Details

analyze1.3s (8.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
9.4%	90.4%	0.2%	11
9.4%	90.4%	0.2%	12
10.1%	89.6%	0.2%	13
20.8%	78.9%	0.2%	14

Compiler

Compiled 14 to 14 computations (0% saved)

sample30.0ms (0.2%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
4.0ms	88×	body	128	invalid

Compiler

Compiled 27 to 32 computations (-18.5% saved)

simplify574.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (478.0ms)

Iter	Nodes	Cost
0	4162	19
1	4162	19

prune3.0ms (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

Error

8.2b

Counts

2 → 1

Compiler

Compiled 26 to 26 computations (0% saved)

localize16.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.2b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
0.2b	(.f64 (.f64 z 9) t)
7.7b	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))

rewrite20.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64_19551` `add-exp-log_binary64_19553`
8×	`pow1_binary64_19576`
6×	`add-cube-cbrt_binary64_19550` `add-sqr-sqrt_binary64_19537` `*-un-lft-identity_binary64_19515`
5×	`add-log-exp_binary64_19554`
4×	`cbrt-unprod_binary64_19548` `prod-exp_binary64_19564`
3×	`times-frac_binary64_19521` `associate-/l_binary64_19460` `pow-prod-down_binary64_19586` `associate-r*_binary64_19455`
2×	`flip3--_binary64_19519` `associate-/l/_binary64_19462` `div-exp_binary64_19566` `cbrt-undiv_binary64_19549` `flip--_binary64_19490`
1×	`associate-l_binary64_19456` `cancel-sign-sub-inv_binary64_19481` `diff-log_binary64_19607` `associate-/r_binary64_19459` `div-inv_binary64_19512` `clear-num_binary64_19514` `sub-neg_binary64_19508` `-commutative_binary64_19446` `div-sub_binary64_19520` `frac-2neg_binary64_19526`

Counts

3 → 54

Calls

3 calls:

8.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
5.0ms	(.f64 (.f64 z 9) t)
4.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))

series134.0ms (0.9%)

Counts

3 → 9

Calls

3 calls:

70.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (.f64 a 2))
49.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
15.0ms	(.f64 (.f64 z 9) t)

simplify75.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4929	1034
1	4929	1034

prune85.0ms (0.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	51	12	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	12	64

Error

4.6b

Counts

64 → 12

Compiler

Compiled 1404 to 877 computations (37.5% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 z 9) t)) 2)
0.2b	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
0.2b	(.f64 (.f64 z 9) t)
7.5b	(.f64 (/.f64 1 a) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) 2))

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`add-sqr-sqrt_binary64_19537`
34×	`times-frac_binary64_19521`
33×	`add-exp-log_binary64_19553`
29×	`*-un-lft-identity_binary64_19515`
27×	`add-cube-cbrt_binary64_19550`
23×	`add-cbrt-cube_binary64_19551`
16×	`associate-r_binary64_19455`
14×	`associate-l_binary64_19456`
11×	`pow1_binary64_19576` `prod-exp_binary64_19564`
9×	`div-exp_binary64_19566`
7×	`cbrt-unprod_binary64_19548`
6×	`add-log-exp_binary64_19554` `unswap-sqr_binary64_19483`
5×	`cbrt-undiv_binary64_19549`
4×	`pow-prod-down_binary64_19586`
3×	`associate-/r_binary64_19459` `div-inv_binary64_19512` `associate-/l_binary64_19460`
2×	`flip3--_binary64_19519` `associate-/l/_binary64_19462` `rec-exp_binary64_19565` `*-commutative_binary64_19446` `1-exp_binary64_19559` `flip--_binary64_19490`
1×	`associate-r/_binary64_19457` `associate-l/_binary64_19458` `cancel-sign-sub-inv_binary64_19481` `diff-log_binary64_19607` `frac-times_binary64_19525` `clear-num_binary64_19514` `sub-neg_binary64_19508` `div-sub_binary64_19520` `frac-2neg_binary64_19526`

Counts

4 → 116

Calls

4 calls:

