Details

analyze541.0ms (6.3%)

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
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
35.9%	64%	0.1%	9
47.6%	49.9%	2.5%	10
49.1%	46.8%	4%	11
51.1%	44.1%	4.8%	12
60.2%	29.9%	9.9%	13
60.6%	27.9%	11.6%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.4s (15.8%)

Symmetry

(sort x y)

Results

949.0ms	8256×	body	128	valid
222.0ms	1644×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify93.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

826×	`associate-*r/_binary64`
769×	`associate-/l/_binary64`
660×	`associate-*l/_binary64`
522×	`associate-/l*_binary64`
421×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	30	16
2	78	14
3	195	14
4	314	14
5	383	14
6	426	14
7	631	14
8	1009	14
9	2204	14
10	2868	14
11	2967	14
12	3079	14
13	3193	14
14	3058	14
15	3712	14
16	4988	14
17	4824	14

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

7.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	9.4b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
	16.9b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))

Compiler

Compiled 78 to 45 computations (42.3% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (/.f64 y (fma.f64 z z z)) z)
✓	6.4b	(/.f64 y (fma.f64 z z z))
✓	8.9b	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))

series174.0ms (2%)

Counts

3 → 84

Calls

3 calls:

94.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
45.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
35.0ms	(/.f64 y (fma.f64 z z z))

rewrite34.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
89×	`add-cube-cbrt_binary64`
43×	`associate-r_binary64`

Counts

3 → 168

Calls

3 calls:

12.0ms	(*.f64 x (/.f64 (/.f64 y (fma.f64 z z z)) z))
4.0ms	(/.f64 (/.f64 y (fma.f64 z z z)) z)
2.0ms	(/.f64 y (fma.f64 z z z))

simplify166.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

805×	`fma-def_binary64`
353×	`fma-neg_binary64`
351×	`*-commutative_binary64`
341×	`associate-/r/_binary64`
275×	`sub-neg_binary64`

Counts

252 → 296

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	287	4846
1	687	4599
2	2304	4515
3	3607	4509
4	4817	4509
5	4963	4509

prune289.0ms (3.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	286	10	296
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	287	11	298

Error

3.0b

Counts

298 → 11

Alt Table

Status	Error	Program
▶	5.0b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
	25.3b	(.f64 (sqrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))) (sqrt.f64 (/.f64 (.f64 y x) (*.f64 z (fma.f64 z z z)))))
	22.8b	(*.f64 x (/.f64 (/.f64 y z) z))
	36.6b	(.f64 x (.f64 (/.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z)) (/.f64 (/.f64 y (sqrt.f64 z)) (hypot.f64 z (sqrt.f64 z)))))
	28.9b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	13.6b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
	9.4b	(*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) x)
	5.1b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	16.9b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
	16.9b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
	19.8b	(.f64 (.f64 x (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (sqrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))

Compiler

Compiled 6348 to 1463 computations (77% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.4b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
✓	4.0b	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))))
✓	4.5b	(/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
✓	23.7b	(cbrt.f64 (fma.f64 z z z))

series1.9s (21.7%)

Counts

4 → 108

Calls

4 calls:

1.2s	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))))
538.0ms	(/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
105.0ms	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
5.0ms	(cbrt.f64 (fma.f64 z z z))

rewrite107.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

231×	`times-frac_binary64`
129×	`associate-r_binary64`
127×	`add-exp-log_binary64`
126×	`add-sqr-sqrt_binary64`
123×	`*-un-lft-identity_binary64`

Counts

4 → 244

Calls

4 calls:

32.0ms	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
8.0ms	(.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z)))))
6.0ms	(/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))
1.0ms	(cbrt.f64 (fma.f64 z z z))

simplify299.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

696×	`associate-*l/_binary64`
421×	`associate-/l*_binary64`
312×	`associate-/r*_binary64`
291×	`times-frac_binary64`
270×	`fma-def_binary64`

Counts

352 → 433

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	562	16302
1	1670	12076
2	4961	12036
3	5102	12036

prune587.0ms (6.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	493	0	493
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	493	11	504

