Details

analyze104.0ms (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
49.9%	49.9%	0.1%	4
49.9%	49.9%	0.1%	5
49.9%	49.9%	0.1%	6
49.9%	25%	25.1%	7
49.9%	25%	25.1%	8
49.9%	25%	25.1%	9
49.9%	12.5%	37.6%	10
49.9%	12.5%	37.6%	11
49.9%	12.5%	37.6%	12
49.9%	6.2%	43.8%	13
49.9%	6.2%	43.8%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample907.0ms (17.2%)

Results

776.0ms	8256×	body	128	valid
95.0ms	1065×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`*-commutative_binary64`
10×	`fma-def_binary64`
2×	`associate-r_binary64`
2×	`associate-l_binary64`
2×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	12
1	23	10
2	35	10
3	41	10
4	39	10

prune3.0ms (0.1%)

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

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))

Compiler

Compiled 40 to 27 computations (32.5% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (sqrt.f64 z) x)
✓	0.2b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))

series40.0ms (0.8%)

Counts

2 → 50

Calls

2 calls:

25.0ms	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
15.0ms	(fma.f64 y (sqrt.f64 z) x)

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

3.0ms	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
0.0ms	(fma.f64 y (sqrt.f64 z) x)

simplify117.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

616×	`associate-l_binary64`
616×	`distribute-lft-in_binary64`
614×	`distribute-rgt-in_binary64`
396×	`associate-+r+_binary64`
396×	`associate-+l+_binary64`

Counts

82 → 43

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	51	803
1	83	752
2	222	751
3	627	751
4	1827	751
5	3859	751
6	4054	751
7	4491	751
8	4947	751

prune52.0ms (1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	37	6	43
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	37	7	44

Error

0.2b

Counts

44 → 7

Alt Table

Status	Error	Program
	33.7b	(.f64 (.f64 1/2 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)))
	1.3b	(.f64 (.f64 1/2 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
▶	1.0b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (fma.f64 y (sqrt.f64 z) x)))
✓	0.3b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	33.7b	(.f64 (sqrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) (sqrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))
	38.4b	(cbrt.f64 (pow.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x)) 3))

Compiler

Compiled 745 to 343 computations (54% saved)

localize21.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 z) x)
✓	0.4b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (fma.f64 y (sqrt.f64 z) x)))
✓	0.6b	(*.f64 (sqrt.f64 1/2) (fma.f64 y (sqrt.f64 z) x))

series100.0ms (1.9%)

Counts

2 → 50

Calls

2 calls:

63.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (fma.f64 y (sqrt.f64 z) x)))
36.0ms	(*.f64 (sqrt.f64 1/2) (fma.f64 y (sqrt.f64 z) x))

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-l_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`

Counts

2 → 53

Calls

2 calls:

12.0ms	(*.f64 (sqrt.f64 1/2) (fma.f64 y (sqrt.f64 z) x))
12.0ms	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (fma.f64 y (sqrt.f64 z) x)))

simplify140.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

969×	`fma-def_binary64`
737×	`unswap-sqr_binary64`
347×	`*-commutative_binary64`
269×	`associate-/r/_binary64`
207×	`sqr-pow_binary64`

Counts

103 → 78

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	1512
1	155	1242
2	483	1242
3	1219	1233
4	1665	1233
5	2371	1233
6	4871	1233
7	5044	1233

prune77.0ms (1.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	91	9	100

Error

0.0b

Counts

100 → 9

Alt Table

Status	Error	Program
	25.9b	(.f64 (sqrt.f64 z) (.f64 1/2 y))
	38.4b	(cbrt.f64 (pow.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x)) 3))
	33.7b	(.f64 (.f64 1/2 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)))
▶	1.3b	(.f64 (.f64 1/2 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	1.0b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (fma.f64 y (sqrt.f64 z) x)))
✓	0.3b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	38.4b	(.f64 (sqrt.f64 1/2) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (fma.f64 y (sqrt.f64 z) x)) 3)))
	33.7b	(.f64 (sqrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) (sqrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))
	1.3b	(.f64 (.f64 (cbrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))

Compiler

Compiled 1756 to 1054 computations (40% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 y (sqrt.f64 z) x)
✓	0.3b	(.f64 (.f64 1/2 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	0.5b	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	5.8b	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

series487.0ms (9.2%)

Counts

3 → 75

Calls

3 calls:

366.0ms

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

87.0ms

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

33.0ms

(*.f64 (*.f64 1/2 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
22×	`cbrt-prod_binary64`
19×	`pow1_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

3 → 81

Calls

3 calls:

17.0ms

(*.f64 (*.f64 1/2 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

8.0ms

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

1.0ms

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

simplify189.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

374×	`cancel-sign-sub-inv_binary64`
347×	`associate-r_binary64`
318×	`associate-l_binary64`
223×	`unswap-sqr_binary64`
222×	`distribute-rgt-in_binary64`

Counts

156 → 186

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	321	4504
1	906	4252
2	3154	3953
3	4965	3953

prune483.0ms (9.1%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	337	4	341
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	338	12	350