14.0ms	(.f64 (/.f64 1 a) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) 2))
6.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 z 9) t)) 2)
5.0ms	(.f64 (.f64 z 9) t)
4.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))

series244.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

123.0ms	(.f64 (/.f64 1 a) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) 2))
56.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 z 9) t)) 2)
48.0ms	(-.f64 (.f64 x y) (.f64 (*.f64 z 9) t))
16.0ms	(.f64 (.f64 z 9) t)

simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4993	2649
1	4993	2649

prune151.0ms (1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	122	6	128
Fresh	5	6	11
Picked	0	1	1
Done	0	0	0
Total	127	13	140

Error

4.6b

Counts

140 → 13

Compiler

Compiled 3012 to 1919 computations (36.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 z 9) t)
0.4b	(/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 z 9) t)) (sqrt.f64 2))
0.5b	(/.f64 (/.f64 1 a) (sqrt.f64 2))
7.5b	(.f64 (/.f64 (/.f64 1 a) (sqrt.f64 2)) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (sqrt.f64 2)))

rewrite113.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

353×	`times-frac_binary64_19521`
259×	`add-sqr-sqrt_binary64_19537`
185×	`*-un-lft-identity_binary64_19515`
179×	`add-cube-cbrt_binary64_19550`
118×	`sqrt-prod_binary64_19531`
83×	`associate-l_binary64_19456`
55×	`add-exp-log_binary64_19553`
37×	`add-cbrt-cube_binary64_19551`
25×	`associate-r_binary64_19455`
24×	`div-exp_binary64_19566`
21×	`unswap-sqr_binary64_19483`
17×	`div-inv_binary64_19512`
16×	`associate-/l*_binary64_19460`
13×	`cbrt-undiv_binary64_19549` `prod-exp_binary64_19564`
12×	`associate-/r*_binary64_19459`
11×	`pow1_binary64_19576`
9×	`cbrt-unprod_binary64_19548`
4×	`add-log-exp_binary64_19554` `pow-prod-down_binary64_19586`
3×	`associate-/l/_binary64_19462` `rec-exp_binary64_19565` `1-exp_binary64_19559`
2×	`clear-num_binary64_19514` `*-commutative_binary64_19446` `frac-2neg_binary64_19526`
1×	`associate-r/_binary64_19457` `flip3--_binary64_19519` `associate-l/_binary64_19458` `frac-times_binary64_19525` `div-sub_binary64_19520` `flip--_binary64_19490`

Counts

4 → 327

Calls

4 calls:

47.0ms	(.f64 (/.f64 (/.f64 1 a) (sqrt.f64 2)) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (sqrt.f64 2)))
8.0ms	(/.f64 (/.f64 1 a) (sqrt.f64 2))
7.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 z 9) t)) (sqrt.f64 2))
5.0ms	(.f64 (.f64 z 9) t)

series455.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

282.0ms	(.f64 (/.f64 (/.f64 1 a) (sqrt.f64 2)) (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (sqrt.f64 2)))
123.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 z 9) t)) (sqrt.f64 2))
34.0ms	(/.f64 (/.f64 1 a) (sqrt.f64 2))
14.0ms	(.f64 (.f64 z 9) t)

simplify152.0ms (1%)

Algorithm

1×	egg-herbie

Counts

339 → 339

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4975	8920
1	4975	8920

prune672.0ms (4.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	335	4	339
Fresh	4	7	11
Picked	1	0	1
Done	0	1	1
Total	340	12	352

Error

4.6b

Counts

352 → 12

Compiler

Compiled 9841 to 6967 computations (29.2% saved)

localize15.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 z 9) t)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
0.3b	(/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 z 9) t)) (sqrt.f64 (sqrt.f64 2)))
0.5b	(/.f64 (/.f64 1 a) (sqrt.f64 2))
7.5b	(.f64 (/.f64 (/.f64 1 a) (sqrt.f64 2)) (/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))

rewrite586.0ms (4%)

