Details

analyze423.0ms (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
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)

sample2.7s (45.1%)

Results

1.4s	2101×	body	1024	valid
684.0ms	4550×	body	128	valid
408.0ms	1092×	body	512	valid
144.0ms	506×	body	256	valid
9.0ms	7×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (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

0.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.1b	(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 3 expressions with local error:

New	Error	Program
✓	0.0b	(cos.f64 y)
✓	0.1b	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
✓	0.1b	(*.f64 z (sin.f64 y))

series21.0ms (0.4%)

Counts

3 → 64

Calls

3 calls:

12.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
7.0ms	(*.f64 z (sin.f64 y))
1.0ms	(cos.f64 y)

rewrite48.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

689×	`log1p-expm1-u_binary64`
689×	`expm1-log1p-u_binary64`
201×	`prod-diff_binary64`
147×	`expm1-udef_binary64`
147×	`log1p-udef_binary64`

Counts

3 → 59

Calls

3 calls:

47.0ms	(cos.f64 y)
47.0ms	(fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))
47.0ms	(*.f64 z (sin.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	21
1	156	21
2	1801	21
3	5105	21

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

607×	`distribute-rgt-neg-in_binary64`
551×	`fma-neg_binary64`
516×	`distribute-lft-neg-in_binary64`
359×	`sub-neg_binary64`
323×	`*-commutative_binary64`

Counts

123 → 84

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	54	656
1	154	644
2	430	627
3	1319	625
4	2979	625
5	4897	625
6	5009	625

prune69.0ms (1.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	76	8	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	8	85

Error

0.1b

Counts

85 → 8

Alt Table

Status	Error	Program
	0.3b	(fma.f64 x (-.f64 (exp.f64 (log1p.f64 (cos.f64 y))) 1) (*.f64 z (sin.f64 y)))
	0.7b	(fma.f64 x (cos.f64 y) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
	26.4b	(fma.f64 x (cos.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))))
▶	0.2b	(fma.f64 x (log1p.f64 (expm1.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	25.0b	(/.f64 (-.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 z (sin.f64 y)) 2)) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))
	36.9b	(/.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))))))
	1.3b	(.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2))
	16.3b	(fma.f64 x (pow.f64 (pow.f64 (cos.f64 y) 3) 1/3) (*.f64 z (sin.f64 y)))

Compiler

Compiled 1403 to 571 computations (59.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (log1p.f64 (expm1.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.2b	(log1p.f64 (expm1.f64 (cos.f64 y)))
✓	0.6b	(expm1.f64 (cos.f64 y))

series19.0ms (0.3%)

Counts

3 → 60

Calls

3 calls:

14.0ms	(fma.f64 x (log1p.f64 (expm1.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
3.0ms	(expm1.f64 (cos.f64 y))
2.0ms	(log1p.f64 (expm1.f64 (cos.f64 y)))

rewrite48.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

765×	`expm1-log1p-u_binary64`
764×	`log1p-expm1-u_binary64`
236×	`prod-diff_binary64`
89×	`add-sqr-sqrt_binary64`
81×	`add-log-exp_binary64`

Counts

3 → 62

Calls

3 calls:

47.0ms	(fma.f64 x (log1p.f64 (expm1.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
47.0ms	(log1p.f64 (expm1.f64 (cos.f64 y)))
47.0ms	(expm1.f64 (cos.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	175	20
2	1994	20
3	5150	20

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

748×	`distribute-rgt-neg-in_binary64`
544×	`fma-neg_binary64`
519×	`sub-neg_binary64`
385×	`neg-mul-1_binary64`
362×	`*-commutative_binary64`

