Details

analyze631.0ms (10.5%)

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
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
37.4%	62.4%	0.1%	8
37.4%	62.4%	0.1%	9
56.2%	43.7%	0.1%	10
65.5%	34.3%	0.1%	11
65.5%	34.3%	0.1%	12
76.5%	23.4%	0.1%	13
81.9%	17.9%	0.1%	14

Compiler

Compiled 13 to 9 computations (30.8% saved)

sample2.2s (37.3%)

Results

920.0ms	5926×	body	128	valid
906.0ms	1298×	body	1024	valid
279.0ms	701×	body	512	valid
90.0ms	326×	body	256	valid
8.0ms	5×	body	2048	valid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`fma-def_binary64`
5×	`+-commutative_binary64`
3×	`associate-+r+_binary64`
3×	`associate-+l+_binary64`
1×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	14	12
2	22	12
3	26	12
4	26	12

prune3.0ms (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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))

Compiler

Compiled 44 to 25 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series8.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

8.0ms

(*.f64 z (cos.f64 y))

rewrite74.0ms (1.2%)

Algorithm

2×	batch-egg-rewrite

Rules

782×	`log1p-udef_binary64`
422×	`log1p-expm1-u_binary64`
422×	`expm1-log1p-u_binary64`
288×	`unpow-prod-down_binary64`
242×	`log-prod_binary64`

Counts

1 → 22

Calls

1 calls:

73.0ms

(*.f64 z (cos.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	97	6
2	1114	6
3	4802	6
4	6294	6
0	0	0
1	0	0

simplify39.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

742×	`distribute-rgt-neg-in_binary64`
671×	`distribute-lft-neg-in_binary64`
484×	`associate-l_binary64`
435×	`distribute-rgt-out--_binary64`
420×	`associate-r_binary64`

Counts

46 → 30

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	190
1	67	189
2	185	181
3	572	175
4	2452	175
5	5173	175

prune18.0ms (0.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	28	2	30
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	28	3	31

Error

0.0b

Counts

31 → 3

Alt Table

Status	Error	Program
	24.5b	(+.f64 (+.f64 x (sin.f64 y)) (cbrt.f64 (pow.f64 (*.f64 z (cos.f64 y)) 3)))
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
▶	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3))

Compiler

Compiled 498 to 219 computations (56% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

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

series785.0ms (13.1%)

Counts

2 → 48

Calls

2 calls:

404.0ms	(cbrt.f64 (*.f64 z (cos.f64 y)))
381.0ms	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)

rewrite82.0ms (1.4%)

Algorithm

2×	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`

Counts

2 → 61

Calls

2 calls:

81.0ms	(cbrt.f64 (*.f64 z (cos.f64 y)))
81.0ms	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3)

Iterations

Useful iterations: 0 (0.0ms)

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

simplify61.0ms (1%)

Algorithm

1×	egg-herbie

Rules

511×	`fma-neg_binary64`
354×	`distribute-rgt-neg-in_binary64`
342×	`distribute-lft-neg-in_binary64`
226×	`unswap-sqr_binary64`
210×	`associate-r_binary64`

Counts

109 → 85

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	67	872
1	191	865
2	517	808
3	1804	464
4	4633	456
5	4939	456

prune135.0ms (2.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	112	3	115
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	113	5	118

Error

Counts

118 → 5

Alt Table

Status	Error	Program
	0.5b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 2))))
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
▶	0.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) z)))
	17.5b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (cbrt.f64 (.f64 z z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
✓	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3))

Compiler

Compiled 2089 to 887 computations (57.5% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(*.f64 (cbrt.f64 (cos.f64 y)) z)
✓	0.2b	(.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) z))
✓	0.2b	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
✓	0.3b	(cbrt.f64 (cos.f64 y))

series791.0ms (13.2%)

Counts

4 → 72

Calls

4 calls:

432.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) z)
207.0ms	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
141.0ms	(cbrt.f64 (cos.f64 y))
10.0ms	(.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) z))

rewrite81.0ms (1.4%)

Algorithm

2×	batch-egg-rewrite

Rules

708×	`log1p-expm1-u_binary64`
708×	`expm1-log1p-u_binary64`
147×	`expm1-udef_binary64`
147×	`log1p-udef_binary64`
85×	`add-sqr-sqrt_binary64`

Counts

4 → 76

Calls

4 calls:

80.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) z)
80.0ms	(.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) z))
80.0ms	(pow.f64 (cbrt.f64 (cos.f64 y)) 2)
80.0ms	(cbrt.f64 (cos.f64 y))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	178	27
2	1887	27
3	4965	27
4	4915	27
0	0	0
1	0	0

simplify83.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

736×	`distribute-rgt-neg-in_binary64`
634×	`fma-neg_binary64`
537×	`sub-neg_binary64`
399×	`neg-mul-1_binary64`
385×	`*-commutative_binary64`

Counts

148 → 104

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	64	628
1	187	621
2	541	604
3	1721	602
4	3700	602
5	4861	602
6	5026	602

prune116.0ms (1.9%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	135	5	140

Error

Counts

140 → 5

Alt Table

Status	Error	Program
▶	0.5b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 2))))
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
✓	0.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) z)))
	17.5b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (cbrt.f64 (.f64 z z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
✓	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3))

Compiler

Compiled 2759 to 1147 computations (58.4% saved)

localize14.0ms (0.2%)

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 z (cos.f64 y))) 2)
	0.6b	(cbrt.f64 (*.f64 z (cos.f64 y)))
✓	0.6b	(cbrt.f64 z)

series416.0ms (7%)

Counts

2 → 36

Calls

2 calls:

382.0ms	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 2)
34.0ms	(cbrt.f64 z)

rewrite47.0ms (0.8%)

Algorithm

2×	batch-egg-rewrite

Rules

668×	`log1p-expm1-u_binary64`
668×	`expm1-log1p-u_binary64`
367×	`log-prod_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`

Counts

2 → 50

Calls

2 calls:

46.0ms	(pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 2)
46.0ms	(cbrt.f64 z)

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	14
1	174	14
2	1785	14
3	5274	14
0	0	0
1	0	0

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

679×	`fma-def_binary64`
580×	`cancel-sign-sub-inv_binary64`
405×	`unswap-sqr_binary64`
316×	`fma-neg_binary64`
263×	`distribute-rgt-neg-in_binary64`

Counts

86 → 65

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	57	556
1	164	544
2	401	493
3	1451	431
4	4260	427
5	4718	403
6	4970	403
7	4911	403

prune106.0ms (1.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	134	0	134
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	134	5	139

Error

Counts

139 → 5

Alt Table

Status	Error	Program
✓	0.5b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (cbrt.f64 z) (.f64 (cbrt.f64 (cos.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 2))))
✓	0.0b	(+.f64 (+.f64 x (sin.f64 y)) (*.f64 z (cos.f64 y)))
✓	0.2b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (pow.f64 (cbrt.f64 (cos.f64 y)) 2) (.f64 (cbrt.f64 (cos.f64 y)) z)))
	17.5b	(+.f64 (+.f64 x (sin.f64 y)) (.f64 (cbrt.f64 (.f64 z z)) (*.f64 (cbrt.f64 z) (cos.f64 y))))
✓	0.6b	(+.f64 (+.f64 x (sin.f64 y)) (pow.f64 (cbrt.f64 (*.f64 z (cos.f64 y))) 3))

Compiler

Compiled 3368 to 1325 computations (60.7% saved)

regimes52.0ms (0.9%)

Accuracy

Total 0.0b remaining (45.8%)

Threshold costs 0.0b (45.8%)

Counts

11 → 1

Compiler

Compiled 720 to 486 computations (32.5% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

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

end90.0ms (1.5%)

Compiler: Compiled 110 to 74 computations (32.7% saved)

Details

analyze631.0ms (10.5%)

sample2.2s (37.3%)

simplify6.0ms (0.1%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series8.0ms (0.1%)

rewrite74.0ms (1.2%)

simplify39.0ms (0.6%)

prune18.0ms (0.3%)

localize11.0ms (0.2%)

series785.0ms (13.1%)

rewrite82.0ms (1.4%)

simplify61.0ms (1%)

prune135.0ms (2.3%)

localize15.0ms (0.2%)

series791.0ms (13.2%)

rewrite81.0ms (1.4%)

simplify83.0ms (1.4%)

prune116.0ms (1.9%)

localize14.0ms (0.2%)

series416.0ms (7%)

rewrite47.0ms (0.8%)

simplify84.0ms (1.4%)

prune106.0ms (1.8%)

regimes52.0ms (0.9%)

simplify2.0ms (0%)

end90.0ms (1.5%)

Profiling