fma.f64 841/108 x 4/29)))
	18.9b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) 3))
	1.8b	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2))
✓	0.1b	(fma.f64 841/108 x 4/29)
▶	0.1b	(+.f64 4/29 (*.f64 841/108 x))
	22.6b	(cbrt.f64 (pow.f64 (fma.f64 841/108 x 4/29) 3))

Compiler

Compiled 502 to 432 computations (13.9% saved)

localize3.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 4/29 (*.f64 841/108 x))
✓	0.1b	(*.f64 841/108 x)

series3.0ms (0.2%)

Counts

2 → 3

Calls

2 calls:

1.0ms	(*.f64 841/108 x)
1.0ms	(+.f64 4/29 (*.f64 841/108 x))

rewrite45.0ms (2.5%)

Algorithm

2×	batch-egg-rewrite

Rules

618×	`log1p-expm1-u_binary64`
618×	`expm1-log1p-u_binary64`
264×	`log-prod_binary64`
120×	`prod-diff_binary64`
116×	`expm1-udef_binary64`

Counts

2 → 57

Calls

2 calls:

44.0ms	(+.f64 4/29 (*.f64 841/108 x))
43.0ms	(*.f64 841/108 x)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	132	9
2	1547	9
3	4947	9
0	0	0
1	0	0

simplify6.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Counts

60 → 58

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	9
1	6	9
2	6	9

prune43.0ms (2.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	55	3	58
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	58	6	64

Error

0.0b

Counts

64 → 6

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (*.f64 841/108 x) 1 4/29)
	18.9b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) 3))
	1.8b	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2))
	22.1b	(/.f64 (fma.f64 594823321/1259712 (pow.f64 x 3) 64/24389) (fma.f64 707281/11664 (.f64 x x) (-.f64 16/841 (.f64 29/27 x))))
✓	0.1b	(fma.f64 841/108 x 4/29)
	15.9b	(/.f64 (fma.f64 707281/11664 (*.f64 x x) -16/841) (fma.f64 841/108 x -4/29))

Compiler

Compiled 698 to 558 computations (20.1% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (*.f64 841/108 x) 1 4/29)
	0.1b	(*.f64 841/108 x)

series2.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

2.0ms

(fma.f64 (*.f64 841/108 x) 1 4/29)

rewrite38.0ms (2.2%)

Algorithm

2×	batch-egg-rewrite

Rules

510×	`log1p-expm1-u_binary64`
510×	`expm1-log1p-u_binary64`
284×	`unpow-prod-down_binary64`
240×	`log-prod_binary64`
153×	`pow2_binary64`

Counts

1 → 33

Calls

1 calls:

37.0ms

(fma.f64 (*.f64 841/108 x) 1 4/29)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	135	7
2	1328	5
3	4897	5
0	0	0
1	0	0

simplify9.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

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

Counts

45 → 35

Iterations

Useful iterations: 1 (0.0ms)

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

prune39.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	51	0	51
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	51	6	57

Error

0.0b

Counts

57 → 6

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (*.f64 841/108 x) 1 4/29)
	18.9b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) 3))
▶	1.8b	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2))
	22.1b	(/.f64 (fma.f64 594823321/1259712 (pow.f64 x 3) 64/24389) (fma.f64 707281/11664 (.f64 x x) (-.f64 16/841 (.f64 29/27 x))))
✓	0.1b	(fma.f64 841/108 x 4/29)
	15.9b	(/.f64 (fma.f64 707281/11664 (*.f64 x x) -16/841) (fma.f64 841/108 x -4/29))

Compiler

Compiled 637 to 540 computations (15.2% saved)

localize6.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 841/108 x 4/29)
✓	0.2b	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2))
✓	0.7b	(cbrt.f64 (fma.f64 841/108 x 4/29))
✓	0.8b	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2)

series15.0ms (0.8%)

Counts

3 → 36

Calls

3 calls:

9.0ms	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2)
4.0ms	(cbrt.f64 (fma.f64 841/108 x 4/29))
2.0ms	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2))

rewrite71.0ms (4.1%)

Algorithm

2×	batch-egg-rewrite

Rules

597×	`log1p-expm1-u_binary64`
597×	`expm1-log1p-u_binary64`
267×	`log-prod_binary64`
174×	`pow2_binary64`
125×	`expm1-udef_binary64`

Counts

3 → 77

Calls

3 calls:

70.0ms	(*.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2))
70.0ms	(cbrt.f64 (fma.f64 841/108 x 4/29))
70.0ms	(pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	165	22
2	1559	22
3	4988	22
4	4846	22
0	0	0
1	0	0

simplify97.0ms (5.5%)

Algorithm

1×	egg-herbie

Rules

636×	`fma-neg_binary64`
420×	`unswap-sqr_binary64`
409×	`fma-def_binary64`
268×	`associate-r_binary64`
249×	`associate-l_binary64`

Counts

113 → 128

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	105	1122
1	304	1052
2	877	820
3	3311	660
4	4873	644
5	4999	644
6	4959	644

prune166.0ms (9.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	256	2	258
Fresh	0	3	3
Picked	1	0	1
Done	0	2	2
Total	257	7	264

Error

0.0b

Counts

264 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (*.f64 841/108 x) 1 4/29)
	18.9b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) 3) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) 3))
	1.9b	(.f64 (cbrt.f64 (.f64 (pow.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 841/108 x 4/29))) 2) 3) (cbrt.f64 (fma.f64 841/108 x 4/29)))) (pow.f64 (cbrt.f64 (fma.f64 841/108 x 4/29)) 2))
	15.9b	(/.f64 (fma.f64 707281/11664 (*.f64 x x) -16/841) (fma.f64 841/108 x -4/29))
	22.1b	(/.f64 (fma.f64 594823321/1259712 (pow.f64 x 3) 64/24389) (fma.f64 707281/11664 (.f64 x x) (-.f64 16/841 (.f64 29/27 x))))
✓	0.1b	(fma.f64 841/108 x 4/29)
	0.7b	(fma.f64 (*.f64 841/108 (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 x) 4/29)

Compiler

Compiled 5296 to 4547 computations (14.1% saved)

regimes214.0ms (12.1%)

Accuracy

Total 0.0b remaining (57.9%)

Threshold costs 0.0b (57.9%)

Counts

62 → 1

Compiler

Compiled 2678 to 2300 computations (14.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	5
1	5	5

end123.0ms (7%)

Compiler: Compiled 107 to 88 computations (17.8% saved)

Details

analyze4.0ms (0.2%)

sample776.0ms (44.1%)

simplify6.0ms (0.3%)

prune3.0ms (0.2%)

localize2.0ms (0.1%)

series2.0ms (0.1%)

rewrite35.0ms (2%)

simplify7.0ms (0.4%)

prune39.0ms (2.2%)

localize3.0ms (0.2%)

series3.0ms (0.2%)

rewrite45.0ms (2.5%)

simplify6.0ms (0.4%)

prune43.0ms (2.5%)

localize4.0ms (0.2%)

series2.0ms (0.1%)

rewrite38.0ms (2.2%)

simplify9.0ms (0.5%)

prune39.0ms (2.2%)

localize6.0ms (0.3%)

series15.0ms (0.8%)

rewrite71.0ms (4.1%)

simplify97.0ms (5.5%)

prune166.0ms (9.4%)

regimes214.0ms (12.1%)

simplify2.0ms (0.1%)

end123.0ms (7%)

Profiling