Details

analyze280.0ms (3.5%)

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)

sample50.0ms (0.6%)

Algorithm

1×

intervals

Symmetry

(sort x y)

Results

12.0ms	256×	body	128	valid
1.0ms	15×	body	128	invalid

Compiler

Compiled 32 to 24 computations (25% 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

prune7.0ms (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

7.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.0b	(/.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
✓	2.7b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
✓	5.5b	(*.f64 y (fma.f64 z z 1))

series99.0ms (1.2%)

Counts

2 → 60

Calls

2 calls:

87.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
12.0ms	(*.f64 y (fma.f64 z z 1))

rewrite15.0ms (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)))
5.0ms	(*.f64 y (fma.f64 z z 1))

simplify116.0ms (1.5%)

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

prune114.0ms (1.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	114	8	122
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	114	9	123

Error

2.4b

Counts

123 → 9

Alt Table

Status	Error	Program
	7.1b	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (fma.f64 z z 1)))
	7.6b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
	14.9b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	7.3b	(/.f64 1 (.f64 y (.f64 (+.f64 1 (pow.f64 z 2)) x)))
	7.6b	(.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)))))
	46.7b	(/.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (*.f64 y (fma.f64 z z 1)) (sqrt.f64 (/.f64 1 x))))
▶	6.6b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
✓	7.0b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
	7.0b	(/.f64 (/.f64 1 x) (.f64 (.f64 y (hypot.f64 1 z)) (sqrt.f64 (fma.f64 z z 1))))

Compiler

Compiled 2383 to 1490 computations (37.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.5b	(/.f64 1 (*.f64 y x))
✓	6.3b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))

series102.0ms (1.3%)

Counts

2 → 36

Calls

2 calls:

94.0ms	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
8.0ms	(/.f64 1 (*.f64 y x))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`times-frac_binary64`
32×	`add-exp-log_binary64`
20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

2 → 84

Calls

2 calls:

7.0ms	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
3.0ms	(/.f64 1 (*.f64 y x))

simplify133.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
468×	`fma-neg_binary64`
445×	`times-frac_binary64`
368×	`associate-/r*_binary64`
345×	`cancel-sign-sub-inv_binary64`

Counts

120 → 121

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	148	2243
1	332	2008
2	900	2006
3	3270	2000
4	4421	2000
5	4793	2000
6	4985	2000
7	4929	2000

prune125.0ms (1.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	117	4	121
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	122	8	130

Error

0.0b

Counts

130 → 8

Alt Table

Status	Error	Program
	7.6b	(/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) (.f64 (*.f64 y (fma.f64 z z 1)) (cbrt.f64 x)))
	3.4b	(.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 (.f64 y x)) (hypot.f64 1 z)))
	14.9b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
▶	0.7b	(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
	46.7b	(/.f64 (sqrt.f64 (/.f64 1 x)) (/.f64 (*.f64 y (fma.f64 z z 1)) (sqrt.f64 (/.f64 1 x))))
	4.0b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 (.f64 y x))) (cbrt.f64 (/.f64 1 (.f64 y x)))) (hypot.f64 1 z)) (/.f64 (cbrt.f64 (/.f64 1 (*.f64 y x))) (hypot.f64 1 z)))
	6.6b	(/.f64 1 (.f64 (fma.f64 z z 1) (.f64 y x)))
✓	7.0b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

Compiler

Compiled 2405 to 1413 computations (41.2% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(hypot.f64 1 z)
✓	0.1b	(/.f64 (/.f64 1 y) (hypot.f64 1 z))
✓	0.1b	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
✓	0.7b	(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))

series200.0ms (2.5%)

Counts

4 → 96

Calls

4 calls:

109.0ms	(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
45.0ms	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
43.0ms	(/.f64 (/.f64 1 y) (hypot.f64 1 z))
3.0ms	(hypot.f64 1 z)

rewrite79.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

322×	`times-frac_binary64`
222×	`add-sqr-sqrt_binary64`
166×	`*-un-lft-identity_binary64`
158×	`add-cube-cbrt_binary64`
122×	`add-exp-log_binary64`

Counts

4 → 308

Calls

4 calls:

32.0ms	(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
4.0ms	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
4.0ms	(/.f64 (/.f64 1 y) (hypot.f64 1 z))
0.0ms	(hypot.f64 1 z)

simplify243.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

620×	`fma-def_binary64`
385×	`associate-/r/_binary64`
378×	`fma-neg_binary64`
359×	`associate-*l/_binary64`
347×	`associate-*r/_binary64`

Counts

404 → 514

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	392	9342
1	1080	8458
2	3045	8346
3	4580	8346
4	5091	8346

prune657.0ms (8.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	541	7	548
Fresh	4	2	6
Picked	1	0	1
Done	0	1	1
Total	546	10	556

