Details

analyze1.3s (8.8%)

Algorithm

2×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5331	64
0	3	3
1	3	3

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
31.2%	68.6%	0.1%	8
35.9%	64%	0.1%	9
35.9%	64%	0.1%	9
47.6%	49.9%	2.5%	10
47.6%	49.9%	2.5%	10
49.1%	46.8%	4%	11
49.1%	46.8%	4%	11
51.1%	44.1%	4.8%	12
51.1%	44.1%	4.8%	12
60.2%	29.9%	9.9%	13
60.2%	29.9%	9.9%	13
60.6%	27.9%	11.6%	14
60.6%	27.9%	11.6%	14

Symmetry

(sort x y)

Compiler

Compiled 24 to 20 computations (16.7% saved)

sample633.0ms (4.4%)

Algorithm

2×

intervals

Results

20.0ms	512×	body	128	valid
7.0ms	164×	body	128	invalid

Compiler

Compiled 4151 to 4494 computations (-8.3% saved)

simplify85.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5346	16

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

Error

14.5b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

0.1b	(.f64 (.f64 z z) (+.f64 z 1))
14.1b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))

rewrite81.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

6.1b

Rules

28×	`add-exp-log_binary64_10687` `add-cbrt-cube_binary64_10685`
12×	`prod-exp_binary64_10698` `cbrt-unprod_binary64_10682`
7×	`pow1_binary64_10710`
6×	`div-exp_binary64_10700` `cbrt-undiv_binary64_10683`
5×	`*-un-lft-identity_binary64_10649`
4×	`add-sqr-sqrt_binary64_10671` `associate-r/_binary64_10591` `associate-r*_binary64_10589`
3×	`add-cube-cbrt_binary64_10684` `pow-prod-down_binary64_10720`
2×	`add-log-exp_binary64_10688` `flip3-+_binary64_10652` `associate-/r/_binary64_10595` `flip-+_binary64_10623`
1×	`frac-2neg_binary64_10660` `times-frac_binary64_10655` `clear-num_binary64_10648` `div-inv_binary64_10646` `associate-/l_binary64_10594` `associate-/r_binary64_10593` `unswap-sqr_binary64_10617` `distribute-rgt-in_binary64_10599` `distribute-lft-in_binary64_10598` `associate-l_binary64_10590` `distribute-lft-out_binary64_10600` `*-commutative_binary64_10580`

Counts

2 → 51

Calls

2 calls:

10.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
8.0ms	(.f64 (.f64 z z) (+.f64 z 1))

Compiler

Compiled 1000 to 448 computations (55.2% saved)

series385.0ms (2.7%)

Error

14.5b

Counts

2 → 24

Calls

2 calls:

306.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
60.0ms	(.f64 (.f64 z z) (+.f64 z 1))

Compiler

Compiled 763 to 504 computations (33.9% saved)

simplify65.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4961	1149
1	4961	1149

prune77.0ms (0.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Error

2.6b

Counts

76 → 7

Compiler

Compiled 1150 to 548 computations (52.3% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (+.f64 z 1))
4.4b	(/.f64 (*.f64 z z) (/.f64 y (+.f64 z 1)))
6.2b	(/.f64 x (/.f64 (*.f64 z z) (/.f64 y (+.f64 z 1))))

rewrite320.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

243×	`times-frac_binary64_10655`
132×	`*-un-lft-identity_binary64_10649`
88×	`add-cube-cbrt_binary64_10684` `add-sqr-sqrt_binary64_10671`
45×	`associate-/r*_binary64_10593`
35×	`add-exp-log_binary64_10687` `add-cbrt-cube_binary64_10685`
22×	`distribute-lft-out_binary64_10600`
20×	`associate-/r/_binary64_10595`
18×	`div-exp_binary64_10700` `cbrt-undiv_binary64_10683`
13×	`div-inv_binary64_10646`
7×	`flip3-+_binary64_10652` `flip-+_binary64_10623` `associate-/l*_binary64_10594`
4×	`prod-exp_binary64_10698` `cbrt-unprod_binary64_10682`
3×	`pow1_binary64_10710` `add-log-exp_binary64_10688` `frac-2neg_binary64_10660` `clear-num_binary64_10648`

