Details

analyze443.0ms (5.2%)

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)

sample3.6s (41.6%)

Results

1.9s	2090×	body	1024	valid
920.0ms	4642×	body	128	valid
533.0ms	1009×	body	512	valid
190.0ms	506×	body	256	valid
12.0ms	9×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify14.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

171×	`fma-def_binary64`
87×	`fma-neg_binary64`
36×	`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	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	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)

localize29.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	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 (0.3%)

Counts

3 → 84

Calls

3 calls:

15.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
7.0ms	(*.f64 z (sin.f64 y))
6.0ms	(*.f64 x (cos.f64 y))

rewrite69.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	26
1	194	26
2	2475	26
3	4984	26

Stop Event

1×	node limit

Counts

3 → 208

Calls

3 calls:

62.0ms	(-.f64 (.f64 x (cos.f64 y)) (.f64 z (sin.f64 y)))
62.0ms	(*.f64 x (cos.f64 y))
62.0ms	(*.f64 z (sin.f64 y))

simplify83.0ms (1%)

Algorithm

1×	egg-herbie

Rules

728×	`distribute-rgt-neg-in_binary64`
651×	`fma-neg_binary64`
403×	`sub-neg_binary64`
381×	`*-commutative_binary64`
370×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	57	850
1	171	841
2	481	822
3	1534	819
4	3510	819
5	4870	819
6	5013	819

Stop Event

1×	node limit

Counts

292 → 232

prune169.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	226	6	232
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	227	6	233

Error

0.0b

Counts

233 → 6

Alt Table

Status	Error	Program
	37.6b	(/.f64 (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (fma.f64 (.f64 z (sin.f64 y)) (fma.f64 z (sin.f64 y) (.f64 x (cos.f64 y))) (pow.f64 (*.f64 x (cos.f64 y)) 2)))
	16.8b	(fma.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x) (neg.f64 (.f64 z (sin.f64 y))))
	27.7b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (neg.f64 (.f64 z (sin.f64 y))))
	30.9b	(-.f64 (pow.f64 (sqrt.f64 (.f64 x (cos.f64 y))) 2) (.f64 z (sin.f64 y)))
	0.9b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))
▶	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)))))

Compiler

Compiled 5106 to 1122 computations (78% saved)

localize15.0ms (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))))
✓	54.0b	(fma.f64 z (neg.f64 (sin.f64 y)) (*.f64 z (sin.f64 y)))

series73.0ms (0.9%)

Counts

3 → 84

Calls

3 calls:

28.0ms

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

27.0ms

(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)))))

18.0ms

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

rewrite55.0ms (0.6%)

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	2346	51
3	5191	51

Stop Event

1×	node limit

Counts

3 → 68

Calls

3 calls:

53.0ms

(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)))))

53.0ms

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

53.0ms

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

simplify71.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

760×	`fma-def_binary64`
658×	`distribute-rgt-neg-in_binary64`
566×	`distribute-lft-neg-in_binary64`
436×	`cancel-sign-sub-inv_binary64`
408×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	726
1	126	720
2	335	708
3	890	704
4	3065	704
5	4465	704
6	4937	704

Stop Event

1×	node limit

Counts

152 → 87

prune85.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	111	6	117

Error

0.0b

Counts

117 → 6

Alt Table

Status	Error	Program
	37.6b	(/.f64 (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (fma.f64 (.f64 z (sin.f64 y)) (fma.f64 z (sin.f64 y) (.f64 x (cos.f64 y))) (pow.f64 (*.f64 x (cos.f64 y)) 2)))
	16.8b	(fma.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x) (neg.f64 (.f64 z (sin.f64 y))))
	27.7b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (neg.f64 (.f64 z (sin.f64 y))))
	30.9b	(-.f64 (pow.f64 (sqrt.f64 (.f64 x (cos.f64 y))) 2) (.f64 z (sin.f64 y)))
▶	0.9b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))
✓	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)))))

Compiler

Compiled 2531 to 722 computations (71.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series876.0ms (10.2%)

Counts

2 → 48

Calls

2 calls:

440.0ms	(cbrt.f64 (*.f64 x (cos.f64 y)))
436.0ms	(pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3)

rewrite75.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

596×	`log1p-expm1-u_binary64`
596×	`expm1-log1p-u_binary64`
319×	`log-prod_binary64`
308×	`fma-def_binary64`
121×	`expm1-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	146	14
2	1576	14
3	4915	14
4	5136	14

Stop Event

1×	node limit

Counts

2 → 60

Calls

2 calls:

74.0ms	(cbrt.f64 (*.f64 x (cos.f64 y)))
74.0ms	(pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 3)

simplify63.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

545×	`fma-neg_binary64`
351×	`distribute-rgt-neg-in_binary64`
345×	`distribute-lft-neg-in_binary64`
226×	`unswap-sqr_binary64`
210×	`associate-r_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	67	872
1	192	865
2	511	808
3	1791	464
4	4691	456
5	4965	456

Stop Event

1×	node limit

Counts

108 → 85

prune116.0ms (1.3%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	132	1	133
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	133	6	139