Error

0.0b

Counts

350 → 12

Alt Table

Status	Error	Program
	26.9b	(.f64 (.f64 1/2 (cbrt.f64 (*.f64 (fma.f64 y (sqrt.f64 z) x) (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	1.0b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (fma.f64 y (sqrt.f64 z) x)))
	25.9b	(.f64 (sqrt.f64 z) (.f64 1/2 y))
	38.4b	(cbrt.f64 (pow.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x)) 3))
	33.7b	(.f64 (.f64 1/2 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	1.3b	(.f64 (.f64 1/2 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	0.3b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	38.4b	(.f64 (sqrt.f64 1/2) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (fma.f64 y (sqrt.f64 z) x)) 3)))
	33.7b	(.f64 (sqrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) (sqrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))
	1.7b	(.f64 (.f64 (.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	27.5b	(.f64 (.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (.f64 (cbrt.f64 y) (pow.f64 z 1/6)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
▶	1.7b	(.f64 (.f64 1/2 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

Compiler

Compiled 13453 to 5416 computations (59.7% saved)

localize87.0ms (1.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
✓	0.5b	(*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
	5.8b	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

series770.0ms (14.6%)

Counts

3 → 75

Calls

3 calls:

379.0ms

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

237.0ms

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

154.0ms

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

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`cbrt-prod_binary64`
35×	`add-sqr-sqrt_binary64`
24×	`pow1_binary64`
23×	`pow1/3_binary64`
17×	`*-un-lft-identity_binary64`

Counts

3 → 101

Calls

3 calls:

10.0ms

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

6.0ms

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

2.0ms

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

simplify156.0ms (3%)

Algorithm

1×	egg-herbie

Rules

409×	`associate-r_binary64`
372×	`unswap-sqr_binary64`
362×	`associate-l_binary64`
253×	`*-commutative_binary64`
219×	`fma-neg_binary64`

Counts

176 → 225

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	417	6702
1	1161	6288
2	3975	5836
3	5186	5836

prune692.0ms (13.1%)

Pruning

13 alts after pruning (9 fresh and 4 done)

	Pruned	Kept	Total
New	609	1	610
Fresh	0	8	8
Picked	0	1	1
Done	0	3	3
Total	609	13	622

Error

Counts

622 → 13

Alt Table

Status	Error	Program
	26.9b	(.f64 (.f64 1/2 (cbrt.f64 (*.f64 (fma.f64 y (sqrt.f64 z) x) (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	1.0b	(.f64 (sqrt.f64 1/2) (.f64 (sqrt.f64 1/2) (fma.f64 y (sqrt.f64 z) x)))
	25.9b	(.f64 (sqrt.f64 z) (.f64 1/2 y))
	38.4b	(cbrt.f64 (pow.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x)) 3))
	33.7b	(.f64 (.f64 1/2 (sqrt.f64 (fma.f64 y (sqrt.f64 z) x))) (sqrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	1.3b	(.f64 (.f64 1/2 (*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	0.3b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	38.4b	(.f64 (sqrt.f64 1/2) (cbrt.f64 (pow.f64 (.f64 (sqrt.f64 1/2) (fma.f64 y (sqrt.f64 z) x)) 3)))
	33.7b	(.f64 (sqrt.f64 (.f64 1/2 (fma.f64 y (sqrt.f64 z) x))) (sqrt.f64 (*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))))
	1.7b	(.f64 (.f64 (.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))
	2.1b	(.f64 (.f64 1/2 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) 6)) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))))
	27.5b	(.f64 (.f64 1/2 (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (.f64 (cbrt.f64 y) (pow.f64 z 1/6)))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))
✓	1.7b	(.f64 (.f64 1/2 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))) (*.f64 (cbrt.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x))))) (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)))

Compiler

Compiled 36805 to 12964 computations (64.8% saved)

regimes576.0ms (10.9%)

Accuracy

Total 0.1b remaining (78.3%)

Threshold costs 0.1b (78.3%)

Counts

58 → 1

Compiler

Compiled 9675 to 5346 computations (44.7% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

end157.0ms (3%)

Compiler: Compiled 333 to 162 computations (51.4% saved)

Details

analyze104.0ms (2%)

sample907.0ms (17.2%)

simplify7.0ms (0.1%)

prune3.0ms (0.1%)

localize5.0ms (0.1%)

series40.0ms (0.8%)

rewrite4.0ms (0.1%)

simplify117.0ms (2.2%)

prune52.0ms (1%)

localize21.0ms (0.4%)

series100.0ms (1.9%)

rewrite28.0ms (0.5%)

simplify140.0ms (2.6%)

prune77.0ms (1.5%)

localize10.0ms (0.2%)

series487.0ms (9.2%)

rewrite38.0ms (0.7%)

simplify189.0ms (3.6%)

prune483.0ms (9.1%)

localize87.0ms (1.6%)

series770.0ms (14.6%)

rewrite31.0ms (0.6%)

simplify156.0ms (3%)

prune692.0ms (13.1%)

regimes576.0ms (10.9%)

simplify6.0ms (0.1%)

end157.0ms (3%)

Profiling