Counts

3 → 205

Calls

3 calls:

13.0ms	(/.f64 x (/.f64 (*.f64 z z) (/.f64 y (+.f64 z 1))))
10.0ms	(/.f64 (*.f64 z z) (/.f64 y (+.f64 z 1)))
6.0ms	(/.f64 y (+.f64 z 1))

Compiler

Compiled 4356 to 2315 computations (46.9% saved)

series593.0ms (4.2%)

Error

2.6b

Counts

3 → 42

Calls

3 calls:

306.0ms	(/.f64 x (/.f64 (*.f64 z z) (/.f64 y (+.f64 z 1))))
160.0ms	(/.f64 (*.f64 z z) (/.f64 y (+.f64 z 1)))
90.0ms	(/.f64 y (+.f64 z 1))

Compiler

Compiled 1383 to 902 computations (34.8% saved)

simplify91.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

247 → 247

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5049	5043

prune276.0ms (1.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	239	8	247
Fresh	4	1	5
Picked	0	1	1
Done	1	0	1
Total	244	10	254

Error

0.0b

Counts

254 → 10

Compiler

Compiled 4520 to 2177 computations (51.8% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (+.f64 z 1))
0.1b	(/.f64 z (/.f64 y (+.f64 z 1)))
3.0b	(/.f64 (/.f64 x z) (/.f64 z (/.f64 y (+.f64 z 1))))

rewrite2.3s (16.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

2681×	`times-frac_binary64_10655`
1369×	`*-un-lft-identity_binary64_10649`
1085×	`add-cube-cbrt_binary64_10684` `add-sqr-sqrt_binary64_10671`
142×	`distribute-lft-out_binary64_10600`
123×	`div-inv_binary64_10646`
110×	`associate-/r/_binary64_10595`
81×	`associate-/r*_binary64_10593`
47×	`flip3-+_binary64_10652` `flip-+_binary64_10623`
31×	`add-exp-log_binary64_10687` `add-cbrt-cube_binary64_10685`
19×	`div-exp_binary64_10700` `cbrt-undiv_binary64_10683` `associate-/l*_binary64_10594`
3×	`pow1_binary64_10710` `add-log-exp_binary64_10688` `frac-2neg_binary64_10660` `clear-num_binary64_10648`
1×	`associate-/l/_binary64_10596`

Counts

3 → 986

Calls

3 calls:

38.0ms	(/.f64 (/.f64 x z) (/.f64 z (/.f64 y (+.f64 z 1))))
9.0ms	(/.f64 z (/.f64 y (+.f64 z 1)))
5.0ms	(/.f64 y (+.f64 z 1))

Compiler

Compiled 29004 to 13274 computations (54.2% saved)

series545.0ms (3.8%)

Error

0.0b

Counts

3 → 42

Calls

3 calls:

304.0ms	(/.f64 (/.f64 x z) (/.f64 z (/.f64 y (+.f64 z 1))))
126.0ms	(/.f64 z (/.f64 y (+.f64 z 1)))
84.0ms	(/.f64 y (+.f64 z 1))

Compiler

Compiled 1391 to 872 computations (37.3% saved)

simplify366.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

1028 → 1028

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4996	38000
1	4996	38000

prune1.5s (10.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	1026	2	1028
Fresh	3	5	8
Picked	0	1	1
Done	0	1	1
Total	1029	9	1038

