Details

analyze153.0ms (3.6%)

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
25%	74.9%	0.1%	4
37.4%	62.4%	0.1%	5
56.2%	43.7%	0.1%	6
56.2%	43.7%	0.1%	7
65.5%	34.3%	0.1%	8
76.5%	23.4%	0.1%	9
76.5%	23.4%	0.1%	10
81.9%	17.9%	0.1%	11
87.8%	12.1%	0.1%	12
87.8%	12.1%	0.1%	13
90.7%	9.2%	0.1%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample755.0ms (17.7%)

Infinites

7.4% of outputs are infinite.

Symmetry

(sort x y)

Results

701.0ms

8256×

body

128

valid

Compiler

Compiled 44 to 32 computations (27.3% saved)

simplify11.0ms (0.3%)

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

6.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.2b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))

Compiler

Compiled 50 to 34 computations (32% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	3.6b	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
✓	5.8b	(*.f64 y (fma.f64 z z 1))

series93.0ms (2.2%)

Counts

2 → 60

Calls

2 calls:

84.0ms	(/.f64 (/.f64 1 x) (*.f64 y (fma.f64 z z 1)))
9.0ms	(*.f64 y (fma.f64 z z 1))

rewrite15.0ms (0.4%)

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 (2.8%)

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

prune113.0ms (2.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	112	10	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	10	123

Error

2.4b

Counts

123 → 10

Alt Table

Status	Error	Program
	5.8b	(.f64 (/.f64 (/.f64 1 (.f64 (cbrt.f64 x) (cbrt.f64 x))) y) (/.f64 (/.f64 1 (cbrt.f64 x)) (fma.f64 z z 1)))
	23.9b	(/.f64 (/.f64 1 x) (cbrt.f64 (pow.f64 (*.f64 y (fma.f64 z z 1)) 3)))
	6.2b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
	23.9b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 (.f64 y (fma.f64 z z 1)) x) 3)))
	23.0b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
▶	4.5b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (fma.f64 z z 1) x)))
	48.8b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
	25.0b	(.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)))))
	4.7b	(/.f64 1 (.f64 y (.f64 (+.f64 1 (pow.f64 z 2)) x)))
	6.3b	(/.f64 1 (.f64 (+.f64 y (.f64 y (pow.f64 z 2))) x))

Compiler

Compiled 2406 to 1511 computations (37.2% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 1 (*.f64 (fma.f64 z z 1) x))
✓	3.1b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (fma.f64 z z 1) x)))
✓	3.1b	(*.f64 (fma.f64 z z 1) x)

series127.0ms (3%)

Counts

3 → 84

Calls

3 calls:

82.0ms	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (fma.f64 z z 1) x)))
33.0ms	(/.f64 1 (*.f64 (fma.f64 z z 1) x))
12.0ms	(*.f64 (fma.f64 z z 1) x)

rewrite22.0ms (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)

simplify173.0ms (4%)

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

prune189.0ms (4.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	211	3	214
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	215	9	224

Error

2.1b

Counts

224 → 9

Alt Table

Status	Error	Program
	47.9b	(.f64 (/.f64 1 y) (/.f64 1 (.f64 (.f64 (hypot.f64 1 z) (sqrt.f64 x)) (.f64 (hypot.f64 1 z) (sqrt.f64 x)))))
	23.0b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	6.2b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
	23.9b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 (.f64 y (fma.f64 z z 1)) x) 3)))
▶	4.5b	(/.f64 (/.f64 1 y) (*.f64 (fma.f64 z z 1) x))
	48.8b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 x)) y) (/.f64 (sqrt.f64 (/.f64 1 x)) (fma.f64 z z 1)))
	25.0b	(.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)))))
	6.3b	(/.f64 1 (.f64 (+.f64 y (.f64 y (pow.f64 z 2))) x))
	22.1b	(.f64 (sqrt.f64 (/.f64 1 y)) (/.f64 (sqrt.f64 (/.f64 1 y)) (fma.f64 x (.f64 z z) x)))

Compiler

Compiled 4197 to 2606 computations (37.9% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
	3.1b	(*.f64 (fma.f64 z z 1) x)
✓	3.3b	(/.f64 (/.f64 1 y) (*.f64 (fma.f64 z z 1) x))

series79.0ms (1.9%)

Counts

1 → 36

Calls

1 calls:

79.0ms

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

rewrite8.0ms (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))

simplify103.0ms (2.4%)

