Details

analyze459.0ms (5.9%)

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

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.9s (37%)

Results

1.5s	2094×	body	1024	valid
756.0ms	4578×	body	128	valid
429.0ms	1082×	body	512	valid
139.0ms	497×	body	256	valid
7.0ms	5×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	12
1	13	12
2	16	12
3	16	12

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

0.2b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.2b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))

Compiler

Compiled 42 to 23 computations (45.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series25.0ms (0.3%)

Counts

2 → 60

Calls

2 calls:

17.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
8.0ms	(*.f64 z (sin.f64 y))

rewrite42.0ms (0.5%)

Algorithm

2×	batch-egg-rewrite

Rules

38× egg-rr

Counts

2 → 38

Calls

2 calls:

41.0ms	((.f64 z (sin.f64 y)) (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	156	18
2	1801	18
3	5105	18
0	0	0
1	0	0

simplify84.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

629×	`distribute-rgt-neg-in_binary64`
582×	`distribute-lft-neg-in_binary64`
523×	`associate-l_binary64`
430×	`associate-r_binary64`
420×	`fma-neg_binary64`

Counts

98 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	600
1	116	592
2	326	580
3	969	579
4	2792	579
5	4930	579
6	5173	579

prune38.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	51	5	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	51	6	57

Error

0.1b

Counts

57 → 6

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)
▶	0.2b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
	41.7b	(/.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (-.f64 (pow.f64 (.f64 z (sin.f64 y)) 2) (.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))
	18.0b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))

Compiler

Compiled 924 to 370 computations (60% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series24.0ms (0.3%)

Counts

2 → 40

Calls

2 calls:

17.0ms	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
8.0ms	(*.f64 (cos.f64 y) x)

rewrite51.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

38× egg-rr

Counts

2 → 38

Calls

2 calls:

50.0ms	((.f64 (cos.f64 y) x) (fma.f64 (sin.f64 y) z (.f64 (cos.f64 y) x)))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	18
1	156	18
2	1801	18
3	5105	18
0	0	0
1	0	0

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

800×	`distribute-rgt-neg-in_binary64`
739×	`cancel-sign-sub-inv_binary64`
699×	`fma-def_binary64`
619×	`distribute-lft-neg-in_binary64`
361×	`fma-neg_binary64`

Counts

78 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	468
1	106	467
2	305	457
3	995	450
4	3071	450
5	4691	450
6	5005	450

prune37.0ms (0.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	55	1	56
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	55	7	62

Error

0.1b

Counts

62 → 7

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
▶	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)
	30.2b	(fma.f64 (sin.f64 y) z (cbrt.f64 (*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))))
✓	0.2b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
	41.7b	(/.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (-.f64 (pow.f64 (.f64 z (sin.f64 y)) 2) (.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))
	18.0b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))

Compiler

Compiled 928 to 381 computations (58.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.6b	(cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))
✓	0.7b	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)

series3.2s (41.4%)

Counts

2 → 72

Calls

2 calls:

2.8s	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)
426.0ms	(cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y))))

rewrite50.0ms (0.6%)

Algorithm

2×	batch-egg-rewrite

Rules

49× egg-rr

Counts

2 → 49

Calls

2 calls:

48.0ms	((pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) 3) (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	26
1	204	26
2	2247	26
3	5578	26
0	0	0
1	0	0

simplify85.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

816×	`fma-def_binary64`
376×	`unswap-sqr_binary64`
311×	`associate-r_binary64`
280×	`times-frac_binary64`
221×	`associate-l_binary64`

Counts

121 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	228	3163
1	822	3059
2	3504	2949
3	5285	2949

prune107.0ms (1.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	190	0	190
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	190	7	197

Error

0.1b

Counts

197 → 7

Alt Table

Status	Error	Program
✓	0.2b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)
	30.2b	(fma.f64 (sin.f64 y) z (cbrt.f64 (*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))))
✓	0.2b	(fma.f64 (sin.f64 y) z (*.f64 (cos.f64 y) x))
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
	41.7b	(/.f64 (+.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (+.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (-.f64 (pow.f64 (.f64 z (sin.f64 y)) 2) (.f64 (.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y))))))
▶	18.0b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))

