Details

analyze170.0ms (4.8%)

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 17 to 17 computations (0% saved)

sample32.0ms (0.9%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
1.0ms	19×	body	128	nan

Compiler

Compiled 33 to 35 computations (-6.1% saved)

simplify169.0ms (4.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	50	23
1	50	23

prune4.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 1.0b

Counts

2 → 1

Compiler

Compiled 28 to 28 computations (0% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.9b	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
1.0b	(+.f64 (*.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
1.0b	(cos.f64 (+.f64 (*.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
1.0b	(*.f64 PI.f64 2/3)

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_1805`
14×	`add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
9×	`times-frac_binary64_1789`
8×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
6×	`div-sub_binary64_1788` `add-log-exp_binary64_1822` `pow1_binary64_1844`
4×	`associate-+r-_binary64_1717`
3×	`associate-/l_binary64_1728` `associate-/r_binary64_1727` `acos-asin_binary64_1964` `associate-l_binary64_1724` `distribute-frac-neg_binary64_1746` `acos-neg_binary64_1966` `associate-r_binary64_1723`
2×	`cos-diff_binary64_1920`
1×	`+-commutative_binary64_1713` `cbrt-unprod_binary64_1816` `prod-exp_binary64_1832` `flip-+_binary64_1757` `div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `sum-log_binary64_1874` `div-exp_binary64_1834` `flip3-+_binary64_1786` `clear-num_binary64_1782` `pow-prod-down_binary64_1854` `unswap-sqr_binary64_1751` `cos-sum_binary64_1917`

Counts

4 → 70

Calls

4 calls:

8.0ms	(cos.f64 (+.f64 (*.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
8.0ms	(+.f64 (*.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
4.0ms	(*.f64 PI.f64 2/3)
4.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)

series210.0ms (5.9%)

Counts

4 → 10

Calls

4 calls:

146.0ms	(cos.f64 (+.f64 (*.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)))
40.0ms	(+.f64 (*.f64 PI.f64 2/3) (/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3))
24.0ms	(/.f64 (acos.f64 (/.f64 (neg.f64 g) h)) 3)
0.0ms	(*.f64 PI.f64 2/3)

simplify94.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5181	1420

prune86.0ms (2.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	2	81

Merged error: 0.9b

Counts

81 → 2

Compiler

Compiled 1593 to 943 computations (40.8% saved)

localize11.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(acos.f64 (/.f64 g h))
0.0b	(cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))
0.9b	(/.f64 (acos.f64 (/.f64 g h)) 3)

rewrite11.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783`
9×	`times-frac_binary64_1789`
5×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
3×	`associate-/l_binary64_1728` `associate-/r_binary64_1727` `acos-asin_binary64_1964` `add-log-exp_binary64_1822` `pow1_binary64_1844`
2×	`div-sub_binary64_1788`
1×	`div-inv_binary64_1780` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782` `cos-diff_binary64_1920`

Counts

3 → 44

Calls

3 calls:

4.0ms	(/.f64 (acos.f64 (/.f64 g h)) 3)
3.0ms	(cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))
1.0ms	(acos.f64 (/.f64 g h))

series106.0ms (3%)

Counts

3 → 9

Calls

3 calls:

80.0ms	(cos.f64 (/.f64 (acos.f64 (/.f64 g h)) 3))
19.0ms	(/.f64 (acos.f64 (/.f64 g h)) 3)
7.0ms	(acos.f64 (/.f64 g h))

simplify139.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (126.0ms)

Iter	Nodes	Cost
0	4749	737
1	4749	737

prune56.0ms (1.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	52	3	55

Merged error: 0b

Counts

55 → 3

Compiler

Compiled 941 to 617 computations (34.4% saved)

localize16.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(acos.f64 (/.f64 g h))
0.0b	(cos.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (/.f64 g h)) (cbrt.f64 3))))
0.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (/.f64 g h)) (cbrt.f64 3)))
0.0b	(/.f64 (acos.f64 (/.f64 g h)) (cbrt.f64 3))

rewrite45.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-sqr-sqrt_binary64_1805`
51×	`add-exp-log_binary64_1821` `times-frac_binary64_1789`
37×	`*-un-lft-identity_binary64_1783`
34×	`add-cube-cbrt_binary64_1818`
24×	`cbrt-prod_binary64_1814`
22×	`associate-r_binary64_1723`
20×	`prod-exp_binary64_1832`
19×	`add-cbrt-cube_binary64_1819`
16×	`div-exp_binary64_1834`
9×	`unswap-sqr_binary64_1751`
8×	`cbrt-unprod_binary64_1816` `cbrt-undiv_binary64_1817`
7×	`associate-l_binary64_1724`
6×	`associate-/r*_binary64_1727` `pow1_binary64_1844`
4×	`1-exp_binary64_1827` `rec-exp_binary64_1833` `add-log-exp_binary64_1822`
3×	`associate-/l*_binary64_1728` `div-inv_binary64_1780`
2×	`acos-asin_binary64_1964`
1×	`div-sub_binary64_1788` `associate-r/_binary64_1725` `associate-l/_binary64_1726` `*-commutative_binary64_1714` `frac-2neg_binary64_1794` `frac-times_binary64_1793` `clear-num_binary64_1782` `pow-prod-down_binary64_1854`

