Details

analyze435.0ms (9.2%)

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)

sample62.0ms (1.3%)

Algorithm

1×

intervals

Results

44.0ms	256×	body	128	valid
3.0ms	18×	body	128	nan

Compiler

Compiled 39 to 35 computations (10.3% saved)

simplify17.0ms (0.4%)

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

prune6.0ms (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)

localize19.0ms (0.4%)

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)))

series69.0ms (1.5%)

Counts

3 → 72

Calls

3 calls:

42.0ms	(cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
17.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
10.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

rewrite11.0ms (0.2%)

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:

5.0ms	(/.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)))
1.0ms	(fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))

simplify171.0ms (3.6%)

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

prune90.0ms (1.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	94	3	97
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	95	3	98

Error

1.0b

Counts

98 → 3

Alt Table

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

Compiler

Compiled 2089 to 1189 computations (43.1% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

series40.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

24.0ms

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

9.0ms

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

7.0ms

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

rewrite7.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`log-pow_binary64`
13×	`exp-prod_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`

Counts

3 → 49

Calls

3 calls:

3.0ms

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

1.0ms

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

0.0ms

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

simplify136.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

589×	`distribute-rgt-out_binary64`
584×	`distribute-rgt-in_binary64`
473×	`distribute-lft-in_binary64`
409×	`associate-l_binary64`
300×	`associate-+l+_binary64`

Counts

121 → 95

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	124	2067
1	163	1961
2	245	1961
3	370	1961
4	680	1961
5	1603	1961
6	3006	1961
7	4830	1961
8	5109	1961

prune316.0ms (6.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	152	3	155

Error

1.0b

Counts

155 → 3

Alt Table

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

Compiler

Compiled 3500 to 2036 computations (41.8% saved)

localize29.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(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)))))

series112.0ms (2.4%)

Counts

2 → 48

Calls

2 calls:

61.0ms	(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
50.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

rewrite3.0ms (0.1%)

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:

1.0ms	(expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))
1.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))))

simplify482.0ms (10.2%)

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

prune173.0ms (3.7%)

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 (cos.f64 (fma.f64 (PI.f64) 2/3 (log.f64 (exp.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
▶	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 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))

Compiler

Compiled 2723 to 1649 computations (39.4% 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))) (*.f64 2/3 (PI.f64)))) 3)
✓	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	(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))

series147.0ms (3.1%)

Counts

4 → 72

Calls

4 calls:

75.0ms	(pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3)
40.0ms	(cbrt.f64 (pow.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))) 3))
32.0ms	(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))

rewrite11.0ms (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))))

simplify171.0ms (3.6%)

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

prune148.0ms (3.1%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	99	1	100
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	99	4	103

Error

Counts

103 → 4

Alt Table

Status	Error	Program
✓	1.0b	(*.f64 2 (cos.f64 (fma.f64 (PI.f64) 2/3 (log.f64 (exp.f64 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
✓	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 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
	0.1b	(.f64 2 (.f64 (cbrt.f64 (pow.f64 (.f64 (cbrt.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)))))) 3)) (cbrt.f64 (pow.f64 (cbrt.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64))))) 3))))

Compiler

Compiled 2499 to 1619 computations (35.2% saved)

regimes373.0ms (7.9%)

Accuracy

Total 0.0b remaining (71.1%)

Threshold costs 0.0b (71.1%)

Counts

20 → 1

Compiler

Compiled 4802 to 3838 computations (20.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
2×	`+-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	18	65
1	27	65
2	31	65
3	34	65
4	35	65
5	35	65

end1.0ms (0%)

Compiler: Compiled 41 to 27 computations (34.1% saved)

sample1.7s (35.2%)

Algorithm

1×

intervals

Results

1.0s	8000×	body	128	valid
56.0ms	510×	body	128	nan

Compiler

Compiled 162 to 126 computations (22.2% saved)

Details

analyze435.0ms (9.2%)

sample62.0ms (1.3%)

simplify17.0ms (0.4%)

prune6.0ms (0.1%)

localize19.0ms (0.4%)

series69.0ms (1.5%)

rewrite11.0ms (0.2%)

simplify171.0ms (3.6%)

prune90.0ms (1.9%)

localize13.0ms (0.3%)

series40.0ms (0.8%)

rewrite7.0ms (0.2%)

simplify136.0ms (2.9%)

prune316.0ms (6.7%)

localize29.0ms (0.6%)

series112.0ms (2.4%)

rewrite3.0ms (0.1%)

simplify482.0ms (10.2%)

prune173.0ms (3.7%)

localize16.0ms (0.3%)

series147.0ms (3.1%)

rewrite11.0ms (0.2%)

simplify171.0ms (3.6%)

prune148.0ms (3.1%)

regimes373.0ms (7.9%)

simplify5.0ms (0.1%)

end1.0ms (0%)

sample1.7s (35.2%)

Profiling