Error

Counts

1038 → 9

Compiler

Compiled 26806 to 10433 computations (61.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (+.f64 z 1))
1.4b	(.f64 (/.f64 1 z) (.f64 (/.f64 x z) (/.f64 y (+.f64 z 1))))
2.7b	(*.f64 (/.f64 x z) (/.f64 y (+.f64 z 1)))

rewrite211.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

94×	`add-exp-log_binary64_10687`
58×	`add-cbrt-cube_binary64_10685`
48×	`*-un-lft-identity_binary64_10649`
46×	`add-sqr-sqrt_binary64_10671` `times-frac_binary64_10655`
40×	`prod-exp_binary64_10698`
34×	`add-cube-cbrt_binary64_10684`
31×	`div-exp_binary64_10700`
26×	`associate-l_binary64_10590`
22×	`cbrt-unprod_binary64_10682`
19×	`associate-r_binary64_10589`
18×	`cbrt-undiv_binary64_10683`
10×	`pow1_binary64_10710`
7×	`distribute-lft-out_binary64_10600`
6×	`frac-times_binary64_10659` `associate-*r/_binary64_10591`
5×	`1-exp_binary64_10693` `rec-exp_binary64_10699`
4×	`pow-prod-down_binary64_10720` `unswap-sqr_binary64_10617` `associate-l/_binary64_10592` `div-inv_binary64_10646` `associate-/r/_binary64_10595` `associate-/r_binary64_10593`
3×	`add-log-exp_binary64_10688` `associate-/l*_binary64_10594`
2×	`flip3-+_binary64_10652` `flip-+_binary64_10623` `*-commutative_binary64_10580`
1×	`frac-2neg_binary64_10660` `clear-num_binary64_10648`

Counts

3 → 149

Calls

3 calls:

15.0ms	(*.f64 (/.f64 x z) (/.f64 y (+.f64 z 1)))
15.0ms	(.f64 (/.f64 1 z) (.f64 (/.f64 x z) (/.f64 y (+.f64 z 1))))
6.0ms	(/.f64 y (+.f64 z 1))

Compiler

Compiled 3240 to 1790 computations (44.8% saved)

series713.0ms (5%)

Error

Counts

3 → 51

Calls

3 calls:

313.0ms	(.f64 (/.f64 1 z) (.f64 (/.f64 x z) (/.f64 y (+.f64 z 1))))
263.0ms	(*.f64 (/.f64 x z) (/.f64 y (+.f64 z 1)))
88.0ms	(/.f64 y (+.f64 z 1))

Compiler

Compiled 1929 to 1230 computations (36.2% saved)

simplify105.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4976	3269
1	4976	3269

prune192.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	199	1	200
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	200	9	209

Error

Counts

209 → 9

Compiler

Compiled 3419 to 1757 computations (48.6% saved)

regimes1.5s (10.4%)

Accuracy

Total 1.2b remaining (100%)

Threshold costs 0b (0%)

Compiler

Compiled 15512 to 11825 computations (23.8% saved)

bsearch0.0ms (0%)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	40
1	15	40

Remove

(sort x y)

Compiler

Compiled 52 to 40 computations (23.1% saved)

end0.0ms (0%)

sample2.9s (20.4%)

Algorithm

1×

intervals

Results

282.0ms	8000×	body	128	valid
93.0ms	2785×	body	128	invalid

Compiler

Compiled 2523 to 1926 computations (23.7% saved)

Details

analyze1.3s (8.8%)

sample633.0ms (4.4%)

simplify85.0ms (0.6%)

prune2.0ms (0%)

localize7.0ms (0%)

rewrite81.0ms (0.6%)

series385.0ms (2.7%)

simplify65.0ms (0.5%)

prune77.0ms (0.5%)

localize7.0ms (0%)

rewrite320.0ms (2.2%)

series593.0ms (4.2%)

simplify91.0ms (0.6%)

prune276.0ms (1.9%)

localize8.0ms (0.1%)

rewrite2.3s (16.2%)

series545.0ms (3.8%)

simplify366.0ms (2.6%)

prune1.5s (10.7%)

localize8.0ms (0.1%)

rewrite211.0ms (1.5%)

series713.0ms (5%)

simplify105.0ms (0.7%)

prune192.0ms (1.3%)

regimes1.5s (10.4%)

bsearch0.0ms (0%)

simplify10.0ms (0.1%)

end0.0ms (0%)

sample2.9s (20.4%)

Profiling