Details

analyze7.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	50%	50%	0
0%	50%	50%	1
0%	50%	50%	2
0%	50%	50%	3
37.5%	12.5%	50%	4
43.7%	6.2%	50%	5
46.9%	3.1%	50%	6
48.4%	1.6%	50%	7
49.2%	0.8%	50%	8
49.6%	0.4%	50%	9
49.8%	0.2%	50%	10
49.9%	0.1%	50%	11
49.9%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 29 to 20 computations (31% saved)

sample22.0ms (0.9%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 54 to 38 computations (29.6% saved)

simplify212.0ms (8.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4983	13
1	4983	13

prune6.0ms (0.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.3b

Counts

2 → 2

Compiler

Compiled 77 to 58 computations (24.7% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 1 (*.f64 i i))
0.3b	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))

rewrite21.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64_2165`
35×	`times-frac_binary64_2149`
33×	`*-un-lft-identity_binary64_2143`
17×	`add-cube-cbrt_binary64_2178`
15×	`add-exp-log_binary64_2181`
12×	`difference-of-squares_binary64_2112`
10×	`pow1_binary64_2204`
9×	`associate-/r*_binary64_2087` `add-cbrt-cube_binary64_2179`
8×	`distribute-lft-out--_binary64_2095`
6×	`associate-/l*_binary64_2088` `div-inv_binary64_2140` `pow-flip_binary64_2217`
5×	`div-exp_binary64_2194`
3×	`cbrt-undiv_binary64_2177` `prod-exp_binary64_2192`
2×	`clear-num_binary64_2142` `add-log-exp_binary64_2182` `associate-/r/_binary64_2089` `1-exp_binary64_2187` `rec-exp_binary64_2193` `frac-2neg_binary64_2154`
1×	`flip--_binary64_2118` `pow2_binary64_2224` `pow-sqr_binary64_2116` `pow-plus_binary64_2206` `pow-prod-up_binary64_2213` `cbrt-unprod_binary64_2176` `flip3--_binary64_2147` `pow-prod-down_binary64_2214` `inv-pow_binary64_2228`

Counts

2 → 81

Calls

2 calls:

9.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
5.0ms	(/.f64 1 (*.f64 i i))

series63.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

35.0ms	(/.f64 1/4 (-.f64 4 (/.f64 1 (*.f64 i i))))
28.0ms	(/.f64 1 (*.f64 i i))

simplify74.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5040	1212

prune145.0ms (6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	86	3	89

Merged error: 0b

Counts

89 → 3

Compiler

Compiled 2251 to 1797 computations (20.2% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
0.1b	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
0.1b	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

rewrite74.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`add-sqr-sqrt_binary64_2165`
96×	`times-frac_binary64_2149` `*-un-lft-identity_binary64_2143`
47×	`add-cube-cbrt_binary64_2178`
30×	`associate-r_binary64_2083`
21×	`associate-l_binary64_2084` `difference-of-squares_binary64_2112`
19×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
18×	`div-inv_binary64_2140`
14×	`distribute-lft-out--_binary64_2095` `distribute-lft-out_binary64_2094`
13×	`associate-/r*_binary64_2087`
8×	`associate-/r/_binary64_2089`
6×	`cbrt-undiv_binary64_2177` `associate-/l*_binary64_2088` `div-exp_binary64_2194`
5×	`pow1_binary64_2204`
4×	`cbrt-unprod_binary64_2176` `prod-exp_binary64_2192` `unswap-sqr_binary64_2111`
3×	`add-log-exp_binary64_2182`
2×	`clear-num_binary64_2142` `flip--_binary64_2118` `flip3--_binary64_2147` `flip3-+_binary64_2146` `flip-+_binary64_2117` `frac-2neg_binary64_2154`
1×	`frac-times_binary64_2153` `pow-prod-down_binary64_2214` `associate-l/_binary64_2086` `associate-r/_binary64_2085` `*-commutative_binary64_2074`

Counts

3 → 161

Calls

3 calls:

