Details

analyze311.0ms (5.4%)

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)

sample959.0ms (16.6%)

Symmetry

(sort x y)

Results

869.0ms	8256×	body	128	valid
49.0ms	449×	body	128	invalid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify9.0ms (0.1%)

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

6.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.5b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

Compiler

Compiled 50 to 34 computations (32% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.4b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
✓	4.5b	(*.f64 y (fma.f64 z z 1))

series88.0ms (1.5%)

Counts

2 → 60

Calls

2 calls:

77.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
11.0ms	(*.f64 y (fma.f64 z z 1))

rewrite13.0ms (0.2%)

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))

simplify120.0ms (2.1%)

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

prune115.0ms (2%)

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
	6.8b	(/.f64 1 (.f64 (+.f64 y (.f64 y (pow.f64 z 2))) x))
▶	6.5b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
	6.7b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (*.f64 (cbrt.f64 (fma.f64 z z 1)) (cbrt.f64 (fma.f64 z z 1)))) (cbrt.f64 (fma.f64 z z 1))))
	7.1b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
	24.5b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 (.f64 y (fma.f64 z z 1)) x) 3)))
	22.7b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	7.1b	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
	7.5b	(/.f64 1 (.f64 y (.f64 (+.f64 1 (pow.f64 z 2)) x)))

Compiler

Compiled 2342 to 1463 computations (37.5% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 y (hypot.f64 1 z))
✓	0.1b	(.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1)))
✓	3.4b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
✓	17.0b	(sqrt.f64 (fma.f64 z z 1))

series199.0ms (3.4%)

Counts

4 → 96

Calls

4 calls:

155.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
23.0ms	(.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1)))
17.0ms	(*.f64 y (hypot.f64 1 z))
2.0ms	(sqrt.f64 (fma.f64 z z 1))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-exp-log_binary64`
32×	`add-cbrt-cube_binary64`
31×	`times-frac_binary64`
26×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`

Counts

4 → 116

Calls

4 calls:

7.0ms	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))
4.0ms	(.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1)))
3.0ms	(*.f64 y (hypot.f64 1 z))
1.0ms	(sqrt.f64 (fma.f64 z z 1))

simplify141.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

697×	`associate-/l*_binary64`
472×	`associate-/l/_binary64`
412×	`fma-def_binary64`
240×	`associate-l_binary64`
198×	`associate-/r*_binary64`

Counts

212 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	243	4001
1	619	2902
2	1916	2883
3	4768	2883
4	4984	2883
5	4965	2883

prune238.0ms (4.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	225	6	231
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	232	7	239

Error

0.1b

Counts

239 → 7

Alt Table

Status	Error	Program
	7.5b	(/.f64 1 (.f64 y (.f64 (fma.f64 z z 1) x)))
	6.8b	(/.f64 1 (.f64 (+.f64 y (.f64 y (pow.f64 z 2))) x))
	2.0b	(.f64 (/.f64 1 (.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
▶	1.4b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 (cbrt.f64 x)) (hypot.f64 1 z)))
	24.3b	(cbrt.f64 (pow.f64 (/.f64 1 (.f64 y (.f64 (fma.f64 z z 1) x))) 3))
	3.4b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (*.f64 1 (hypot.f64 1 z))))
	3.6b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (.f64 (.f64 (cbrt.f64 (hypot.f64 1 z)) (cbrt.f64 (hypot.f64 1 z))) (cbrt.f64 (hypot.f64 1 z)))))

Compiler

Compiled 5119 to 3423 computations (33.1% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 1 (cbrt.f64 x))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)
✓	2.5b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 y (hypot.f64 1 z)))

series599.0ms (10.4%)

Counts

4 → 72

Calls

4 calls:

483.0ms	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 y (hypot.f64 1 z)))
49.0ms	(/.f64 1 (cbrt.f64 x))
36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
30.0ms	(cbrt.f64 x)

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-exp-log_binary64`
40×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`
31×	`cbrt-prod_binary64`

Counts

4 → 149

Calls

4 calls:

7.0ms	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 y (hypot.f64 1 z)))
6.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
3.0ms	(/.f64 1 (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify118.0ms (2%)

Algorithm

1×	egg-herbie

Rules

851×	`associate-/l*_binary64`
620×	`associate-/l/_binary64`
499×	`fma-def_binary64`
381×	`fma-neg_binary64`
268×	`cancel-sign-sub-inv_binary64`

Counts

221 → 228

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	224	3983
1	507	3052
2	1668	2773
3	4551	2771
4	4966	2771

prune259.0ms (4.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	261	3	264
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	262	9	271