Compiler

Compiled 5046 to 2445 computations (51.5% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.2b	(pow.f64 (*.f64 z (sin.f64 y)) 3)
✓	33.1b	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))

series69.0ms (0.9%)

Counts

3 → 84

Calls

3 calls:

28.0ms	(pow.f64 (*.f64 z (sin.f64 y)) 3)
23.0ms	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))
17.0ms	(cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))

rewrite57.0ms (0.7%)

Algorithm

2×	batch-egg-rewrite

Rules

82× egg-rr

Counts

3 → 82

Calls

2 calls:

53.0ms	((cbrt.f64 (pow.f64 (.f64 z (sin.f64 y)) 3)) (pow.f64 (.f64 z (sin.f64 y)) 3) (fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3))))
0.0ms	()

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	27
1	206	27
2	2277	27
3	5704	27
0	0	0
1	0	0

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Rules

429×	`distribute-rgt-neg-in_binary64`
422×	`distribute-lft-neg-in_binary64`
368×	`associate-l_binary64`
361×	`associate-r_binary64`
336×	`fma-def_binary64`

Counts

166 → 111

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	64	1020
1	201	992
2	677	964
3	2507	963
4	4829	960
5	4939	960

prune92.0ms (1.2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	130	4	134
Fresh	1	2	3
Picked	0	1	1
Done	1	2	3
Total	132	9	141

Error

0.1b

Counts

141 → 9

Alt Table

Status	Error	Program
	0.5b	(fma.f64 x (cos.f64 y) (.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (.f64 (cbrt.f64 (sin.f64 y)) z)))
	30.2b	(fma.f64 (sin.f64 y) z (cbrt.f64 (*.f64 (pow.f64 (cos.f64 y) 3) (pow.f64 x 3))))
✓	0.2b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
✓	1.3b	(pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 3)
	0.6b	(fma.f64 x (cos.f64 y) (.f64 (.f64 z (pow.f64 (cbrt.f64 (sin.f64 y)) 2)) (cbrt.f64 (sin.f64 y))))
	29.9b	(fma.f64 x (cos.f64 y) (.f64 (sqrt.f64 (sin.f64 y)) (.f64 (sqrt.f64 (sin.f64 y)) z)))
	15.5b	(fma.f64 x (cos.f64 y) (.f64 (cbrt.f64 (.f64 z z)) (*.f64 (cbrt.f64 z) (sin.f64 y))))
	32.8b	(pow.f64 (sqrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2)
✓	18.0b	(fma.f64 x (cos.f64 y) (cbrt.f64 (pow.f64 (*.f64 z (sin.f64 y)) 3)))

Compiler

Compiled 2143 to 924 computations (56.9% saved)

regimes125.0ms (1.6%)

Accuracy

Total 0.1b remaining (49.8%)

Threshold costs 0.1b (49.8%)

Counts

32 → 1

Compiler

Compiled 1740 to 1090 computations (37.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	9	12
2	9	12

end129.0ms (1.7%)

Compiler: Compiled 160 to 105 computations (34.4% saved)

Details

analyze459.0ms (5.9%)

sample2.9s (37%)

simplify8.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series25.0ms (0.3%)

rewrite42.0ms (0.5%)

simplify84.0ms (1.1%)

prune38.0ms (0.5%)

localize7.0ms (0.1%)

series24.0ms (0.3%)

rewrite51.0ms (0.7%)

simplify70.0ms (0.9%)

prune37.0ms (0.5%)

localize9.0ms (0.1%)

series3.2s (41.4%)

rewrite50.0ms (0.6%)

simplify85.0ms (1.1%)

prune107.0ms (1.4%)

localize10.0ms (0.1%)

series69.0ms (0.9%)

rewrite57.0ms (0.7%)

simplify74.0ms (1%)

prune92.0ms (1.2%)

regimes125.0ms (1.6%)

simplify2.0ms (0%)

end129.0ms (1.7%)

Profiling