Details

analyze283.0ms (6.5%)

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
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
43.7%	56.2%	0.1%	8
62.4%	37.4%	0.1%	9
65.5%	34.3%	0.1%	10
71.8%	27.7%	0.5%	11
79.2%	19.7%	1.1%	12
80.2%	18.7%	1.1%	13
82.8%	15%	2.2%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample56.0ms (1.3%)

Algorithm

1×

intervals

Symmetry

(sort x y)

Results

11.0ms	256×	body	128	valid
1.0ms	13×	body	128	invalid

Compiler

Compiled 32 to 24 computations (25% saved)

simplify10.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

44×	`fma-def_binary64`
37×	`associate-l_binary64`
36×	`associate-r_binary64`
20×	`*-commutative_binary64`
19×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	24	14
2	41	14
3	94	14
4	122	14
5	149	14
6	153	14
7	146	14

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

4.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	4.6b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

Compiler

Compiled 50 to 34 computations (32% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.5b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
✓	3.6b	(*.f64 y (fma.f64 z z 1))

series106.0ms (2.4%)

Counts

2 → 60

Calls

2 calls:

91.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
15.0ms	(*.f64 y (fma.f64 z z 1))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64`
26×	`add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
18×	`add-cube-cbrt_binary64`

Counts

2 → 74

Calls

2 calls:

5.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
3.0ms	(*.f64 y (fma.f64 z z 1))

simplify131.0ms (3%)

Algorithm

1×	egg-herbie

Rules

469×	`associate-/r*_binary64`
451×	`associate-l_binary64`
414×	`associate-/l*_binary64`
336×	`associate-/l/_binary64`
296×	`associate-r_binary64`

Counts

134 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	154	2203
1	330	1967
2	1107	1965
3	3956	1963
4	4482	1963
5	4806	1963
6	4938	1963

prune126.0ms (2.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	10	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Error

3.4b

Counts

123 → 10

Alt Table

Status	Error	Program
	5.4b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
	21.7b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	5.3b	(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))
	22.5b	(.f64 (sqrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1)))) (sqrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
	5.3b	(/.f64 (/.f64 1 x) (.f64 (.f64 (cbrt.f64 (.f64 y (fma.f64 z z 1))) (cbrt.f64 (.f64 y (fma.f64 z z 1)))) (cbrt.f64 (*.f64 y (fma.f64 z z 1)))))
	27.9b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 (.f64 y (fma.f64 z z 1)) x) 3)))
▶	4.7b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
	7.1b	(/.f64 1 (.f64 y (+.f64 (.f64 (pow.f64 z 2) x) x)))
	48.3b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
	6.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))

Compiler

Compiled 2436 to 1531 computations (37.2% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (*.f64 y (fma.f64 z z 1)))
✓	2.5b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
	3.6b	(*.f64 y (fma.f64 z z 1))

series126.0ms (2.9%)

Counts

2 → 60

Calls

2 calls:

88.0ms	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
37.0ms	(/.f64 1 (*.f64 y (fma.f64 z z 1)))

rewrite27.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`add-exp-log_binary64`
43×	`prod-exp_binary64`
34×	`div-exp_binary64`
28×	`add-cbrt-cube_binary64`
20×	`add-sqr-sqrt_binary64`

Counts

2 → 105

Calls

2 calls:

15.0ms	(.f64 (/.f64 1 x) (/.f64 1 (.f64 y (fma.f64 z z 1))))
3.0ms	(/.f64 1 (*.f64 y (fma.f64 z z 1)))

simplify143.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

775×	`times-frac_binary64`
432×	`associate-/r*_binary64`
421×	`associate-l_binary64`
389×	`cancel-sign-sub-inv_binary64`
328×	`associate-/l*_binary64`

Counts

165 → 176

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	175	2996
1	394	2649
2	1088	2618
3	4075	2618
4	4768	2618
5	4973	2618
6	4954	2618

prune198.0ms (4.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	203	5	208
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	209	9	218

