Details

analyze77.0ms (1.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
0%	50%	50%	4
6.2%	43.7%	50%	5
9.4%	28.1%	62.5%	6
12.5%	25%	62.5%	7
15.6%	15.6%	68.8%	8
16.8%	14.4%	68.8%	9
18.5%	8.8%	72.7%	10
19.2%	7.7%	73.1%	11
20.1%	4.6%	75.2%	12
20.5%	4%	75.5%	13
21%	2.4%	76.6%	14

Compiler

Compiled 21 to 20 computations (4.8% saved)

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
1.0ms	11×	body	128	invalid
0.0ms	5×	body	128	nan

Compiler

Compiled 41 to 41 computations (0% saved)

simplify231.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	1030	21
1	1030	21

prune6.0ms (0.1%)

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: 0.1b

Counts

2 → 2

Compiler

Compiled 82 to 77 computations (6.1% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (-.f64 a 1/3) 9)
0.1b	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.3b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

rewrite52.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64_2165`
23×	`*-un-lft-identity_binary64_2143`
17×	`add-cube-cbrt_binary64_2178`
12×	`times-frac_binary64_2149`
11×	`pow1_binary64_2204`
10×	`add-exp-log_binary64_2181` `associate-l_binary64_2084` `add-cbrt-cube_binary64_2179`
8×	`associate-*l/_binary64_2086`
7×	`associate-r_binary64_2083`
6×	`flip--_binary64_2118` `flip3--_binary64_2147`
5×	`sqrt-prod_binary64_2159`
4×	`sqrt-div_binary64_2160` `add-log-exp_binary64_2182` `associate-/r*_binary64_2087` `frac-times_binary64_2153`
3×	`associate-/l*_binary64_2088` `pow-prod-down_binary64_2214` `flip3-+_binary64_2146` `flip-+_binary64_2117`
2×	`associate-/r/_binary64_2089` `distribute-lft-out--_binary64_2095` `cbrt-unprod_binary64_2176` `prod-exp_binary64_2192` `associate-r/_binary64_2085` `unswap-sqr_binary64_2111` `sqrt-pow1_binary64_2161` `-commutative_binary64_2074` `difference-of-squares_binary64_2112`
1×	`pow1/2_binary64_2223` `cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `distribute-rgt-in_binary64_2093` `div-inv_binary64_2140` `distribute-lft-out_binary64_2094` `distribute-lft-in_binary64_2092` `div-exp_binary64_2194` `frac-2neg_binary64_2154`

Counts

4 → 99

Calls

4 calls:

17.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
9.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
8.0ms	(*.f64 (-.f64 a 1/3) 9)
6.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series297.0ms (7%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
89.0ms	(.f64 (-.f64 a 1/3) (+.f64 1 (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
43.0ms	(*.f64 (-.f64 a 1/3) 9)
38.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify52.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5478	2236

prune396.0ms (9.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	104	7	111
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	105	8	113

Merged error: 0.0b

Counts

113 → 8

Compiler

Compiled 6621 to 5584 computations (15.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
0.2b	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
0.3b	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))
5.6b	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))

rewrite53.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2165`
25×	`times-frac_binary64_2149` `*-un-lft-identity_binary64_2143`
23×	`add-cube-cbrt_binary64_2178`
18×	`associate-r_binary64_2083`
14×	`flip--_binary64_2118` `flip3--_binary64_2147`
12×	`associate-*l/_binary64_2086`
11×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
10×	`frac-add_binary64_2151`
9×	`pow1_binary64_2204` `add-log-exp_binary64_2182`
8×	`sqrt-prod_binary64_2159`
6×	`sqrt-div_binary64_2160` `frac-times_binary64_2153`
5×	`associate-l_binary64_2084`
4×	`associate-/r/_binary64_2089` `associate-/r*_binary64_2087` `associate-+l+_binary64_2076`
3×	`associate-/l_binary64_2088` `associate-r/_binary64_2085` `cancel-sign-sub-inv_binary64_2109`
2×	`cbrt-undiv_binary64_2177` `div-inv_binary64_2140` `cbrt-unprod_binary64_2176` `sum-log_binary64_2234` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `unswap-sqr_binary64_2111` `sqrt-pow1_binary64_2161` `div-exp_binary64_2194`
1×	`pow1/2_binary64_2223` `+-commutative_binary64_2073` `diff-log_binary64_2235` `clear-num_binary64_2142` `sub-neg_binary64_2136` `associate-+l-_binary64_2078` `distribute-lft-out--_binary64_2095` `flip3-+_binary64_2146` `flip-+_binary64_2117` `*-commutative_binary64_2074` `difference-of-squares_binary64_2112` `frac-2neg_binary64_2154`

