Details

analyze215.0ms (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)

sample269.0ms (6.2%)

Algorithm

1×

intervals

Results

238.0ms	256×	body	128	valid
2.0ms	23×	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))
✓	0.9b	(/.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)))

series35.0ms (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 (0.2%)

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:

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))

simplify125.0ms (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

prune123.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	93	5	98

Error

0.9b

Counts

98 → 5

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))))
	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 (.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))))))
	1.5b	(.f64 2 (cbrt.f64 (.f64 (*.f64 (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))) (cos.f64 (fma.f64 (PI.f64) 2/3 (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))))))
▶	1.0b	(.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64)))))))

Compiler

Compiled 2260 to 1294 computations (42.7% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(expm1.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))))
✓	1.0b	(log1p.f64 (expm1.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))

series76.0ms (1.8%)

Counts

4 → 72

Calls

4 calls:

30.0ms	(expm1.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))))
23.0ms	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))
23.0ms	(log1p.f64 (expm1.f64 (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))

rewrite6.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

3.0ms	(*.f64 2/3 (PI.f64))
1.0ms	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))
0.0ms	(expm1.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64)))))
0.0ms	(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))))

simplify145.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

932×	`unsub-neg_binary64`
354×	`distribute-rgt-in_binary64`
336×	`associate-l_binary64`
295×	`distribute-lft-in_binary64`
293×	`sub-neg_binary64`

Counts

124 → 74

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	90	2335
1	114	2204
2	190	2204
3	276	2204
4	549	2204
5	1957	2204
6	3689	2204
7	4592	2204
8	4818	2204

prune85.0ms (2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	3	0	3
Picked	1	0	1
Done	0	1	1
Total	76	3	79

Error

0.9b

Counts

79 → 3

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))))
	1.0b	(.f64 2 (log1p.f64 (-.f64 (exp.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64))))) 1)))
▶	1.0b	(.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (.f64 2/3 (PI.f64)) 3)))))))

Compiler

Compiled 1685 to 1091 computations (35.3% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(log1p.f64 (expm1.f64 (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	(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)

series67.0ms (1.5%)

Counts

3 → 48

Calls

3 calls:

36.0ms

(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (*.f64 2/3 (PI.f64)) 3))))))

31.0ms

(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)

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 45

Calls

3 calls:

3.0ms

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

0.0ms

(log1p.f64 (expm1.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (*.f64 2/3 (PI.f64)) 3))))))

simplify122.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

552×	`*-commutative_binary64`
437×	`fma-def_binary64`
388×	`log-prod_binary64`
382×	`exp-prod_binary64`
335×	`unswap-sqr_binary64`

Counts

93 → 67

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	82	1711
1	122	1627
2	284	1619
3	1270	1619
4	2903	1616
5	4686	1616
6	5000	1616
7	4896	1616

prune89.0ms (2.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	89	0	89
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	89	3	92

Error

0.9b

Counts

92 → 3

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))))
▶	1.0b	(.f64 2 (log1p.f64 (-.f64 (exp.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64))))) 1)))
✓	1.0b	(.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (.f64 2/3 (PI.f64)) 3)))))))

Compiler

Compiled 2164 to 1503 computations (30.5% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	1.0b	(log1p.f64 (-.f64 (exp.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))) 1))
	1.0b	(cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))
✓	1.0b	(-.f64 (exp.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))) 1)
	1.0b	(*.f64 2/3 (PI.f64))

series1.1s (26%)

Counts

2 → 48

Calls

2 calls:

1.1s

(log1p.f64 (-.f64 (exp.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))) 1))

29.0ms

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

rewrite8.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`
9×	`prod-diff_binary64`
4×	`add-log-exp_binary64`

Counts

2 → 45

Calls

2 calls:

5.0ms

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

0.0ms

(log1p.f64 (-.f64 (exp.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (*.f64 2/3 (PI.f64))))) 1))

simplify127.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

439×	`sub-neg_binary64`
380×	`times-frac_binary64`
280×	`*-commutative_binary64`
275×	`unsub-neg_binary64`
239×	`associate-l_binary64`

Counts

93 → 71

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	2023
1	110	1868
2	183	1859
3	460	1857
4	1652	1857
5	3397	1857
6	4385	1857
7	4891	1857

prune113.0ms (2.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	113	3	116

Error

0.9b

Counts

116 → 3

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))))
✓	1.0b	(.f64 2 (log1p.f64 (-.f64 (exp.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (.f64 2/3 (PI.f64))))) 1)))
✓	1.0b	(.f64 2 (log1p.f64 (expm1.f64 (cos.f64 (fma.f64 1/3 (acos.f64 (neg.f64 (/.f64 g h))) (cbrt.f64 (pow.f64 (.f64 2/3 (PI.f64)) 3)))))))

Compiler

Compiled 3042 to 2046 computations (32.7% saved)

regimes308.0ms (7.1%)

Accuracy

Total 0.0b remaining (1.5%)

Threshold costs 0.0b (1.5%)

Counts

35 → 1

Compiler

Compiled 6606 to 5658 computations (14.4% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

3×	`*-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	14	21
1	21	21
2	25	21
3	28	21
4	29	21
5	29	21

end1.0ms (0%)

Compiler: Compiled 15 to 13 computations (13.3% saved)

sample1.2s (27.9%)

Algorithm

1×

intervals

Results

821.0ms	8000×	body	128	valid
49.0ms	575×	body	128	nan

Compiler

Compiled 90 to 80 computations (11.1% saved)

Details

analyze215.0ms (5%)

sample269.0ms (6.2%)

simplify9.0ms (0.2%)

prune3.0ms (0.1%)

localize11.0ms (0.2%)

series35.0ms (0.8%)

rewrite7.0ms (0.2%)

simplify125.0ms (2.9%)

prune123.0ms (2.8%)

localize13.0ms (0.3%)

series76.0ms (1.8%)

rewrite6.0ms (0.1%)

simplify145.0ms (3.4%)

prune85.0ms (2%)

localize16.0ms (0.4%)

series67.0ms (1.5%)

rewrite5.0ms (0.1%)

simplify122.0ms (2.8%)

prune89.0ms (2.1%)

localize15.0ms (0.3%)

series1.1s (26%)

rewrite8.0ms (0.2%)

simplify127.0ms (2.9%)

prune113.0ms (2.6%)

regimes308.0ms (7.1%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.2s (27.9%)

Profiling