Details

analyze220.0ms (4.9%)

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
25%	68.7%	6.3%	5
25%	65.6%	9.5%	6
37.5%	39%	23.5%	7
37.5%	36.7%	25.9%	8
43.7%	20.7%	35.6%	9
43.7%	19.3%	37%	10
46.8%	10.6%	42.5%	11
46.8%	9.9%	43.3%	12
48.4%	5.4%	46.2%	13
48.4%	5%	46.6%	14

Compiler

Compiled 19 to 17 computations (10.5% saved)

sample1.4s (32.3%)

Results

1.3s	8256×	body	128	valid
74.0ms	522×	body	128	invalid

Compiler

Compiled 56 to 50 computations (10.7% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

16×	`fma-def_binary64`
7×	`sub-neg_binary64`
6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`div-sub_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	26	23
2	40	21
3	49	21
4	56	21
5	63	21
6	74	21
7	73	21
8	62	21

prune3.0ms (0.1%)

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

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

Compiler

Compiled 61 to 49 computations (19.7% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
✓	1.0b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
✓	1.0b	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

series34.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

21.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
7.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
6.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

rewrite63.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

532×	`log-prod_binary64`
216×	`expm1-udef_binary64`
216×	`log1p-udef_binary64`
201×	`prod-diff_binary64`
183×	`log-pow_binary64`

Counts

3 → 85

Calls

3 calls:

61.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
61.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
61.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	45
1	261	39
2	2885	39
3	5140	39

simplify61.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

18×	`fma-def_binary64`
8×	`sub-neg_binary64`
5×	`+-commutative_binary64`
5×	`*-commutative_binary64`
4×	`fma-neg_binary64`

Counts

157 → 91

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	1080
1	22	1080
2	31	1080
3	37	1080
4	43	1080
5	49	1080
6	54	1080
7	59	1080
8	67	1080
9	64	1080
10	55	1080

prune50.0ms (1.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	3	92

Error

0.0b

Counts

92 → 3

Alt Table

Status	Error	Program
	2.1b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))) (.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (/.f64 (acos.f64 (/.f64 g h)) 3)))))
▶	1.1b	(.f64 2 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3))))) (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3))))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3))))))))
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

Compiler

Compiled 1854 to 1197 computations (35.4% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3))
✓	0.0b	(cbrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3)))))
✓	1.0b	(/.f64 (acos.f64 (/.f64 g h)) 3)
✓	1.0b	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3)))

series780.0ms (17.4%)

Counts

4 → 96

Calls

4 calls:

748.0ms	(cbrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3)))))
20.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3)))
7.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3))
5.0ms	(/.f64 (acos.f64 (/.f64 g h)) 3)

rewrite73.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

591×	`log-prod_binary64`
240×	`expm1-udef_binary64`
240×	`log1p-udef_binary64`
212×	`log-pow_binary64`
176×	`prod-diff_binary64`

Counts

4 → 117

Calls

4 calls:

70.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3))
70.0ms	(cbrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3)))))
70.0ms	(/.f64 (acos.f64 (/.f64 g h)) 3)
70.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	59
1	268	59
2	3150	59
3	5658	59

simplify312.0ms (7%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-def_binary64`
473×	`sqr-pow_binary64`
434×	`unswap-sqr_binary64`
301×	`*-commutative_binary64`
299×	`pow-sqr_binary64`

Counts

213 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	14	1440
1	21	1440
2	30	1416
3	40	1416
4	63	1416
5	110	1416
6	216	1416
7	532	1416
8	1272	1416
9	1799	1416
10	2077	1416
11	2413	1416
12	2992	1416
13	4976	1416
14	4686	1416

prune465.0ms (10.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	369	0	369
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	369	3	372

Error

0.0b

Counts

372 → 3

Alt Table

Status	Error	Program
▶	2.1b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))) (.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (/.f64 (acos.f64 (/.f64 g h)) 3)))))
✓	1.1b	(.f64 2 (+.f64 (log.f64 (.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3))))) (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3))))))) (log.f64 (cbrt.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 g h)) 3))))))))
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

Compiler

Compiled 18203 to 11917 computations (34.5% saved)

localize18.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(/.f64 (acos.f64 (/.f64 g h)) 3)
✓	1.0b	(sin.f64 (*.f64 (PI.f64) 2/3))
✓	1.0b	(*.f64 (PI.f64) 2/3)
✓	1.6b	(cos.f64 (*.f64 (PI.f64) 2/3))

series0.0ms (0%)

Counts

3 → 0

Calls

3 calls:

0.0ms	(cos.f64 (*.f64 (PI.f64) 2/3))
0.0ms	(sin.f64 (*.f64 (PI.f64) 2/3))
0.0ms	(*.f64 (PI.f64) 2/3)

rewrite83.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

866×	`prod-diff_binary64`
486×	`log1p-expm1-u_binary64`
486×	`expm1-log1p-u_binary64`
287×	`unpow-prod-down_binary64`
257×	`log-prod_binary64`

Counts

3 → 76

Calls

3 calls:

82.0ms	(sin.f64 (*.f64 (PI.f64) 2/3))
82.0ms	(*.f64 (PI.f64) 2/3)
82.0ms	(cos.f64 (*.f64 (PI.f64) 2/3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	19
1	118	19
2	1281	19
3	4876	19
4	6127	19

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune114.0ms (2.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	152	2	154

Error

0.0b

Counts

154 → 2

Alt Table

Status	Error	Program
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
▶	1.1b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))) (.f64 (log1p.f64 (expm1.f64 (sin.f64 (*.f64 (PI.f64) 2/3)))) (sin.f64 (/.f64 (acos.f64 (/.f64 g h)) 3)))))

Status

Error

Program

✓

1.0b

(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

▶

1.1b

(*.f64 2 (-.f64 (*.f64 (cos.f64 (*.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))) (*.f64 (log1p.f64 (expm1.f64 (sin.f64 (*.f64 (PI.f64) 2/3)))) (sin.f64 (/.f64 (acos.f64 (/.f64 g h)) 3)))))

Compiler

Compiled 4967 to 3300 computations (33.6% saved)

localize20.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(sin.f64 (*.f64 (PI.f64) 2/3))
	1.0b	(*.f64 (PI.f64) 2/3)
✓	1.0b	(expm1.f64 (sin.f64 (*.f64 (PI.f64) 2/3)))
	1.6b	(cos.f64 (*.f64 (PI.f64) 2/3))

series0.0ms (0%)

Counts

1 → 0

Calls

1 calls:

0.0ms

(expm1.f64 (sin.f64 (*.f64 (PI.f64) 2/3)))

rewrite73.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

684×	`prod-diff_binary64`
476×	`log1p-expm1-u_binary64`
476×	`expm1-log1p-u_binary64`
286×	`unpow-prod-down_binary64`
251×	`log-prod_binary64`

Counts

1 → 33

Calls

1 calls:

72.0ms

(expm1.f64 (sin.f64 (*.f64 (PI.f64) 2/3)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	9
1	116	9
2	1254	9
3	4914	9
4	5851	9

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune120.0ms (2.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	126	2	128

Error

0.0b

Counts

128 → 2

Alt Table

Status	Error	Program
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
✓	1.1b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))) (.f64 (log1p.f64 (expm1.f64 (sin.f64 (*.f64 (PI.f64) 2/3)))) (sin.f64 (/.f64 (acos.f64 (/.f64 g h)) 3)))))

Status

Error

Program

✓

1.0b

(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

✓

1.1b

(*.f64 2 (-.f64 (*.f64 (cos.f64 (*.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))) (*.f64 (log1p.f64 (expm1.f64 (sin.f64 (*.f64 (PI.f64) 2/3)))) (sin.f64 (/.f64 (acos.f64 (/.f64 g h)) 3)))))

Compiler

Compiled 4497 to 3181 computations (29.3% saved)

regimes402.0ms (9%)

Accuracy

Total 1.0b remaining (96.8%)

Threshold costs 1.0b (96.8%)

Counts

38 → 1

Compiler

Compiled 10521 to 8133 computations (22.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	21
1	21	21
2	25	21
3	28	21
4	29	21
5	29	21

end85.0ms (1.9%)

Compiler: Compiled 76 to 63 computations (17.1% saved)

Details

analyze220.0ms (4.9%)

sample1.4s (32.3%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series34.0ms (0.8%)

rewrite63.0ms (1.4%)

simplify61.0ms (1.4%)

prune50.0ms (1.1%)

localize17.0ms (0.4%)

series780.0ms (17.4%)

rewrite73.0ms (1.6%)

simplify312.0ms (7%)

prune465.0ms (10.4%)

localize18.0ms (0.4%)

series0.0ms (0%)

rewrite83.0ms (1.9%)

simplify8.0ms (0.2%)

prune114.0ms (2.5%)

localize20.0ms (0.5%)

series0.0ms (0%)

rewrite73.0ms (1.6%)

simplify7.0ms (0.1%)

prune120.0ms (2.7%)

regimes402.0ms (9%)

simplify5.0ms (0.1%)

end85.0ms (1.9%)

Profiling