Details

analyze591.0ms (9.6%)

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
25%	74.9%	0.1%	6
34.3%	40.6%	25.1%	7
35.9%	39%	25.1%	8
42.1%	32.8%	25.1%	9
42.9%	19.5%	37.6%	10
43.3%	19.1%	37.6%	11
45%	17.5%	37.6%	12
45.1%	10.3%	44.6%	13
45.2%	10.2%	44.6%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample2.4s (38.3%)

Results

1.9s	8256×	body	128	valid
349.0ms	1561×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify13.0ms (0.2%)

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

prune6.0ms (0.1%)

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
▶	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))

Compiler

Compiled 66 to 47 computations (28.8% saved)

localize23.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (sqrt.f64 z)))
✓	0.3b	(*.f64 y (sqrt.f64 z))

series44.0ms (0.7%)

Counts

2 → 16

Calls

2 calls:

24.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
20.0ms	(*.f64 y (sqrt.f64 z))

rewrite83.0ms (1.3%)

Algorithm

2×	batch-egg-rewrite

Rules

791×	`prod-diff_binary64`
729×	`log1p-expm1-u_binary64`
729×	`expm1-log1p-u_binary64`
75×	`add-sqr-sqrt_binary64`
70×	`add-log-exp_binary64`

Counts

2 → 50

Calls

2 calls:

81.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
81.0ms	(*.f64 y (sqrt.f64 z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	147	13
2	1850	13
3	5937	13
0	0	0
1	0	0

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`fma-def_binary64`
1×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Counts

66 → 53

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	85
1	10	85
2	11	85
3	11	85

prune98.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	48	5	53
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	49	6	55

Error

0.0b

Counts

55 → 6

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
	23.5b	(.f64 (/.f64 1 2) (+.f64 x (cbrt.f64 (pow.f64 (.f64 y (sqrt.f64 z)) 3))))
	34.7b	(.f64 (/.f64 1 2) (.f64 (-.f64 (.f64 x x) (.f64 z (.f64 y y))) (/.f64 1 (-.f64 x (.f64 y (sqrt.f64 z))))))
▶	1.4b	(.f64 (/.f64 1 2) (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)))
	26.6b	(.f64 (/.f64 1 2) (+.f64 x (sqrt.f64 (.f64 z (*.f64 y y)))))
	29.2b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2)))

Compiler

Compiled 1013 to 531 computations (47.6% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (sqrt.f64 z) x)
✓	0.3b	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)
✓	0.6b	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

series400.0ms (6.5%)

Counts

4 → 100

Calls

4 calls:

224.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)
150.0ms	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))
14.0ms	(fma.f64 y (sqrt.f64 z) x)
12.0ms	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))

rewrite116.0ms (1.9%)

Algorithm

2×	batch-egg-rewrite

Rules

689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
144×	`expm1-udef_binary64`
144×	`log1p-udef_binary64`
137×	`log-pow_binary64`

Counts

4 → 110

Calls

4 calls:

112.0ms	(fma.f64 y (sqrt.f64 z) x)
112.0ms	(*.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2))
112.0ms	(pow.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) 2)
112.0ms	(cbrt.f64 (fma.f64 y (sqrt.f64 z) x))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	35
1	180	33
2	1822	33
3	4960	33
4	4999	33
5	4946	33
0	0	0
1	0	0

simplify124.0ms (2%)

Algorithm

1×	egg-herbie

Rules

379×	`cancel-sign-sub-inv_binary64`
295×	`associate-/r/_binary64`
241×	`unswap-sqr_binary64`
234×	`associate-r_binary64`
204×	`fma-neg_binary64`

Counts

210 → 171

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	251	3102
1	791	3040
2	2783	2799
3	4811	2479
4	4980	2479
5	4954	2479

prune192.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	241	4	245
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	244	7	251

Error

0.0b

Counts

251 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
	0.4b	(.f64 (/.f64 1 2) (fma.f64 (.f64 y (cbrt.f64 z)) (cbrt.f64 (sqrt.f64 z)) x))
	0.7b	(.f64 (/.f64 1 2) (fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (sqrt.f64 z)) x))
	32.9b	(.f64 (/.f64 1 2) (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 z)) (/.f64 -1 y))) 2)))
▶	0.2b	(.f64 (/.f64 1 2) (fma.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4) x))
	34.7b	(.f64 (/.f64 1 2) (.f64 (-.f64 (.f64 x x) (.f64 z (.f64 y y))) (/.f64 1 (-.f64 x (.f64 y (sqrt.f64 z))))))
	29.2b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2)))

Compiler

Compiled 8750 to 4961 computations (43.3% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 (*.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4) x)
✓	0.2b	(*.f64 y (pow.f64 z 1/4))

series474.0ms (7.7%)

Counts

2 → 40

Calls

2 calls:

242.0ms	(*.f64 y (pow.f64 z 1/4))
232.0ms	(fma.f64 (*.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4) x)

rewrite86.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

684×	`log1p-expm1-u_binary64`
684×	`expm1-log1p-u_binary64`
143×	`expm1-udef_binary64`
143×	`log1p-udef_binary64`
130×	`log-pow_binary64`

Counts

2 → 41

Calls

2 calls:

84.0ms	(fma.f64 (*.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4) x)
84.0ms	(*.f64 y (pow.f64 z 1/4))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	166	16
2	1803	14
3	4925	14
4	4897	14
0	0	0
1	0	0

simplify111.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

818×	`div-sub_binary64`
613×	`fma-neg_binary64`
543×	`fma-def_binary64`
538×	`log-prod_binary64`
465×	`associate-l_binary64`

