Details

analyze544.0ms (9.6%)

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
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
37.4%	62.4%	0.1%	7
43.7%	56.2%	0.1%	8
43.7%	56.2%	0.1%	9
65.5%	34.3%	0.1%	10
70.2%	29.6%	0.1%	11
70.2%	29.6%	0.1%	12
81.9%	17.9%	0.1%	13
84.6%	15.2%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.9s (51.1%)

Results

1.5s	2041×	body	1024	valid
798.0ms	4659×	body	128	valid
453.0ms	1035×	body	512	valid
145.0ms	510×	body	256	valid
15.0ms	11×	body	2048	valid

Compiler

Compiled 26 to 18 computations (30.8% saved)

preprocess20.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

16×	`fma-def_binary64`
8×	`*-commutative_binary64`
4×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	48
1	38	48
2	50	48
0	3	3

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`fma-def_binary64`
2×	`*-commutative_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	16	12

Stop Event

1×

saturated

Counts

1 → 2

prune3.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))
✓	0.2b	(*.f64 z (cos.f64 y))

series21.0ms (0.4%)

Counts

2 → 60

Calls

15 calls:

2.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))	z	0
2.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))	z	-inf
2.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))	x	-inf
2.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))	z	inf
2.0ms	(fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))	x	inf

rewrite38.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
147×	`log1p-udef_binary64`
81×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	156	18
2	1869	18

Stop Event

1×	node limit

Counts

2 → 38

simplify41.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

744×	`cancel-sign-sub-inv_binary64`
697×	`fma-def_binary64`
362×	`fma-neg_binary64`
276×	`sub-neg_binary64`
234×	`*-commutative_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	588
1	107	587
2	326	576
3	1247	568
4	4695	568

Stop Event

1×	node limit

Counts

98 → 55

prune37.0ms (0.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	48	7	55
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	7	56

Error

0.1b

Counts

56 → 7

Alt Table

Status	Error	Program
▶	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
	1.3b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
	32.9b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	32.9b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3)))
	22.5b	(expm1.f64 (log1p.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	28.3b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 3)

Compiler

Compiled 920 to 384 computations (58.3% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
✓	0.1b	(*.f64 (sin.f64 y) x)

series21.0ms (0.4%)

Counts

2 → 40

Calls

15 calls:

3.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))	z	-inf
2.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))	x	-inf
2.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))	x	0
2.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))	z	inf
2.0ms	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))	x	inf

rewrite43.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
147×	`log1p-udef_binary64`
81×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	156	18
2	1869	18

Stop Event

1×	node limit

Counts

2 → 38

simplify44.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-def_binary64`
505×	`associate-l_binary64`
422×	`associate-r_binary64`
410×	`fma-neg_binary64`
224×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	480
1	118	472
2	358	460
3	1240	451
4	4701	451

Stop Event

1×	node limit

Counts

78 → 57

prune39.0ms (0.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	57	7	64

Error

0.1b

Counts

64 → 7

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
▶	1.3b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
	32.9b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	32.9b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3)))
	22.5b	(expm1.f64 (log1p.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
	28.3b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 3)

Compiler

Compiled 913 to 379 computations (58.5% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(*.f64 z (cos.f64 y))
✓	0.3b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
✓	0.5b	(cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))

series233.0ms (4.1%)

Counts

3 → 76

Calls

27 calls:

40.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)	y	inf
40.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)	y	-inf
36.0ms	(cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))	y	-inf
36.0ms	(cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))	y	inf
8.0ms	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)	y	0

rewrite58.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

879×	`log1p-expm1-u_binary64`
879×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
107×	`add-sqr-sqrt_binary64`
99×	`add-cube-cbrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	43
1	238	43
2	2498	43

Stop Event

1×	node limit

Counts

3 → 60

simplify61.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

622×	`cancel-sign-sub-inv_binary64`
475×	`times-frac_binary64`
329×	`unswap-sqr_binary64`
267×	`associate-r_binary64`
226×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	2427
1	628	2381
2	2441	2379

Stop Event

1×	node limit

Counts

136 → 123

prune139.0ms (2.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	213	5	218
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	215	10	225

