Details

analyze170.0ms (6.1%)

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 (45.2%)

Results

1.2s	8256×	body	128	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 101 to 65 computations (35.6% saved)

simplify29.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

693×	`fma-def_binary64`
312×	`+-commutative_binary64`
277×	`fma-neg_binary64`
232×	`associate-+l+_binary64`
211×	`associate-l_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	20	42
1	63	40
2	193	36
3	742	36
4	2867	32
5	4882	32

Stop Event

1×	node limit

Counts

1 → 2

prune5.0ms (0.2%)

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
▶	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1)))) -1))
	0.1b	(-.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)

Status

Error

Program

▶

0.0b

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

0.1b

(-.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)

Compiler

Compiled 172 to 109 computations (36.6% saved)

localize14.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

series27.0ms (1%)

Counts

4 → 84

Calls

4 calls:

11.0ms	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))
9.0ms	(.f64 b (.f64 b (fma.f64 a -3 1)))
5.0ms	(*.f64 b (fma.f64 a -3 1))
1.0ms	(fma.f64 a -3 1)

rewrite50.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

830×	`log1p-expm1-u_binary64`
830×	`expm1-log1p-u_binary64`
328×	`prod-diff_binary64`
95×	`add-sqr-sqrt_binary64`
87×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	43
1	195	43
2	2244	43

Stop Event

1×	node limit

Counts

4 → 80

Calls

4 calls:

48.0ms	(fma.f64 a -3 1)
48.0ms	(fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1))))
48.0ms	(.f64 b (.f64 b (fma.f64 a -3 1)))
48.0ms	(*.f64 b (fma.f64 a -3 1))

simplify39.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

571×	`cancel-sign-sub-inv_binary64`
533×	`fma-neg_binary64`
442×	`fma-def_binary64`
373×	`associate-l_binary64`
263×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	1077
1	86	1002
2	240	838
3	691	834
4	2627	834

Stop Event

1×	node limit

Counts

164 → 107

prune107.0ms (3.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	107	2	109

Error

0.0b

Counts

109 → 2

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1)))) -1))
▶	0.1b	(-.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)

Status

Error

Program

✓

0.0b

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

▶

0.1b

(-.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)

Compiler

Compiled 2892 to 1590 computations (45% saved)

localize16.0ms (0.6%)

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))))))
✓	0.0b	(.f64 (.f64 a a) (+.f64 1 a))
✓	0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
✓	0.6b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

series47.0ms (1.7%)

Counts

4 → 84

Calls

4 calls:

23.0ms	(+.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))))))
11.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
10.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
3.0ms	(.f64 (.f64 a a) (+.f64 1 a))

rewrite43.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

209×	`log1p-expm1-u_binary64`
209×	`expm1-log1p-u_binary64`
205×	`add-sqr-sqrt_binary64`
202×	`add-cbrt-cube_binary64`
195×	`add-log-exp_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	73
1	442	65

Stop Event

1×	node limit

Counts

4 → 82

Calls

4 calls:

41.0ms	(+.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))))))
41.0ms	(.f64 (.f64 a a) (+.f64 1 a))
41.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2)
41.0ms	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))

simplify45.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

589×	`fma-def_binary64`
528×	`cancel-sign-sub-inv_binary64`
408×	`associate--l+_binary64`
384×	`associate-+l+_binary64`
323×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	1606
1	180	1537
2	611	1321
3	2857	1298

Stop Event

1×	node limit

Counts

166 → 124

prune145.0ms (5.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	123	3	126

Error

Counts

126 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1)))) -1))
✓	0.1b	(-.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)
▶	46.0b	(-.f64 (+.f64 (/.f64 (.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (+.f64 (pow.f64 a 6) (pow.f64 b 6))) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (pow.f64 a 4) (-.f64 (pow.f64 b 4) (pow.f64 (.f64 a b) 2))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)

