Details

analyze225.0ms (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)

sample1.6s (34.4%)

Results

1.4s	8256×	body	128	valid
85.0ms	544×	body	128	invalid

Compiler

Compiled 56 to 50 computations (10.7% saved)

simplify8.0ms (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))
✓	0.9b	(/.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)))

series38.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

23.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
8.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
7.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
5×	`add-cbrt-cube_binary64`

Counts

3 → 51

Calls

3 calls:

2.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
1.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
0.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))

simplify134.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

516×	`distribute-rgt-in_binary64`
515×	`fma-neg_binary64`
508×	`associate-/l/_binary64`
495×	`distribute-lft-in_binary64`
420×	`distribute-rgt-out_binary64`

Counts

123 → 97

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	105	2186
1	150	2070
2	246	2070
3	411	2070
4	874	2070
5	2199	2070
6	4684	2070
7	5109	2070

prune145.0ms (3.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	92	5	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	5	98

Error

0.9b

Counts

98 → 5

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (.f64 (*.f64 (cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)) (cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cbrt.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.0b	(*.f64 2 (log.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
▶	1.0b	(.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))))

Compiler

Compiled 2225 to 1285 computations (42.2% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))
✓	0.9b	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
✓	1.0b	(cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))
✓	1.0b	(/.f64 1 (sqrt.f64 3))

series183.0ms (3.9%)

Counts

4 → 72

Calls

4 calls:

97.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))
69.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
16.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))
0.0ms	(/.f64 1 (sqrt.f64 3))

rewrite39.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`add-sqr-sqrt_binary64`
94×	`times-frac_binary64`
66×	`*-un-lft-identity_binary64`
60×	`add-cube-cbrt_binary64`
53×	`sqrt-prod_binary64`

Counts

4 → 185

Calls

4 calls:

17.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
3.0ms	(/.f64 1 (sqrt.f64 3))
3.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))
1.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))

simplify220.0ms (4.8%)

Algorithm

1×	egg-herbie

Rules

794×	`fma-def_binary64`
500×	`times-frac_binary64`
416×	`associate-/l*_binary64`
322×	`*-commutative_binary64`
314×	`fma-neg_binary64`

Counts

257 → 252

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	179	5264
1	352	4590
2	993	4409
3	2295	4361
4	2691	4361
5	3479	4361
6	4441	4361
7	4886	4361

prune360.0ms (7.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	253	4	257

Error

0.9b

Counts

257 → 4

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))
▶	1.0b	(.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))))
	1.0b	(*.f64 2 (log.f64 (exp.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.0b	(*.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 7035 to 4810 computations (31.6% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))
✓	0.9b	(*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
✓	1.0b	(cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))
	1.0b	(/.f64 1 (sqrt.f64 3))

series157.0ms (3.4%)

Counts

2 → 48

Calls

2 calls:

94.0ms

(cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))

63.0ms

(*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))

rewrite43.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`times-frac_binary64`
37×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
26×	`associate-l_binary64`

Counts

2 → 77

Calls

2 calls:

34.0ms

(*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))

1.0ms

(cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))

simplify166.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

713×	`fma-neg_binary64`
481×	`fma-def_binary64`
266×	`associate-/l*_binary64`
261×	`associate-*l/_binary64`
250×	`*-commutative_binary64`

Counts

125 → 122

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	142	2824
1	265	2494
2	740	2270
3	1700	2221
4	1992	2221
5	3143	2221
6	4232	2221
7	4891	2221
8	4903	2221

prune174.0ms (3.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	240	2	242

Error

Counts

242 → 2

Alt Table

Status	Error	Program
▶	0.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))) (.f64 (sin.f64 (.f64 (PI.f64) 2/3)) (sin.f64 (*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))))
✓	1.0b	(.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))))

Status

Error

Program

▶

0.0b

(*.f64 2 (-.f64 (*.f64 (cos.f64 (*.f64 (PI.f64) 2/3)) (cos.f64 (*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))) (*.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))))

✓

1.0b

(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))))

Compiler

Compiled 6966 to 4896 computations (29.7% saved)

localize28.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(sin.f64 (*.f64 (PI.f64) 2/3))
	1.0b	(/.f64 1 (sqrt.f64 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	(*.f64 (PI.f64) 2/3)
0.0ms	(sin.f64 (*.f64 (PI.f64) 2/3))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 38

Calls

3 calls:

3.0ms	(*.f64 (PI.f64) 2/3)
1.0ms	(sin.f64 (*.f64 (PI.f64) 2/3))
1.0ms	(cos.f64 (*.f64 (PI.f64) 2/3))

simplify87.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

603×	`unswap-sqr_binary64`
428×	`associate-*l/_binary64`
378×	`associate-*r/_binary64`
293×	`log-div_binary64`
277×	`*-commutative_binary64`

Counts

38 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	55	383
1	83	337
2	169	337
3	229	337
4	293	337
5	442	337
6	806	337
7	1343	337
8	3492	337
9	4632	337
10	4833	337
11	4757	337

prune267.0ms (5.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	162	0	162
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	162	2	164

Error

Counts

164 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))) (.f64 (sin.f64 (.f64 (PI.f64) 2/3)) (sin.f64 (*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))))
✓	1.0b	(.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))))

Status

Error

Program

✓

0.0b

(*.f64 2 (-.f64 (*.f64 (cos.f64 (*.f64 (PI.f64) 2/3)) (cos.f64 (*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))) (*.f64 (sin.f64 (*.f64 (PI.f64) 2/3)) (sin.f64 (*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))))))

✓

1.0b

(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (*.f64 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))))

Compiler

Compiled 8184 to 6168 computations (24.6% saved)

regimes591.0ms (12.8%)

Accuracy

Total 0.0b remaining (61.6%)

Threshold costs 0.0b (61.6%)

Counts

49 → 1

Compiler

Compiled 9914 to 8428 computations (15% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
6×	`+-commutative_binary64`
6×	`sub-neg_binary64`
5×	`neg-sub0_binary64`
5×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	75
1	49	75
2	61	75
3	70	75
4	75	75
5	76	75
6	75	75

end106.0ms (2.3%)

Compiler: Compiled 162 to 136 computations (16% saved)

Details

analyze225.0ms (4.9%)

sample1.6s (34.4%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series38.0ms (0.8%)

rewrite8.0ms (0.2%)

simplify134.0ms (2.9%)

prune145.0ms (3.1%)

localize14.0ms (0.3%)

series183.0ms (3.9%)

rewrite39.0ms (0.8%)

simplify220.0ms (4.8%)

prune360.0ms (7.8%)

localize17.0ms (0.4%)

series157.0ms (3.4%)

rewrite43.0ms (0.9%)

simplify166.0ms (3.6%)

prune174.0ms (3.8%)

localize28.0ms (0.6%)

series0.0ms (0%)

rewrite6.0ms (0.1%)

simplify87.0ms (1.9%)

prune267.0ms (5.8%)

regimes591.0ms (12.8%)

simplify5.0ms (0.1%)

end106.0ms (2.3%)

Profiling