Details

analyze1.7s (12.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0.4%	99.4%	0.2%	13
0.8%	99%	0.2%	14

Compiler

Compiled 20 to 12 computations (40% saved)

sample7.9s (56.4%)

Results

6.5s	7599×	body	8192	exit
1.4s	8256×	body	128	valid

Compiler

Compiled 59 to 35 computations (40.7% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`associate-/l*_binary64`
6×	`associate-*r/_binary64`
6×	`associate-/r/_binary64`
6×	`fma-def_binary64`
4×	`associate-/r*_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	22
1	25	20
2	45	20
3	55	20
4	55	20
5	55	20

prune4.0ms (0%)

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

28.9b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	28.9b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
	33.9b	(+.f64 (/.f64 (.f64 x x) (.f64 y y)) (/.f64 (.f64 z z) (.f64 t t)))

Compiler

Compiled 107 to 55 computations (48.6% saved)

localize11.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	3.7b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
✓	11.2b	(/.f64 x (*.f64 y y))
✓	21.7b	(/.f64 (.f64 z z) (.f64 t t))

series171.0ms (1.2%)

Counts

3 → 96

Calls

3 calls:

111.0ms	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))
32.0ms	(/.f64 (.f64 z z) (.f64 t t))
28.0ms	(/.f64 x (*.f64 y y))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
6×	`cbrt-undiv_binary64`
6×	`div-exp_binary64`
5×	`*-un-lft-identity_binary64`

Counts

3 → 56

Calls

3 calls:

5.0ms	(/.f64 (.f64 z z) (.f64 t t))
4.0ms	(/.f64 x (*.f64 y y))
0.0ms	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z z) (*.f64 t t)))

simplify115.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

652×	`times-frac_binary64`
469×	`unswap-sqr_binary64`
438×	`associate-/l*_binary64`
258×	`associate-*l/_binary64`
229×	`associate-/r*_binary64`

Counts

152 → 75

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	106	2182
1	224	1962
2	656	1913
3	2597	1888
4	4392	1885
5	4944	1885
6	4965	1885

prune84.0ms (0.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	65	10	75
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	67	10	77

Error

0.1b

Counts

77 → 10

Alt Table

Status	Error	Program
	22.0b	(fma.f64 x (/.f64 1 (/.f64 y (/.f64 x y))) (/.f64 (.f64 z z) (.f64 t t)))
	17.0b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z (/.f64 z t)) t))
	21.8b	(fma.f64 x (.f64 (/.f64 1 y) (/.f64 x y)) (/.f64 (.f64 z z) (*.f64 t t)))
	24.8b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (/.f64 (.f64 z z) t) t))
	41.1b	(fma.f64 x (.f64 (/.f64 (sqrt.f64 x) y) (/.f64 (sqrt.f64 x) y)) (/.f64 (.f64 z z) (*.f64 t t)))
	16.8b	(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
	21.8b	(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (.f64 z z) (.f64 t t)))
	22.1b	(fma.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 x) y)) (/.f64 (.f64 z z) (.f64 t t)))
	40.8b	(/.f64 (pow.f64 x 2) (pow.f64 y 2))
▶	0.4b	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))

Compiler

Compiled 1798 to 483 computations (73.1% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 (/.f64 z t) (/.f64 x y))
✓	0.4b	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))

series347.0ms (2.5%)

Counts

2 → 96

Calls

2 calls:

294.0ms	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
53.0ms	(hypot.f64 (/.f64 z t) (/.f64 x y))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
5×	`hypot-udef_binary64`

Counts

2 → 39

Calls

2 calls:

3.0ms	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))
0.0ms	(hypot.f64 (/.f64 z t) (/.f64 x y))

simplify93.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

928×	`associate-/l*_binary64`
772×	`associate-/r*_binary64`
212×	`fma-def_binary64`
151×	`unswap-sqr_binary64`
148×	`associate-/r/_binary64`

Counts

135 → 87

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	117	3714
1	342	3389
2	1314	3211
3	5268	3211

prune142.0ms (1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	122	7	129
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	127	12	139

