Details

analyze229.0ms (5.2%)

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)

sample1.5s (32.7%)

Results

1.3s	8256×	body	128	valid
80.0ms	537×	body	128	invalid

Compiler

Compiled 56 to 50 computations (10.7% saved)

simplify25.0ms (0.6%)

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)

localize10.0ms (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)))

series36.0ms (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)))
8.0ms	(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))

simplify127.0ms (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

prune96.0ms (2.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	95	3	98

Error

1.0b

Counts

98 → 3

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

Compiler

Compiled 2096 to 1186 computations (43.4% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(expm1.f64 (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)
	1.0b	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
✓	1.0b	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

series51.0ms (1.2%)

Counts

2 → 48

Calls

2 calls:

29.0ms	(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
22.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`log1p-expm1-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
0.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

simplify272.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

1392×	`sqr-pow_binary64`
724×	`unswap-sqr_binary64`
592×	`cube-prod_binary64`
500×	`fabs-mul_binary64`
470×	`pow-sqr_binary64`

Counts

70 → 42

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	45	1455
1	59	1377
2	74	1377
3	87	1377
4	100	1377
5	122	1377
6	170	1377
7	270	1377
8	614	1377
9	1210	1377
10	1349	1377
11	1612	1377
12	1917	1377
13	2211	1377
14	2613	1377
15	2967	1377
16	3150	1377
17	3407	1377
18	3546	1377
19	3625	1377
20	3705	1377
21	4463	1377
22	4855	1377

prune129.0ms (2.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	119	3	122

Error

1.0b

Counts

122 → 3

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

Compiler

Compiled 2747 to 1661 computations (39.5% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(/.f64 (acos.f64 (/.f64 (neg.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)

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))

simplify91.0ms (2.1%)

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

prune131.0ms (3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	0	0	0
Picked	1	0	1
Done	1	1	2
Total	178	3	181

Error

Counts

181 → 3

Alt Table

Status	Error	Program
	1.5b	(.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 (.f64 (cbrt.f64 (acos.f64 (/.f64 (neg.f64 g) h))) (cbrt.f64 (acos.f64 (/.f64 (neg.f64 g) h)))) (/.f64 3 (cbrt.f64 (acos.f64 (neg.f64 (/.f64 g h))))))))))
▶	0.0b	(.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 (expm1.f64 (log1p.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 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

Compiler

Compiled 6485 to 3805 computations (41.3% saved)

localize20.0ms (0.5%)

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 (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))))

rewrite2.0ms (0.1%)

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:

2.0ms

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

simplify132.0ms (3%)

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

prune187.0ms (4.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	184	1	185
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	186	2	188

Error

Counts

188 → 2

Alt Table

Status	Error	Program
	0.0b	(.f64 2 (-.f64 (.f64 (log.f64 (exp.f64 (cos.f64 (.f64 (PI.f64) 2/3)))) (cos.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (.f64 (sin.f64 (expm1.f64 (log1p.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 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))

Status

Error

Program

0.0b

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

Compiler

Compiled 6972 to 4244 computations (39.1% saved)

regimes1.3s (29.5%)

Accuracy

Total 0.0b remaining (54.8%)

Threshold costs 0.0b (54.8%)

Counts

56 → 1

Compiler

Compiled 14715 to 11913 computations (19% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

9×	`*-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	24	57
1	39	57
2	51	57
3	60	57
4	65	57
5	66	57
6	66	57

end80.0ms (1.8%)

Compiler: Compiled 120 to 94 computations (21.7% saved)

Details

analyze229.0ms (5.2%)

sample1.5s (32.7%)

simplify25.0ms (0.6%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

series36.0ms (0.8%)

rewrite7.0ms (0.1%)

simplify127.0ms (2.9%)

prune96.0ms (2.2%)

localize14.0ms (0.3%)

series51.0ms (1.2%)

rewrite2.0ms (0%)

simplify272.0ms (6.1%)

prune129.0ms (2.9%)

localize17.0ms (0.4%)

series0.0ms (0%)

rewrite6.0ms (0.1%)

simplify91.0ms (2.1%)

prune131.0ms (3%)

localize20.0ms (0.5%)

series0.0ms (0%)

rewrite2.0ms (0.1%)

simplify132.0ms (3%)

prune187.0ms (4.2%)

regimes1.3s (29.5%)

simplify4.0ms (0.1%)

end80.0ms (1.8%)

Profiling