Error

3.4b

Counts

218 → 9

Alt Table

Status	Error	Program
	5.4b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
	21.7b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
▶	4.6b	(/.f64 (/.f64 1 (fma.f64 y (*.f64 z z) y)) x)
	17.7b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 (fma.f64 y (.f64 z z) y))) x) (sqrt.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1)))))
	4.7b	(.f64 1 (/.f64 1 (.f64 (fma.f64 y (*.f64 z z) y) x)))
	21.7b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (.f64 (sqrt.f64 y) (hypot.f64 1 z)))))
	6.4b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) y) (/.f64 (cbrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
	4.7b	(*.f64 (/.f64 1 x) (/.f64 (/.f64 1 y) (fma.f64 z z 1)))
	5.3b	(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))

Compiler

Compiled 4104 to 2557 computations (37.7% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (fma.f64 y (*.f64 z z) y))
✓	2.4b	(/.f64 (/.f64 1 (fma.f64 y (*.f64 z z) y)) x)
✓	3.5b	(fma.f64 y (*.f64 z z) y)

series151.0ms (3.5%)

Counts

3 → 84

Calls

3 calls:

104.0ms	(/.f64 (/.f64 1 (fma.f64 y (*.f64 z z) y)) x)
39.0ms	(/.f64 1 (fma.f64 y (*.f64 z z) y))
8.0ms	(fma.f64 y (*.f64 z z) y)

rewrite18.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
53×	`*-un-lft-identity_binary64`
53×	`add-sqr-sqrt_binary64`
53×	`add-cube-cbrt_binary64`
16×	`associate-/l*_binary64`

Counts

3 → 117

Calls

3 calls:

4.0ms	(/.f64 (/.f64 1 (fma.f64 y (*.f64 z z) y)) x)
2.0ms	(/.f64 1 (fma.f64 y (*.f64 z z) y))
0.0ms	(fma.f64 y (*.f64 z z) y)

simplify145.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

483×	`fma-def_binary64`
391×	`distribute-rgt-in_binary64`
321×	`fma-neg_binary64`
317×	`associate-/r*_binary64`
235×	`associate-l_binary64`

Counts

201 → 213

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	173	4051
1	369	3773
2	875	3771
3	2854	3761
4	4522	3757
5	4966	3757

prune184.0ms (4.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	211	2	213
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	213	9	222

Error

3.4b

Counts

222 → 9

Alt Table

Status	Error	Program
	5.4b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
	21.7b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
✓	4.6b	(/.f64 (/.f64 1 (fma.f64 y (*.f64 z z) y)) x)
	5.3b	(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))
	4.7b	(/.f64 1 (.f64 x (fma.f64 y (.f64 z z) y)))
	22.3b	(log1p.f64 (expm1.f64 (/.f64 1 (.f64 y (.f64 (fma.f64 z z 1) x)))))
	17.7b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 (fma.f64 y (.f64 z z) y))) x) (sqrt.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1)))))
	21.7b	(.f64 (/.f64 1 x) (/.f64 1 (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (.f64 (sqrt.f64 y) (hypot.f64 1 z)))))
▶	4.7b	(*.f64 (/.f64 1 x) (/.f64 (/.f64 1 y) (fma.f64 z z 1)))

Compiler

Compiled 4526 to 2162 computations (52.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	2.5b	(*.f64 (/.f64 1 x) (/.f64 (/.f64 1 y) (fma.f64 z z 1)))
✓	3.6b	(/.f64 (/.f64 1 y) (fma.f64 z z 1))

series127.0ms (2.9%)

Counts

2 → 60

Calls

2 calls:

86.0ms	(*.f64 (/.f64 1 x) (/.f64 (/.f64 1 y) (fma.f64 z z 1)))
41.0ms	(/.f64 (/.f64 1 y) (fma.f64 z z 1))

rewrite48.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

173×	`times-frac_binary64`
126×	`add-sqr-sqrt_binary64`
93×	`*-un-lft-identity_binary64`
86×	`add-cube-cbrt_binary64`
76×	`add-exp-log_binary64`

Counts

2 → 182

Calls

2 calls:

20.0ms	(*.f64 (/.f64 1 x) (/.f64 (/.f64 1 y) (fma.f64 z z 1)))
4.0ms	(/.f64 (/.f64 1 y) (fma.f64 z z 1))

simplify168.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

616×	`fma-def_binary64`
518×	`fma-neg_binary64`
496×	`associate-/r*_binary64`
322×	`cancel-sign-sub-inv_binary64`
263×	`*-commutative_binary64`

Counts

242 → 302

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	235	5243
1	573	4561
2	1660	4502
3	3098	4460
4	4619	4456
5	4956	4456

prune283.0ms (6.5%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	298	4	302
Fresh	3	4	7
Picked	0	1	1
Done	0	1	1
Total	301	10	311

Error

1.7b

Counts

311 → 10

Alt Table

Status	Error	Program
	21.7b	(.f64 (/.f64 1 x) (.f64 (/.f64 (/.f64 1 (sqrt.f64 y)) (hypot.f64 1 z)) (/.f64 (/.f64 1 (sqrt.f64 y)) (hypot.f64 1 z))))
	17.7b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 (fma.f64 y (.f64 z z) y))) x) (sqrt.f64 (/.f64 1 (*.f64 y (fma.f64 z z 1)))))
	5.3b	(/.f64 (/.f64 (/.f64 1 x) y) (fma.f64 z z 1))
	4.7b	(/.f64 1 (.f64 x (fma.f64 y (.f64 z z) y)))
	22.3b	(log1p.f64 (expm1.f64 (/.f64 1 (.f64 y (.f64 (fma.f64 z z 1) x)))))
	2.6b	(.f64 (/.f64 1 x) (.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 y) (hypot.f64 1 z))))
	48.1b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) (.f64 (hypot.f64 1 z) (sqrt.f64 y))) (/.f64 (sqrt.f64 (/.f64 1 x)) (*.f64 (hypot.f64 1 z) (sqrt.f64 y))))
	21.7b	(.f64 (/.f64 1 x) (.f64 (/.f64 (sqrt.f64 (/.f64 1 y)) (hypot.f64 1 z)) (/.f64 (sqrt.f64 (/.f64 1 y)) (hypot.f64 1 z))))
✓	4.7b	(*.f64 (/.f64 1 x) (/.f64 (/.f64 1 y) (fma.f64 z z 1)))
✓	4.6b	(/.f64 (/.f64 1 (fma.f64 y (*.f64 z z) y)) x)

Compiler

Compiled 6825 to 4565 computations (33.1% saved)

regimes1.0s (23%)

Accuracy

Total 2.2b remaining (67.2%)

Threshold costs 0b (0%)

Counts

138 → 1

Compiler

Compiled 20760 to 14715 computations (29.1% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	16	25
2	15	25

end6.0ms (0.1%)

Compiler: Compiled 60 to 48 computations (20% saved)

sample967.0ms (22.2%)

Algorithm

1×

intervals

Results

340.0ms	8000×	body	128	valid
19.0ms	460×	body	128	invalid

Compiler

Compiled 225 to 165 computations (26.7% saved)

Details

analyze283.0ms (6.5%)

sample56.0ms (1.3%)

simplify10.0ms (0.2%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series106.0ms (2.4%)

rewrite12.0ms (0.3%)

simplify131.0ms (3%)

prune126.0ms (2.9%)

localize12.0ms (0.3%)

series126.0ms (2.9%)

rewrite27.0ms (0.6%)

simplify143.0ms (3.3%)

prune198.0ms (4.6%)

localize6.0ms (0.1%)

series151.0ms (3.5%)

rewrite18.0ms (0.4%)

simplify145.0ms (3.3%)

prune184.0ms (4.2%)

localize7.0ms (0.2%)

series127.0ms (2.9%)

rewrite48.0ms (1.1%)

simplify168.0ms (3.9%)

prune283.0ms (6.5%)

regimes1.0s (23%)

simplify2.0ms (0.1%)

end6.0ms (0.1%)

sample967.0ms (22.2%)

Profiling