Error

0.0b

Counts

139 → 12

Alt Table

Status	Error	Program
	17.0b	(fma.f64 x (/.f64 x (.f64 y y)) (/.f64 (.f64 z (/.f64 z t)) t))
	15.0b	(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (cbrt.f64 (pow.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) 3)))
	0.8b	(pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4) 1)
	0.6b	(.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
▶	0.4b	(+.f64 (.f64 (/.f64 z t) (/.f64 z t)) (.f64 (/.f64 x y) (/.f64 x y)))
	1.2b	(.f64 (.f64 (cbrt.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))) (cbrt.f64 (.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y))))) (cbrt.f64 (*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (hypot.f64 (/.f64 z t) (/.f64 x y)))))
	21.8b	(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (.f64 z z) (.f64 t t)))
	16.8b	(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
	22.1b	(fma.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) y) (/.f64 (cbrt.f64 x) y)) (/.f64 (.f64 z z) (.f64 t t)))
	40.8b	(/.f64 (pow.f64 x 2) (pow.f64 y 2))
	0.6b	(.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
	1.1b	(.f64 (.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))

Compiler

Compiled 4249 to 1483 computations (65.1% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.3b	(*.f64 (/.f64 z t) (/.f64 z t))
✓	0.3b	(*.f64 (/.f64 x y) (/.f64 x y))

series63.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

32.0ms	(*.f64 (/.f64 z t) (/.f64 z t))
31.0ms	(*.f64 (/.f64 x y) (/.f64 x y))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

82×	`add-sqr-sqrt_binary64`
80×	`times-frac_binary64`
58×	`*-un-lft-identity_binary64`
58×	`add-cube-cbrt_binary64`
26×	`associate-r_binary64`

Counts

2 → 138

Calls

2 calls:

9.0ms	(*.f64 (/.f64 z t) (/.f64 z t))
8.0ms	(*.f64 (/.f64 x y) (/.f64 x y))

simplify145.0ms (1%)

Algorithm

1×	egg-herbie

Rules

816×	`times-frac_binary64`
418×	`associate-/r*_binary64`
300×	`associate-/r/_binary64`
256×	`associate-*r/_binary64`
248×	`associate-*l/_binary64`

Counts

186 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	213	2820
1	610	2390
2	1926	2062
3	4024	1998
4	4863	1998
5	5073	1998

prune237.0ms (1.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	203	7	210
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	210	12	222

Error

0.0b

Counts

222 → 12

Alt Table

Status	Error	Program
	1.3b	(+.f64 (.f64 (.f64 (/.f64 z t) (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) 1)) (/.f64 (cbrt.f64 z) t)) (.f64 (/.f64 x y) (/.f64 x y)))
	30.1b	(+.f64 (.f64 (/.f64 z t) (/.f64 z t)) (.f64 (/.f64 (sqrt.f64 x) 1) (*.f64 (/.f64 (sqrt.f64 x) y) (/.f64 x y))))
	33.4b	(+.f64 (.f64 (/.f64 z t) (/.f64 z t)) (.f64 (/.f64 x (pow.f64 y 3/2)) (/.f64 x (sqrt.f64 y))))
	1.0b	(+.f64 (.f64 (/.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (*.f64 (/.f64 x y) (/.f64 x y)))
	3.6b	(+.f64 (.f64 (/.f64 z t) (/.f64 z t)) (/.f64 (.f64 x (/.f64 x y)) y))
	1.1b	(.f64 (.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
	3.6b	(+.f64 (.f64 (/.f64 z t) (/.f64 z t)) (.f64 (/.f64 1 y) (*.f64 x (/.f64 x y))))
▶	0.6b	(.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
	3.5b	(+.f64 (/.f64 (.f64 z (/.f64 z t)) t) (.f64 (/.f64 x y) (/.f64 x y)))
	21.8b	(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (.f64 z z) (.f64 t t)))
	0.8b	(pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4) 1)
	16.8b	(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))

Compiler

Compiled 5326 to 1253 computations (76.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 (/.f64 z t) (/.f64 x y))
✓	0.4b	(.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))
✓	0.5b	(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))
✓	2.9b	(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

series434.0ms (3.1%)

Counts

3 → 120

Calls

3 calls:

299.0ms

(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))

80.0ms

(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

54.0ms

(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))

rewrite22.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`pow1_binary64`
32×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
15×	`pow-prod-up_binary64`
15×	`sqrt-pow1_binary64`

Counts

3 → 97

Calls

3 calls:

8.0ms

(*.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))))

5.0ms

(*.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))))

1.0ms

(sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))

simplify130.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

960×	`associate-/r*_binary64`
363×	`fma-def_binary64`
200×	`cancel-sign-sub-inv_binary64`
194×	`unswap-sqr_binary64`
169×	`associate-/r/_binary64`

Counts

217 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	202	5798
1	520	5228
2	1905	5086
3	5297	5086

prune292.0ms (2.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	320	1	321
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	321	12	333

Error

Counts

333 → 12

Alt Table

Status	Error	Program
	21.8b	(fma.f64 x (/.f64 (/.f64 x y) y) (/.f64 (.f64 z z) (.f64 t t)))
	0.7b	(.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)) (.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 3))))
	1.3b	(+.f64 (.f64 (.f64 (/.f64 z t) (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) 1)) (/.f64 (cbrt.f64 z) t)) (.f64 (/.f64 x y) (/.f64 x y)))
	30.1b	(+.f64 (.f64 (/.f64 z t) (/.f64 z t)) (.f64 (/.f64 (sqrt.f64 x) 1) (*.f64 (/.f64 (sqrt.f64 x) y) (/.f64 x y))))
	33.4b	(+.f64 (.f64 (/.f64 z t) (/.f64 z t)) (.f64 (/.f64 x (pow.f64 y 3/2)) (/.f64 x (sqrt.f64 y))))
	1.0b	(+.f64 (.f64 (/.f64 (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t))) (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 z (.f64 (cbrt.f64 t) (cbrt.f64 t)))) (*.f64 (/.f64 x y) (/.f64 x y)))
	3.6b	(+.f64 (.f64 (/.f64 z t) (/.f64 z t)) (/.f64 (.f64 x (/.f64 x y)) y))
	1.1b	(.f64 (.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y)))) (*.f64 (cbrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) (hypot.f64 (/.f64 z t) (/.f64 x y))))
	3.5b	(+.f64 (/.f64 (.f64 z (/.f64 z t)) t) (.f64 (/.f64 x y) (/.f64 x y)))
	0.8b	(pow.f64 (pow.f64 (sqrt.f64 (hypot.f64 (/.f64 z t) (/.f64 x y))) 4) 1)
	16.8b	(fma.f64 x (/.f64 x (*.f64 y y)) (/.f64 z (/.f64 t (/.f64 z t))))
	3.6b	(+.f64 (.f64 (/.f64 z t) (/.f64 z t)) (.f64 (/.f64 1 y) (*.f64 x (/.f64 x y))))

Compiler

Compiled 12155 to 3609 computations (70.3% saved)

regimes1.9s (13.5%)

Accuracy

Total 0.4b remaining (90.1%)

Threshold costs 0.4b (90.1%)

Counts

178 → 1

Compiler

Compiled 50289 to 24813 computations (50.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	13
1	16	13
2	13	13

end151.0ms (1.1%)

Compiler: Compiled 315 to 160 computations (49.2% saved)

Details

analyze1.7s (12.1%)

sample7.9s (56.4%)

simplify11.0ms (0.1%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series171.0ms (1.2%)

rewrite12.0ms (0.1%)

simplify115.0ms (0.8%)

prune84.0ms (0.6%)

localize7.0ms (0%)

series347.0ms (2.5%)

rewrite8.0ms (0.1%)

simplify93.0ms (0.7%)

prune142.0ms (1%)

localize7.0ms (0.1%)

series63.0ms (0.4%)

rewrite29.0ms (0.2%)

simplify145.0ms (1%)

prune237.0ms (1.7%)

localize9.0ms (0.1%)

series434.0ms (3.1%)

rewrite22.0ms (0.2%)

simplify130.0ms (0.9%)

prune292.0ms (2.1%)

regimes1.9s (13.5%)

simplify2.0ms (0%)

end151.0ms (1.1%)

Profiling