Error

0.0b

Counts

271 → 9

Alt Table

Status	Error	Program
	7.5b	(/.f64 1 (.f64 y (.f64 (fma.f64 z z 1) x)))
	6.8b	(/.f64 1 (.f64 (+.f64 y (.f64 y (pow.f64 z 2))) x))
▶	1.5b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x)))) (hypot.f64 1 z)))
	3.3b	(.f64 (/.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (hypot.f64 1 z)) (/.f64 (/.f64 1 (cbrt.f64 x)) (hypot.f64 1 z)))
	2.0b	(.f64 (/.f64 1 (.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 y (hypot.f64 1 z)))) (cbrt.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 y (hypot.f64 1 z))))) (cbrt.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 y (hypot.f64 1 z))))) (/.f64 (/.f64 1 (cbrt.f64 x)) (hypot.f64 1 z)))
	24.3b	(cbrt.f64 (pow.f64 (/.f64 1 (.f64 y (.f64 (fma.f64 z z 1) x))) 3))
	3.4b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (*.f64 1 (hypot.f64 1 z))))
	3.6b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (.f64 (.f64 (cbrt.f64 (hypot.f64 1 z)) (cbrt.f64 (hypot.f64 1 z))) (cbrt.f64 (hypot.f64 1 z)))))

Compiler

Compiled 7961 to 4802 computations (39.7% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 x)
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
✓	0.6b	(cbrt.f64 (cbrt.f64 x))
	2.5b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 y (hypot.f64 1 z)))

series519.0ms (9%)

Counts

2 → 24

Calls

2 calls:

273.0ms	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
246.0ms	(cbrt.f64 (cbrt.f64 x))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`cbrt-prod_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 27

Calls

2 calls:

2.0ms	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
1.0ms	(cbrt.f64 (cbrt.f64 x))

simplify103.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

693×	`sqr-pow_binary64`
622×	`fma-def_binary64`
548×	`unswap-sqr_binary64`
376×	`distribute-rgt-in_binary64`
318×	`*-commutative_binary64`

Counts

51 → 42

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	474
1	78	474
2	138	474
3	283	468
4	779	450
5	1271	450
6	1449	450
7	1730	450
8	2156	450
9	2689	450
10	3638	450
11	4799	450
12	4840	450

prune249.0ms (4.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	222	2	224
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	222	11	233

Error

Counts

233 → 11

Alt Table

Status	Error	Program
	7.5b	(/.f64 1 (.f64 y (.f64 (fma.f64 z z 1) x)))
	6.8b	(/.f64 1 (.f64 (+.f64 y (.f64 y (pow.f64 z 2))) x))
	1.7b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x))))) (.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x)))) (hypot.f64 1 z)))
✓	1.5b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (cbrt.f64 (cbrt.f64 x)))) (hypot.f64 1 z)))
	1.5b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 (.f64 (.f64 (sqrt.f64 (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (sqrt.f64 (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x))))) (cbrt.f64 (cbrt.f64 x)))) (hypot.f64 1 z)))
	3.3b	(.f64 (/.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (hypot.f64 1 z)) (/.f64 (/.f64 1 (cbrt.f64 x)) (hypot.f64 1 z)))
	2.0b	(.f64 (/.f64 1 (.f64 y (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
	1.6b	(.f64 (.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 y (hypot.f64 1 z)))) (cbrt.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 y (hypot.f64 1 z))))) (cbrt.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (*.f64 y (hypot.f64 1 z))))) (/.f64 (/.f64 1 (cbrt.f64 x)) (hypot.f64 1 z)))
	24.3b	(cbrt.f64 (pow.f64 (/.f64 1 (.f64 y (.f64 (fma.f64 z z 1) x))) 3))
	3.4b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (*.f64 1 (hypot.f64 1 z))))
	3.6b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (.f64 (.f64 (cbrt.f64 (hypot.f64 1 z)) (cbrt.f64 (hypot.f64 1 z))) (cbrt.f64 (hypot.f64 1 z)))))

Compiler

Compiled 8453 to 4150 computations (50.9% saved)

regimes1.3s (22.3%)

Accuracy

Total 1.8b remaining (97.4%)

Threshold costs 0b (0%)

Counts

107 → 3

Compiler

Compiled 17072 to 12058 computations (29.4% saved)

bsearch3.0ms (0.1%)

Compiler: Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	83
1	30	83
2	29	83

end345.0ms (6%)

Compiler: Compiled 539 to 370 computations (31.4% saved)

Details

analyze311.0ms (5.4%)

sample959.0ms (16.6%)

simplify9.0ms (0.1%)

prune3.0ms (0.1%)

localize7.0ms (0.1%)

series88.0ms (1.5%)

rewrite13.0ms (0.2%)

simplify120.0ms (2.1%)

prune115.0ms (2%)

localize9.0ms (0.2%)

series199.0ms (3.4%)

rewrite22.0ms (0.4%)

simplify141.0ms (2.4%)

prune238.0ms (4.1%)

localize11.0ms (0.2%)

series599.0ms (10.4%)

rewrite25.0ms (0.4%)

simplify118.0ms (2%)

prune259.0ms (4.5%)

localize15.0ms (0.3%)

series519.0ms (9%)

rewrite4.0ms (0.1%)

simplify103.0ms (1.8%)

prune249.0ms (4.3%)

regimes1.3s (22.3%)

bsearch3.0ms (0.1%)

simplify4.0ms (0.1%)

end345.0ms (6%)

Profiling