Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample1.0s (7.4%)

Results

960.0ms

8256×

body

128

valid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify60.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

725×	`fma-def_binary64`
669×	`unsub-neg_binary64`
596×	`cancel-sign-sub-inv_binary64`
340×	`+-commutative_binary64`
277×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	170	36
3	542	36
4	1867	32
5	3281	32
6	4881	32
7	4958	32

prune4.0ms (0%)

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

13.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	13.5b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 106 to 66 computations (37.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 a -3 1)
✓	3.2b	(.f64 (.f64 b b) (fma.f64 a -3 1))
✓	4.5b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	9.0b	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))

series68.0ms (0.5%)

Counts

4 → 84

Calls

4 calls:

41.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
13.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
12.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
2.0ms	(fma.f64 a -3 1)

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
9×	`pow1_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`

Counts

4 → 53

Calls

4 calls:

5.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
0.0ms	(fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4))
0.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
0.0ms	(fma.f64 a -3 1)

simplify105.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

786×	`fma-def_binary64`
528×	`fma-neg_binary64`
415×	`associate-+l+_binary64`
313×	`cancel-sign-sub-inv_binary64`
229×	`associate-+r+_binary64`

Counts

137 → 125

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	125	2832
1	318	2352
2	969	2192
3	3184	2169
4	4818	2143
5	4983	2143

prune210.0ms (1.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	124	2	126

Error

0.0b

Counts

126 → 2

Alt Table

Status	Error	Program
▶	14.2b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
✓	13.5b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Status

Error

Program

▶

14.2b

(+.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) -1)

✓

13.5b

(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (*.f64 (*.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 3472 to 1988 computations (42.7% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
✓	0.0b	(.f64 2 (.f64 b b))
✓	0.0b	(*.f64 a (+.f64 4 a))
✓	8.6b	(.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))

series59.0ms (0.4%)

Counts

4 → 72

Calls

4 calls:

31.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
24.0ms	(.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))
2.0ms	(.f64 2 (.f64 b b))
2.0ms	(*.f64 a (+.f64 4 a))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-cbrt-cube_binary64`
16×	`add-exp-log_binary64`
16×	`pow1_binary64`
12×	`associate-*r/_binary64`
12×	`add-sqr-sqrt_binary64`

Counts

4 → 91

Calls

4 calls:

12.0ms	(.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))
11.0ms	(+.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1)
4.0ms	(.f64 2 (.f64 b b))
4.0ms	(*.f64 a (+.f64 4 a))

simplify80.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

436×	`associate-+r+_binary64`
424×	`associate-+l+_binary64`
363×	`associate-l_binary64`
290×	`associate-r_binary64`
215×	`fma-neg_binary64`

Counts

163 → 164

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	3291
1	628	2667
2	2480	2630
3	5183	2630

prune173.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	163	3	166

Error

Counts

166 → 3

Alt Table

Status	Error	Program
▶	19.0b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 a a)) (.f64 (.f64 (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))))) -1)
	46.1b	(/.f64 (-.f64 (.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))))) (.f64 -1 -1)) (-.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1))
✓	13.5b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 4861 to 3015 computations (38% saved)

localize20.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))
✓	0.2b	(.f64 (.f64 a a) (*.f64 a a))
✓	13.2b	(.f64 (.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 a a)) (.f64 (.f64 (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))))
✓	14.7b	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 a a)) (.f64 (.f64 (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))))

series152.0ms (1.1%)

Counts

4 → 84

Calls

4 calls:

93.0ms	(.f64 (.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 a a)) (.f64 (.f64 (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))))
32.0ms	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 a a)) (.f64 (.f64 (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))))
24.0ms	(.f64 (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))
3.0ms	(.f64 (.f64 a a) (*.f64 a a))

rewrite1.5s (10.9%)

Algorithm

1×	rewrite-expression-head

Rules

2018×	`associate-*r/_binary64`
1540×	`flip-+_binary64`
1540×	`flip3-+_binary64`
1232×	`frac-add_binary64`
1217×	`pow1_binary64`

Counts

4 → 1116

Calls

4 calls:

189.0ms	(cbrt.f64 (.f64 (.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 a a)) (.f64 (.f64 (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))))
151.0ms	(.f64 (.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 a a)) (.f64 (.f64 (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))))
15.0ms	(.f64 (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))
7.0ms	(.f64 (.f64 a a) (*.f64 a a))

simplify1.7s (12.6%)

