Details

analyze229.0ms (2.5%)

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)

sample39.0ms (0.4%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
2.0ms	19×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify12.0ms (0.1%)

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%)

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 (0.1%)

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)))

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:

3.0ms	(/.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))

series112.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

64.0ms	(cos.f64 (fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
29.0ms	(fma.f64 PI.f64 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
19.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

simplify146.0ms (1.6%)

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 → 239

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

prune91.0ms (1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	237	2	239
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	238	2	240

Error

1.0b

Counts

240 → 2

Alt Table

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

Status

Error

Program

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))))))

▶

1.0b

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

Compiler

Compiled 2073 to 1163 computations (43.9% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`log-prod_binary64`
6×	`cbrt-prod_binary64`

Counts

4 → 55

Calls

4 calls:

3.0ms	(cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))
2.0ms	(log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))))
1.0ms	(cos.f64 (fma.f64 PI.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))))))
0.0ms	(fma.f64 PI.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))

series6.3s (69.6%)

Counts

4 → 96

Calls

4 calls:

1.8s	(cos.f64 (fma.f64 PI.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))))))
1.8s	(fma.f64 PI.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))
1.8s	(log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))))
869.0ms	(cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))

simplify181.0ms (2%)

Algorithm

1×	egg-herbie

Rules

462×	`*-commutative_binary64`
422×	`log-prod_binary64`
389×	`unswap-sqr_binary64`
336×	`distribute-rgt-out_binary64`
323×	`distribute-rgt-in_binary64`

Counts

151 → 287

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	98	2531
1	113	2412
2	188	2412
3	442	2412
4	1935	2388
5	3027	2326
6	4715	2326
7	4971	2326
8	4763	2326

prune109.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	286	1	287
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	286	3	289

Error

1.0b

Counts

289 → 3

Alt Table

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

Compiler

Compiled 2034 to 964 computations (52.6% saved)

localize21.0ms (0.2%)

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	(*.f64 PI.f64 2/3)
✓	1.6b	(cos.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	(cos.f64 (*.f64 PI.f64 2/3))
1.0ms	(sin.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)

simplify93.0ms (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 → 46

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

prune48.0ms (0.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	0	1
Picked	1	0	1
Done	0	1	1
Total	73	2	75

Error

Counts

75 → 2

Alt Table

Status	Error	Program
▶	0.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 PI.f64 2/3)) (cos.f64 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))) (.f64 (log1p.f64 (expm1.f64 (sin.f64 (*.f64 PI.f64 2/3)))) (sin.f64 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))))))))
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))))

Status

Error

Program

▶

0.0b

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

✓

1.0b

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

Compiler

Compiled 2325 to 984 computations (57.7% saved)

localize24.0ms (0.3%)

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	(*.f64 PI.f64 2/3)
	1.6b	(cos.f64 (*.f64 PI.f64 2/3))

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune51.0ms (0.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

Counts

178 → 2

Alt Table

Status	Error	Program
✓	0.0b	(.f64 2 (-.f64 (.f64 (cos.f64 (.f64 PI.f64 2/3)) (cos.f64 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))) (.f64 (log1p.f64 (expm1.f64 (sin.f64 (*.f64 PI.f64 2/3)))) (sin.f64 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h))))))))))
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 PI.f64 2/3 (log.f64 (cbrt.f64 (exp.f64 (acos.f64 (neg.f64 (/.f64 g h)))))))))

Status

Error

Program

✓

0.0b

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

✓

1.0b

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

Compiler

Compiled 2416 to 1086 computations (55% saved)

regimes305.0ms (3.4%)

Accuracy

Total 0.0b remaining (43.6%)

Threshold costs 0.0b (43.6%)

Compiler

Compiled 8036 to 5794 computations (27.9% saved)

simplify6.0ms (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	23	59
1	38	59
2	50	59
3	59	59
4	64	59
5	65	59
6	65	59

end1.0ms (0%)

Compiler: Compiled 35 to 24 computations (31.4% saved)

sample1.2s (13.5%)

Algorithm

1×

intervals

Results

790.0ms	8000×	body	128	valid
42.0ms	513×	body	128	nan

Compiler

Compiled 107 to 81 computations (24.3% saved)

Details

analyze229.0ms (2.5%)

sample39.0ms (0.4%)

simplify12.0ms (0.1%)

prune3.0ms (0%)

localize10.0ms (0.1%)

rewrite7.0ms (0.1%)

series112.0ms (1.2%)

simplify146.0ms (1.6%)

prune91.0ms (1%)

localize12.0ms (0.1%)

rewrite8.0ms (0.1%)

series6.3s (69.6%)

simplify181.0ms (2%)

prune109.0ms (1.2%)

localize21.0ms (0.2%)

rewrite6.0ms (0.1%)

series0.0ms (0%)

simplify93.0ms (1%)

prune48.0ms (0.5%)

localize24.0ms (0.3%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify10.0ms (0.1%)

prune51.0ms (0.6%)

regimes305.0ms (3.4%)

simplify6.0ms (0.1%)

end1.0ms (0%)

sample1.2s (13.5%)

Profiling