Counts

4 → 125

Calls

4 calls:

21.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (/.f64 g h)) (cbrt.f64 3)))
5.0ms	(/.f64 (acos.f64 (/.f64 g h)) (cbrt.f64 3))
2.0ms	(cos.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (/.f64 g h)) (cbrt.f64 3))))
1.0ms	(acos.f64 (/.f64 g h))

series297.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

158.0ms	(cos.f64 (.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (/.f64 g h)) (cbrt.f64 3))))
78.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3))) (/.f64 (acos.f64 (/.f64 g h)) (cbrt.f64 3)))
53.0ms	(/.f64 (acos.f64 (/.f64 g h)) (cbrt.f64 3))
7.0ms	(acos.f64 (/.f64 g h))

simplify101.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5041	2593

prune193.0ms (5.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	137	0	137
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	137	3	140

Merged error: 0b

Counts

140 → 3

Compiler

Compiled 3388 to 2499 computations (26.2% saved)

localize13.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(asin.f64 (/.f64 (neg.f64 g) h))
0.1b	(/.f64 (asin.f64 (/.f64 (neg.f64 g) h)) 3)
1.0b	(cos.f64 (-.f64 (*.f64 PI.f64 5/6) (/.f64 (asin.f64 (/.f64 (neg.f64 g) h)) 3)))

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1805` `add-cube-cbrt_binary64_1818` `*-un-lft-identity_binary64_1783` `times-frac_binary64_1789`
15×	`cos-sum_binary64_1917`
13×	`cancel-sign-sub-inv_binary64_1749`
5×	`add-cbrt-cube_binary64_1819` `add-exp-log_binary64_1821`
3×	`associate-/l_binary64_1728` `associate-/r_binary64_1727` `asin-acos_binary64_1963` `distribute-frac-neg_binary64_1746` `add-log-exp_binary64_1822` `pow1_binary64_1844`
2×	`div-sub_binary64_1788` `asin-neg_binary64_1965` `div-inv_binary64_1780`
1×	`associate--r-_binary64_1722` `cbrt-undiv_binary64_1817` `frac-2neg_binary64_1794` `div-exp_binary64_1834` `clear-num_binary64_1782` `cos-diff_binary64_1920` `sub-neg_binary64_1776`

Counts

3 → 61

Calls

3 calls:

11.0ms	(cos.f64 (-.f64 (*.f64 PI.f64 5/6) (/.f64 (asin.f64 (/.f64 (neg.f64 g) h)) 3)))
4.0ms	(/.f64 (asin.f64 (/.f64 (neg.f64 g) h)) 3)
1.0ms	(asin.f64 (/.f64 (neg.f64 g) h))

series188.0ms (5.3%)

Counts

3 → 9

Calls

3 calls:

155.0ms	(cos.f64 (-.f64 (*.f64 PI.f64 5/6) (/.f64 (asin.f64 (/.f64 (neg.f64 g) h)) 3)))
24.0ms	(/.f64 (asin.f64 (/.f64 (neg.f64 g) h)) 3)
9.0ms	(asin.f64 (/.f64 (neg.f64 g) h))

simplify76.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4941	1610
1	4941	1610

prune72.0ms (2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	70	3	73

Merged error: 0b

Counts

73 → 3

Compiler

Compiled 1499 to 868 computations (42.1% saved)

regimes226.0ms (6.4%)

Compiler: Compiled 1872 to 1880 computations (-0.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	31
1	41	31

end0.0ms (0%)

sample1.2s (32.7%)

Algorithm

1×

intervals

Results

688.0ms	8000×	body	128	valid
35.0ms	524×	body	128	nan

Compiler

Compiled 202 to 204 computations (-1% saved)

Details

analyze170.0ms (4.8%)

sample32.0ms (0.9%)

simplify169.0ms (4.8%)

prune4.0ms (0.1%)

localize13.0ms (0.4%)

rewrite31.0ms (0.9%)

series210.0ms (5.9%)

simplify94.0ms (2.6%)

prune86.0ms (2.4%)

localize11.0ms (0.3%)

rewrite11.0ms (0.3%)

series106.0ms (3%)

simplify139.0ms (3.9%)

prune56.0ms (1.6%)

localize16.0ms (0.5%)

rewrite45.0ms (1.3%)

series297.0ms (8.4%)

simplify101.0ms (2.8%)

prune193.0ms (5.5%)

localize13.0ms (0.4%)

rewrite23.0ms (0.7%)

series188.0ms (5.3%)

simplify76.0ms (2.2%)

prune72.0ms (2%)

regimes226.0ms (6.4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (32.7%)

Profiling