Counts

122 → 88

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	606
1	159	598
2	446	585
3	1449	577
4	3490	577
5	4838	577
6	5013	577

prune82.0ms (1.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	112	8	120

Error

0.1b

Counts

120 → 8

Alt Table

Status	Error	Program
▶	0.3b	(fma.f64 x (-.f64 (exp.f64 (log1p.f64 (cos.f64 y))) 1) (*.f64 z (sin.f64 y)))
	0.7b	(fma.f64 x (cos.f64 y) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
	26.4b	(fma.f64 x (cos.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))))
✓	0.2b	(fma.f64 x (log1p.f64 (expm1.f64 (cos.f64 y))) (*.f64 z (sin.f64 y)))
	25.0b	(/.f64 (-.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 z (sin.f64 y)) 2)) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))
	36.9b	(/.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))))))
	1.3b	(.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (.f64 z (sin.f64 y)))) (pow.f64 (cbrt.f64 (fma.f64 x (cos.f64 y) (*.f64 z (sin.f64 y)))) 2))
	16.3b	(fma.f64 x (pow.f64 (pow.f64 (cos.f64 y) 3) 1/3) (*.f64 z (sin.f64 y)))

Compiler

Compiled 1889 to 752 computations (60.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(*.f64 z (sin.f64 y))
✓	0.2b	(exp.f64 (log1p.f64 (cos.f64 y)))
✓	0.3b	(log1p.f64 (cos.f64 y))
✓	0.4b	(-.f64 (exp.f64 (log1p.f64 (cos.f64 y))) 1)

series405.0ms (6.7%)

Counts

3 → 36

Calls

3 calls:

139.0ms	(-.f64 (exp.f64 (log1p.f64 (cos.f64 y))) 1)
134.0ms	(exp.f64 (log1p.f64 (cos.f64 y)))
132.0ms	(log1p.f64 (cos.f64 y))

rewrite51.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

519×	`expm1-log1p-u_binary64`
518×	`log1p-expm1-u_binary64`
313×	`unpow-prod-down_binary64`
236×	`log-prod_binary64`
160×	`prod-diff_binary64`

Counts

3 → 143

Calls

3 calls:

48.0ms	(exp.f64 (log1p.f64 (cos.f64 y)))
48.0ms	(log1p.f64 (cos.f64 y))
48.0ms	(-.f64 (exp.f64 (log1p.f64 (cos.f64 y))) 1)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	120	14
2	1317	14
3	5056	14

simplify90.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

653×	`fma-def_binary64`
635×	`distribute-rgt-neg-in_binary64`
547×	`distribute-lft-neg-in_binary64`
426×	`associate-l_binary64`
365×	`associate-r_binary64`

Counts

179 → 165

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	284
1	106	276
2	261	266
3	778	260
4	2799	260
5	4914	260
6	4973	260
7	4932	260

prune198.0ms (3.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	186	3	189
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	189	8	197

Error

0.1b

Counts

197 → 8

Alt Table

Status	Error	Program
	0.7b	(fma.f64 x (.f64 (expm1.f64 (.f64 (log1p.f64 (cos.f64 y)) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 (cos.f64 y) 1) 2) (+.f64 (+.f64 (cos.f64 y) 1) 1)))) (*.f64 z (sin.f64 y)))
	26.4b	(fma.f64 x (cos.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))))
▶	0.4b	(fma.f64 x (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y)))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y))))) (*.f64 z (sin.f64 y)))
✓	0.3b	(fma.f64 x (-.f64 (exp.f64 (log1p.f64 (cos.f64 y))) 1) (*.f64 z (sin.f64 y)))
	0.7b	(fma.f64 x (cos.f64 y) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
	25.0b	(/.f64 (-.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 z (sin.f64 y)) 2)) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))
	36.9b	(/.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))))))
	8.1b	(fma.f64 x (-.f64 (exp.f64 (sqrt.f64 (pow.f64 (log1p.f64 (cos.f64 y)) 2))) 1) (*.f64 z (sin.f64 y)))

Compiler

Compiled 3774 to 1913 computations (49.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y)))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y))))) (*.f64 z (sin.f64 y)))
✓	0.1b	(sqrt.f64 (exp.f64 (cos.f64 y)))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.7b	(log.f64 (sqrt.f64 (exp.f64 (cos.f64 y))))

series416.0ms (6.9%)

Counts

3 → 44

Calls

3 calls:

257.0ms

(fma.f64 x (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y)))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y))))) (*.f64 z (sin.f64 y)))

154.0ms

(log.f64 (sqrt.f64 (exp.f64 (cos.f64 y))))

5.0ms

(sqrt.f64 (exp.f64 (cos.f64 y)))

rewrite88.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

533×	`prod-diff_binary64`
493×	`log-prod_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`
175×	`log-pow_binary64`