Error

0.0b

Counts

139 → 6

Alt Table

Status	Error	Program
	37.6b	(/.f64 (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (fma.f64 (.f64 z (sin.f64 y)) (fma.f64 z (sin.f64 y) (.f64 x (cos.f64 y))) (pow.f64 (*.f64 x (cos.f64 y)) 2)))
▶	0.8b	(-.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 2))) (.f64 z (sin.f64 y)))
	16.8b	(fma.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x) (neg.f64 (.f64 z (sin.f64 y))))
	27.7b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (neg.f64 (.f64 z (sin.f64 y))))
✓	0.9b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))
✓	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)))))

Compiler

Compiled 2502 to 1054 computations (57.9% saved)

localize57.0ms (0.7%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(cbrt.f64 (cos.f64 y))
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 2)
	0.6b	(cbrt.f64 (*.f64 x (cos.f64 y)))
✓	0.6b	(cbrt.f64 x)

series612.0ms (7.1%)

Counts

3 → 48

Calls

3 calls:

451.0ms	(pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 2)
129.0ms	(cbrt.f64 (cos.f64 y))
32.0ms	(cbrt.f64 x)

rewrite43.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

726×	`log1p-expm1-u_binary64`
726×	`expm1-log1p-u_binary64`
153×	`expm1-udef_binary64`
153×	`log1p-udef_binary64`
89×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	19
1	190	19
2	1946	19
3	4914	19

Stop Event

1×	node limit

Counts

3 → 63

Calls

3 calls:

42.0ms	(cbrt.f64 (cos.f64 y))
42.0ms	(pow.f64 (cbrt.f64 (*.f64 x (cos.f64 y))) 2)
42.0ms	(cbrt.f64 x)

simplify102.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

490×	`unswap-sqr_binary64`
463×	`fma-neg_binary64`
379×	`distribute-rgt-neg-in_binary64`
368×	`distribute-lft-neg-in_binary64`
237×	`neg-mul-1_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	71	648
1	200	636
2	517	567
3	1900	527
4	4705	523
5	4855	523
6	4991	523
7	4996	523
8	4913	523

Stop Event

1×	node limit

Counts

111 → 89

prune111.0ms (1.3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	125	8	133

Error

0.0b

Counts

133 → 8

Alt Table

Status	Error	Program
	0.8b	(-.f64 (.f64 (cbrt.f64 x) (.f64 (log1p.f64 (expm1.f64 (cbrt.f64 (cos.f64 y)))) (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 2))) (.f64 z (sin.f64 y)))
✓	0.8b	(-.f64 (.f64 (cbrt.f64 x) (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 2))) (.f64 z (sin.f64 y)))
	0.9b	(-.f64 (.f64 (cbrt.f64 x) (.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (cos.f64 y))) 3) (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 2))) (.f64 z (sin.f64 y)))
	16.8b	(fma.f64 (sqrt.f64 (cos.f64 y)) (.f64 (sqrt.f64 (cos.f64 y)) x) (neg.f64 (.f64 z (sin.f64 y))))
	37.6b	(/.f64 (-.f64 (pow.f64 (.f64 x (cos.f64 y)) 3) (pow.f64 (.f64 z (sin.f64 y)) 3)) (fma.f64 (.f64 z (sin.f64 y)) (fma.f64 z (sin.f64 y) (.f64 x (cos.f64 y))) (pow.f64 (*.f64 x (cos.f64 y)) 2)))
	27.7b	(fma.f64 (sqrt.f64 x) (.f64 (sqrt.f64 x) (cos.f64 y)) (neg.f64 (.f64 z (sin.f64 y))))
✓	0.9b	(-.f64 (pow.f64 (cbrt.f64 (.f64 x (cos.f64 y))) 3) (.f64 z (sin.f64 y)))
✓	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)))))

Compiler

Compiled 3259 to 1302 computations (60% saved)

regimes1.6s (19%)

Accuracy

Total 0.1b remaining (67.8%)

Threshold costs 0.1b (67.8%)

Counts

108 → 1

Compiler

Compiled 7368 to 4766 computations (35.3% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
2×	`*-rgt-identity_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	20	14
2	23	14
3	24	14
4	22	14

Stop Event

1×

saturated

end167.0ms (1.9%)

Compiler: Compiled 200 to 124 computations (38% saved)

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14

Details

analyze443.0ms (5.2%)

sample3.6s (41.6%)

simplify14.0ms (0.2%)

prune2.0ms (0%)

localize29.0ms (0.3%)

series29.0ms (0.3%)

rewrite69.0ms (0.8%)

simplify83.0ms (1%)

prune169.0ms (2%)

localize15.0ms (0.2%)

series73.0ms (0.9%)

rewrite55.0ms (0.6%)

simplify71.0ms (0.8%)

prune85.0ms (1%)

localize11.0ms (0.1%)

series876.0ms (10.2%)

rewrite75.0ms (0.9%)

simplify63.0ms (0.7%)

prune116.0ms (1.3%)

localize57.0ms (0.7%)

series612.0ms (7.1%)

rewrite43.0ms (0.5%)

simplify102.0ms (1.2%)

prune111.0ms (1.3%)

regimes1.6s (19%)

simplify6.0ms (0.1%)

end167.0ms (1.9%)

Profiling

Iter	Nodes	Cost
0	9	14
1	17	14
2	28	14
3	45	14
4	67	14
5	101	14
6	153	14
7	214	14
8	258	14
9	280	14
10	300	14
11	306	14
12	275	14