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

prune118.0ms (2.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	129	8	137

Error

2.1b

Counts

137 → 8

Alt Table

Status	Error	Program
	6.2b	(/.f64 (/.f64 1 (*.f64 y x)) (fma.f64 z z 1))
	23.9b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 (.f64 y (fma.f64 z z 1)) x) 3)))
	23.0b	(/.f64 (/.f64 1 x) (.f64 (.f64 (sqrt.f64 y) (hypot.f64 1 z)) (*.f64 (sqrt.f64 y) (hypot.f64 1 z))))
	47.8b	(/.f64 (/.f64 1 y) (.f64 (.f64 (hypot.f64 1 z) (sqrt.f64 x)) (*.f64 (hypot.f64 1 z) (sqrt.f64 x))))
▶	4.4b	(/.f64 (/.f64 1 y) (.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 x (hypot.f64 1 z))))
	25.0b	(.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)))))
	6.3b	(/.f64 1 (.f64 (+.f64 y (.f64 y (pow.f64 z 2))) x))
	22.1b	(.f64 (sqrt.f64 (/.f64 1 y)) (/.f64 (sqrt.f64 (/.f64 1 y)) (fma.f64 x (.f64 z z) x)))

Compiler

Compiled 2441 to 1415 computations (42% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (hypot.f64 1 z))
✓	0.1b	(.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 x (hypot.f64 1 z)))
✓	3.3b	(/.f64 (/.f64 1 y) (.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 x (hypot.f64 1 z))))
✓	16.6b	(sqrt.f64 (fma.f64 z z 1))

series203.0ms (4.8%)

Counts

4 → 96

Calls

4 calls:

161.0ms	(/.f64 (/.f64 1 y) (.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 x (hypot.f64 1 z))))
26.0ms	(.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 x (hypot.f64 1 z)))
13.0ms	(*.f64 x (hypot.f64 1 z))
3.0ms	(sqrt.f64 (fma.f64 z z 1))

rewrite24.0ms (0.6%)

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:

8.0ms	(/.f64 (/.f64 1 y) (.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 x (hypot.f64 1 z))))
5.0ms	(.f64 (sqrt.f64 (fma.f64 z z 1)) (.f64 x (hypot.f64 1 z)))
3.0ms	(*.f64 x (hypot.f64 1 z))
1.0ms	(sqrt.f64 (fma.f64 z z 1))

simplify126.0ms (3%)

Algorithm

1×	egg-herbie

Rules

553×	`associate-/l*_binary64`
381×	`fma-def_binary64`
364×	`associate-/l/_binary64`
233×	`associate-*l/_binary64`
195×	`associate-*r/_binary64`

Counts

212 → 231

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	238	3977
1	597	2892
2	1737	2869
3	4629	2869
4	4937	2869
5	4976	2869

prune433.0ms (10.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	226	5	231
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	231	8	239

Error

0.0b

Counts

239 → 8

Alt Table

Status	Error	Program
	19.8b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 y)) (hypot.f64 1 z)) (/.f64 (sqrt.f64 (/.f64 1 y)) (.f64 x (hypot.f64 1 z))))
	3.2b	(/.f64 (/.f64 1 y) (.f64 (.f64 x (hypot.f64 1 z)) (hypot.f64 1 z)))
	1.8b	(/.f64 (/.f64 (/.f64 1 y) (hypot.f64 1 z)) (*.f64 x (hypot.f64 1 z)))
	22.1b	(/.f64 (/.f64 1 (sqrt.f64 y)) (.f64 (.f64 (fma.f64 z z 1) x) (sqrt.f64 y)))
	25.0b	(.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)))))
	23.9b	(cbrt.f64 (/.f64 1 (pow.f64 (.f64 (.f64 y (fma.f64 z z 1)) x) 3)))
	6.3b	(/.f64 1 (.f64 (+.f64 y (.f64 y (pow.f64 z 2))) x))
	3.9b	(.f64 (/.f64 1 (hypot.f64 1 z)) (/.f64 (/.f64 1 (.f64 y x)) (hypot.f64 1 z)))

Compiler

Compiled 4997 to 3333 computations (33.3% saved)

regimes1.1s (26.2%)

Accuracy

Total 1.5b remaining (97.9%)

Threshold costs 0b (0%)

Counts

136 → 1

Compiler

Compiled 19068 to 13552 computations (28.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	37
1	17	37
2	16	37

end251.0ms (5.9%)

Compiler: Compiled 253 to 190 computations (24.9% saved)

Details

analyze153.0ms (3.6%)

sample755.0ms (17.7%)

simplify11.0ms (0.3%)

prune3.0ms (0.1%)

localize7.0ms (0.2%)

series93.0ms (2.2%)

rewrite15.0ms (0.4%)

simplify118.0ms (2.8%)

prune113.0ms (2.6%)

localize8.0ms (0.2%)

series127.0ms (3%)

rewrite22.0ms (0.5%)

simplify173.0ms (4%)

prune189.0ms (4.4%)

localize7.0ms (0.2%)

series79.0ms (1.9%)

rewrite8.0ms (0.2%)

simplify103.0ms (2.4%)

prune118.0ms (2.8%)

localize10.0ms (0.2%)

series203.0ms (4.8%)

rewrite24.0ms (0.6%)

simplify126.0ms (3%)

prune433.0ms (10.1%)

regimes1.1s (26.2%)

simplify2.0ms (0.1%)

end251.0ms (5.9%)

Profiling