Counts

3 → 87

Calls

3 calls:

86.0ms

(fma.f64 x (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y)))) (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y))))) (*.f64 z (sin.f64 y)))

86.0ms

(sqrt.f64 (exp.f64 (cos.f64 y)))

86.0ms

(log.f64 (sqrt.f64 (exp.f64 (cos.f64 y))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	220	25
2	2463	25
3	4981	25
4	5199	25

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

585×	`fma-def_binary64`
496×	`sub-neg_binary64`
422×	`associate-r_binary64`
324×	`associate-l_binary64`
301×	`cancel-sign-sub-inv_binary64`

Counts

131 → 113

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	120	1198
1	327	1023
2	1043	974
3	3970	974
4	4868	974
5	4921	974

prune319.0ms (5.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	207	2	209
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	209	8	217

Error

0.1b

Counts

217 → 8

Alt Table

Status	Error	Program
	0.7b	(fma.f64 x (.f64 (expm1.f64 (.f64 (log1p.f64 (cos.f64 y)) 3)) (/.f64 1 (+.f64 (pow.f64 (+.f64 (cos.f64 y) 1) 2) (+.f64 (+.f64 (cos.f64 y) 1) 1)))) (*.f64 z (sin.f64 y)))
	26.4b	(fma.f64 x (cos.f64 y) (cbrt.f64 (*.f64 (pow.f64 z 3) (pow.f64 (sin.f64 y) 3))))
✓	0.3b	(fma.f64 x (-.f64 (exp.f64 (log1p.f64 (cos.f64 y))) 1) (*.f64 z (sin.f64 y)))
	0.7b	(fma.f64 x (cos.f64 y) (pow.f64 (cbrt.f64 (*.f64 z (sin.f64 y))) 3))
	0.3b	(fma.f64 x (+.f64 (log.f64 (sqrt.f64 (exp.f64 (cos.f64 y)))) (.f64 1/2 (cos.f64 y))) (.f64 z (sin.f64 y)))
	25.0b	(/.f64 (-.f64 (.f64 (.f64 x (cos.f64 y)) (.f64 x (cos.f64 y))) (pow.f64 (.f64 z (sin.f64 y)) 2)) (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y))))
	36.9b	(/.f64 (+.f64 (pow.f64 (.f64 (cos.f64 y) x) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (fma.f64 (.f64 (cos.f64 y) x) (.f64 (cos.f64 y) x) (-.f64 (pow.f64 (.f64 z (sin.f64 y)) 2) (.f64 (.f64 (cos.f64 y) x) (.f64 z (sin.f64 y))))))
	8.1b	(fma.f64 x (-.f64 (exp.f64 (sqrt.f64 (pow.f64 (log1p.f64 (cos.f64 y)) 2))) 1) (*.f64 z (sin.f64 y)))

Compiler

Compiled 5069 to 2018 computations (60.2% saved)

regimes612.0ms (10.2%)

Accuracy

Total 0.0b remaining (32.5%)

Threshold costs 0.0b (32.5%)

Counts

130 → 1

Compiler

Compiled 9584 to 6558 computations (31.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`*-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	12
1	13	12
2	12	12

end135.0ms (2.3%)

Compiler: Compiled 206 to 128 computations (37.9% saved)

Details

analyze423.0ms (7%)

sample2.7s (45.1%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series21.0ms (0.4%)

rewrite48.0ms (0.8%)

simplify73.0ms (1.2%)

prune69.0ms (1.2%)

localize11.0ms (0.2%)

series19.0ms (0.3%)

rewrite48.0ms (0.8%)

simplify75.0ms (1.2%)

prune82.0ms (1.4%)

localize11.0ms (0.2%)

series405.0ms (6.7%)

rewrite51.0ms (0.8%)

simplify90.0ms (1.5%)

prune198.0ms (3.3%)

localize13.0ms (0.2%)

series416.0ms (6.9%)

rewrite88.0ms (1.5%)

simplify79.0ms (1.3%)

prune319.0ms (5.3%)

regimes612.0ms (10.2%)

simplify2.0ms (0%)

end135.0ms (2.3%)

Profiling