Details

analyze12.0ms (0.4%)

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)

sample22.0ms (0.7%)

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)

simplify418.0ms (13.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5184	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: 19.1b

Counts

2 → 1

Compiler

Compiled 30 to 18 computations (40% saved)

localize8.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
18.8b	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))

rewrite22.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`associate-/l/_binary64_1402`
7×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
5×	`flip-+_binary64_1429` `flip3-+_binary64_1458`
4×	`add-sqr-sqrt_binary64_1477` `add-log-exp_binary64_1494` `frac-times_binary64_1465` `add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
3×	`associate-/r*_binary64_1399` `flip--_binary64_1430` `times-frac_binary64_1461` `flip3--_binary64_1459`
2×	`associate-r/_binary64_1397` `associate-/r/_binary64_1401` `pow1_binary64_1516` `div-exp_binary64_1506` `cbrt-undiv_binary64_1489` `associate-l/_binary64_1398`
1×	`prod-exp_binary64_1504` `clear-num_binary64_1454` `frac-2neg_binary64_1466` `associate-/l*_binary64_1400` `cbrt-unprod_binary64_1488` `div-inv_binary64_1452` `sum-log_binary64_1546` `+-commutative_binary64_1385`

Counts

2 → 42

Calls

2 calls:

14.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series130.0ms (4.3%)

Counts

2 → 6

Calls

2 calls:

87.0ms	(/.f64 (.f64 (-.f64 x y) (+.f64 x y)) (+.f64 (.f64 x x) (*.f64 y y)))
43.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify34.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5033	969

prune90.0ms (2.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	42	6	48
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	43	6	49

Merged error: 0.7b

Counts

49 → 6

Compiler

Compiled 1937 to 656 computations (66.1% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 y y) (.f64 x x))
0.0b	(+.f64 (.f64 x x) (.f64 y y))
18.8b	(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (neg.f64 (+.f64 (.f64 x x) (.f64 y y))))

rewrite30.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`times-frac_binary64_1461`
29×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490` `*-un-lft-identity_binary64_1455`
15×	`distribute-rgt-neg-in_binary64_1413` `distribute-lft-neg-in_binary64_1412`
12×	`difference-of-squares_binary64_1424`
10×	`associate-/r*_binary64_1399`
7×	`add-log-exp_binary64_1494`
5×	`neg-mul-1_binary64_1451` `add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
4×	`associate-/l*_binary64_1400`
3×	`pow1_binary64_1516`
2×	`associate-/r/_binary64_1401` `flip-+_binary64_1429` `associate-/l/_binary64_1402` `flip--_binary64_1430` `flip3-+_binary64_1458` `flip3--_binary64_1459` `distribute-neg-frac_binary64_1419`
1×	`div-exp_binary64_1506` `clear-num_binary64_1454` `cbrt-undiv_binary64_1489` `frac-2neg_binary64_1466` `diff-log_binary64_1547` `cancel-sign-sub-inv_binary64_1421` `sub-neg_binary64_1448` `div-inv_binary64_1452` `sum-log_binary64_1546` `+-commutative_binary64_1385` `div-sub_binary64_1460`

Counts

3 → 95

Calls

3 calls:

11.0ms	(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (neg.f64 (+.f64 (.f64 x x) (.f64 y y))))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))
4.0ms	(-.f64 (.f64 y y) (.f64 x x))

series166.0ms (5.4%)

Counts

3 → 9

Calls

3 calls:

86.0ms	(/.f64 (-.f64 (.f64 y y) (.f64 x x)) (neg.f64 (+.f64 (.f64 x x) (.f64 y y))))
43.0ms	(-.f64 (.f64 y y) (.f64 x x))
37.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify75.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5898	3152

prune86.0ms (2.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	104	0	104
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	104	6	110

Merged error: 0.7b

Counts

110 → 6

Compiler

Compiled 2864 to 419 computations (85.4% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
0.1b	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
18.7b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
18.7b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

rewrite91.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

115×	`add-sqr-sqrt_binary64_1477`
96×	`times-frac_binary64_1461`
95×	`*-un-lft-identity_binary64_1455`
57×	`sqrt-prod_binary64_1471` `add-cube-cbrt_binary64_1490`
36×	`associate-l_binary64_1396`
30×	`associate-r_binary64_1395`
18×	`add-cbrt-cube_binary64_1491` `add-exp-log_binary64_1493`
13×	`distribute-lft-out--_binary64_1407` `difference-of-squares_binary64_1424`
10×	`sqrt-div_binary64_1472`
9×	`unswap-sqr_binary64_1423`
8×	`pow1_binary64_1516`
6×	`distribute-lft-out_binary64_1406` `associate-/r/_binary64_1401` `associate-/r*_binary64_1399`
5×	`flip-+_binary64_1429` `div-exp_binary64_1506` `cbrt-undiv_binary64_1489` `associate-/l*_binary64_1400` `flip3-+_binary64_1458`
4×	`prod-exp_binary64_1504` `add-log-exp_binary64_1494` `cbrt-unprod_binary64_1488`
3×	`div-inv_binary64_1452`
2×	`sqrt-pow1_binary64_1473` `rem-sqrt-square_binary64_1468` `associate-/l/_binary64_1402` `pow1/2_binary64_1535`
1×	`associate-r/_binary64_1397` `clear-num_binary64_1454` `frac-times_binary64_1465` `-commutative_binary64_1386` `flip--_binary64_1430` `frac-2neg_binary64_1466` `flip3--_binary64_1459` `div-sub_binary64_1460` `associate-*l/_binary64_1398` `pow-prod-down_binary64_1526`

