Details

analyze441.0ms (8.2%)

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
18.7%	81.1%	0.1%	8
28.1%	71.8%	0.1%	9
37.4%	49.9%	12.6%	10
43.7%	43.7%	12.6%	11
49.1%	38.2%	12.6%	12
54.6%	26.5%	18.9%	13
58.5%	22.6%	18.9%	14

Compiler

Compiled 11 to 7 computations (36.4% saved)

sample874.0ms (16.3%)

Results

773.0ms	8256×	body	128	valid
67.0ms	702×	body	128	invalid

Compiler

Compiled 32 to 20 computations (37.5% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`associate-r_binary64`
1×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	12	8
2	16	8
3	17	8
4	17	8

prune2.0ms (0%)

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 z (*.f64 y z) x)

Compiler

Compiled 34 to 17 computations (50% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.2%)

Counts

1 → 36

Calls

1 calls:

8.0ms

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

rewrite1.0ms (0%)

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 z (*.f64 y z) x)

simplify65.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

557×	`fma-def_binary64`
534×	`unswap-sqr_binary64`
444×	`*-commutative_binary64`
374×	`distribute-rgt-in_binary64`
370×	`distribute-lft-in_binary64`

Counts

46 → 23

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	382
1	32	365
2	56	365
3	152	365
4	615	365
5	2186	365
6	2764	365
7	4969	365
8	5049	365

prune12.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	20	3	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	20	4	24

Error

0.0b

Counts

24 → 4

Alt Table

Status	Error	Program
	33.0b	(.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x)) (sqrt.f64 (fma.f64 z (*.f64 y z) x)))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x))) (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
	6.2b	(fma.f64 y (*.f64 z z) x)
✓	0.1b	(fma.f64 z (*.f64 y z) x)

Compiler

Compiled 342 to 99 computations (71.1% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 z (*.f64 y z) x)
✓	0.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x))) (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
✓	0.5b	(.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
✓	0.6b	(cbrt.f64 (fma.f64 z (*.f64 y z) x))

series103.0ms (1.9%)

Counts

3 → 108

Calls

3 calls:

53.0ms

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

41.0ms

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

9.0ms

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

rewrite19.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
24×	`add-sqr-sqrt_binary64`
23×	`cbrt-prod_binary64`
16×	`pow1/3_binary64`
14×	`*-un-lft-identity_binary64`

Counts

3 → 93

Calls

3 calls:

8.0ms

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

4.0ms

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

1.0ms

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

simplify131.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

418×	`cancel-sign-sub-inv_binary64`
325×	`associate-r_binary64`
317×	`unswap-sqr_binary64`
245×	`times-frac_binary64`
239×	`associate-l_binary64`

Counts

201 → 234

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	363	6351
1	1102	5908
2	3621	5539
3	4984	5539

prune529.0ms (9.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	449	4	453
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	450	7	457

Error

0.0b

Counts

457 → 7

Alt Table

Status	Error	Program
	7.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x))) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 z z) x))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 y (*.f64 z z) x)))))
	33.0b	(.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x)) (sqrt.f64 (fma.f64 z (*.f64 y z) x)))
	7.9b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 z z) x))) 4)) (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
	33.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x))))) (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
▶	1.6b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))))
	6.2b	(fma.f64 y (*.f64 z z) x)
✓	0.1b	(fma.f64 z (*.f64 y z) x)

Compiler

Compiled 18456 to 6971 computations (62.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
✓	0.5b	(cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (*.f64 y z) x))))
	0.6b	(cbrt.f64 (fma.f64 z (*.f64 y z) x))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))

series112.0ms (2.1%)

Counts

2 → 72

Calls

2 calls:

61.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
50.0ms	(cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (*.f64 y z) x))))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (*.f64 y z) x))))
1.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))

simplify146.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

469×	`cancel-sign-sub-inv_binary64`
301×	`unswap-sqr_binary64`
282×	`associate-r_binary64`
248×	`associate-/r*_binary64`
245×	`times-frac_binary64`

