Details

analyze462.0ms (18.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
12.5%	87.4%	0.1%	7
25%	74.9%	0.1%	8
31.2%	64%	4.8%	9
31.2%	42.1%	26.7%	10
35.9%	37.1%	27.1%	11
38.2%	32.2%	29.6%	12
47.8%	21.6%	30.6%	13
50.2%	19%	30.8%	14

Compiler

Compiled 19 to 9 computations (52.6% saved)

sample26.0ms (1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
0.0ms	12×	body	128	invalid

Compiler

Compiled 40 to 20 computations (50% saved)

simplify7.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

32×	`fma-def_binary64`
5×	`*-commutative_binary64`
4×	`associate-+l+_binary64`
4×	`associate-r_binary64`
3×	`+-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	17	15
2	34	11
3	54	11
4	68	11
5	72	11
6	70	11

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
	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
▶	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

Compiler

Compiled 84 to 41 computations (51.2% saved)

localize7.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 x y) (.f64 z z))
✓	0.1b	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))

series23.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

13.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
10.0ms	(+.f64 (.f64 x y) (.f64 z z))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-log-exp_binary64`
7×	`sum-log_binary64`
4×	`fma-def_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`

Counts

2 → 33

Calls

2 calls:

6.0ms	(+.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z)) (.f64 z z))
3.0ms	(+.f64 (.f64 x y) (.f64 z z))

simplify74.0ms (3%)

Algorithm

1×	egg-herbie

Rules

442×	`fma-def_binary64`
364×	`fma-neg_binary64`
350×	`distribute-rgt-out_binary64`
344×	`cancel-sign-sub-inv_binary64`
302×	`distribute-rgt-in_binary64`

Counts

105 → 61

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	1215
1	201	1103
2	643	1026
3	2473	1026
4	4449	1026
5	4937	1026

prune42.0ms (1.7%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	57	4	61
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	58	5	63

Error

0.0b

Counts

63 → 5

Alt Table

Status	Error	Program
	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	1.0b	(+.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (fma.f64 z z (.f64 y x))) (cbrt.f64 (fma.f64 z z (.f64 y x)))) (cbrt.f64 (fma.f64 z z (.f64 y x)))) (.f64 z z)) (*.f64 z z))
▶	0.1b	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 2 (.f64 z z)))
	1.2b	(.f64 (.f64 (cbrt.f64 (fma.f64 3 (.f64 z z) (.f64 y x))) (cbrt.f64 (fma.f64 3 (.f64 z z) (.f64 y x)))) (cbrt.f64 (fma.f64 3 (.f64 z z) (.f64 y x))))
	20.8b	(fma.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (sqrt.f64 (+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 z z))) (*.f64 z z))

Compiler

Compiled 1528 to 369 computations (75.9% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 2 (.f64 z z))
	0.0b	(+.f64 (.f64 x y) (.f64 z z))
✓	0.1b	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 2 (.f64 z z)))

series20.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

17.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 2 (.f64 z z)))
2.0ms	(.f64 2 (.f64 z z))

rewrite11.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
7×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`

Counts

2 → 39

Calls

2 calls:

5.0ms	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 2 (.f64 z z)))
4.0ms	(.f64 2 (.f64 z z))

simplify68.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

368×	`associate-l_binary64`
360×	`sub-neg_binary64`
329×	`fma-def_binary64`
301×	`cancel-sign-sub-inv_binary64`
295×	`associate-r_binary64`

Counts

87 → 60

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	72	918
1	186	883
2	592	850
3	2383	850
4	4459	840
5	5027	840

prune63.0ms (2.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	3	1	4
Picked	1	0	1
Done	0	0	0
Total	88	4	92

Error

0.0b

Counts

92 → 4

Alt Table

Status	Error	Program
	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	20.8b	(fma.f64 (sqrt.f64 (+.f64 (.f64 x y) (.f64 z z))) (sqrt.f64 (+.f64 (.f64 x y) (.f64 z z))) (.f64 2 (.f64 z z)))
▶	0.1b	(+.f64 (fma.f64 x y (.f64 z z)) (.f64 2 (*.f64 z z)))
	0.2b	(+.f64 (+.f64 (.f64 x y) (.f64 z z)) (.f64 (sqrt.f64 2) (.f64 z (*.f64 z (sqrt.f64 2)))))