38.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
10.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))
9.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))

series84.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

45.0ms	(*.f64 (/.f64 1/2 (+.f64 2 (/.f64 1 i))) (/.f64 1/2 (-.f64 2 (/.f64 1 i))))
19.0ms	(/.f64 1/2 (+.f64 2 (/.f64 1 i)))
19.0ms	(/.f64 1/2 (-.f64 2 (/.f64 1 i)))

simplify92.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5149	3334

prune248.0ms (10.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	170	3	173

Merged error: 0b

Counts

173 → 3

Compiler

Compiled 3835 to 3336 computations (13% saved)

localize10.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.1b	(.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (/.f64 (cbrt.f64 1/4) (-.f64 4 (/.f64 1 (*.f64 i i)))))
0.3b	(/.f64 1 (*.f64 i i))
0.4b	(/.f64 (cbrt.f64 1/4) (-.f64 4 (/.f64 1 (*.f64 i i))))

rewrite69.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`times-frac_binary64_2149`
123×	`add-sqr-sqrt_binary64_2165`
105×	`*-un-lft-identity_binary64_2143`
54×	`associate-r_binary64_2083`
53×	`add-cube-cbrt_binary64_2178`
52×	`cbrt-prod_binary64_2174`
39×	`difference-of-squares_binary64_2112`
28×	`add-exp-log_binary64_2181`
26×	`distribute-lft-out--_binary64_2095`
16×	`pow1_binary64_2204` `div-inv_binary64_2140`
15×	`add-cbrt-cube_binary64_2179`
9×	`associate-/r_binary64_2087` `associate-/l_binary64_2088` `prod-exp_binary64_2192`
7×	`cbrt-unprod_binary64_2176` `div-exp_binary64_2194`
6×	`pow-flip_binary64_2217`
5×	`cbrt-undiv_binary64_2177`
4×	`associate-/r/_binary64_2089` `pow-prod-down_binary64_2214`
3×	`add-log-exp_binary64_2182` `unswap-sqr_binary64_2111`
2×	`clear-num_binary64_2142` `flip--_binary64_2118` `1-exp_binary64_2187` `rec-exp_binary64_2193` `flip3--_binary64_2147` `frac-2neg_binary64_2154`
1×	`pow2_binary64_2224` `pow-sqr_binary64_2116` `pow-plus_binary64_2206` `pow-prod-up_binary64_2213` `associate-l_binary64_2084` `associate-r/_binary64_2085` `-commutative_binary64_2074` `inv-pow_binary64_2228`

Counts

3 → 185

Calls

3 calls:

29.0ms	(.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (/.f64 (cbrt.f64 1/4) (-.f64 4 (/.f64 1 (*.f64 i i)))))
10.0ms	(/.f64 (cbrt.f64 1/4) (-.f64 4 (/.f64 1 (*.f64 i i))))
9.0ms	(/.f64 1 (*.f64 i i))

series172.0ms (7.1%)

Counts

3 → 9

Calls

3 calls:

98.0ms	(.f64 (.f64 (cbrt.f64 1/4) (cbrt.f64 1/4)) (/.f64 (cbrt.f64 1/4) (-.f64 4 (/.f64 1 (*.f64 i i)))))
52.0ms	(/.f64 (cbrt.f64 1/4) (-.f64 4 (/.f64 1 (*.f64 i i))))
22.0ms	(/.f64 1 (*.f64 i i))

simplify107.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4871	3931
1	4871	3931

prune283.0ms (11.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	194	3	197

Merged error: 0b

Counts

197 → 3

Compiler

Compiled 4462 to 3750 computations (16% saved)

regimes12.0ms (0.5%)

Compiler: Compiled 42 to 39 computations (7.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	22
1	34	22

end0.0ms (0%)

sample707.0ms (29.2%)

Algorithm

1×

intervals

Results

399.0ms	8000×	body	128	valid
96.0ms	8000×	pre	128	true

Compiler

Compiled 84 to 72 computations (14.3% saved)

Details

analyze7.0ms (0.3%)

sample22.0ms (0.9%)

simplify212.0ms (8.8%)

prune6.0ms (0.3%)

localize6.0ms (0.2%)

rewrite21.0ms (0.8%)

series63.0ms (2.6%)

simplify74.0ms (3.1%)

prune145.0ms (6%)

localize8.0ms (0.3%)

rewrite74.0ms (3.1%)

series84.0ms (3.5%)

simplify92.0ms (3.8%)

prune248.0ms (10.2%)

localize10.0ms (0.4%)

rewrite69.0ms (2.9%)

series172.0ms (7.1%)

simplify107.0ms (4.4%)

prune283.0ms (11.7%)

regimes12.0ms (0.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample707.0ms (29.2%)

Profiling