Details

analyze17.0ms (0.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	18.7%	81.3%	0
0%	18.7%	81.3%	1
0%	18.7%	81.3%	2
0%	18.7%	81.3%	3
0%	18.7%	81.3%	4
4.7%	14%	81.3%	5
5.3%	13.5%	81.3%	6
18.1%	0.6%	81.3%	7
18.1%	0.6%	81.3%	8
18.6%	0.1%	81.3%	9
18.6%	0.1%	81.3%	10
18.7%	0%	81.3%	11
18.7%	0%	81.3%	12
18.7%	0%	81.3%	13
18.7%	0%	81.3%	14

Compiler

Compiled 23 to 15 computations (34.8% saved)

sample23.0ms (1.1%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify262.0ms (12.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (170.0ms)

Iter	Nodes	Cost
0	4979	22
1	4979	22

prune2.0ms (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: 22.1b

Counts

2 → 1

Compiler

Compiled 30 to 18 computations (40% saved)

localize9.0ms (0.4%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
21.8b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite24.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64_1389`
7×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
5×	`flip3-+_binary64_1445` `flip-+_binary64_1416`
4×	`add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464` `frac-times_binary64_1452` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
3×	`associate-/r*_binary64_1386` `times-frac_binary64_1448` `flip3--_binary64_1446` `flip--_binary64_1417`
2×	`associate-r/_binary64_1384` `cbrt-undiv_binary64_1476` `associate-/r/_binary64_1388` `pow1_binary64_1503` `associate-l/_binary64_1385` `div-exp_binary64_1493`
1×	`cbrt-unprod_binary64_1475` `sum-log_binary64_1533` `div-inv_binary64_1439` `clear-num_binary64_1441` `associate-/l*_binary64_1387` `+-commutative_binary64_1372` `frac-2neg_binary64_1453` `prod-exp_binary64_1491`

Counts

2 → 42

Calls

2 calls:

16.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series68.0ms (3.2%)

Counts

2 → 6

Calls

2 calls:

47.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
22.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify33.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5131	969

prune44.0ms (2.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	44	4	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	45	4	49

Merged error: 0.5b

Counts

49 → 4

Compiler

Compiled 1065 to 207 computations (80.6% saved)

localize0.0ms (0%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify6.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune3.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	3	3
Picked	1	1
Done	0	0
Total	4	4

Merged error: 0.5b

Counts

4 → 4

Compiler

Compiled 33 to 21 computations (36.4% saved)

localize8.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(-.f64 (.f64 x x) (.f64 y y))
0.0b	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y))))
21.8b	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y)))

rewrite49.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64_1448`
64×	`add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
22×	`associate-/r*_binary64_1386`
17×	`add-exp-log_binary64_1480` `difference-of-squares_binary64_1411`
11×	`add-cbrt-cube_binary64_1478` `associate-/r/_binary64_1388`
8×	`add-log-exp_binary64_1481` `div-exp_binary64_1493`
6×	`div-inv_binary64_1439` `associate-/l*_binary64_1387` `flip3--_binary64_1446` `flip--_binary64_1417`
5×	`pow1_binary64_1503`
4×	`cbrt-undiv_binary64_1476`
2×	`associate-/l/_binary64_1389` `clear-num_binary64_1441` `1-exp_binary64_1486` `rec-exp_binary64_1492` `frac-2neg_binary64_1453` `flip3-+_binary64_1445` `flip-+_binary64_1416`
1×	`inv-pow_binary64_1527` `cancel-sign-sub-inv_binary64_1408` `sum-log_binary64_1533` `sub-neg_binary64_1435` `+-commutative_binary64_1372` `pow-flip_binary64_1516` `diff-log_binary64_1534`

Counts

4 → 155

Calls

4 calls:

12.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y))))
9.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(-.f64 (.f64 x x) (.f64 y y))

series115.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y)))
36.0ms	(/.f64 1 (/.f64 (+.f64 (.f64 x x) (.f64 y y)) (-.f64 (.f64 x x) (.f64 y y))))
21.0ms	(-.f64 (.f64 x x) (.f64 y y))
21.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify87.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5172	5202

prune127.0ms (6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	167	4	171

Merged error: 0.5b

Counts

171 → 4

Compiler

Compiled 4545 to 734 computations (83.9% saved)

localize9.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.2b	(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (+.f64 (.f64 x x) (*.f64 y y))))
21.4b	(/.f64 (+.f64 x y) (+.f64 (.f64 x x) (.f64 y y)))

rewrite38.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_1442`
28×	`add-sqr-sqrt_binary64_1464`
25×	`times-frac_binary64_1448`
21×	`add-cube-cbrt_binary64_1477`
18×	`associate-r_binary64_1382`
10×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480`
7×	`distribute-lft-out_binary64_1393`
5×	`associate-l_binary64_1383` `add-log-exp_binary64_1481` `pow1_binary64_1503`
4×	`associate-/r/_binary64_1388` `associate-/l*_binary64_1387` `flip3-+_binary64_1445` `flip-+_binary64_1416`
3×	`associate-/r*_binary64_1386`
2×	`cbrt-undiv_binary64_1476` `cbrt-unprod_binary64_1475` `associate-/l/_binary64_1389` `div-inv_binary64_1439` `flip3--_binary64_1446` `flip--_binary64_1417` `frac-times_binary64_1452` `prod-exp_binary64_1491` `associate-*l/_binary64_1385` `div-exp_binary64_1493` `unswap-sqr_binary64_1410`
1×	`associate-r/_binary64_1384` `sum-log_binary64_1533` `clear-num_binary64_1441` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `-commutative_binary64_1373` `frac-2neg_binary64_1453` `difference-of-squares_binary64_1411` `distribute-lft-out--_binary64_1394`

Counts

3 → 89

Calls

3 calls:

16.0ms	(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (+.f64 (.f64 x x) (*.f64 y y))))
10.0ms	(/.f64 (+.f64 x y) (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series91.0ms (4.3%)

Counts

3 → 9

Calls

3 calls:

41.0ms	(.f64 (-.f64 x y) (/.f64 (+.f64 x y) (+.f64 (.f64 x x) (*.f64 y y))))
30.0ms	(/.f64 (+.f64 x y) (+.f64 (.f64 x x) (.f64 y y)))
20.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify64.0ms (3%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5381	2173

prune59.0ms (2.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	98	0	98
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	98	4	102

Merged error: 0.5b

Counts

102 → 4

Compiler

Compiled 2245 to 324 computations (85.6% saved)

regimes95.0ms (4.5%)

Compiler: Compiled 504 to 254 computations (49.6% saved)

bsearch59.0ms (2.8%)

Steps

Iters	Range	Point
11	2.5861234271314185e-184	2.7405716536391272e-160	1.5816817489251754e-162
11	-2.794123426034212e-152	-4.04374074168056e-183	-1.5469202841278558e-162
9	-2.3830503814251755e+154	-2.141513692869074e+149	-1.3534529294603233e+154

Iters

Range

Point

2.5861234271314185e-184

2.7405716536391272e-160

1.5816817489251754e-162

-2.794123426034212e-152

-4.04374074168056e-183

-1.5469202841278558e-162

-2.3830503814251755e+154

-2.141513692869074e+149

-1.3534529294603233e+154

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	47	67
1	47	67

end0.0ms (0%)

sample813.0ms (38.6%)

Algorithm

1×

intervals

Results

308.0ms	8000×	body	128	valid
171.0ms	8000×	pre	128	true

Compiler

Compiled 246 to 128 computations (48% saved)

Details

analyze17.0ms (0.8%)

sample23.0ms (1.1%)

simplify262.0ms (12.5%)

prune2.0ms (0.1%)

localize9.0ms (0.4%)

rewrite24.0ms (1.1%)

series68.0ms (3.2%)

simplify33.0ms (1.6%)

prune44.0ms (2.1%)

localize0.0ms (0%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify6.0ms (0.3%)

prune3.0ms (0.1%)

localize8.0ms (0.4%)

rewrite49.0ms (2.3%)

series115.0ms (5.5%)

simplify87.0ms (4.1%)

prune127.0ms (6%)

localize9.0ms (0.4%)

rewrite38.0ms (1.8%)

series91.0ms (4.3%)

simplify64.0ms (3%)

prune59.0ms (2.8%)

regimes95.0ms (4.5%)

bsearch59.0ms (2.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample813.0ms (38.6%)

Profiling