Details

analyze332.0ms (6.6%)

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
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)

sample1.0s (20.3%)

Symmetry

(sort x y)

Results

917.0ms	8256×	body	128	valid
56.0ms	484×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify8.0ms (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

6.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.9b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

Compiler

Compiled 50 to 34 computations (32% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.7b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
✓	4.5b	(*.f64 y (fma.f64 z z 1))

series101.0ms (2%)

Counts

2 → 60

Calls

2 calls:

91.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
10.0ms	(*.f64 y (fma.f64 z z 1))

rewrite16.0ms (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))

simplify118.0ms (2.4%)

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

prune128.0ms (2.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	114	8	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	8	123

Error

3.4b

Counts

123 → 8

Alt Table

Status	Error	Program
	22.9b	(.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)))))
	7.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1)))) (cbrt.f64 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1))))) (cbrt.f64 (/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))))
	7.4b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
	7.0b	(/.f64 1 (/.f64 y (/.f64 1 (*.f64 (fma.f64 z z 1) x))))
	6.9b	(.f64 1 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1))))
	21.9b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
▶	6.7b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (fma.f64 z z 1) x)))
	6.9b	(/.f64 1 (.f64 y (.f64 (+.f64 1 (pow.f64 z 2)) x)))

Compiler

Compiled 2382 to 1489 computations (37.5% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (*.f64 (fma.f64 z z 1) x))
✓	3.5b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (fma.f64 z z 1) x)))
✓	4.8b	(*.f64 (fma.f64 z z 1) x)

series132.0ms (2.6%)

Counts

3 → 84

Calls

3 calls:

87.0ms	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (fma.f64 z z 1) x)))
35.0ms	(/.f64 1 (*.f64 (fma.f64 z z 1) x))
11.0ms	(*.f64 (fma.f64 z z 1) x)

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

99×	`add-exp-log_binary64`
44×	`prod-exp_binary64`
34×	`div-exp_binary64`
31×	`add-cbrt-cube_binary64`
25×	`add-sqr-sqrt_binary64`

Counts

3 → 125

Calls

3 calls:

8.0ms	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (fma.f64 z z 1) x)))
3.0ms	(/.f64 1 (*.f64 (fma.f64 z z 1) x))
3.0ms	(*.f64 (fma.f64 z z 1) x)

simplify165.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

493×	`associate-/r*_binary64`
425×	`associate-*l/_binary64`
361×	`fma-neg_binary64`
354×	`associate-/l*_binary64`
287×	`associate-*r/_binary64`

Counts

209 → 214

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	188	3383
1	420	3024
2	1301	2998
3	4200	2994
4	4574	2990
5	4922	2990
6	4985	2990
7	4941	2990

prune193.0ms (3.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	210	4	214
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	215	7	222

Error

3.0b

Counts

222 → 7

Alt Table

Status	Error	Program
	6.9b	(/.f64 1 (.f64 (fma.f64 x (.f64 z z) x) y))
	7.0b	(/.f64 1 (/.f64 y (/.f64 1 (*.f64 (fma.f64 z z 1) x))))
	46.6b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (.f64 (hypot.f64 1 z) (sqrt.f64 x)) (.f64 (hypot.f64 1 z) (sqrt.f64 x)))))
▶	6.7b	(/.f64 (/.f64 1 (fma.f64 x (*.f64 z z) x)) y)
	6.9b	(.f64 1 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1))))
	21.9b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	6.7b	(/.f64 (/.f64 1 y) (*.f64 (fma.f64 z z 1) x))

Compiler

Compiled 4095 to 2530 computations (38.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (fma.f64 x (*.f64 z z) x))
✓	3.4b	(/.f64 (/.f64 1 (fma.f64 x (*.f64 z z) x)) y)
✓	4.8b	(fma.f64 x (*.f64 z z) x)

series139.0ms (2.8%)

Counts

3 → 84

Calls

3 calls:

90.0ms	(/.f64 (/.f64 1 (fma.f64 x (*.f64 z z) x)) y)
39.0ms	(/.f64 1 (fma.f64 x (*.f64 z z) x))
10.0ms	(fma.f64 x (*.f64 z z) x)

rewrite17.0ms (0.3%)

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:

6.0ms	(/.f64 (/.f64 1 (fma.f64 x (*.f64 z z) x)) y)
2.0ms	(/.f64 1 (fma.f64 x (*.f64 z z) x))
0.0ms	(fma.f64 x (*.f64 z z) x)

simplify168.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

844×	`fma-def_binary64`
356×	`associate-/r*_binary64`
318×	`times-frac_binary64`
261×	`associate-l_binary64`
248×	`associate-r_binary64`

Counts

201 → 214

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	167	4025
1	370	3773
2	997	3771
3	3458	3767
4	4499	3767
5	4997	3767
6	4968	3767

prune165.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	213	1	214
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	213	8	221