Counts

81 → 47

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	307
1	39	307
2	71	287
3	204	259
4	561	259
5	1689	259
6	2917	259
7	4433	259
8	4842	259
9	4997	259
10	4771	259

prune33.0ms (0.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	47	7	54

Error

0.0b

Counts

54 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
▶	0.4b	(.f64 (/.f64 1 2) (fma.f64 (.f64 y (cbrt.f64 z)) (cbrt.f64 (sqrt.f64 z)) x))
	0.7b	(.f64 (/.f64 1 2) (fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (sqrt.f64 z)) x))
	32.9b	(.f64 (/.f64 1 2) (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 z)) (/.f64 -1 y))) 2)))
✓	0.2b	(.f64 (/.f64 1 2) (fma.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4) x))
	34.7b	(.f64 (/.f64 1 2) (.f64 (-.f64 (.f64 x x) (.f64 z (.f64 y y))) (/.f64 1 (-.f64 x (.f64 y (sqrt.f64 z))))))
	29.2b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2)))

Compiler

Compiled 930 to 608 computations (34.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series516.0ms (8.4%)

Counts

4 → 76

Calls

4 calls:

245.0ms	(*.f64 y (cbrt.f64 z))
219.0ms	(fma.f64 (*.f64 y (cbrt.f64 z)) (cbrt.f64 (sqrt.f64 z)) x)
28.0ms	(cbrt.f64 z)
24.0ms	(cbrt.f64 (sqrt.f64 z))

rewrite91.0ms (1.5%)

Algorithm

2×	batch-egg-rewrite

Rules

701×	`log1p-expm1-u_binary64`
701×	`expm1-log1p-u_binary64`
145×	`expm1-udef_binary64`
145×	`log1p-udef_binary64`
87×	`egg-rr`

Counts

4 → 87

Calls

4 calls:

89.0ms	(fma.f64 (*.f64 y (cbrt.f64 z)) (cbrt.f64 (sqrt.f64 z)) x)
89.0ms	(*.f64 y (cbrt.f64 z))
89.0ms	(cbrt.f64 z)
89.0ms	(cbrt.f64 (sqrt.f64 z))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	28
1	170	22
2	1861	20
3	4977	20
4	4948	20
0	0	0
1	0	0

simplify165.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

862×	`sqr-pow_binary64`
634×	`associate-l_binary64`
556×	`cube-prod_binary64`
514×	`fabs-mul_binary64`
501×	`*-commutative_binary64`

Counts

163 → 97

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	471
1	41	471
2	74	471
3	144	471
4	353	471
5	1058	471
6	1435	471
7	1547	471
8	1727	471
9	1951	471
10	2203	471
11	2529	471
12	2866	471
13	3351	471
14	4065	471
15	4329	471
16	4572	471
17	4751	471
18	4750	471

prune74.0ms (1.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	97	7	104

Error

0.0b

Counts

104 → 7

Alt Table

Status	Error	Program
✓	0.1b	(.f64 (/.f64 1 2) (+.f64 x (.f64 y (sqrt.f64 z))))
✓	0.4b	(.f64 (/.f64 1 2) (fma.f64 (.f64 y (cbrt.f64 z)) (cbrt.f64 (sqrt.f64 z)) x))
	0.7b	(.f64 (/.f64 1 2) (fma.f64 (pow.f64 (cbrt.f64 y) 2) (.f64 (cbrt.f64 y) (sqrt.f64 z)) x))
	32.9b	(.f64 (/.f64 1 2) (.f64 (cbrt.f64 (fma.f64 y (sqrt.f64 z) x)) (pow.f64 (cbrt.f64 (/.f64 (neg.f64 (sqrt.f64 z)) (/.f64 -1 y))) 2)))
✓	0.2b	(.f64 (/.f64 1 2) (fma.f64 (.f64 y (pow.f64 z 1/4)) (pow.f64 z 1/4) x))
	34.7b	(.f64 (/.f64 1 2) (.f64 (-.f64 (.f64 x x) (.f64 z (.f64 y y))) (/.f64 1 (-.f64 x (.f64 y (sqrt.f64 z))))))
	29.2b	(.f64 (/.f64 1 2) (+.f64 x (pow.f64 (sqrt.f64 (.f64 y (sqrt.f64 z))) 2)))

Compiler

Compiled 1640 to 920 computations (43.9% saved)

regimes375.0ms (6.1%)

Accuracy

Total 0.1b remaining (80.6%)

Threshold costs 0.1b (80.6%)

Counts

45 → 1

Compiler

Compiled 6157 to 4336 computations (29.6% saved)

simplify2.0ms (0%)

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

end110.0ms (1.8%)

Compiler: Compiled 149 to 110 computations (26.2% saved)

Details

analyze591.0ms (9.6%)

sample2.4s (38.3%)

simplify13.0ms (0.2%)

prune6.0ms (0.1%)

localize23.0ms (0.4%)

series44.0ms (0.7%)

rewrite83.0ms (1.3%)

simplify15.0ms (0.2%)

prune98.0ms (1.6%)

localize22.0ms (0.4%)

series400.0ms (6.5%)

rewrite116.0ms (1.9%)

simplify124.0ms (2%)

prune192.0ms (3.1%)

localize12.0ms (0.2%)

series474.0ms (7.7%)

rewrite86.0ms (1.4%)

simplify111.0ms (1.8%)

prune33.0ms (0.5%)

localize10.0ms (0.2%)

series516.0ms (8.4%)

rewrite91.0ms (1.5%)

simplify165.0ms (2.7%)

prune74.0ms (1.2%)

regimes375.0ms (6.1%)

simplify2.0ms (0%)

end110.0ms (1.8%)

Profiling