Algorithm

1×	egg-herbie

Rules

996×	`associate-l_binary64`
396×	`distribute-lft-in_binary64`
396×	`distribute-rgt-in_binary64`
119×	`fma-def_binary64`
20×	`sqr-pow_binary64`

Counts

1200 → 1732

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2018	137901
1	5869	137901

prune5.5s (39.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	1732	0	1732
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	1732	3	1735

Error

Counts

1735 → 3

Alt Table

Status	Error	Program
✓	19.0b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 a a)) (.f64 (.f64 (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))))) -1)
▶	46.1b	(/.f64 (-.f64 (.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))))) (.f64 -1 -1)) (-.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1))
✓	13.5b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 259985 to 168424 computations (35.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 a (+.f64 4 a))
✓	0.1b	(.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))))
	8.6b	(.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b)))))
✓	27.4b	(/.f64 (-.f64 (.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))))) (.f64 -1 -1)) (-.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1))

series291.0ms (2.1%)

Counts

2 → 48

Calls

2 calls:

251.0ms

(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b)))))) (*.f64 -1 -1)) (-.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) -1))

40.0ms

(*.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))))

rewrite113.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

146×	`associate-*r/_binary64`
116×	`pow1_binary64`
70×	`flip-+_binary64`
70×	`flip3-+_binary64`
66×	`pow-prod-down_binary64`

Counts

2 → 152

Calls

2 calls:

37.0ms

(/.f64 (-.f64 (*.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b)))))) (*.f64 -1 -1)) (-.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) -1))

20.0ms

(*.f64 (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))) (*.f64 (*.f64 a a) (+.f64 (*.f64 a (+.f64 4 a)) (+.f64 4 (*.f64 2 (*.f64 b b))))))

simplify215.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

644×	`distribute-rgt-in_binary64`
631×	`distribute-lft-in_binary64`
587×	`fma-def_binary64`
175×	`times-frac_binary64`
152×	`*-commutative_binary64`

Counts

200 → 241

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	559	16384
1	1944	14659
2	6098	14659

prune799.0ms (5.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	553	0	553
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	553	3	556

Error

Counts

556 → 3

Alt Table

Status	Error	Program
✓	19.0b	(+.f64 (cbrt.f64 (.f64 (.f64 (.f64 (.f64 a a) (.f64 a a)) (.f64 a a)) (.f64 (.f64 (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))))) -1)
✓	46.1b	(/.f64 (-.f64 (.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b))))) (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (.f64 b b)))))) (.f64 -1 -1)) (-.f64 (.f64 (.f64 a a) (+.f64 (.f64 a (+.f64 4 a)) (+.f64 4 (.f64 2 (*.f64 b b))))) -1))
✓	13.5b	(+.f64 (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1))) (pow.f64 (hypot.f64 a b) 4)) -1)

Compiler

Compiled 47765 to 30022 computations (37.1% saved)

regimes1.5s (11%)

Accuracy

Total 0.5b remaining (98.6%)

Threshold costs 0.5b (98.6%)

Counts

222 → 1

Compiler

Compiled 46039 to 31903 computations (30.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	17
1	11	17
2	11	17

end85.0ms (0.6%)

Compiler: Compiled 172 to 111 computations (35.5% saved)

Details

analyze2.0ms (0%)

sample1.0s (7.4%)

simplify60.0ms (0.4%)

prune4.0ms (0%)

localize14.0ms (0.1%)

series68.0ms (0.5%)

rewrite8.0ms (0.1%)

simplify105.0ms (0.8%)

prune210.0ms (1.5%)

localize12.0ms (0.1%)

series59.0ms (0.4%)

rewrite40.0ms (0.3%)

simplify80.0ms (0.6%)

prune173.0ms (1.3%)

localize20.0ms (0.1%)

series152.0ms (1.1%)

rewrite1.5s (10.9%)

simplify1.7s (12.6%)

prune5.5s (39.7%)

localize15.0ms (0.1%)

series291.0ms (2.1%)

rewrite113.0ms (0.8%)

simplify215.0ms (1.6%)

prune799.0ms (5.8%)

regimes1.5s (11%)

simplify2.0ms (0%)

end85.0ms (0.6%)

Profiling