Counts

4 → 116

Calls

4 calls:

18.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
9.0ms	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
8.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
5.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

series381.0ms (9.1%)

Counts

4 → 12

Calls

4 calls:

135.0ms	(/.f64 rand (sqrt.f64 (*.f64 (-.f64 a 1/3) 9)))
112.0ms	(.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9))))
99.0ms	(+.f64 (-.f64 a 1/3) (.f64 (-.f64 a 1/3) (/.f64 rand (sqrt.f64 (.f64 (-.f64 a 1/3) 9)))))
34.0ms	(sqrt.f64 (*.f64 (-.f64 a 1/3) 9))

simplify78.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4969	3316
1	4969	3316

prune254.0ms (6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	127	1	128
Fresh	4	2	6
Picked	0	1	1
Done	1	0	1
Total	132	4	136

Merged error: 0b

Counts

136 → 4

Compiler

Compiled 4713 to 3655 computations (22.4% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 a 1/3)
0.0b	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
0.4b	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
0.5b	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))

rewrite91.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

147×	`add-sqr-sqrt_binary64_2165`
117×	`*-un-lft-identity_binary64_2143`
110×	`times-frac_binary64_2149`
70×	`sqrt-prod_binary64_2159`
59×	`add-cube-cbrt_binary64_2178`
46×	`associate-l_binary64_2084`
29×	`distribute-lft-out--_binary64_2095` `difference-of-squares_binary64_2112`
22×	`associate-r_binary64_2083`
18×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
11×	`add-log-exp_binary64_2182`
9×	`pow1_binary64_2204` `unswap-sqr_binary64_2111`
8×	`associate-/r*_binary64_2087`
7×	`flip--_binary64_2118` `flip3--_binary64_2147`
6×	`cancel-sign-sub-inv_binary64_2109` `frac-add_binary64_2151`
5×	`cbrt-undiv_binary64_2177` `associate-/l*_binary64_2088` `div-exp_binary64_2194`
4×	`sqrt-div_binary64_2160` `associate-/r/_binary64_2089` `cbrt-unprod_binary64_2176` `associate-+l+_binary64_2076` `prod-exp_binary64_2192`
3×	`frac-times_binary64_2153` `div-inv_binary64_2140` `associate-l/_binary64_2086` `associate-r/_binary64_2085`
2×	`diff-log_binary64_2235` `sub-neg_binary64_2136` `pow-div_binary64_2218` `sum-log_binary64_2234` `associate-/l/_binary64_2090`
1×	`pow1/2_binary64_2223` `+-commutative_binary64_2073` `clear-num_binary64_2142` `associate-+l-_binary64_2078` `pow-prod-down_binary64_2214` `flip3-+_binary64_2146` `sqrt-pow1_binary64_2161` `flip-+_binary64_2117` `*-commutative_binary64_2074` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 208

Calls

4 calls:

40.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
11.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))
9.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
4.0ms	(-.f64 a 1/3)

series404.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

245.0ms	(*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9)))
93.0ms	(+.f64 (-.f64 a 1/3) (*.f64 (/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3))) (/.f64 rand (sqrt.f64 9))))
39.0ms	(/.f64 (-.f64 a 1/3) (sqrt.f64 (-.f64 a 1/3)))
27.0ms	(-.f64 a 1/3)

simplify96.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

220 → 220

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4928	4400
1	4928	4400

prune364.0ms (8.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	219	5	224

Merged error: 0b

Counts

224 → 5

Compiler

Compiled 5665 to 4407 computations (22.2% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 a 1/3)
0.0b	(+.f64 (-.f64 a 1/3) (/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9)))
0.2b	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
0.2b	(/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9))

rewrite43.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64_2143`
21×	`add-sqr-sqrt_binary64_2165`
13×	`add-cube-cbrt_binary64_2178`
12×	`sqrt-prod_binary64_2159`
11×	`add-log-exp_binary64_2182` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
8×	`associate-l_binary64_2084`
6×	`pow1_binary64_2204` `associate-/r*_binary64_2087` `cancel-sign-sub-inv_binary64_2109` `times-frac_binary64_2149`
4×	`sqrt-div_binary64_2160` `flip--_binary64_2118` `associate-+l+_binary64_2076` `flip3--_binary64_2147` `associate-*l/_binary64_2086`
3×	`associate-r_binary64_2083` `distribute-lft-out--_binary64_2095`
2×	`cbrt-undiv_binary64_2177` `diff-log_binary64_2235` `sub-neg_binary64_2136` `cbrt-unprod_binary64_2176` `sum-log_binary64_2234` `prod-exp_binary64_2192` `distribute-lft-out_binary64_2094` `unswap-sqr_binary64_2111` `difference-of-squares_binary64_2112` `div-exp_binary64_2194` `associate-/l/_binary64_2090` `frac-add_binary64_2151`
1×	`+-commutative_binary64_2073` `clear-num_binary64_2142` `associate-/l_binary64_2088` `associate-+l-_binary64_2078` `div-inv_binary64_2140` `pow-prod-down_binary64_2214` `flip3-+_binary64_2146` `flip-+_binary64_2117` `-commutative_binary64_2074` `frac-2neg_binary64_2154`

Counts

4 → 92

Calls

4 calls:

12.0ms	(/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9))
11.0ms	(+.f64 (-.f64 a 1/3) (/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9)))
8.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
4.0ms	(-.f64 a 1/3)

series278.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9))
85.0ms	(*.f64 (sqrt.f64 (-.f64 a 1/3)) rand)
65.0ms	(+.f64 (-.f64 a 1/3) (/.f64 (*.f64 (sqrt.f64 (-.f64 a 1/3)) rand) (sqrt.f64 9)))
25.0ms	(-.f64 a 1/3)

simplify62.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4909	1790
1	4909	1790

prune128.0ms (3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	104	5	109

Merged error: 0b

Counts

109 → 5

Compiler

Compiled 2173 to 1659 computations (23.7% saved)

regimes26.0ms (0.6%)

Compiler: Compiled 168 to 156 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	23	18
1	23	18

end0.0ms (0%)

sample780.0ms (18.5%)

Algorithm

1×

intervals

Results

468.0ms	8000×	body	128	valid
17.0ms	267×	body	128	nan
15.0ms	259×	body	128	invalid

Compiler

Compiled 115 to 107 computations (7% saved)

Details

analyze77.0ms (1.8%)

sample23.0ms (0.5%)

simplify231.0ms (5.5%)

prune6.0ms (0.1%)

localize9.0ms (0.2%)

rewrite52.0ms (1.2%)

series297.0ms (7%)

simplify52.0ms (1.2%)

prune396.0ms (9.4%)

localize9.0ms (0.2%)

rewrite53.0ms (1.3%)

series381.0ms (9.1%)

simplify78.0ms (1.8%)

prune254.0ms (6%)

localize10.0ms (0.2%)

rewrite91.0ms (2.2%)

series404.0ms (9.6%)

simplify96.0ms (2.3%)

prune364.0ms (8.6%)

localize8.0ms (0.2%)

rewrite43.0ms (1%)

series278.0ms (6.6%)

simplify62.0ms (1.5%)

prune128.0ms (3%)

regimes26.0ms (0.6%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample780.0ms (18.5%)

Profiling