Error

3.0b

Counts

504 → 11

Alt Table

Status	Error	Program
✓	5.0b	(.f64 (.f64 x (/.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (cbrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
	25.3b	(.f64 (sqrt.f64 (/.f64 (.f64 y x) (.f64 z (fma.f64 z z z)))) (sqrt.f64 (/.f64 (.f64 y x) (*.f64 z (fma.f64 z z z)))))
	22.8b	(*.f64 x (/.f64 (/.f64 y z) z))
	36.6b	(.f64 x (.f64 (/.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z)) (/.f64 (/.f64 y (sqrt.f64 z)) (hypot.f64 z (sqrt.f64 z)))))
	28.9b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	13.6b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
	9.4b	(*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) x)
▶	5.1b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	16.9b	(.f64 (.f64 y x) (/.f64 (/.f64 1 (fma.f64 z z z)) z))
	16.9b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
	19.8b	(.f64 (.f64 x (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (sqrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))

Compiler

Compiled 21557 to 4321 computations (80% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
✓	4.3b	(*.f64 x (/.f64 y (fma.f64 z z z)))
	6.4b	(/.f64 y (fma.f64 z z z))

series163.0ms (1.9%)

Counts

2 → 72

Calls

2 calls:

97.0ms	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
66.0ms	(*.f64 x (/.f64 y (fma.f64 z z z)))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
13×	`associate-r_binary64`
13×	`times-frac_binary64`

Counts

2 → 60

Calls

2 calls:

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

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

604×	`fma-neg_binary64`
483×	`associate-l_binary64`
433×	`associate-/r*_binary64`
417×	`associate-r_binary64`
378×	`associate-/r/_binary64`

Counts

132 → 124

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	2289
1	397	2096
2	1539	1990
3	4439	1990
4	4968	1990

prune171.0ms (2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	171	4	175
Fresh	4	5	9
Picked	0	1	1
Done	1	0	1
Total	176	10	186

Error

1.2b

Counts

186 → 10

Alt Table

Status	Error	Program
	36.6b	(.f64 x (.f64 (/.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z)) (/.f64 (/.f64 y (sqrt.f64 z)) (hypot.f64 z (sqrt.f64 z)))))
	40.6b	(/.f64 (.f64 x (.f64 (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))) (/.f64 (sqrt.f64 y) (hypot.f64 z (sqrt.f64 z))))) z)
	9.5b	(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
	19.8b	(.f64 (.f64 x (/.f64 (sqrt.f64 y) (*.f64 (cbrt.f64 (fma.f64 z z z)) (cbrt.f64 (fma.f64 z z z))))) (/.f64 (/.f64 (sqrt.f64 y) (cbrt.f64 (fma.f64 z z z))) z))
	31.9b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
	28.9b	(*.f64 (/.f64 y z) (-.f64 (/.f64 x z) x))
	13.6b	(.f64 (.f64 x (/.f64 (/.f64 1 (sqrt.f64 (fma.f64 z z z))) 1)) (/.f64 (/.f64 y (sqrt.f64 (fma.f64 z z z))) z))
▶	9.4b	(/.f64 1 (/.f64 z (/.f64 (*.f64 y x) (fma.f64 z z z))))
	9.4b	(*.f64 (/.f64 (/.f64 y (fma.f64 z z z)) z) x)
✓	5.1b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)

Compiler

Compiled 3317 to 942 computations (71.6% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 z (/.f64 (*.f64 y x) (fma.f64 z z z))))
✓	0.3b	(/.f64 z (/.f64 (*.f64 y x) (fma.f64 z z z)))
✓	11.4b	(/.f64 (*.f64 y x) (fma.f64 z z z))

series201.0ms (2.3%)

Counts

3 → 108

Calls

3 calls:

94.0ms	(/.f64 1 (/.f64 z (/.f64 (*.f64 y x) (fma.f64 z z z))))
68.0ms	(/.f64 (*.f64 y x) (fma.f64 z z z))
39.0ms	(/.f64 z (/.f64 (*.f64 y x) (fma.f64 z z z)))