Counts

99 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	361	4995
1	1095	4745
2	3540	4610
3	4970	4590
4	4935	4590

prune570.0ms (10.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	715	3	718
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	716	9	725

Error

0.0b

Counts

725 → 9

Alt Table

Status	Error	Program
	7.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x))) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 z z) x))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 y (*.f64 z z) x)))))
	33.0b	(.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x)) (sqrt.f64 (fma.f64 z (*.f64 y z) x)))
▶	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x))))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))))))
	6.2b	(fma.f64 y (*.f64 z z) x)
	10.2b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 z z) x))) 6))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))))
	36.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (exp.f64 (log.f64 (cbrt.f64 (fma.f64 y (.f64 z z) x)))))) (cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))))
	7.9b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 z z) x))) 4)) (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
	33.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x))))) (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
✓	0.1b	(fma.f64 z (*.f64 y z) x)

Compiler

Compiled 46277 to 15595 computations (66.3% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x))))
	0.5b	(cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (*.f64 y z) x))))
	0.6b	(cbrt.f64 (fma.f64 z (*.f64 y z) x))
	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))

series42.0ms (0.8%)

Counts

1 → 36

Calls

1 calls:

42.0ms

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

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 19

Calls

1 calls:

1.0ms

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

simplify72.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

935×	`associate-/r*_binary64`
527×	`fma-def_binary64`
242×	`associate-/r/_binary64`
234×	`cancel-sign-sub-inv_binary64`
173×	`unswap-sqr_binary64`

Counts

55 → 84

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	218	2615
1	628	2509
2	2030	2390
3	5330	2390

prune1.2s (22.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	1046	0	1046
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	1046	9	1055

Error

0.0b

Counts

1055 → 9

Alt Table

Status	Error	Program
	7.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x))) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 z z) x))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 y (*.f64 z z) x)))))
	33.0b	(.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x)) (sqrt.f64 (fma.f64 z (*.f64 y z) x)))
✓	1.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x))))) (cbrt.f64 (cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))))))
	6.2b	(fma.f64 y (*.f64 z z) x)
	10.2b	(.f64 (expm1.f64 (log1p.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 z z) x))) 6))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))))
	36.8b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x))) (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (exp.f64 (log.f64 (cbrt.f64 (fma.f64 y (.f64 z z) x)))))) (cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))))
	7.9b	(.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (.f64 z z) x))) 4)) (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
	33.5b	(.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (.f64 (cbrt.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x))) (cbrt.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x))))) (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
✓	0.1b	(fma.f64 z (*.f64 y z) x)

Compiler

Compiled 91479 to 25356 computations (72.3% saved)

regimes874.0ms (16.3%)

Accuracy

Total 0.1b remaining (67.2%)

Threshold costs 0.1b (67.2%)

Counts

161 → 1

Compiler

Compiled 34520 to 10614 computations (69.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	7	8
2	7	8

end123.0ms (2.3%)

Compiler: Compiled 319 to 120 computations (62.4% saved)

Details

analyze441.0ms (8.2%)

sample874.0ms (16.3%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series8.0ms (0.2%)

rewrite1.0ms (0%)

simplify65.0ms (1.2%)

prune12.0ms (0.2%)

localize15.0ms (0.3%)

series103.0ms (1.9%)

rewrite19.0ms (0.4%)

simplify131.0ms (2.4%)

prune529.0ms (9.9%)

localize11.0ms (0.2%)

series112.0ms (2.1%)

rewrite5.0ms (0.1%)

simplify146.0ms (2.7%)

prune570.0ms (10.6%)

localize14.0ms (0.3%)

series42.0ms (0.8%)

rewrite2.0ms (0%)

simplify72.0ms (1.3%)

prune1.2s (22.1%)

regimes874.0ms (16.3%)

simplify2.0ms (0%)

end123.0ms (2.3%)

Profiling