Details

analyze244.0ms (3.9%)

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
12.5%	87.4%	0.1%	4
12.5%	87.4%	0.1%	5
15.6%	84.3%	0.1%	6
32.8%	67.1%	0.1%	7
38.2%	61.6%	0.1%	8
46%	53.8%	0.1%	9
62.6%	37.3%	0.1%	10
67.2%	32.7%	0.1%	11
71.1%	28.8%	0.1%	12
81.6%	18.2%	0.1%	13
84.1%	15.7%	0.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample15.0ms (0.2%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify177.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	56	13
1	56	13

prune2.0ms (0%)

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: 7.1b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 1 (/.f64 y z))
7.1b	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))

rewrite32.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

71×	`add-sqr-sqrt_binary64_10077`
65×	`*-un-lft-identity_binary64_10055`
53×	`times-frac_binary64_10061`
24×	`difference-of-squares_binary64_10024`
23×	`add-cube-cbrt_binary64_10090`
13×	`cancel-sign-sub-inv_binary64_10021`
9×	`distribute-lft-out_binary64_10006`
8×	`associate-/r*_binary64_9999`
6×	`distribute-lft-out--_binary64_10007`
4×	`associate-/l*_binary64_10000` `add-exp-log_binary64_10093` `add-log-exp_binary64_10094` `add-cbrt-cube_binary64_10091`
2×	`div-inv_binary64_10052` `flip--_binary64_10030` `flip3--_binary64_10059` `associate-/r/_binary64_10001` `pow1_binary64_10116` `associate-/l/_binary64_10002`
1×	`div-exp_binary64_10106` `flip3-+_binary64_10058` `diff-log_binary64_10147` `clear-num_binary64_10054` `cbrt-undiv_binary64_10089` `sub-neg_binary64_10048` `frac-2neg_binary64_10066` `flip-+_binary64_10029`

Counts

2 → 89

Calls

2 calls:

13.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
10.0ms	(-.f64 1 (/.f64 y z))

series119.0ms (1.9%)

Counts

2 → 6

Calls

2 calls:

91.0ms	(/.f64 (+.f64 x y) (-.f64 1 (/.f64 y z)))
28.0ms	(-.f64 1 (/.f64 y z))

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	6064	1764

prune197.0ms (3.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	7	96

Merged error: 5.9b

Counts

96 → 7

Compiler

Compiled 3830 to 2074 computations (45.8% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 1 (/.f64 y z))
0.2b	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
7.1b	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))

rewrite82.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

327×	`times-frac_binary64_10061`
291×	`add-sqr-sqrt_binary64_10077`
285×	`*-un-lft-identity_binary64_10055`
115×	`add-cube-cbrt_binary64_10090`
88×	`difference-of-squares_binary64_10024`
42×	`associate-/r*_binary64_9999`
41×	`distribute-lft-out_binary64_10006`
22×	`distribute-lft-out--_binary64_10007`
16×	`add-exp-log_binary64_10093`
13×	`cancel-sign-sub-inv_binary64_10021`
11×	`associate-/l*_binary64_10000` `associate-/r/_binary64_10001`
10×	`add-cbrt-cube_binary64_10091`
8×	`div-exp_binary64_10106`
7×	`div-inv_binary64_10052`
5×	`flip3-+_binary64_10058` `add-log-exp_binary64_10094` `flip-+_binary64_10029`
4×	`cbrt-undiv_binary64_10089` `pow1_binary64_10116`
2×	`clear-num_binary64_10054` `1-exp_binary64_10099` `flip--_binary64_10030` `frac-2neg_binary64_10066` `flip3--_binary64_10059` `rec-exp_binary64_10105` `associate-/l/_binary64_10002`
1×	`div-sub_binary64_10060` `diff-log_binary64_10147` `pow-flip_binary64_10129` `inv-pow_binary64_10140` `sub-neg_binary64_10048`

Counts

3 → 266

Calls

3 calls:

20.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
15.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))
9.0ms	(-.f64 1 (/.f64 y z))

series269.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

166.0ms	(/.f64 1 (/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y)))
77.0ms	(/.f64 (-.f64 1 (/.f64 y z)) (+.f64 x y))
25.0ms	(-.f64 1 (/.f64 y z))

simplify109.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4992	6775
1	4992	6775

prune303.0ms (4.8%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	275	0	275
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	275	7	282

Merged error: 5.9b

Counts

282 → 7

Compiler

Compiled 6360 to 2940 computations (53.8% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (+.f64 x y))
0.6b	(cbrt.f64 (+.f64 x y))
1.8b	(/.f64 (cbrt.f64 (+.f64 x y)) (-.f64 1 (/.f64 y z)))
5.4b	(.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (/.f64 (cbrt.f64 (+.f64 x y)) (-.f64 1 (/.f64 y z))))