Algorithm

1×	rewrite-expression-head

Rules

1648×	`times-frac_binary64_19521`
1383×	`sqrt-prod_binary64_19531`
1156×	`add-sqr-sqrt_binary64_19537`
749×	`*-un-lft-identity_binary64_19515`
723×	`add-cube-cbrt_binary64_19550`
283×	`associate-r_binary64_19455`
91×	`unswap-sqr_binary64_19483`
82×	`associate-l_binary64_19456`
80×	`add-exp-log_binary64_19553`
52×	`add-cbrt-cube_binary64_19551`
47×	`associate-/l*_binary64_19460`
43×	`div-exp_binary64_19566`
37×	`div-inv_binary64_19512`
25×	`cbrt-undiv_binary64_19549`
24×	`associate-/r*_binary64_19459`
15×	`prod-exp_binary64_19564`
9×	`cbrt-unprod_binary64_19548`
6×	`pow1_binary64_19576`
4×	`associate-/l/_binary64_19462` `add-log-exp_binary64_19554` `rec-exp_binary64_19565` `1-exp_binary64_19559`
3×	`clear-num_binary64_19514` `div-sub_binary64_19520` `frac-2neg_binary64_19526`
1×	`associate-r/_binary64_19457` `flip3--_binary64_19519` `associate-l/_binary64_19458` `frac-times_binary64_19525` `*-commutative_binary64_19446` `flip--_binary64_19490` `pow-prod-down_binary64_19586`

Counts

4 → 995

Calls

4 calls:

340.0ms	(.f64 (/.f64 (/.f64 1 a) (sqrt.f64 2)) (/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
20.0ms	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 z 9) t)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
9.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 z 9) t)) (sqrt.f64 (sqrt.f64 2)))
8.0ms	(/.f64 (/.f64 1 a) (sqrt.f64 2))

series583.0ms (4%)

Counts

4 → 12

Calls

4 calls:

283.0ms	(.f64 (/.f64 (/.f64 1 a) (sqrt.f64 2)) (/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 (.f64 z 9) t)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2))))
148.0ms	(/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 z 9) t)) (sqrt.f64 (sqrt.f64 2)))
120.0ms	(/.f64 (/.f64 (-.f64 (.f64 x y) (.f64 (*.f64 z 9) t)) (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
32.0ms	(/.f64 (/.f64 1 a) (sqrt.f64 2))

simplify399.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1007 → 1007

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5501	41982

prune4.3s (29.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	1002	5	1007
Fresh	6	4	10
Picked	1	0	1
Done	0	1	1
Total	1009	10	1019

Error

4.6b

Counts

1019 → 10

Compiler

Compiled 39292 to 29139 computations (25.8% saved)

regimes2.1s (14.3%)

Accuracy

Total 0.7b remaining (16.2%)

Threshold costs 0.7b (16.2%)

Compiler

Compiled 23568 to 21336 computations (9.5% saved)

bsearch3.0ms (0%)

Compiler: Compiled 9 to 10 computations (-11.1% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	114	79
1	114	79

end0.0ms (0%)

sample2.4s (16.3%)

Algorithm

1×

intervals

Results

353.0ms	8000×	body	128	valid
131.0ms	3146×	body	128	invalid

Compiler

Compiled 1796 to 1602 computations (10.8% saved)

Details

analyze1.3s (8.9%)

sample30.0ms (0.2%)

simplify574.0ms (3.9%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite20.0ms (0.1%)

series134.0ms (0.9%)

simplify75.0ms (0.5%)

prune85.0ms (0.6%)

localize16.0ms (0.1%)

rewrite39.0ms (0.3%)

series244.0ms (1.7%)

simplify78.0ms (0.5%)

prune151.0ms (1%)

localize13.0ms (0.1%)

rewrite113.0ms (0.8%)

series455.0ms (3.1%)

simplify152.0ms (1%)

prune672.0ms (4.6%)

localize15.0ms (0.1%)

rewrite586.0ms (4%)

series583.0ms (4%)

simplify399.0ms (2.7%)

prune4.3s (29.9%)

regimes2.1s (14.3%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.4s (16.3%)

Profiling