Details

analyze141.0ms (4.2%)

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)

sample1.5s (45.1%)

Infinites

6.1% of outputs are infinite.

Results

1.3s	8256×	body	128	valid
162.0ms	1115×	body	128	invalid

Compiler

Compiled 41 to 32 computations (22% saved)

simplify8.0ms (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

prune3.0ms (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)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 y (sqrt.f64 z)))
✓	0.2b	(*.f64 y (sqrt.f64 z))

series23.0ms (0.7%)

Counts

2 → 16

Calls

2 calls:

13.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))
10.0ms	(*.f64 y (sqrt.f64 z))

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
6×	`associate-r_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
4×	`sqrt-prod_binary64`

Counts

2 → 40

Calls

2 calls:

3.0ms	(*.f64 y (sqrt.f64 z))
2.0ms	(+.f64 x (*.f64 y (sqrt.f64 z)))

simplify111.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

895×	`fma-neg_binary64`
773×	`fma-def_binary64`
544×	`distribute-rgt-in_binary64`
537×	`unsub-neg_binary64`
453×	`distribute-lft-in_binary64`

Counts

56 → 52

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	63	469
1	148	454
2	387	452
3	951	452
4	2044	452
5	3250	452
6	4140	452
7	4878	452
8	4998	452
9	4834	452

prune58.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	45	7	52
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	46	8	54

Error

0.0b

Counts

54 → 8

Alt Table

Status	Error	Program
▶	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 y (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))) (cbrt.f64 (sqrt.f64 z)))))
	30.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (sqrt.f64 z)))))
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (sqrt.f64 z)))))
	30.7b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (sqrt.f64 y) (sqrt.f64 (sqrt.f64 z))) (.f64 (sqrt.f64 y) (sqrt.f64 (sqrt.f64 z))))))
	32.3b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))

Compiler

Compiled 1098 to 577 computations (47.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

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

series11.0ms (0.3%)

Counts

1 → 25

Calls

1 calls:

11.0ms

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

simplify98.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

642×	`distribute-rgt-in_binary64`
492×	`distribute-lft-in_binary64`
436×	`distribute-rgt-out_binary64`
421×	`associate-l_binary64`
413×	`*-commutative_binary64`

Counts

35 → 15

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	262
1	20	247
2	43	247
3	104	247
4	281	247
5	915	247
6	1563	247
7	2177	247
8	2401	247
9	3023	247
10	3557	247
11	4430	247
12	4903	247

prune21.0ms (0.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	15	0	15
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	15	8	23

Error

0.0b

Counts

23 → 8

Alt Table

Status	Error	Program
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
▶	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))))
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 y (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))) (cbrt.f64 (sqrt.f64 z)))))
	30.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (sqrt.f64 z)))))
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 y) (sqrt.f64 z)))))
	30.7b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (sqrt.f64 y) (sqrt.f64 (sqrt.f64 z))) (.f64 (sqrt.f64 y) (sqrt.f64 (sqrt.f64 z))))))
	32.3b	(.f64 (/.f64 1 2) (/.f64 (-.f64 (.f64 x x) (.f64 y (.f64 y z))) (-.f64 x (*.f64 y (sqrt.f64 z)))))

Compiler

Compiled 446 to 250 computations (43.9% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z))))
✓	0.2b	(sqrt.f64 (sqrt.f64 z))
✓	0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
✓	0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

series369.0ms (10.9%)

Counts

4 → 65

Calls

4 calls:

324.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
21.0ms	(sqrt.f64 (sqrt.f64 z))
14.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z))))
10.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))

rewrite20.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`sqrt-prod_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`associate-r_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-cube-cbrt_binary64`

Counts

4 → 91

Calls

4 calls:

6.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z)))
4.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
3.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (sqrt.f64 (sqrt.f64 z))))
1.0ms	(sqrt.f64 (sqrt.f64 z))

simplify164.0ms (4.9%)

Algorithm

1×	egg-herbie

Rules

776×	`fma-def_binary64`
518×	`distribute-rgt-in_binary64`
436×	`distribute-lft-in_binary64`
278×	`unsub-neg_binary64`
230×	`fma-neg_binary64`