Counts

4 → 183

Calls

4 calls:

44.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
11.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

series294.0ms (9.6%)

Counts

4 → 12

Calls

4 calls:

103.0ms	(/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y))))
96.0ms	(.f64 (/.f64 (-.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))) (/.f64 (+.f64 x y) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y y)))))
48.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))
47.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y y)))

simplify99.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4964	5945
1	4964	5945

prune172.0ms (5.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	195	0	195
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	195	6	201

Merged error: 0.7b

Counts

201 → 6

Compiler

Compiled 6727 to 640 computations (90.5% saved)

localize10.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.3b	(/.f64 1 (+.f64 (.f64 x x) (.f64 y y)))
20.7b	(.f64 (.f64 (-.f64 x y) (+.f64 x y)) (/.f64 1 (+.f64 (.f64 x x) (.f64 y y))))

rewrite41.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-exp-log_binary64_1493`
18×	`add-sqr-sqrt_binary64_1477` `add-cube-cbrt_binary64_1490` `times-frac_binary64_1461` `*-un-lft-identity_binary64_1455`
17×	`add-cbrt-cube_binary64_1491`
16×	`frac-times_binary64_1465`
15×	`associate-r_binary64_1395`
12×	`prod-exp_binary64_1504` `associate-*l/_binary64_1398`
9×	`flip-+_binary64_1429` `pow1_binary64_1516` `flip3-+_binary64_1458`
6×	`div-exp_binary64_1506` `flip--_binary64_1430` `cbrt-unprod_binary64_1488` `flip3--_binary64_1459`
5×	`associate-*r/_binary64_1397` `add-log-exp_binary64_1494`
4×	`associate-/r/_binary64_1401`
3×	`1-exp_binary64_1499` `associate-/r_binary64_1399` `cbrt-undiv_binary64_1489` `associate-/l_binary64_1400` `rec-exp_binary64_1505` `pow-prod-down_binary64_1526`
2×	`div-inv_binary64_1452`
1×	`inv-pow_binary64_1540` `clear-num_binary64_1454` `pow-flip_binary64_1529` `-commutative_binary64_1386` `un-div-inv_binary64_1453` `frac-2neg_binary64_1466` `sum-log_binary64_1546` `+-commutative_binary64_1385` `associate-l*_binary64_1396`

Counts

3 → 100

Calls

3 calls:

19.0ms	(.f64 (.f64 (-.f64 x y) (+.f64 x y)) (/.f64 1 (+.f64 (.f64 x x) (.f64 y y))))
6.0ms	(/.f64 1 (+.f64 (.f64 x x) (.f64 y y)))
4.0ms	(+.f64 (.f64 x x) (.f64 y y))

series168.0ms (5.5%)

Counts

3 → 9

Calls

3 calls:

90.0ms	(.f64 (.f64 (-.f64 x y) (+.f64 x y)) (/.f64 1 (+.f64 (.f64 x x) (.f64 y y))))
43.0ms	(/.f64 1 (+.f64 (.f64 x x) (.f64 y y)))
35.0ms	(+.f64 (.f64 x x) (.f64 y y))

simplify76.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4925	2336
1	4925	2336

prune83.0ms (2.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	109	6	115

Merged error: 0.7b

Counts

115 → 6

Compiler

Compiled 2546 to 540 computations (78.8% saved)

regimes51.0ms (1.7%)

Compiler: Compiled 170 to 104 computations (38.8% saved)

bsearch55.0ms (1.8%)

Steps

Iters	Range	Point
8	4.310635927458171e-165	3.0118780988792484e-162	1.5801171599198037e-162
10	-1.6464378207315332e-152	-3.4206412201262403e-165	-1.561338403315553e-162
9	-1.6908961132726686e-17	-1.8874625850684502e-23	-1.6640725549120233e-17

Iters

Range

Point

4.310635927458171e-165

3.0118780988792484e-162

1.5801171599198037e-162

-1.6464378207315332e-152

-3.4206412201262403e-165

-1.561338403315553e-162

-1.6908961132726686e-17

-1.8874625850684502e-23

-1.6640725549120233e-17

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	65	46
1	65	46

end0.0ms (0%)

sample793.0ms (26%)

Algorithm

1×

intervals

Results

304.0ms	8000×	body	128	valid
171.0ms	8000×	pre	128	true

Compiler

Compiled 173 to 107 computations (38.2% saved)

Details

analyze12.0ms (0.4%)

sample22.0ms (0.7%)

simplify418.0ms (13.7%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

rewrite22.0ms (0.7%)

series130.0ms (4.3%)

simplify34.0ms (1.1%)

prune90.0ms (2.9%)

localize10.0ms (0.3%)

rewrite30.0ms (1%)

series166.0ms (5.4%)

simplify75.0ms (2.4%)

prune86.0ms (2.8%)

localize11.0ms (0.4%)

rewrite91.0ms (3%)

series294.0ms (9.6%)

simplify99.0ms (3.2%)

prune172.0ms (5.6%)

localize10.0ms (0.3%)

rewrite41.0ms (1.3%)

series168.0ms (5.5%)

simplify76.0ms (2.5%)

prune83.0ms (2.7%)

regimes51.0ms (1.7%)

bsearch55.0ms (1.8%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample793.0ms (26%)

Profiling