Details

analyze238.0ms (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 (33%)

Results

1.5s	8256×	body	128	valid
90.0ms	572×	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	(cos.f64 (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)

series37.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

22.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
9.0ms	(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)

rewrite7.0ms (0.1%)

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))

simplify129.0ms (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

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

prune98.0ms (2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	1	98

Error

1.0b

Counts

98 → 1

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))))))

Compiler

Compiled 2027 to 1135 computations (44% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(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 (/.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))

series438.0ms (9%)

Counts

4 → 72

Calls

4 calls:

294.0ms	(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)))))
75.0ms	(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)))
0.0ms	(/.f64 1 (sqrt.f64 3))

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

91×	`add-sqr-sqrt_binary64`
76×	`times-frac_binary64`
51×	`*-un-lft-identity_binary64`
45×	`add-cube-cbrt_binary64`
41×	`sqrt-prod_binary64`

Counts

4 → 152

Calls

4 calls:

16.0ms	(*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3)))
3.0ms	(/.f64 1 (sqrt.f64 3))
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)))))
0.0ms	(fma.f64 (PI.f64) 2/3 (*.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))

simplify226.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

625×	`fma-neg_binary64`
551×	`fma-def_binary64`
469×	`times-frac_binary64`
379×	`associate-/l*_binary64`
296×	`*-commutative_binary64`

Counts

224 → 206

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	4593
1	330	3862
2	933	3699
3	2132	3651
4	2660	3651
5	4263	3651
6	4937	3651
7	5174	3651

prune224.0ms (4.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	205	1	206
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	205	2	207

Error

1.0b

Counts

207 → 2

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

Compiler

Compiled 5584 to 3882 computations (30.5% 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))

rewrite7.0ms (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))

simplify89.0ms (1.8%)

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

prune166.0ms (3.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	161	1	162
Fresh	0	0	0
Picked	1	0	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 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))) (.f64 (sin.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) 2/3)))) (sin.f64 (*.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 (/.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 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))) (*.f64 (sin.f64 (expm1.f64 (log1p.f64 (*.f64 (PI.f64) 2/3)))) (sin.f64 (*.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 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))))

Compiler

Compiled 7577 to 5553 computations (26.7% saved)

localize29.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(/.f64 1 (sqrt.f64 3))
	1.0b	(*.f64 (PI.f64) 2/3)
✓	1.0b	(sin.f64 (expm1.f64 (log1p.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

(sin.f64 (expm1.f64 (log1p.f64 (*.f64 (PI.f64) 2/3))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

1.0ms

(sin.f64 (expm1.f64 (log1p.f64 (*.f64 (PI.f64) 2/3))))

simplify150.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

1333×	`sqr-pow_binary64`
715×	`pow-sqr_binary64`
529×	`cube-prod_binary64`
481×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

10 → 17

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	140
1	30	125
2	32	125
3	37	125
4	42	125
5	51	125
6	71	125
7	124	125
8	299	125
9	604	125
10	608	125
11	738	125
12	892	125
13	1060	125
14	1289	125
15	1590	125
16	1938	125
17	2413	125
18	3031	125
19	3227	125
20	3401	125
21	3515	125
22	3562	125
23	3614	125
24	4492	125
25	4797	125

prune238.0ms (4.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	169	0	169
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	169	2	171

Error

Counts

171 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 (PI.f64) 2/3)) (cos.f64 (.f64 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))) (.f64 (sin.f64 (expm1.f64 (log1p.f64 (.f64 (PI.f64) 2/3)))) (sin.f64 (*.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 (/.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 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))) (*.f64 (sin.f64 (expm1.f64 (log1p.f64 (*.f64 (PI.f64) 2/3)))) (sin.f64 (*.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 (/.f64 1 (sqrt.f64 3)) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) (sqrt.f64 3))))))

Compiler

Compiled 8194 to 6090 computations (25.7% saved)

regimes975.0ms (20%)

Accuracy

Total 0.0b remaining (72.7%)

Threshold costs 0.0b (72.7%)

Counts

93 → 1

Compiler

Compiled 21095 to 17533 computations (16.9% 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	28	71
1	46	71
2	58	71
3	67	71
4	72	71
5	73	71
6	72	71

end102.0ms (2.1%)

Compiler: Compiled 154 to 128 computations (16.9% saved)

Details

analyze238.0ms (4.9%)

sample1.6s (33%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series37.0ms (0.8%)

rewrite7.0ms (0.1%)

simplify129.0ms (2.6%)

prune98.0ms (2%)

localize13.0ms (0.3%)

series438.0ms (9%)

rewrite34.0ms (0.7%)

simplify226.0ms (4.6%)

prune224.0ms (4.6%)

localize28.0ms (0.6%)

series0.0ms (0%)

rewrite7.0ms (0.1%)

simplify89.0ms (1.8%)

prune166.0ms (3.4%)

localize29.0ms (0.6%)

series0.0ms (0%)

rewrite1.0ms (0%)

simplify150.0ms (3.1%)

prune238.0ms (4.9%)

regimes975.0ms (20%)

simplify5.0ms (0.1%)

end102.0ms (2.1%)

Profiling