Compiler

Compiled 4470 to 2831 computations (36.7% saved)

localize28.0ms (1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (pow.f64 a 4) (-.f64 (pow.f64 b 4) (pow.f64 (.f64 a b) 2))))
✓	0.2b	(pow.f64 (*.f64 a b) 2)
	0.6b	(.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))
✓	47.6b	(/.f64 (.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (+.f64 (pow.f64 a 6) (pow.f64 b 6))) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (pow.f64 a 4) (-.f64 (pow.f64 b 4) (pow.f64 (*.f64 a b) 2)))))

series73.0ms (2.6%)

Counts

3 → 72

Calls

3 calls:

50.0ms

(/.f64 (*.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (+.f64 (pow.f64 a 6) (pow.f64 b 6))) (*.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (+.f64 (pow.f64 a 4) (-.f64 (pow.f64 b 4) (pow.f64 (*.f64 a b) 2)))))

16.0ms

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

7.0ms

(pow.f64 (*.f64 a b) 2)

rewrite41.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

259×	`log1p-expm1-u_binary64`
259×	`expm1-log1p-u_binary64`
247×	`add-cbrt-cube_binary64`
238×	`add-log-exp_binary64`
237×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	93
1	542	93

Stop Event

1×	node limit

Counts

3 → 49

Calls

3 calls:

38.0ms

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

38.0ms

(pow.f64 (*.f64 a b) 2)

38.0ms

(/.f64 (*.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (+.f64 (pow.f64 a 6) (pow.f64 b 6))) (*.f64 (-.f64 (*.f64 a a) (*.f64 b b)) (+.f64 (pow.f64 a 4) (-.f64 (pow.f64 b 4) (pow.f64 (*.f64 a b) 2)))))

simplify52.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

824×	`unswap-sqr_binary64`
692×	`fma-def_binary64`
379×	`cancel-sign-sub-inv_binary64`
328×	`fma-neg_binary64`
213×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	1218
1	88	1194
2	268	1155
3	1092	1146
4	3980	1146

Stop Event

1×	node limit

Counts

121 → 72

prune113.0ms (4.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	92	3	95

Error

Counts

95 → 3

Alt Table

Status	Error	Program
✓	0.0b	(+.f64 (pow.f64 (hypot.f64 a b) 4) (fma.f64 4 (fma.f64 a (fma.f64 a a a) (.f64 b (.f64 b (fma.f64 a -3 1)))) -1))
✓	0.1b	(-.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)
✓	46.0b	(-.f64 (+.f64 (/.f64 (.f64 (-.f64 (pow.f64 a 4) (pow.f64 b 4)) (+.f64 (pow.f64 a 6) (pow.f64 b 6))) (.f64 (-.f64 (.f64 a a) (.f64 b b)) (+.f64 (pow.f64 a 4) (-.f64 (pow.f64 b 4) (pow.f64 (.f64 a b) 2))))) (.f64 4 (+.f64 (.f64 (.f64 a a) (+.f64 1 a)) (.f64 (.f64 b b) (-.f64 1 (*.f64 3 a)))))) 1)

Compiler

Compiled 5537 to 3409 computations (38.4% saved)

regimes359.0ms (13%)

Accuracy

Total 0.0b remaining (64.1%)

Threshold costs 0.0b (64.1%)

Counts

56 → 1

Compiler

Compiled 8236 to 5729 computations (30.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	32
1	20	32

Stop Event

1×

saturated

end110.0ms (4%)

Compiler: Compiled 169 to 112 computations (33.7% saved)

Details

analyze170.0ms (6.1%)

sample1.3s (45.2%)

simplify29.0ms (1.1%)

prune5.0ms (0.2%)

localize14.0ms (0.5%)

series27.0ms (1%)

rewrite50.0ms (1.8%)

simplify39.0ms (1.4%)

prune107.0ms (3.9%)

localize16.0ms (0.6%)

series47.0ms (1.7%)

rewrite43.0ms (1.6%)

simplify45.0ms (1.6%)

prune145.0ms (5.2%)

localize28.0ms (1%)

series73.0ms (2.6%)

rewrite41.0ms (1.5%)

simplify52.0ms (1.9%)

prune113.0ms (4.1%)

regimes359.0ms (13%)

simplify2.0ms (0.1%)

end110.0ms (4%)

Profiling