Details

analyze4.0ms (0.3%)

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
75%	12.5%	12.5%	5
75%	6.2%	18.8%	6
75%	3.1%	21.9%	7
75%	1.6%	23.5%	8
75%	0.8%	24.3%	9
75%	0.4%	24.6%	10
75%	0.2%	24.8%	11
75%	0.1%	24.9%	12
75%	0%	25%	13
75%	0%	25%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample657.0ms (51.2%)

Results

622.0ms

8256×

body

128

valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify7.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

3×	`fma-neg_binary64`
2×	`+-commutative_binary64`
2×	`sub-neg_binary64`
1×	`*-commutative_binary64`
1×	`associate-/l*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	8
1	15	8
2	21	8
3	24	8
4	26	8
5	27	8
6	24	8

prune2.0ms (0.2%)

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	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 28 to 20 computations (28.6% saved)

localize3.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)

series3.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(/.f64 (fma.f64 x x -3) 6)

rewrite3.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 29

Calls

1 calls:

2.0ms

(/.f64 (fma.f64 x x -3) 6)

simplify50.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

822×	`distribute-rgt-in_binary64`
507×	`associate-/l*_binary64`
396×	`associate-/l/_binary64`
383×	`fma-def_binary64`
343×	`times-frac_binary64`

Counts

41 → 39

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	64	533
1	103	499
2	216	499
3	434	499
4	1114	499
5	3350	499
6	4886	499

prune32.0ms (2.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	33	6	39
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	33	7	40

Error

Counts

40 → 7

Alt Table

Status	Error	Program
	43.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
	1.1b	(.f64 (.f64 (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)) (cbrt.f64 (/.f64 (fma.f64 x x -3) 6))) (cbrt.f64 (/.f64 (fma.f64 x x -3) 6)))
	43.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
	20.8b	(log.f64 (exp.f64 (/.f64 (fma.f64 x x -3) 6)))
▶	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)
	0.4b	(/.f64 (*.f64 (cbrt.f64 (fma.f64 x x -3)) (cbrt.f64 (fma.f64 x x -3))) (/.f64 6 (cbrt.f64 (fma.f64 x x -3))))
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 651 to 482 computations (26% saved)

localize3.0ms (0.3%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)

series4.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(fma.f64 1/6 (*.f64 x x) -1/2)

rewrite1.0ms (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:

0.0ms

(fma.f64 1/6 (*.f64 x x) -1/2)

simplify46.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-def_binary64`
474×	`unswap-sqr_binary64`
438×	`*-commutative_binary64`
374×	`distribute-rgt-in_binary64`
370×	`distribute-lft-in_binary64`

Counts

22 → 16

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	214
1	30	197
2	59	197
3	156	197
4	622	197
5	2186	197
6	2781	197
7	5148	197

prune13.0ms (1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	17	6	23

Error

Counts

23 → 6

Alt Table

Status	Error	Program
	43.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
▶	2.0b	(expm1.f64 (log1p.f64 (fma.f64 1/6 (*.f64 x x) -1/2)))
	43.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
	20.8b	(log.f64 (exp.f64 (/.f64 (fma.f64 x x -3) 6)))
✓	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 254 to 171 computations (32.7% saved)

localize7.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (fma.f64 1/6 (*.f64 x x) -1/2))
	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	2.0b	(expm1.f64 (log1p.f64 (fma.f64 1/6 (*.f64 x x) -1/2)))

series8.0ms (0.6%)

Counts

2 → 24

Calls

2 calls:

5.0ms	(log1p.f64 (fma.f64 1/6 (*.f64 x x) -1/2))
2.0ms	(expm1.f64 (log1p.f64 (fma.f64 1/6 (*.f64 x x) -1/2)))

rewrite1.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-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:

0.0ms	(log1p.f64 (fma.f64 1/6 (*.f64 x x) -1/2))
0.0ms	(expm1.f64 (log1p.f64 (fma.f64 1/6 (*.f64 x x) -1/2)))

simplify52.0ms (4%)

Algorithm

1×	egg-herbie

Rules

582×	`fma-def_binary64`
425×	`sub-neg_binary64`
404×	`times-frac_binary64`
352×	`associate-l_binary64`
312×	`unswap-sqr_binary64`