Error

3.0b

Counts

221 → 8

Alt Table

Status	Error	Program
	6.9b	(/.f64 1 (.f64 (fma.f64 x (.f64 z z) x) y))
	7.0b	(/.f64 1 (/.f64 y (/.f64 1 (*.f64 (fma.f64 z z 1) x))))
	21.9b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	7.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (fma.f64 x (.f64 z z) x))) (cbrt.f64 (/.f64 1 (fma.f64 x (.f64 z z) x)))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 (/.f64 1 (fma.f64 x (.f64 z z) x))) (cbrt.f64 y)))
	46.6b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (.f64 (hypot.f64 1 z) (sqrt.f64 x)) (.f64 (hypot.f64 1 z) (sqrt.f64 x)))))
✓	6.7b	(/.f64 (/.f64 1 (fma.f64 x (*.f64 z z) x)) y)
	6.9b	(.f64 1 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1))))
▶	6.7b	(/.f64 (/.f64 1 y) (*.f64 (fma.f64 z z 1) x))

Compiler

Compiled 4546 to 2154 computations (52.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.5b	(/.f64 (/.f64 1 y) (*.f64 (fma.f64 z z 1) x))
	4.8b	(*.f64 (fma.f64 z z 1) x)

series85.0ms (1.7%)

Counts

1 → 36

Calls

1 calls:

84.0ms

(/.f64 (/.f64 1 y) (*.f64 (fma.f64 z z 1) x))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`times-frac_binary64`
23×	`add-exp-log_binary64`
15×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`

Counts

1 → 52

Calls

1 calls:

5.0ms

(/.f64 (/.f64 1 y) (*.f64 (fma.f64 z z 1) x))

simplify94.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

811×	`times-frac_binary64`
419×	`associate-/r*_binary64`
366×	`associate-/l*_binary64`
364×	`associate-l_binary64`
314×	`unswap-sqr_binary64`

Counts

88 → 91

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	132	1760
1	301	1567
2	866	1565
3	3851	1565
4	4517	1563
5	4982	1563

prune123.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	128	8	136

Error

3.0b

Counts

136 → 8

Alt Table

Status	Error	Program
	6.9b	(/.f64 1 (.f64 (fma.f64 x (.f64 z z) x) y))
	7.0b	(/.f64 1 (/.f64 y (/.f64 1 (*.f64 (fma.f64 z z 1) x))))
	21.9b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	7.5b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (fma.f64 x (.f64 z z) x))) (cbrt.f64 (/.f64 1 (fma.f64 x (.f64 z z) x)))) (.f64 (cbrt.f64 y) (cbrt.f64 y))) (/.f64 (cbrt.f64 (/.f64 1 (fma.f64 x (.f64 z z) x))) (cbrt.f64 y)))
	46.6b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (.f64 (hypot.f64 1 z) (sqrt.f64 x)) (.f64 (hypot.f64 1 z) (sqrt.f64 x)))))
✓	6.7b	(/.f64 (/.f64 1 (fma.f64 x (*.f64 z z) x)) y)
	6.9b	(.f64 1 (/.f64 (/.f64 1 x) (.f64 y (fma.f64 z z 1))))
✓	6.7b	(/.f64 (/.f64 1 y) (*.f64 (fma.f64 z z 1) x))

Compiler

Compiled 2301 to 1306 computations (43.2% saved)

regimes1.6s (31.4%)

Accuracy

Total 1.0b remaining (30%)

Threshold costs 1.0b (30%)

Counts

108 → 3

Compiler

Compiled 15420 to 11079 computations (28.2% saved)

bsearch68.0ms (1.4%)

Steps

Iters	Range		Point
11	3.42197931123005e-96	3.198613718985946e-63	8.980294761979465e-80
9	1.320286140231934e-303	1.4378817530320796e-294	1.3416652531759415e-303

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0.1%)

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	27	68
1	32	68
2	31	68

end290.0ms (5.8%)

Compiler: Compiled 348 to 225 computations (35.3% saved)

Details

analyze332.0ms (6.6%)

sample1.0s (20.3%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series101.0ms (2%)

rewrite16.0ms (0.3%)

simplify118.0ms (2.4%)

prune128.0ms (2.6%)

localize7.0ms (0.1%)

series132.0ms (2.6%)

rewrite24.0ms (0.5%)

simplify165.0ms (3.3%)

prune193.0ms (3.9%)

localize6.0ms (0.1%)

series139.0ms (2.8%)

rewrite17.0ms (0.3%)

simplify168.0ms (3.4%)

prune165.0ms (3.3%)

localize6.0ms (0.1%)

series85.0ms (1.7%)

rewrite9.0ms (0.2%)

simplify94.0ms (1.9%)

prune123.0ms (2.5%)

regimes1.6s (31.4%)

bsearch68.0ms (1.4%)

simplify3.0ms (0.1%)

end290.0ms (5.8%)

Profiling