Error

0.0b

Counts

225 → 10

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
✓	1.3b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
	32.9b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	1.7b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) 2)) (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))))
	32.9b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3)))
	14.3b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 4))))
	30.3b	(.f64 (exp.f64 (log.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))))) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
▶	1.6b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) 3) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
	28.3b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	51.6b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (.f64 x (.f64 x (pow.f64 (sin.f64 y) 2)))))

Compiler

Compiled 7752 to 3282 computations (57.7% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	0.5b	(cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))
✓	0.6b	(cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))
✓	0.8b	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))) 3)

series617.0ms (10.9%)

Counts

2 → 72

Calls

18 calls:

139.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))) 3)	y	-inf
134.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))) 3)	y	inf
117.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))	y	inf
113.0ms	(cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))	y	-inf
13.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y))))) 3)	z	inf

rewrite45.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

485×	`log-prod_binary64`
201×	`prod-diff_binary64`
189×	`expm1-udef_binary64`
189×	`log1p-udef_binary64`
186×	`pow1/3_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	30
1	234	30
2	2537	30

Stop Event

1×	node limit

Counts

2 → 47

simplify71.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

528×	`times-frac_binary64`
433×	`associate-l_binary64`
355×	`associate-/l*_binary64`
323×	`associate-/r*_binary64`
229×	`fma-def_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	362	4987
1	1343	4838

Stop Event

1×	node limit

Counts

119 → 163

prune244.0ms (4.3%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	303	2	305
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	303	12	315

Error

0.0b

Counts

315 → 12

Alt Table

Status	Error	Program
✓	0.1b	(fma.f64 (cos.f64 y) z (*.f64 (sin.f64 y) x))
✓	1.3b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
	1.9b	(.f64 (pow.f64 (cbrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) 3)) 3) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
	58.0b	(.f64 (pow.f64 (exp.f64 (.f64 1/9 (-.f64 (log.f64 (sin.f64 y)) (log.f64 (/.f64 1 x))))) 3) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
	32.9b	(fma.f64 x (sin.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (cos.f64 y) 3))))
	1.7b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (.f64 (.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) 2)) (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))))))
	32.9b	(fma.f64 x (sin.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3)))
	14.3b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) 2) (cbrt.f64 (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 4))))
	30.3b	(.f64 (exp.f64 (log.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))))) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
✓	1.6b	(.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y))))) 3) (pow.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2))
	28.3b	(pow.f64 (sqrt.f64 (fma.f64 x (sin.f64 y) (*.f64 z (cos.f64 y)))) 2)
	51.6b	(.f64 (cbrt.f64 (fma.f64 x (sin.f64 y) (.f64 z (cos.f64 y)))) (cbrt.f64 (.f64 x (.f64 x (pow.f64 (sin.f64 y) 2)))))

Compiler

Compiled 15054 to 7207 computations (52.1% saved)

regimes218.0ms (3.8%)

Accuracy

Total 0.1b remaining (46.1%)

Threshold costs 0.1b (46.1%)

Counts

50 → 1

Compiler

Compiled 3908 to 2290 computations (41.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12

Stop Event

1×

saturated

end180.0ms (3.2%)

Stop Event

1×

fuel

Compiler

Compiled 318 to 173 computations (45.6% saved)

Details

analyze544.0ms (9.6%)

sample2.9s (51.1%)

preprocess20.0ms (0.3%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

series21.0ms (0.4%)

rewrite38.0ms (0.7%)

simplify41.0ms (0.7%)

prune37.0ms (0.7%)

localize9.0ms (0.2%)

series21.0ms (0.4%)

rewrite43.0ms (0.8%)

simplify44.0ms (0.8%)

prune39.0ms (0.7%)

localize10.0ms (0.2%)

series233.0ms (4.1%)

rewrite58.0ms (1%)

simplify61.0ms (1.1%)

prune139.0ms (2.4%)

localize16.0ms (0.3%)

series617.0ms (10.9%)

rewrite45.0ms (0.8%)

simplify71.0ms (1.3%)

prune244.0ms (4.3%)

regimes218.0ms (3.8%)

simplify3.0ms (0.1%)

end180.0ms (3.2%)

Profiling