Counts

156 → 116

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	103	1305
1	232	1272
2	689	1265
3	1315	1265
4	2693	1265
5	4269	1265
6	4492	1265
7	4845	1247
8	4996	1247
9	4819	1247

prune139.0ms (4.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	138	8	146

Error

Counts

146 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 z))) (cbrt.f64 (sqrt.f64 (sqrt.f64 z))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 z))))))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
▶	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))))
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 y (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))) (cbrt.f64 (sqrt.f64 z)))))
	30.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (sqrt.f64 z)))))
	30.7b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (sqrt.f64 y) (sqrt.f64 (sqrt.f64 z))) (.f64 (sqrt.f64 y) (sqrt.f64 (sqrt.f64 z))))))
	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))))

Compiler

Compiled 3027 to 1282 computations (57.6% saved)

localize12.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4)))
	0.2b	(sqrt.f64 (sqrt.f64 z))
	0.3b	(*.f64 y (sqrt.f64 (sqrt.f64 z)))
✓	0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))

series32.0ms (0.9%)

Counts

2 → 37

Calls

2 calls:

19.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4)))
12.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))

rewrite10.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64`
9×	`prod-exp_binary64`
7×	`associate-r_binary64`
7×	`add-cbrt-cube_binary64`
5×	`*-un-lft-identity_binary64`

Counts

2 → 42

Calls

2 calls:

6.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))
3.0ms	(+.f64 x (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4)))

simplify84.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

747×	`unswap-sqr_binary64`
691×	`fma-neg_binary64`
434×	`*-commutative_binary64`
321×	`cancel-sign-sub-inv_binary64`
285×	`distribute-rgt-neg-in_binary64`

Counts

79 → 67

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	87	978
1	219	920
2	734	899
3	1613	622
4	2662	621
5	4850	621
6	5021	621

prune126.0ms (3.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	119	8	127

Error

Counts

127 → 8

Alt Table

Status	Error	Program
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (.f64 y (sqrt.f64 (sqrt.f64 z))) (*.f64 (cbrt.f64 (sqrt.f64 (sqrt.f64 z))) (cbrt.f64 (sqrt.f64 (sqrt.f64 z))))) (cbrt.f64 (sqrt.f64 (sqrt.f64 z))))))
✓	0.1b	(*.f64 1/2 (fma.f64 y (sqrt.f64 z) x))
	0.4b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (fabs.f64 (cbrt.f64 z))) (sqrt.f64 (cbrt.f64 z)))))
✓	0.2b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (sqrt.f64 (sqrt.f64 z))) (pow.f64 z 1/4))))
	0.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 y (.f64 (cbrt.f64 (sqrt.f64 z)) (cbrt.f64 (sqrt.f64 z)))) (cbrt.f64 (sqrt.f64 z)))))
	30.6b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (sqrt.f64 y) (*.f64 (sqrt.f64 y) (sqrt.f64 z)))))
	30.7b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (.f64 (sqrt.f64 y) (sqrt.f64 (sqrt.f64 z))) (.f64 (sqrt.f64 y) (sqrt.f64 (sqrt.f64 z))))))
	0.3b	(.f64 (/.f64 1 2) (+.f64 x (.f64 (*.f64 y (pow.f64 (sqrt.f64 (sqrt.f64 z)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 z))))))

Compiler

Compiled 2534 to 1406 computations (44.5% saved)

regimes275.0ms (8.2%)

Accuracy

Total 0.1b remaining (74.1%)

Threshold costs 0.1b (74.1%)

Counts

38 → 1

Compiler

Compiled 4938 to 3489 computations (29.3% saved)

simplify5.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	12
1	17	12
2	15	12

end110.0ms (3.3%)

Compiler: Compiled 179 to 118 computations (34.1% saved)

Details

analyze141.0ms (4.2%)

sample1.5s (45.1%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series23.0ms (0.7%)

rewrite7.0ms (0.2%)

simplify111.0ms (3.3%)

prune58.0ms (1.7%)

localize5.0ms (0.2%)

series11.0ms (0.3%)

rewrite1.0ms (0%)

simplify98.0ms (2.9%)

prune21.0ms (0.6%)

localize9.0ms (0.3%)

series369.0ms (10.9%)

rewrite20.0ms (0.6%)

simplify164.0ms (4.9%)

prune139.0ms (4.1%)

localize12.0ms (0.4%)

series32.0ms (0.9%)

rewrite10.0ms (0.3%)

simplify84.0ms (2.5%)

prune126.0ms (3.7%)

regimes275.0ms (8.2%)

simplify5.0ms (0.2%)

end110.0ms (3.3%)

Profiling