Details

analyze466.0ms (9.3%)

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)

sample2.8s (55.1%)

Results

1.4s	2052×	body	1024	valid
704.0ms	4648×	body	128	valid
437.0ms	1053×	body	512	valid
147.0ms	495×	body	256	valid
11.0ms	8×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify12.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

171×	`fma-def_binary64`
87×	`fma-neg_binary64`
37×	`cancel-sign-sub-inv_binary64`
23×	`distribute-rgt-neg-in_binary64`
20×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	17	14
2	32	14
3	49	14
4	76	14
5	124	14
6	205	14
7	306	14
8	408	14
9	524	14
10	582	14
11	588	14

Stop Event

1×

saturated

Counts

1 → 1

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

0.1b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series29.0ms (0.6%)

Counts

4 → 88

Calls

4 calls:

15.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
6.0ms	(*.f64 z (sin.f64 y))
6.0ms	(*.f64 x (cos.f64 y))
1.0ms	(cos.f64 y)

rewrite67.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

518×	`log-prod_binary64`
391×	`fma-def_binary64`
228×	`egg-rr`
190×	`fma-neg_binary64`
184×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	29
1	198	29
2	2648	29

Stop Event

1×	node limit

Counts

4 → 228

Calls

4 calls:

61.0ms	(cos.f64 y)
61.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
61.0ms	(*.f64 x (cos.f64 y))
61.0ms	(*.f64 z (sin.f64 y))

simplify39.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

762×	`fma-neg_binary64`
283×	`distribute-lft-neg-in_binary64`
280×	`distribute-rgt-neg-in_binary64`
261×	`fma-def_binary64`
209×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	906
1	198	891
2	596	866
3	2235	865

Stop Event

1×	node limit

Counts

316 → 259

prune198.0ms (4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	248	11	259
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	249	11	260

Error

0.0b

Counts

260 → 11

Alt Table

Status	Error	Program
	21.6b	(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (cos.f64 y)) (*.f64 (sin.f64 y) (neg.f64 z)))
▶	0.1b	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 x (cos.f64 y)))
	0.2b	(-.f64 (.f64 x (expm1.f64 (log1p.f64 (cos.f64 y)))) (.f64 z (sin.f64 y)))
	15.6b	(fma.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))
	0.9b	(fma.f64 (cbrt.f64 (.f64 x (cos.f64 y))) (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 2) (*.f64 (sin.f64 y) (neg.f64 z)))
	0.2b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	29.9b	(-.f64 (cbrt.f64 (pow.f64 (.f64 x (cos.f64 y)) 3)) (.f64 z (sin.f64 y)))
	26.1b	(fma.f64 (sqrt.f64 (.f64 (sin.f64 y) (neg.f64 z))) (sqrt.f64 (.f64 (sin.f64 y) (neg.f64 z))) (*.f64 x (cos.f64 y)))
	0.4b	(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))
	33.4b	(pow.f64 (sqrt.f64 (-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))) 2)
	35.2b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (sin.f64 y) (neg.f64 z)))

Compiler

Compiled 5602 to 1373 computations (75.5% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series14.0ms (0.3%)

Counts

1 → 36

Calls

1 calls:

14.0ms

(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 x (cos.f64 y)))

rewrite35.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

718×	`log1p-expm1-u_binary64`
718×	`expm1-log1p-u_binary64`
216×	`prod-diff_binary64`
93×	`add-sqr-sqrt_binary64`
84×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	179	12
2	2204	12

Stop Event

1×	node limit

Counts

1 → 23

Calls

1 calls:

34.0ms

(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 x (cos.f64 y)))

simplify28.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

864×	`fma-neg_binary64`
804×	`cancel-sign-sub-inv_binary64`
381×	`distribute-rgt-neg-in_binary64`
336×	`distribute-lft-neg-in_binary64`
319×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	458
1	75	458
2	197	458
3	565	454
4	2280	454

Stop Event

1×	node limit

Counts

59 → 34

prune89.0ms (1.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	89	9	98

Error

0.0b

Counts

98 → 9

Alt Table

Status	Error	Program
	0.2b	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
	0.4b	(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))
	0.2b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	26.1b	(fma.f64 (sqrt.f64 (.f64 (sin.f64 y) (neg.f64 z))) (sqrt.f64 (.f64 (sin.f64 y) (neg.f64 z))) (*.f64 x (cos.f64 y)))
	21.6b	(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (cos.f64 y)) (*.f64 (sin.f64 y) (neg.f64 z)))
▶	0.2b	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y)))))
	35.2b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (sin.f64 y) (neg.f64 z)))
	15.6b	(fma.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))
	0.9b	(fma.f64 z (neg.f64 (sin.f64 y)) (pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3))

Compiler

Compiled 1497 to 623 computations (58.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y)))))
✓	0.1b	(*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y))))
✓	0.1b	(expm1.f64 (log1p.f64 (cos.f64 y)))
✓	0.3b	(log1p.f64 (cos.f64 y))

series165.0ms (3.3%)

Counts

4 → 84

Calls

4 calls:

142.0ms	(log1p.f64 (cos.f64 y))
14.0ms	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y)))))
8.0ms	(*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y))))
1.0ms	(expm1.f64 (log1p.f64 (cos.f64 y)))

rewrite53.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

793×	`expm1-log1p-u_binary64`
792×	`log1p-expm1-u_binary64`
251×	`prod-diff_binary64`
101×	`add-sqr-sqrt_binary64`
91×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	200	26
2	2411	26

Stop Event

1×	node limit

Counts

4 → 75

Calls

4 calls:

