Details

analyze423.0ms (8.7%)

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)

sample2.3s (47.2%)

Results

926.0ms	5907×	body	128	valid
925.0ms	1329×	body	1024	valid
279.0ms	694×	body	512	valid
89.0ms	317×	body	256	valid
12.0ms	9×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify18.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

228×	`fma-def_binary64`
171×	`fma-neg_binary64`
68×	`cancel-sign-sub-inv_binary64`
44×	`distribute-rgt-in_binary64`
42×	`associate--r+_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	18	14
2	38	14
3	67	14
4	118	14
5	183	14
6	324	14
7	531	14
8	681	14
9	846	14
10	950	14
11	960	14

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

0.1b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 45 to 26 computations (42.2% saved)

localize7.0ms (0.1%)

Local error

Found 3 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 z (sin.f64 y))

series20.0ms (0.4%)

Counts

3 → 64

Calls

3 calls:

13.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
6.0ms	(*.f64 z (sin.f64 y))
1.0ms	(cos.f64 y)

rewrite63.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

521×	`log-prod_binary64`
460×	`fma-def_binary64`
217×	`fma-neg_binary64`
194×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	202	23
2	2964	23

Stop Event

1×	node limit

Counts

3 → 170

Calls

3 calls:

60.0ms	(cos.f64 y)
60.0ms	(-.f64 (+.f64 x (cos.f64 y)) (*.f64 z (sin.f64 y)))
60.0ms	(*.f64 z (sin.f64 y))

simplify44.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

514×	`fma-neg_binary64`
427×	`sub-neg_binary64`
268×	`unswap-sqr_binary64`
267×	`*-commutative_binary64`
204×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	715
1	176	703
2	508	687
3	1785	681
4	4289	681

Stop Event

1×	node limit

Counts

234 → 200

prune144.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	195	5	200
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	196	5	201

Error

0.0b

Counts

201 → 5

Alt Table

Status	Error	Program
	0.3b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 z (sin.f64 y))) 2) (neg.f64 (cbrt.f64 (.f64 z (sin.f64 y)))) (+.f64 x (cos.f64 y)))
	21.5b	(-.f64 x (fma.f64 y z -1))
	33.3b	(fma.f64 (*.f64 (neg.f64 z) (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	0.7b	(fma.f64 (*.f64 (neg.f64 z) (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
▶	0.1b	(+.f64 (cos.f64 y) (-.f64 x (*.f64 z (sin.f64 y))))

Compiler

Compiled 3689 to 1039 computations (71.8% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series23.0ms (0.5%)

Counts

2 → 72

Calls

2 calls:

12.0ms	(+.f64 (cos.f64 y) (-.f64 x (*.f64 z (sin.f64 y))))
11.0ms	(-.f64 x (*.f64 z (sin.f64 y)))

rewrite65.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

520×	`log-prod_binary64`
423×	`fma-def_binary64`
213×	`fma-neg_binary64`
194×	`expm1-udef_binary64`
194×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	202	23
2	2921	23

Stop Event

1×	node limit

Counts

2 → 168

Calls

2 calls:

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

simplify43.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

705×	`fma-def_binary64`
468×	`distribute-rgt-neg-in_binary64`
362×	`cancel-sign-sub-inv_binary64`
305×	`sub-neg_binary64`
285×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	40	770
1	119	769
2	325	763
3	1027	749
4	3893	749

Stop Event

1×	node limit

Counts

240 → 190

prune164.0ms (3.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	242	1	243
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	243	5	248

Error

0.0b

Counts

248 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (cos.f64 y) (-.f64 x (*.f64 z (sin.f64 y))))
▶	0.3b	(+.f64 (cos.f64 y) (fma.f64 (*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 (sin.f64 y)) 2)) (cbrt.f64 (sin.f64 y)) x))
	33.3b	(fma.f64 (*.f64 (neg.f64 z) (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	0.7b	(fma.f64 (*.f64 (neg.f64 z) (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	21.5b	(-.f64 x (fma.f64 y z -1))

Compiler

Compiled 4275 to 1263 computations (70.5% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 (*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 (sin.f64 y)) 2)) (cbrt.f64 (sin.f64 y)) x)
✓	0.2b	(*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 (sin.f64 y)) 2))
✓	0.5b	(pow.f64 (cbrt.f64 (sin.f64 y)) 2)
✓	0.6b	(cbrt.f64 (sin.f64 y))

series254.0ms (5.2%)

Counts

4 → 69

Calls

4 calls:

125.0ms	(fma.f64 (*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 (sin.f64 y)) 2)) (cbrt.f64 (sin.f64 y)) x)
71.0ms	(*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 (sin.f64 y)) 2))
43.0ms	(pow.f64 (cbrt.f64 (sin.f64 y)) 2)
15.0ms	(cbrt.f64 (sin.f64 y))

rewrite53.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

826×	`log1p-expm1-u_binary64`
826×	`expm1-log1p-u_binary64`
109×	`add-sqr-sqrt_binary64`
101×	`add-cbrt-cube_binary64`
100×	`add-exp-log_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	47
1	223	33
2	2650	33

Stop Event

1×	node limit

Counts

4 → 81

Calls

4 calls:

52.0ms	(fma.f64 (*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 (sin.f64 y)) 2)) (cbrt.f64 (sin.f64 y)) x)
52.0ms	(*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 (sin.f64 y)) 2))
52.0ms	(pow.f64 (cbrt.f64 (sin.f64 y)) 2)
52.0ms	(cbrt.f64 (sin.f64 y))

simplify52.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

860×	`fma-def_binary64`
658×	`unswap-sqr_binary64`
346×	`associate-l_binary64`
219×	`fma-neg_binary64`
217×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	626
1	43	626
2	86	626
3	191	626
4	463	626
5	1421	626
6	2490	626
7	4521	626

