Details

analyze178.0ms (3.7%)

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
25%	74.9%	0.1%	5
25%	68.7%	6.3%	6
25%	56.2%	18.8%	7
25%	48.4%	26.6%	8
25%	35.1%	39.9%	9
28.1%	18.3%	53.6%	10
31.6%	12.3%	56.1%	11
33.4%	5.9%	60.8%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

Compiler

Compiled 34 to 22 computations (35.3% saved)

sample1.3s (26.5%)

Results

1.2s	8256×	body	128	valid
1.0ms	5×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify68.0ms (1.4%)

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

prune5.0ms (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
▶	0.0b	(+.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

0.2b

(-.f64 (+.f64 (pow.f64 (+.f64 (*.f64 a a) (*.f64 b b)) 2) (*.f64 4 (+.f64 (*.f64 (*.f64 a a) (+.f64 1 a)) (*.f64 (*.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)

▶

0.0b

(+.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 172 to 108 computations (37.2% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a -3 1)
✓	0.0b	(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))
✓	0.1b	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
✓	0.4b	(.f64 (.f64 b b) (fma.f64 a -3 1))

series83.0ms (1.7%)

Counts

4 → 84

Calls

4 calls:

42.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
29.0ms	(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))
11.0ms	(fma.f64 a (fma.f64 a a a) (.f64 (.f64 b b) (fma.f64 a -3 1)))
2.0ms	(fma.f64 a -3 1)

rewrite12.0ms (0.3%)

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×	`fma-udef_binary64`

Counts

4 → 53

Calls

4 calls:

9.0ms	(.f64 (.f64 b b) (fma.f64 a -3 1))
0.0ms	(fma.f64 a (fma.f64 a a a) (.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 -3 1)

simplify101.0ms (2.1%)

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	2754
1	318	2352
2	969	2192
3	3184	2169
4	4818	2143
5	4983	2143

prune178.0ms (3.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	123	4	127

Error

Counts

127 → 4

Alt Table

Status	Error	Program
	10.7b	(+.f64 (*.f64 (pow.f64 a 3) (+.f64 4 a)) -1)
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
	15.8b	(+.f64 (cbrt.f64 (.f64 (.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)) (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))) (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)
▶	0.0b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -1)

Compiler

Compiled 3757 to 2115 computations (43.7% saved)

localize22.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))
✓	0.2b	(.f64 12 (.f64 a (pow.f64 b 2)))
✓	0.5b	(*.f64 a (pow.f64 b 2))
✓	1.6b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series54.0ms (1.1%)

Counts

4 → 15

Calls

4 calls:

23.0ms	(+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))
12.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
10.0ms	(.f64 12 (.f64 a (pow.f64 b 2)))
8.0ms	(*.f64 a (pow.f64 b 2))

rewrite55.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
31×	`add-exp-log_binary64`
20×	`unswap-sqr_binary64`
19×	`prod-exp_binary64`
18×	`unpow-prod-down_binary64`

Counts

4 → 121

Calls

4 calls:

21.0ms	(.f64 12 (.f64 a (pow.f64 b 2)))
18.0ms	(+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))
6.0ms	(*.f64 (pow.f64 a 2) (pow.f64 b 2))
4.0ms	(*.f64 a (pow.f64 b 2))

simplify65.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

721×	`distribute-rgt-in_binary64`
689×	`distribute-lft-in_binary64`
537×	`fma-def_binary64`
217×	`associate-l_binary64`
214×	`unswap-sqr_binary64`

Counts

136 → 188

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	184	2295
1	409	1991
2	1507	1840
3	5493	1840

prune425.0ms (8.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	187	1	188
Fresh	1	2	3
Picked	0	1	1
Done	0	0	0
Total	188	4	192

Error

Counts

192 → 4

Alt Table

Status	Error	Program
	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
	15.8b	(+.f64 (cbrt.f64 (.f64 (.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)) (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))) (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)
✓	0.0b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -1)
▶	0.1b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 (pow.f64 a 3) (+.f64 4 a)) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4))))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -1)

Compiler

Compiled 9861 to 7501 computations (23.9% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (pow.f64 a 3) (+.f64 4 a))
	0.2b	(.f64 12 (.f64 a (pow.f64 b 2)))
	0.5b	(*.f64 a (pow.f64 b 2))
	1.6b	(*.f64 (pow.f64 a 2) (pow.f64 b 2))