52.0ms	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y)))))
52.0ms	(*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y))))
52.0ms	(expm1.f64 (log1p.f64 (cos.f64 y)))
52.0ms	(log1p.f64 (cos.f64 y))

simplify35.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

619×	`fma-neg_binary64`
324×	`*-commutative_binary64`
235×	`distribute-rgt-neg-in_binary64`
229×	`distribute-lft-neg-in_binary64`
215×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	66	828
1	186	821
2	530	805
3	1977	803

Stop Event

1×	node limit

Counts

159 → 108

prune88.0ms (1.8%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	108	9	117

Error

0.0b

Counts

117 → 9

Alt Table

Status	Error	Program
	0.2b	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
	0.4b	(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))
▶	0.2b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	26.1b	(fma.f64 (sqrt.f64 (.f64 (sin.f64 y) (neg.f64 z))) (sqrt.f64 (.f64 (sin.f64 y) (neg.f64 z))) (*.f64 x (cos.f64 y)))
	21.6b	(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (cos.f64 y)) (*.f64 (sin.f64 y) (neg.f64 z)))
✓	0.2b	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y)))))
	35.2b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (sin.f64 y) (neg.f64 z)))
	15.6b	(fma.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))
	0.9b	(fma.f64 z (neg.f64 (sin.f64 y)) (pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3))

Compiler

Compiled 1845 to 815 computations (55.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	0.1b	(*.f64 z (sin.f64 y))
✓	0.1b	(fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y))))
✓	52.4b	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))

series54.0ms (1.1%)

Counts

3 → 84

Calls

3 calls:

23.0ms

(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))

16.0ms

(fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y))))

14.0ms

(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))

rewrite50.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

897×	`expm1-log1p-u_binary64`
708×	`prod-diff_binary64`
114×	`add-sqr-sqrt_binary64`
104×	`log1p-expm1-u_binary64`
103×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	64
1	220	51
2	2745	51

Stop Event

1×	node limit

Counts

3 → 68

Calls

3 calls:

49.0ms

(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))

49.0ms

(fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y))))

49.0ms

(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))

simplify45.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
433×	`cancel-sign-sub-inv_binary64`
408×	`fma-neg_binary64`
399×	`associate-l_binary64`
325×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	726
1	127	720
2	359	708
3	1157	704
4	4458	704

Stop Event

1×	node limit

Counts

152 → 89

prune93.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	112	10	122

Error

0.0b

Counts

122 → 10

Alt Table

Status	Error	Program
	0.2b	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 x (cbrt.f64 (pow.f64 (cos.f64 y) 3))))
	0.4b	(fma.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))
✓	0.2b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))))
	26.1b	(fma.f64 (sqrt.f64 (.f64 (sin.f64 y) (neg.f64 z))) (sqrt.f64 (.f64 (sin.f64 y) (neg.f64 z))) (*.f64 x (cos.f64 y)))
	21.6b	(fma.f64 (cbrt.f64 (.f64 x x)) (.f64 (cbrt.f64 x) (cos.f64 y)) (*.f64 (sin.f64 y) (neg.f64 z)))
✓	0.2b	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 x (expm1.f64 (log1p.f64 (cos.f64 y)))))
	30.9b	(fma.f64 x (cos.f64 y) (fma.f64 z (neg.f64 (sin.f64 y)) (fma.f64 z (neg.f64 (sin.f64 y)) (pow.f64 (sqrt.f64 (*.f64 z (sin.f64 y))) 2))))
	35.2b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (.f64 (sin.f64 y) (neg.f64 z)))
	15.6b	(fma.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x) (.f64 (sin.f64 y) (neg.f64 z)))
	0.9b	(fma.f64 z (neg.f64 (sin.f64 y)) (pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3))

Compiler

Compiled 2505 to 710 computations (71.7% saved)

regimes500.0ms (10%)

Accuracy

Total 0.1b remaining (78.3%)

Threshold costs 0.1b (78.3%)

Counts

121 → 1

Compiler

Compiled 7608 to 5078 computations (33.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	18	14
2	20	14
3	21	14

Stop Event

1×

saturated

end141.0ms (2.8%)

Compiler: Compiled 203 to 125 computations (38.4% saved)

Iter	Nodes	Cost
0	9	14
1	17	14
2	32	14
3	49	14
4	76	14
5	124	14
6	205	14
7	306	14
8	408	14
9	524	14
10	582	14
11	588	14

Iter	Nodes	Cost
0	9	14
1	17	14
2	32	14
3	49	14
4	76	14
5	124	14
6	205	14
7	306	14
8	408	14
9	524	14
10	582	14
11	588	14

Details

analyze466.0ms (9.3%)

sample2.8s (55.1%)

simplify12.0ms (0.2%)

prune2.0ms (0%)

localize8.0ms (0.2%)

series29.0ms (0.6%)

rewrite67.0ms (1.3%)

simplify39.0ms (0.8%)

prune198.0ms (4%)

localize9.0ms (0.2%)

series14.0ms (0.3%)

rewrite35.0ms (0.7%)

simplify28.0ms (0.6%)

prune89.0ms (1.8%)

localize10.0ms (0.2%)

series165.0ms (3.3%)

rewrite53.0ms (1.1%)

simplify35.0ms (0.7%)

prune88.0ms (1.8%)

localize11.0ms (0.2%)

series54.0ms (1.1%)

rewrite50.0ms (1%)

simplify45.0ms (0.9%)

prune93.0ms (1.9%)

regimes500.0ms (10%)

simplify2.0ms (0%)

end141.0ms (2.8%)

Profiling

Iter	Nodes	Cost
0	9	14
1	17	14
2	32	14
3	49	14
4	76	14
5	124	14
6	205	14
7	306	14
8	408	14
9	524	14
10	582	14
11	588	14