Error

Counts

556 → 10

Alt Table

Status	Error	Program
✓	7.0b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
▶	0.5b	(/.f64 (*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (hypot.f64 1 z))) (hypot.f64 1 z))
	14.9b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	12.6b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 y)) (sqrt.f64 (hypot.f64 1 z))) (.f64 (/.f64 (sqrt.f64 (/.f64 1 y)) (sqrt.f64 (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
	1.3b	(.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))
	0.7b	(*.f64 (/.f64 (/.f64 (/.f64 1 y) 1) (hypot.f64 1 z)) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
	21.5b	(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (cbrt.f64 (pow.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) 3)))
	1.2b	(.f64 (/.f64 (.f64 (cbrt.f64 (/.f64 1 y)) (cbrt.f64 (/.f64 1 y))) (sqrt.f64 (hypot.f64 1 z))) (*.f64 (/.f64 (cbrt.f64 (/.f64 1 y)) (sqrt.f64 (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
	6.6b	(/.f64 1 (.f64 (fma.f64 z z 1) (.f64 y x)))
	12.9b	(.f64 (/.f64 (/.f64 1 (sqrt.f64 y)) (.f64 (hypot.f64 1 z) (sqrt.f64 y))) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))

Compiler

Compiled 14437 to 10497 computations (27.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(hypot.f64 1 z)
✓	0.0b	(/.f64 (*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (hypot.f64 1 z))) (hypot.f64 1 z))
	0.1b	(/.f64 (/.f64 1 x) (hypot.f64 1 z))
✓	2.5b	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))

series202.0ms (2.5%)

Counts

2 → 72

Calls

2 calls:

104.0ms	(/.f64 (*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (hypot.f64 1 z))) (hypot.f64 1 z))
98.0ms	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))

rewrite49.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

154×	`add-exp-log_binary64`
101×	`times-frac_binary64`
89×	`div-exp_binary64`
86×	`add-sqr-sqrt_binary64`
53×	`*-un-lft-identity_binary64`

Counts

2 → 158

Calls

2 calls:

18.0ms	(*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (hypot.f64 1 z)))
10.0ms	(/.f64 (*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (hypot.f64 1 z))) (hypot.f64 1 z))

simplify191.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

773×	`fma-def_binary64`
523×	`associate-/r/_binary64`
464×	`fma-neg_binary64`
401×	`*-commutative_binary64`
218×	`associate-/l*_binary64`

Counts

230 → 275

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	277	5240
1	738	4487
2	2410	4368
3	4033	4332
4	4882	4332
5	4991	4332
6	4943	4332

prune760.0ms (9.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	450	4	454
Fresh	5	3	8
Picked	0	1	1
Done	0	1	1
Total	455	9	464

Error

Counts

464 → 9

Alt Table

Status	Error	Program
	1.3b	(.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (.f64 (*.f64 (cbrt.f64 (/.f64 1 x)) (cbrt.f64 (/.f64 1 x))) (/.f64 (cbrt.f64 (/.f64 1 x)) (hypot.f64 1 z))))
	0.5b	(/.f64 (/.f64 (/.f64 1 x) (*.f64 y (hypot.f64 1 z))) (hypot.f64 1 z))
✓	7.0b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
✓	0.5b	(/.f64 (*.f64 (/.f64 1 y) (/.f64 (/.f64 1 x) (hypot.f64 1 z))) (hypot.f64 1 z))
	7.0b	(/.f64 (/.f64 1 y) (.f64 x (.f64 (hypot.f64 1 z) (hypot.f64 1 z))))
	2.7b	(/.f64 (.f64 1 (/.f64 1 x)) (.f64 (hypot.f64 1 z) (*.f64 y (hypot.f64 1 z))))
	12.6b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 y)) (sqrt.f64 (hypot.f64 1 z))) (.f64 (/.f64 (sqrt.f64 (/.f64 1 y)) (sqrt.f64 (hypot.f64 1 z))) (/.f64 (/.f64 1 x) (hypot.f64 1 z))))
	21.5b	(*.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (cbrt.f64 (pow.f64 (/.f64 (/.f64 1 x) (hypot.f64 1 z)) 3)))
	3.4b	(/.f64 (.f64 (/.f64 1 (.f64 y x)) (/.f64 1 (hypot.f64 1 z))) (hypot.f64 1 z))

Compiler

Compiled 11092 to 7927 computations (28.5% saved)

regimes3.6s (45.3%)

Accuracy

Total 1.6b remaining (98.2%)

Threshold costs 0b (0%)

Counts

314 → 1

Compiler

Compiled 57326 to 43038 computations (24.9% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	12	19
2	11	19

end7.0ms (0.1%)

Remove: (sort x y)
Compiler: Compiled 48 to 36 computations (25% saved)

sample858.0ms (10.8%)

Algorithm

1×

intervals

Results

435.0ms	8000×	body	128	valid
21.0ms	452×	body	128	invalid

Compiler

Compiled 213 to 165 computations (22.5% saved)

Details

analyze280.0ms (3.5%)

sample50.0ms (0.6%)

simplify9.0ms (0.1%)

prune7.0ms (0.1%)

localize7.0ms (0.1%)

series99.0ms (1.2%)

rewrite15.0ms (0.2%)

simplify116.0ms (1.5%)

prune114.0ms (1.4%)

localize6.0ms (0.1%)

series102.0ms (1.3%)

rewrite15.0ms (0.2%)

simplify133.0ms (1.7%)

prune125.0ms (1.6%)

localize8.0ms (0.1%)

series200.0ms (2.5%)

rewrite79.0ms (1%)

simplify243.0ms (3.1%)

prune657.0ms (8.3%)

localize11.0ms (0.1%)

series202.0ms (2.5%)

rewrite49.0ms (0.6%)

simplify191.0ms (2.4%)

prune760.0ms (9.6%)

regimes3.6s (45.3%)

simplify3.0ms (0%)

end7.0ms (0.1%)

sample858.0ms (10.8%)

Profiling