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64`
104×	`*-un-lft-identity_binary64`
104×	`add-sqr-sqrt_binary64`
104×	`add-cube-cbrt_binary64`
51×	`add-exp-log_binary64`

Counts

3 → 211

Calls

3 calls:

9.0ms	(/.f64 1 (/.f64 z (/.f64 (*.f64 y x) (fma.f64 z z z))))
4.0ms	(/.f64 z (/.f64 (*.f64 y x) (fma.f64 z z z)))
3.0ms	(/.f64 (*.f64 y x) (fma.f64 z z z))

simplify175.0ms (2%)

Algorithm

1×	egg-herbie

Rules

655×	`fma-neg_binary64`
346×	`fma-def_binary64`
268×	`cancel-sign-sub-inv_binary64`
236×	`associate-/r/_binary64`
190×	`distribute-rgt-in_binary64`

Counts

319 → 329

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	7399
1	561	6479
2	2328	6233
3	4447	6233
4	4962	6233

prune289.0ms (3.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	325	4	329
Fresh	6	2	8
Picked	0	1	1
Done	0	1	1
Total	331	8	339

Error

0.9b

Counts

339 → 8

Alt Table

Status	Error	Program
	32.7b	(*.f64 (/.f64 (/.f64 y (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z)) (/.f64 (/.f64 x (hypot.f64 z (sqrt.f64 z))) (sqrt.f64 z)))
✓	5.1b	(/.f64 (*.f64 x (/.f64 y (fma.f64 z z z))) z)
	10.0b	(/.f64 y (/.f64 z (/.f64 x (fma.f64 z z z))))
	9.7b	(/.f64 1 (.f64 (/.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z)) 1) (/.f64 (cbrt.f64 z) (/.f64 (*.f64 y x) (fma.f64 z z z)))))
	9.5b	(/.f64 x (/.f64 z (/.f64 y (fma.f64 z z z))))
	32.7b	(*.f64 (/.f64 y (hypot.f64 z (sqrt.f64 z))) (/.f64 (/.f64 x (hypot.f64 z (sqrt.f64 z))) z))
	31.9b	(/.f64 (.f64 x (.f64 (/.f64 1 (hypot.f64 z (sqrt.f64 z))) (/.f64 y (hypot.f64 z (sqrt.f64 z))))) z)
✓	9.4b	(/.f64 1 (/.f64 z (/.f64 (*.f64 y x) (fma.f64 z z z))))

Compiler

Compiled 7309 to 1952 computations (73.3% saved)

regimes1.6s (19%)

Accuracy

Total 2.5b remaining (73.1%)

Threshold costs 0b (0%)

Counts

231 → 2

Compiler

Compiled 27961 to 14600 computations (47.8% saved)

bsearch47.0ms (0.5%)

Steps

Iters	Range		Point
3	-3.3959039301260996e-293	1.1286652475146936e-273	5.615096020682109e-280

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	69
1	29	69
2	28	69

end247.0ms (2.9%)

Compiler: Compiled 334 to 166 computations (50.3% saved)

Details

analyze541.0ms (6.3%)

sample1.4s (15.8%)

simplify93.0ms (1.1%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series174.0ms (2%)

rewrite34.0ms (0.4%)

simplify166.0ms (1.9%)

prune289.0ms (3.4%)

localize14.0ms (0.2%)

series1.9s (21.7%)

rewrite107.0ms (1.2%)

simplify299.0ms (3.5%)

prune587.0ms (6.8%)

localize6.0ms (0.1%)

series163.0ms (1.9%)

rewrite15.0ms (0.2%)

simplify78.0ms (0.9%)

prune171.0ms (2%)

localize7.0ms (0.1%)

series201.0ms (2.3%)

rewrite37.0ms (0.4%)

simplify175.0ms (2%)

prune289.0ms (3.4%)

regimes1.6s (19%)

bsearch47.0ms (0.5%)

simplify3.0ms (0%)

end247.0ms (2.9%)

Profiling