Counts

46 → 58

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	644
1	177	593
2	416	575
3	1112	575
4	3592	575
5	4951	575

prune41.0ms (3.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	74	6	80

Error

Counts

80 → 6

Alt Table

Status	Error	Program
	43.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
✓	2.0b	(expm1.f64 (log1p.f64 (fma.f64 1/6 (*.f64 x x) -1/2)))
	43.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
▶	20.8b	(log.f64 (exp.f64 (/.f64 (fma.f64 x x -3) 6)))
✓	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 1091 to 802 computations (26.5% saved)

localize7.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(exp.f64 (/.f64 (fma.f64 x x -3) 6))
	0.1b	(/.f64 (fma.f64 x x -3) 6)
✓	0.5b	(log.f64 (exp.f64 (/.f64 (fma.f64 x x -3) 6)))

series5.0ms (0.4%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(log.f64 (exp.f64 (/.f64 (fma.f64 x x -3) 6)))
2.0ms	(exp.f64 (/.f64 (fma.f64 x x -3) 6))

rewrite7.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`exp-prod_binary64`
18×	`times-frac_binary64`
17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
17×	`add-cube-cbrt_binary64`

Counts

2 → 50

Calls

2 calls:

3.0ms	(log.f64 (exp.f64 (/.f64 (fma.f64 x x -3) 6)))
2.0ms	(exp.f64 (/.f64 (fma.f64 x x -3) 6))

simplify68.0ms (5.3%)

Algorithm

1×	egg-herbie

Rules

512×	`distribute-rgt-in_binary64`
420×	`associate-l_binary64`
393×	`fma-def_binary64`
377×	`distribute-lft-out_binary64`
374×	`distribute-rgt-out_binary64`

Counts

74 → 88

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	97	936
1	155	883
2	308	881
3	677	869
4	1905	866
5	4093	866
6	5308	866

prune72.0ms (5.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	127	6	133

Error

Counts

133 → 6

Alt Table

Status	Error	Program
	43.1b	(*.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 (sqrt.f64 (fma.f64 x x -3)) 6))
✓	2.0b	(expm1.f64 (log1p.f64 (fma.f64 1/6 (*.f64 x x) -1/2)))
	43.1b	(/.f64 (sqrt.f64 (fma.f64 x x -3)) (/.f64 6 (sqrt.f64 (fma.f64 x x -3))))
✓	20.8b	(log.f64 (exp.f64 (/.f64 (fma.f64 x x -3) 6)))
✓	0.2b	(fma.f64 1/6 (*.f64 x x) -1/2)
✓	0.1b	(/.f64 (fma.f64 x x -3) 6)

Compiler

Compiled 1930 to 1506 computations (22% saved)

regimes112.0ms (8.7%)

Accuracy

Total 0.1b remaining (55.7%)

Threshold costs 0.1b (55.7%)

Counts

30 → 1

Compiler

Compiled 1654 to 1270 computations (23.2% saved)

simplify2.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	11
1	10	11
2	9	11

end72.0ms (5.6%)

Compiler: Compiled 78 to 58 computations (25.6% saved)

Details

analyze4.0ms (0.3%)

sample657.0ms (51.2%)

simplify7.0ms (0.6%)

prune2.0ms (0.2%)

localize3.0ms (0.3%)

series3.0ms (0.2%)

rewrite3.0ms (0.2%)

simplify50.0ms (3.9%)

prune32.0ms (2.5%)

localize3.0ms (0.3%)

series4.0ms (0.3%)

rewrite1.0ms (0.1%)

simplify46.0ms (3.6%)

prune13.0ms (1%)

localize7.0ms (0.5%)

series8.0ms (0.6%)

rewrite1.0ms (0.1%)

simplify52.0ms (4%)

prune41.0ms (3.2%)

localize7.0ms (0.5%)

series5.0ms (0.4%)

rewrite7.0ms (0.6%)

simplify68.0ms (5.3%)

prune72.0ms (5.6%)

regimes112.0ms (8.7%)

simplify2.0ms (0.2%)

end72.0ms (5.6%)

Profiling