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

(*.f64 (pow.f64 a 3) (+.f64 4 a))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`associate-l_binary64`
12×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64`
6×	`add-exp-log_binary64`
5×	`add-cube-cbrt_binary64`

Counts

1 → 38

Calls

1 calls:

9.0ms

(*.f64 (pow.f64 a 3) (+.f64 4 a))

simplify63.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

971×	`fma-def_binary64`
348×	`sqr-pow_binary64`
340×	`*-commutative_binary64`
308×	`associate-+l+_binary64`
297×	`associate-+r+_binary64`

Counts

50 → 47

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	69	623
1	178	591
2	818	591
3	2091	567
4	4420	567
5	5174	567

prune414.0ms (8.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	193	0	193
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	193	4	197

Error

Counts

197 → 4

Alt Table

Status	Error	Program
▶	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
	15.8b	(+.f64 (cbrt.f64 (.f64 (.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)) (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))) (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)
✓	0.0b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -1)
✓	0.1b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 (pow.f64 a 3) (+.f64 4 a)) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4))))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -1)

Compiler

Compiled 9713 to 7369 computations (24.1% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
✓	0.1b	(.f64 (.f64 a a) (+.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.4b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series49.0ms (1%)

Counts

4 → 84

Calls

4 calls:

25.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
12.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
9.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
3.0ms	(.f64 (.f64 a a) (+.f64 1 a))

rewrite31.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64`
15×	`pow1_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`

Counts

4 → 102

Calls

4 calls:

8.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a))))))
8.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
6.0ms	(.f64 (.f64 a a) (+.f64 1 a))
4.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)

simplify114.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

870×	`distribute-rgt-in_binary64`
807×	`distribute-lft-in_binary64`
278×	`cancel-sign-sub-inv_binary64`
257×	`associate-l_binary64`
213×	`associate-r_binary64`

Counts

186 → 190

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	3661
1	577	3211
2	1997	3007
3	5819	3007

prune290.0ms (6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	1	0	1
Picked	0	1	1
Done	1	1	2
Total	191	3	194

Error

Counts

194 → 3

Alt Table

Status	Error	Program
	0.5b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (pow.f64 (hypot.f64 a b) 4)) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (cbrt.f64 (pow.f64 (hypot.f64 a b) 4))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.2b	(-.f64 (+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (.f64 3 a)))))) 1)
✓	0.0b	(+.f64 (-.f64 (+.f64 (.f64 4 (pow.f64 a 2)) (+.f64 (.f64 4 (pow.f64 a 3)) (+.f64 (pow.f64 a 4) (+.f64 (.f64 2 (.f64 (pow.f64 a 2) (pow.f64 b 2))) (+.f64 (.f64 4 (pow.f64 b 2)) (pow.f64 b 4)))))) (.f64 12 (*.f64 a (pow.f64 b 2)))) -1)

Compiler

Compiled 7146 to 4049 computations (43.3% saved)

regimes1.2s (23.8%)

Accuracy

Total 0.0b remaining (33.9%)

Threshold costs 0.0b (33.9%)

Counts

188 → 1

Compiler

Compiled 28798 to 19952 computations (30.7% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

8×	`+-commutative_binary64`
8×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`distribute-lft-neg-in_binary64`
2×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	56
1	45	56
2	52	56
3	56	56
4	59	56
5	60	56
6	57	56

end130.0ms (2.7%)

Compiler: Compiled 204 to 143 computations (29.9% saved)

Details

analyze178.0ms (3.7%)

sample1.3s (26.5%)

simplify68.0ms (1.4%)

prune5.0ms (0.1%)

localize13.0ms (0.3%)

series83.0ms (1.7%)

rewrite12.0ms (0.3%)

simplify101.0ms (2.1%)

prune178.0ms (3.7%)

localize22.0ms (0.5%)

series54.0ms (1.1%)

rewrite55.0ms (1.1%)

simplify65.0ms (1.4%)

prune425.0ms (8.8%)

localize22.0ms (0.4%)

series3.0ms (0.1%)

rewrite11.0ms (0.2%)

simplify63.0ms (1.3%)

prune414.0ms (8.6%)

localize16.0ms (0.3%)

series49.0ms (1%)

rewrite31.0ms (0.6%)

simplify114.0ms (2.4%)

prune290.0ms (6%)

regimes1.2s (23.8%)

simplify3.0ms (0.1%)

end130.0ms (2.7%)

Profiling