Details

analyze230.0ms (4.4%)

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)

sample37.0ms (0.7%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
2.0ms	19×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% 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 4 expressions with local error:

New	Error	Program
✓	0.0b	(acos.f64 (/.f64 (neg.f64 g) h))
✓	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)))

series39.0ms (0.7%)

Counts

4 → 96

Calls

4 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))
5.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
3.0ms	(acos.f64 (/.f64 (neg.f64 g) h))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 62

Calls

4 calls:

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

simplify136.0ms (2.6%)

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

158 → 118

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	108	2519
1	152	2386
2	248	2386
3	413	2386
4	876	2386
5	2201	2386
6	4686	2386
7	5111	2386

prune180.0ms (3.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	112	6	118
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	113	6	119

Error

0.9b

Counts

119 → 6

Alt Table

Status	Error	Program
▶	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))))))
	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 (sqrt.f64 (acos.f64 (/.f64 (neg.f64 g) h))) (sqrt.f64 3)) (/.f64 (sqrt.f64 (acos.f64 (/.f64 (neg.f64 g) h))) (sqrt.f64 3))))))
	1.0b	(.f64 2 (.f64 (*.f64 (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.5b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 2706 to 1540 computations (43.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))
✓	1.0b	(*.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))

series179.0ms (3.4%)

Counts

4 → 72

Calls

4 calls:

98.0ms	(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)))))
66.0ms	(*.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))

rewrite38.0ms (0.7%)

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:

14.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
4.0ms	(/.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)))))

simplify221.0ms (4.2%)

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

prune391.0ms (7.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	251	1	252
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	253	5	258

Error

0.9b

Counts

258 → 5

Alt Table

Status	Error	Program
	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 (log.f64 (exp.f64 (/.f64 1 (sqrt.f64 3)))) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))))
	1.0b	(.f64 2 (.f64 (*.f64 (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))) (cbrt.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	1.5b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (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)))))

Compiler

Compiled 7165 to 4888 computations (31.8% saved)

localize16.0ms (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))
✓	1.0b	(*.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))

series165.0ms (3.1%)

Counts

2 → 48

Calls

2 calls:

99.0ms

(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)))))

66.0ms

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

rewrite26.0ms (0.5%)

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:

17.0ms

(*.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)))))

simplify164.0ms (3.1%)

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

prune163.0ms (3.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	237	1	238
Fresh	4	0	4
Picked	0	1	1
Done	0	0	0
Total	241	2	243

Error

0.0b

Counts

243 → 2

Alt Table

Status	Error	Program
✓	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))))))
▶	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)))))))

Status

Error

Program

✓

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))))))

▶

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)))))))

Compiler

Compiled 6966 to 4896 computations (29.7% saved)

localize24.0ms (0.4%)

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	(sin.f64 (*.f64 (PI.f64) 2/3))
0.0ms	(*.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	(cos.f64 (*.f64 (PI.f64) 2/3))
1.0ms	(sin.f64 (*.f64 (PI.f64) 2/3))

simplify83.0ms (1.6%)

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

prune275.0ms (5.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	160	2	162
Fresh	0	0	0
Picked	0	1	1
Done	1	0	1
Total	161	3	164

Error

Counts

164 → 3

Alt Table

Status	Error	Program
	0.0b	(.f64 2 (-.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cos.f64 (.f64 (PI.f64) 2/3))) (cbrt.f64 (cos.f64 (.f64 (PI.f64) 2/3)))) (cbrt.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)))))))
	0.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (.f64 (log.f64 (exp.f64 (cbrt.f64 (/.f64 1/3 (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)))))))
✓	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)))))))

Compiler

Compiled 8269 to 6237 computations (24.6% saved)

regimes1.0s (18.9%)

Accuracy

Total 0.0b remaining (75.8%)

Threshold costs 0.0b (75.8%)

Counts

110 → 1

Compiler

Compiled 24971 to 20995 computations (15.9% 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	29	101
1	47	101
2	59	101
3	68	101
4	73	101
5	74	101
6	73	101

end1.0ms (0%)

Compiler: Compiled 60 to 50 computations (16.7% saved)

sample1.9s (35.2%)

Algorithm

1×

intervals

Results

1.1s	8000×	body	128	valid
64.0ms	553×	body	128	nan

Compiler

Compiled 236 to 198 computations (16.1% saved)

Details

analyze230.0ms (4.4%)

sample37.0ms (0.7%)

simplify8.0ms (0.2%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series39.0ms (0.7%)

rewrite8.0ms (0.1%)

simplify136.0ms (2.6%)

prune180.0ms (3.4%)

localize13.0ms (0.2%)

series179.0ms (3.4%)

rewrite38.0ms (0.7%)

simplify221.0ms (4.2%)

prune391.0ms (7.4%)

localize16.0ms (0.3%)

series165.0ms (3.1%)

rewrite26.0ms (0.5%)

simplify164.0ms (3.1%)

prune163.0ms (3.1%)

localize24.0ms (0.4%)

series0.0ms (0%)

rewrite6.0ms (0.1%)

simplify83.0ms (1.6%)

prune275.0ms (5.2%)

regimes1.0s (18.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.9s (35.2%)

Profiling