Stop Event

1×	node limit

Counts

150 → 90

prune99.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	113	6	119

Error

0.0b

Counts

119 → 6

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (cos.f64 y) (-.f64 x (*.f64 z (sin.f64 y))))
✓	0.3b	(+.f64 (cos.f64 y) (fma.f64 (*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 (sin.f64 y)) 2)) (cbrt.f64 (sin.f64 y)) x))
	33.3b	(fma.f64 (*.f64 (neg.f64 z) (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	0.7b	(fma.f64 (*.f64 (neg.f64 z) (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
▶	0.3b	(+.f64 (cos.f64 y) (fma.f64 (*.f64 (neg.f64 z) (pow.f64 (cbrt.f64 (sin.f64 y)) 2)) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) 3) x))
	21.5b	(-.f64 x (fma.f64 y z -1))

Compiler

Compiled 2187 to 871 computations (60.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.5b	(pow.f64 (cbrt.f64 (sin.f64 y)) 2)
	0.6b	(cbrt.f64 (sin.f64 y))
✓	0.6b	(cbrt.f64 (cbrt.f64 (sin.f64 y)))
✓	0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) 3)

series263.0ms (5.4%)

Counts

2 → 24

Calls

2 calls:

136.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) 3)
127.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 y)))

rewrite40.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

473×	`log1p-expm1-u_binary64`
473×	`expm1-log1p-u_binary64`
385×	`unpow-prod-down_binary64`
234×	`log-prod_binary64`
136×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	12
1	136	12
2	1347	12

Stop Event

1×	node limit

Counts

2 → 82

Calls

2 calls:

38.0ms	(cbrt.f64 (cbrt.f64 (sin.f64 y)))
38.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) 3)

simplify36.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

511×	`fma-def_binary64`
427×	`distribute-rgt-neg-in_binary64`
353×	`distribute-lft-neg-in_binary64`
279×	`fma-neg_binary64`
264×	`sub-neg_binary64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	47	384
1	141	382
2	359	378
3	1066	372
4	3493	284

Stop Event

1×	node limit

Counts

106 → 100

prune191.0ms (3.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	166	1	167
Fresh	0	3	3
Picked	1	0	1
Done	1	1	2
Total	168	5	173

Error

Counts

173 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (cos.f64 y) (-.f64 x (*.f64 z (sin.f64 y))))
	0.4b	(+.f64 (cos.f64 y) (fma.f64 (.f64 (neg.f64 z) (pow.f64 (cbrt.f64 (sin.f64 y)) 2)) (.f64 (pow.f64 (*.f64 (pow.f64 (cbrt.f64 (sin.f64 y)) 2) (pow.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))) 2)) 1/3) (cbrt.f64 (cbrt.f64 (cbrt.f64 (sin.f64 y))))) x))
	33.3b	(fma.f64 (*.f64 (neg.f64 z) (sqrt.f64 (sin.f64 y))) (sqrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	0.7b	(fma.f64 (*.f64 (neg.f64 z) (cbrt.f64 (pow.f64 (sin.f64 y) 2))) (cbrt.f64 (sin.f64 y)) (+.f64 x (cos.f64 y)))
	21.5b	(-.f64 x (fma.f64 y z -1))

Compiler

Compiled 4239 to 1949 computations (54% saved)

regimes434.0ms (8.9%)

Accuracy

Total 0.0b remaining (43.9%)

Threshold costs 0.0b (43.9%)

Counts

96 → 1

Compiler

Compiled 7948 to 5338 computations (32.8% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	16	14
2	28	14
3	34	14
4	38	14
5	39	14

Stop Event

1×

saturated

end95.0ms (1.9%)

Compiler: Compiled 117 to 75 computations (35.9% saved)

Iter	Nodes	Cost
0	9	14
1	18	14
2	38	14
3	67	14
4	118	14
5	183	14
6	324	14
7	531	14
8	681	14
9	846	14
10	950	14
11	960	14

Iter	Nodes	Cost
0	9	14
1	18	14
2	38	14
3	67	14
4	118	14
5	183	14
6	324	14
7	531	14
8	681	14
9	846	14
10	950	14
11	960	14

Details

analyze423.0ms (8.7%)

sample2.3s (47.2%)

simplify18.0ms (0.4%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series20.0ms (0.4%)

rewrite63.0ms (1.3%)

simplify44.0ms (0.9%)

prune144.0ms (3%)

localize7.0ms (0.1%)

series23.0ms (0.5%)

rewrite65.0ms (1.3%)

simplify43.0ms (0.9%)

prune164.0ms (3.4%)

localize13.0ms (0.3%)

series254.0ms (5.2%)

rewrite53.0ms (1.1%)

simplify52.0ms (1.1%)

prune99.0ms (2%)

localize14.0ms (0.3%)

series263.0ms (5.4%)

rewrite40.0ms (0.8%)

simplify36.0ms (0.7%)

prune191.0ms (3.9%)

regimes434.0ms (8.9%)

simplify2.0ms (0%)

end95.0ms (1.9%)

Profiling

Iter	Nodes	Cost
0	9	14
1	18	14
2	38	14
3	67	14
4	118	14
5	183	14
6	324	14
7	531	14
8	681	14
9	846	14
10	950	14
11	960	14