rewrite98.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

181×	`add-sqr-sqrt_binary64_10077`
154×	`*-un-lft-identity_binary64_10055`
144×	`times-frac_binary64_10061`
77×	`cbrt-prod_binary64_10086`
62×	`associate-r_binary64_9995`
60×	`difference-of-squares_binary64_10024`
56×	`add-cube-cbrt_binary64_10090`
30×	`cbrt-div_binary64_10087`
19×	`distribute-lft-out_binary64_10006`
18×	`add-exp-log_binary64_10093`
16×	`frac-times_binary64_10065`
15×	`flip3-+_binary64_10058` `flip-+_binary64_10029` `distribute-lft-out--_binary64_10007`
12×	`associate-*l/_binary64_9998`
11×	`add-cbrt-cube_binary64_10091`
9×	`pow1_binary64_10116`
8×	`associate-/r*_binary64_9999`
7×	`associate-/l*_binary64_10000`
6×	`cbrt-unprod_binary64_10088` `prod-exp_binary64_10104`
5×	`associate-*r/_binary64_9997`
4×	`add-log-exp_binary64_10094` `associate-/r/_binary64_10001`
3×	`div-exp_binary64_10106` `cbrt-undiv_binary64_10089` `pow-prod-down_binary64_10126` `unswap-sqr_binary64_10023`
2×	`div-inv_binary64_10052` `flip--_binary64_10030` `flip3--_binary64_10059` `pow1/3_binary64_10137` `associate-/l/_binary64_10002`
1×	`clear-num_binary64_10054` `associate-l_binary64_9996` `*-commutative_binary64_9986` `frac-2neg_binary64_10066`

Counts

4 → 216

Calls

4 calls:

40.0ms	(.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (/.f64 (cbrt.f64 (+.f64 x y)) (-.f64 1 (/.f64 y z))))
15.0ms	(/.f64 (cbrt.f64 (+.f64 x y)) (-.f64 1 (/.f64 y z)))
3.0ms	(cbrt.f64 (+.f64 x y))
3.0ms	(cbrt.f64 (+.f64 x y))

series1.1s (17.6%)

Counts

4 → 12

Calls

4 calls:

516.0ms	(/.f64 (cbrt.f64 (+.f64 x y)) (-.f64 1 (/.f64 y z)))
224.0ms	(cbrt.f64 (+.f64 x y))
216.0ms	(cbrt.f64 (+.f64 x y))
153.0ms	(.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (/.f64 (cbrt.f64 (+.f64 x y)) (-.f64 1 (/.f64 y z))))

simplify113.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5093	5854

prune281.0ms (4.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	228	7	235

Merged error: 5.9b

Counts

235 → 7

Compiler

Compiled 7264 to 2563 computations (64.7% saved)

localize354.0ms (5.6%)

Local error

Found 4 expressions with local error:

1.6b	(/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
7.4b	(cbrt.f64 (-.f64 1 (/.f64 y z)))
7.4b	(cbrt.f64 (-.f64 1 (/.f64 y z)))
7.4b	(cbrt.f64 (-.f64 1 (/.f64 y z)))

rewrite70.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64_10077`
30×	`cbrt-div_binary64_10087`
24×	`cbrt-prod_binary64_10086`
19×	`*-un-lft-identity_binary64_10055`
16×	`add-exp-log_binary64_10093`
12×	`difference-of-squares_binary64_10024`
9×	`flip--_binary64_10030` `flip3--_binary64_10059`
8×	`frac-times_binary64_10065` `associate-/r/_binary64_10001` `add-cbrt-cube_binary64_10091` `associate-/l/_binary64_10002`
7×	`times-frac_binary64_10061` `add-cube-cbrt_binary64_10090`
6×	`flip3-+_binary64_10058` `flip-+_binary64_10029`
4×	`div-exp_binary64_10106` `associate-l/_binary64_9998` `cbrt-unprod_binary64_10088` `cbrt-undiv_binary64_10089` `add-log-exp_binary64_10094` `associate-r/_binary64_9997` `prod-exp_binary64_10104` `pow1_binary64_10116`
3×	`distribute-lft-out--_binary64_10007` `pow1/3_binary64_10137`
1×	`associate-/l_binary64_10000` `clear-num_binary64_10054` `div-inv_binary64_10052` `associate-/r_binary64_9999` `frac-2neg_binary64_10066`

Counts

4 → 91

Calls

4 calls:

32.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
8.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))
8.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))
8.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))

series1.7s (27%)

Counts

4 → 12

Calls

4 calls:

874.0ms	(/.f64 (.f64 (cbrt.f64 (+.f64 x y)) (cbrt.f64 (+.f64 x y))) (.f64 (cbrt.f64 (-.f64 1 (/.f64 y z))) (cbrt.f64 (-.f64 1 (/.f64 y z)))))
283.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))
282.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))
265.0ms	(cbrt.f64 (-.f64 1 (/.f64 y z)))

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4862	2089
1	4862	2089

prune151.0ms (2.4%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	103	0	103
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	103	7	110

Merged error: 5.9b

Counts

110 → 7

Compiler

Compiled 4141 to 1751 computations (57.7% saved)

regimes69.0ms (1.1%)

Compiler: Compiled 576 to 398 computations (30.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	13
1	27	13

end0.0ms (0%)

sample608.0ms (9.6%)

Algorithm

1×

intervals

Results

252.0ms	7999×	body	128	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 190 to 129 computations (32.1% saved)

Details

analyze244.0ms (3.9%)

sample15.0ms (0.2%)

simplify177.0ms (2.8%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite32.0ms (0.5%)

series119.0ms (1.9%)

simplify73.0ms (1.2%)

prune197.0ms (3.1%)

localize10.0ms (0.2%)

rewrite82.0ms (1.3%)

series269.0ms (4.3%)

simplify109.0ms (1.7%)

prune303.0ms (4.8%)

localize11.0ms (0.2%)

rewrite98.0ms (1.6%)

series1.1s (17.6%)

simplify113.0ms (1.8%)

prune281.0ms (4.5%)

localize354.0ms (5.6%)

rewrite70.0ms (1.1%)

series1.7s (27%)

simplify94.0ms (1.5%)

prune151.0ms (2.4%)

regimes69.0ms (1.1%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample608.0ms (9.6%)

Profiling