Details

analyze228.0ms (6%)

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)

sample1.6s (42.6%)

Results

1.5s	8256×	body	128	valid
91.0ms	522×	body	128	invalid

Compiler

Compiled 56 to 50 computations (10.7% saved)

prune2.0ms (0.1%)

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

1.0b

Counts

2 → 1

Alt Table

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

Compiler

Compiled 54 to 48 computations (11.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series38.0ms (1%)

Counts

4 → 72

Calls

4 calls:

24.0ms	(cos.f64 (+.f64 (/.f64 (*.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
8.0ms	(+.f64 (/.f64 (*.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
6.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
0.0ms	(/.f64 (*.f64 2 (PI.f64)) 3)

rewrite85.0ms (2.2%)

Algorithm

1×	batch-egg-rewrite

Rules

283×	`expm1-udef_binary64`
283×	`log1p-udef_binary64`
168×	`add-sqr-sqrt_binary64`
160×	`log1p-expm1-u_binary64`
160×	`expm1-log1p-u_binary64`

Counts

4 → 145

Calls

4 calls:

82.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
82.0ms	(+.f64 (/.f64 (*.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
82.0ms	(cos.f64 (+.f64 (/.f64 (*.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
82.0ms	(/.f64 (*.f64 2 (PI.f64)) 3)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	63
1	326	44
2	4169	44
3	4861	44

prune194.0ms (5.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	215	3	218

Error

1.0b

Counts

218 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 2 (cos.f64 (+.f64 (/.f64 (.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
	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)))))
▶	1.0b	(.f64 2 (cos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) 2/3) 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

Compiler

Compiled 4259 to 2909 computations (31.7% saved)

localize14.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series45.0ms (1.2%)

Counts

4 → 48

Calls

4 calls:

30.0ms	(cos.f64 (+.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) 2/3) 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
14.0ms	(+.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) 2/3) 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
0.0ms	(pow.f64 (*.f64 (PI.f64) 2/3) 3)
0.0ms	(*.f64 (PI.f64) 2/3)

rewrite76.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

382×	`fma-def_binary64`
269×	`expm1-udef_binary64`
269×	`log1p-udef_binary64`
220×	`fma-neg_binary64`
162×	`add-sqr-sqrt_binary64`

Counts

4 → 135

Calls

4 calls:

72.0ms	(cos.f64 (+.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) 2/3) 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
72.0ms	(+.f64 (cbrt.f64 (pow.f64 (*.f64 (PI.f64) 2/3) 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
72.0ms	(*.f64 (PI.f64) 2/3)
72.0ms	(pow.f64 (*.f64 (PI.f64) 2/3) 3)

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	51
1	323	43
2	3806	43
3	5023	43

prune197.0ms (5.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	183	3	186

Error

1.0b

Counts

186 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 2 (cos.f64 (+.f64 (/.f64 (.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
▶	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)))))
✓	1.0b	(.f64 2 (cos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) 2/3) 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

Compiler

Compiled 4062 to 2741 computations (32.5% saved)

localize17.0ms (0.5%)

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))

series5.0ms (0.1%)

Counts

4 → 24

Calls

4 calls:

5.0ms	(/.f64 (acos.f64 (/.f64 g h)) 3)
0.0ms	(cos.f64 (*.f64 (PI.f64) 2/3))
0.0ms	(*.f64 (PI.f64) 2/3)
0.0ms	(sin.f64 (*.f64 (PI.f64) 2/3))

rewrite63.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

575×	`log-prod_binary64`
230×	`expm1-udef_binary64`
230×	`log1p-udef_binary64`
199×	`log-pow_binary64`
181×	`prod-diff_binary64`

Counts

4 → 89

Calls

4 calls:

61.0ms	(/.f64 (acos.f64 (/.f64 g h)) 3)
61.0ms	(sin.f64 (*.f64 (PI.f64) 2/3))
61.0ms	(*.f64 (PI.f64) 2/3)
61.0ms	(cos.f64 (*.f64 (PI.f64) 2/3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	28
1	254	28
2	3002	28
3	5317	28

prune159.0ms (4.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	182	3	185

Error

0.0b

Counts

185 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 2 (cos.f64 (+.f64 (/.f64 (.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
✓	1.0b	(.f64 2 (cos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) 2/3) 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 5633 to 3667 computations (34.9% saved)

localize19.0ms (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

4 → 0

Calls

4 calls:

0.0ms	(cos.f64 (*.f64 (PI.f64) 2/3))
0.0ms	(expm1.f64 (sin.f64 (*.f64 (PI.f64) 2/3)))
0.0ms	(sin.f64 (*.f64 (PI.f64) 2/3))
0.0ms	(*.f64 (PI.f64) 2/3)

rewrite77.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

555×	`log1p-expm1-u_binary64`
555×	`expm1-log1p-u_binary64`
295×	`log-prod_binary64`
171×	`prod-diff_binary64`
170×	`pow2_binary64`

Counts

4 → 87

Calls

4 calls:

75.0ms	(sin.f64 (*.f64 (PI.f64) 2/3))
75.0ms	(*.f64 (PI.f64) 2/3)
75.0ms	(expm1.f64 (sin.f64 (*.f64 (PI.f64) 2/3)))
75.0ms	(cos.f64 (*.f64 (PI.f64) 2/3))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	28
1	135	28
2	1465	28
3	4948	28
4	5002	28

prune98.0ms (2.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	103	3	106

Error

0.0b

Counts

106 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 2 (cos.f64 (+.f64 (/.f64 (.f64 2 (PI.f64)) 3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
✓	1.0b	(.f64 2 (cos.f64 (+.f64 (cbrt.f64 (pow.f64 (.f64 (PI.f64) 2/3) 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 3585 to 2518 computations (29.8% saved)

regimes772.0ms (20.2%)

Accuracy

Total 1.0b remaining (97%)

Threshold costs 1.0b (97%)

Counts

92 → 1

Compiler

Compiled 17793 to 14658 computations (17.6% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-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	15	23
1	24	23
2	28	23
3	31	23
4	32	23
5	32	23

end87.0ms (2.3%)

Compiler: Compiled 100 to 85 computations (15% saved)

Details

analyze228.0ms (6%)

sample1.6s (42.6%)

prune2.0ms (0.1%)

localize13.0ms (0.3%)

series38.0ms (1%)

rewrite85.0ms (2.2%)

prune194.0ms (5.1%)

localize14.0ms (0.4%)

series45.0ms (1.2%)

rewrite76.0ms (2%)

prune197.0ms (5.1%)

localize17.0ms (0.5%)

series5.0ms (0.1%)

rewrite63.0ms (1.6%)

prune159.0ms (4.2%)

localize19.0ms (0.5%)

series0.0ms (0%)

rewrite77.0ms (2%)

prune98.0ms (2.6%)

regimes772.0ms (20.2%)

simplify2.0ms (0.1%)

end87.0ms (2.3%)

Profiling