Details

analyze431.0ms (8.5%)

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
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)

sample911.0ms (17.8%)

Results

817.0ms	8256×	body	128	valid
63.0ms	685×	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)

series9.0ms (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)

simplify64.0ms (1.3%)

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

prune15.0ms (0.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	19	4	23
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	19	5	24

Error

0.0b

Counts

24 → 5

Alt Table

Status	Error	Program
	28.8b	(.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x)) (sqrt.f64 (fma.f64 z (*.f64 y z) x)))
▶	1.3b	(.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)))
	42.5b	(cbrt.f64 (.f64 (.f64 (fma.f64 z (.f64 y z) x) (fma.f64 z (.f64 y z) x)) (fma.f64 z (*.f64 y z) x)))
	6.6b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
✓	0.1b	(fma.f64 z (*.f64 y z) x)

Compiler

Compiled 392 to 119 computations (69.6% saved)

localize8.0ms (0.2%)

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))

series122.0ms (2.4%)

Counts

3 → 108

Calls

3 calls:

63.0ms

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

50.0ms

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

10.0ms

(*.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)))

rewrite18.0ms (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:

6.0ms

(*.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)))

6.0ms

(*.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))

simplify132.0ms (2.6%)

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

prune449.0ms (8.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	449	4	453
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	450	8	458

Error

0.0b

Counts

458 → 8

Alt Table

Status	Error	Program
	6.6b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
▶	1.5b	(.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)))))
✓	0.1b	(fma.f64 z (*.f64 y z) x)
	1.7b	(.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 (fma.f64 z (.f64 y z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))))
	32.8b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x))) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 z z) x))) 3)) (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
	28.8b	(.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x)) (sqrt.f64 (fma.f64 z (*.f64 y z) x)))
✓	1.3b	(.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)))
	1.7b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x))))) (cbrt.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)))

Compiler

Compiled 18530 to 6971 computations (62.4% 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)))

series144.0ms (2.8%)

Counts

2 → 72

Calls

2 calls:

87.0ms	(cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (*.f64 y z) x))))
57.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))

rewrite4.0ms (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)))

simplify194.0ms (3.8%)

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

prune517.0ms (10.1%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	718	0	718
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	718	8	726

Error

0.0b

Counts

726 → 8

Alt Table

Status	Error	Program
	6.6b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
✓	1.5b	(.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)))))
✓	0.1b	(fma.f64 z (*.f64 y z) x)
	1.7b	(.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 (fma.f64 z (.f64 y z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))))
	32.8b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x))) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 z z) x))) 3)) (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
	28.8b	(.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x)) (sqrt.f64 (fma.f64 z (*.f64 y z) x)))
✓	1.3b	(.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)))
▶	1.7b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x))))) (cbrt.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)))

Compiler

Compiled 46091 to 15506 computations (66.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series75.0ms (1.5%)

Counts

1 → 36

Calls

1 calls:

75.0ms

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

rewrite7.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt_binary64`
8×	`cbrt-prod_binary64`
8×	`pow1_binary64`
6×	`pow1/3_binary64`
5×	`*-un-lft-identity_binary64`

Counts

1 → 36

Calls

1 calls:

4.0ms

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

simplify119.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

544×	`fma-def_binary64`
493×	`associate-*r/_binary64`
367×	`associate-*l/_binary64`
227×	`cancel-sign-sub-inv_binary64`
209×	`associate-/r/_binary64`

Counts

72 → 94

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	203	3875
1	600	3519
2	2073	3158
3	4465	2965
4	4937	2965
5	4886	2965

prune1.2s (23.6%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	1123	0	1123
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	1123	8	1131

Error

0.0b

Counts

1131 → 8

Alt Table

Status	Error	Program
	6.6b	(+.f64 (*.f64 y (pow.f64 z 2)) x)
✓	1.5b	(.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)))))
✓	0.1b	(fma.f64 z (*.f64 y z) x)
	1.7b	(.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 (fma.f64 z (.f64 y z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 z (*.f64 y z) x)))))
	32.8b	(.f64 (.f64 (sqrt.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x))) (pow.f64 (sqrt.f64 (cbrt.f64 (fma.f64 y (.f64 z z) x))) 3)) (cbrt.f64 (fma.f64 z (*.f64 y z) x)))
	28.8b	(.f64 (sqrt.f64 (fma.f64 z (.f64 y z) x)) (sqrt.f64 (fma.f64 z (*.f64 y z) x)))
✓	1.3b	(.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)))
✓	1.7b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x)))) (cbrt.f64 (.f64 (cbrt.f64 (fma.f64 z (.f64 y z) x)) (cbrt.f64 (fma.f64 z (.f64 y z) x))))) (cbrt.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)))

Compiler

Compiled 88926 to 25046 computations (71.8% saved)

regimes545.0ms (10.7%)

Accuracy

Total 0.1b remaining (72.6%)

Threshold costs 0.1b (72.6%)

Counts

99 → 1

Compiler

Compiled 20835 to 6744 computations (67.6% 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

end97.0ms (1.9%)

Compiler: Compiled 261 to 85 computations (67.4% saved)

Details

analyze431.0ms (8.5%)

sample911.0ms (17.8%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize4.0ms (0.1%)

series9.0ms (0.2%)

rewrite1.0ms (0%)

simplify64.0ms (1.3%)

prune15.0ms (0.3%)

localize8.0ms (0.2%)

series122.0ms (2.4%)

rewrite18.0ms (0.4%)

simplify132.0ms (2.6%)

prune449.0ms (8.8%)

localize11.0ms (0.2%)

series144.0ms (2.8%)

rewrite4.0ms (0.1%)

simplify194.0ms (3.8%)

prune517.0ms (10.1%)

localize10.0ms (0.2%)

series75.0ms (1.5%)

rewrite7.0ms (0.1%)

simplify119.0ms (2.3%)

prune1.2s (23.6%)

regimes545.0ms (10.7%)

simplify2.0ms (0%)

end97.0ms (1.9%)

Profiling