Details

analyze210.0ms (4.1%)

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)

sample55.0ms (1.1%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
2.0ms	18×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% 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	(/.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 (0.7%)

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)))
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)

rewrite6.0ms (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))

simplify128.0ms (2.5%)

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

prune80.0ms (1.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	95	2	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	2	98

Error

1.0b

Counts

98 → 2

Alt Table

Status	Error	Program
	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 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) 3)))

Status

Error

Program

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 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3)))

Compiler

Compiled 2053 to 1157 computations (43.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series309.0ms (6.1%)

Counts

4 → 72

Calls

4 calls:

261.0ms	(pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3)
25.0ms	(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3))
24.0ms	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))
0.0ms	(*.f64 2/3 (PI.f64))

rewrite10.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`cbrt-prod_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
7×	`add-cbrt-cube_binary64`

Counts

4 → 78

Calls

4 calls:

3.0ms	(*.f64 2/3 (PI.f64))
2.0ms	(pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3)
2.0ms	(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3))
1.0ms	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))

simplify145.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

740×	`sqr-pow_binary64`
574×	`fma-def_binary64`
454×	`*-commutative_binary64`
386×	`log-prod_binary64`
384×	`exp-prod_binary64`

Counts

150 → 100

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	112	3222
1	166	2982
2	368	2966
3	1272	2966
4	2315	2963
5	4112	2963
6	4941	2963

prune91.0ms (1.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	99	3	102

Error

0.0b

Counts

102 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) 3)))
	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (.f64 2/3 (PI.f64)) 3)))) 3)))
▶	0.1b	(.f64 2 (.f64 (cbrt.f64 (.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))))

Compiler

Compiled 2541 to 1647 computations (35.2% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series1.3s (26.2%)

Counts

2 → 48

Calls

2 calls:

1.3s

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

37.0ms

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

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64`
6×	`add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 41

Calls

2 calls:

4.0ms

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

2.0ms

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

simplify152.0ms (3%)

Algorithm

1×	egg-herbie

Rules

661×	`sqr-pow_binary64`
655×	`unswap-sqr_binary64`
614×	`distribute-rgt-in_binary64`
547×	`distribute-lft-in_binary64`
457×	`fma-def_binary64`

Counts

89 → 66

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	73	2203
1	110	1993
2	281	1965
3	1007	1933
4	2002	1930
5	3678	1930
6	4254	1930
7	5176	1930

prune219.0ms (4.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	191	1	192
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	191	4	195

Error

Counts

195 → 4

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (.f64 (pow.f64 (pow.f64 (cos.f64 (+.f64 (.f64 2/3 (PI.f64)) (.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h)))))) 2) 1/3) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))))))
✓	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) 3)))
▶	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (.f64 2/3 (PI.f64)) 3)))) 3)))
✓	0.1b	(.f64 2 (.f64 (cbrt.f64 (.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))))

Compiler

Compiled 8773 to 4983 computations (43.2% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (*.f64 2/3 (PI.f64)) 3)))) 3)
✓	1.0b	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (*.f64 2/3 (PI.f64)) 3))))
	1.0b	(*.f64 2/3 (PI.f64))
✓	1.6b	(pow.f64 (*.f64 2/3 (PI.f64)) 3)

series113.0ms (2.2%)

Counts

3 → 48

Calls

3 calls:

78.0ms

(pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (*.f64 2/3 (PI.f64)) 3)))) 3)

35.0ms

(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (*.f64 2/3 (PI.f64)) 3))))

0.0ms

(pow.f64 (*.f64 2/3 (PI.f64)) 3)

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
7×	`pow1_binary64`
7×	`*-un-lft-identity_binary64`
7×	`add-sqr-sqrt_binary64`

Counts

3 → 59

Calls

3 calls:

3.0ms

(pow.f64 (*.f64 2/3 (PI.f64)) 3)

2.0ms

(pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (*.f64 2/3 (PI.f64)) 3)))) 3)

1.0ms

(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (*.f64 2/3 (PI.f64)) 3))))

simplify111.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

929×	`fma-def_binary64`
627×	`associate-l_binary64`
503×	`associate-r_binary64`
366×	`log-prod_binary64`
352×	`exp-prod_binary64`

Counts

107 → 92

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	92	2207
1	171	2092
2	475	2068
3	2297	2068
4	4654	2068
5	5392	2068

prune90.0ms (1.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	114	4	118

Error

Counts

118 → 4

Alt Table

Status	Error	Program
	1.0b	(.f64 2 (.f64 (pow.f64 (pow.f64 (cos.f64 (+.f64 (.f64 2/3 (PI.f64)) (.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h)))))) 2) 1/3) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))))))
✓	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) 3)))
✓	1.0b	(.f64 2 (cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (.f64 2/3 (PI.f64)) 3)))) 3)))
✓	0.1b	(.f64 2 (.f64 (cbrt.f64 (.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))) (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))) (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))))

Compiler

Compiled 2961 to 2062 computations (30.4% saved)

regimes642.0ms (12.7%)

Accuracy

Total 0.0b remaining (69.6%)

Threshold costs 0.0b (69.6%)

Counts

50 → 1

Compiler

Compiled 12173 to 9815 computations (19.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
3×	`+-commutative_binary64`
2×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	51
1	35	51
2	39	51
3	42	51
4	43	51
5	43	51

end1.0ms (0%)

Compiler: Compiled 33 to 25 computations (24.2% saved)

sample1.3s (24.8%)

Algorithm

1×

intervals

Results

829.0ms	8000×	body	128	valid
54.0ms	600×	body	128	nan

Compiler

Compiled 167 to 131 computations (21.6% saved)

Details

analyze210.0ms (4.1%)

sample55.0ms (1.1%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series38.0ms (0.7%)

rewrite6.0ms (0.1%)

simplify128.0ms (2.5%)

prune80.0ms (1.6%)

localize13.0ms (0.3%)

series309.0ms (6.1%)

rewrite10.0ms (0.2%)

simplify145.0ms (2.9%)

prune91.0ms (1.8%)

localize15.0ms (0.3%)

series1.3s (26.2%)

rewrite8.0ms (0.2%)

simplify152.0ms (3%)

prune219.0ms (4.3%)

localize16.0ms (0.3%)

series113.0ms (2.2%)

rewrite8.0ms (0.2%)

simplify111.0ms (2.2%)

prune90.0ms (1.8%)

regimes642.0ms (12.7%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample1.3s (24.8%)

Profiling