Compiler

Compiled 1744 to 610 computations (65% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x y (*.f64 z z))
	0.0b	(.f64 2 (.f64 z z))
✓	0.1b	(+.f64 (fma.f64 x y (.f64 z z)) (.f64 2 (*.f64 z z)))

series24.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

14.0ms	(+.f64 (fma.f64 x y (.f64 z z)) (.f64 2 (*.f64 z z)))
9.0ms	(fma.f64 x y (*.f64 z z))

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`fma-def_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(+.f64 (fma.f64 x y (.f64 z z)) (.f64 2 (*.f64 z z)))
0.0ms	(fma.f64 x y (*.f64 z z))

simplify48.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

703×	`associate-+l+_binary64`
666×	`associate-+r+_binary64`
266×	`cancel-sign-sub-inv_binary64`
257×	`fma-neg_binary64`
247×	`associate-l_binary64`

Counts

99 → 54

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	46	1075
1	127	962
2	424	935
3	1786	935
4	5266	935

prune51.0ms (2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	2	1	3
Picked	1	0	1
Done	0	0	0
Total	82	3	85

Error

0.0b

Counts

85 → 3

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	0.2b	(+.f64 (fma.f64 x y (.f64 z z)) (.f64 (sqrt.f64 2) (.f64 z (.f64 z (sqrt.f64 2)))))
	20.8b	(fma.f64 (sqrt.f64 (fma.f64 x y (.f64 z z))) (sqrt.f64 (fma.f64 x y (.f64 z z))) (.f64 2 (.f64 z z)))

Compiler

Compiled 1480 to 539 computations (63.6% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))

series10.0ms (0.4%)

Counts

1 → 36

Calls

1 calls:

10.0ms

(fma.f64 z (*.f64 z 3) (*.f64 x y))

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma.f64 z (*.f64 z 3) (*.f64 x y))

simplify61.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

893×	`fma-def_binary64`
483×	`distribute-rgt-out_binary64`
466×	`distribute-rgt-in_binary64`
458×	`distribute-lft-in_binary64`
301×	`*-commutative_binary64`

Counts

46 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	23	508
1	34	485
2	65	485
3	184	485
4	750	485
5	2905	485
6	3790	485
7	4921	485

prune16.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	23	3	26

Error

0.0b

Counts

26 → 3

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 z (.f64 z 3) (.f64 x y))
	0.2b	(+.f64 (fma.f64 x y (.f64 z z)) (.f64 (sqrt.f64 2) (.f64 z (.f64 z (sqrt.f64 2)))))
	20.8b	(fma.f64 (sqrt.f64 (fma.f64 x y (.f64 z z))) (sqrt.f64 (fma.f64 x y (.f64 z z))) (.f64 2 (.f64 z z)))

Compiler

Compiled 338 to 170 computations (49.7% saved)

regimes765.0ms (30.6%)

Accuracy

Total 0.1b remaining (90.6%)

Threshold costs 0.1b (90.6%)

Counts

82 → 1

Compiler

Compiled 9929 to 5544 computations (44.2% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	9	11
2	9	11

end6.0ms (0.2%)

Remove: (sort x y)
Compiler: Compiled 33 to 21 computations (36.4% saved)

sample674.0ms (27%)

Algorithm

1×

intervals

Results

303.0ms	8000×	body	128	valid
17.0ms	487×	body	128	invalid

Compiler

Compiled 86 to 48 computations (44.2% saved)

Details

analyze462.0ms (18.5%)

sample26.0ms (1%)

simplify7.0ms (0.3%)

prune5.0ms (0.2%)

localize7.0ms (0.3%)

series23.0ms (0.9%)

rewrite11.0ms (0.4%)

simplify74.0ms (3%)

prune42.0ms (1.7%)

localize7.0ms (0.3%)

series20.0ms (0.8%)

rewrite11.0ms (0.4%)

simplify68.0ms (2.7%)

prune63.0ms (2.5%)

localize6.0ms (0.3%)

series24.0ms (0.9%)

rewrite4.0ms (0.2%)

simplify48.0ms (1.9%)

prune51.0ms (2%)

localize5.0ms (0.2%)

series10.0ms (0.4%)

rewrite2.0ms (0.1%)

simplify61.0ms (2.4%)

prune16.0ms (0.7%)

regimes765.0ms (30.6%)

simplify2.0ms (0.1%)

end6.0ms (0.2%)

sample674.0ms (27%)

Profiling