Details

analyze51.0ms (1.8%)

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
0%	74.9%	25.1%	4
18.7%	56.2%	25.1%	5
28.1%	34.3%	37.6%	6
34.3%	28.1%	37.6%	7
39%	17.2%	43.8%	8
41%	13.7%	45.4%	9
43.1%	8.4%	48.5%	10
44%	6.7%	49.3%	11
45%	4.1%	50.8%	12
45.4%	3.3%	51.2%	13
45.9%	2.1%	52%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample14.0ms (0.5%)

Algorithm

1×

intervals

Results

8.0ms	256×	body	128	valid
0.0ms	3×	body	128	nan
0.0ms	1×	body	128	invalid

Compiler

Compiled 17 to 17 computations (0% saved)

simplify173.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	188	12
1	188	12

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: 0.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
0.2b	(*.f64 y (sqrt.f64 x))

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2165`
7×	`add-log-exp_binary64_2182`
6×	`associate-r_binary64_2083` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
4×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `sqrt-prod_binary64_2159` `associate-+l+_binary64_2076` `add-cbrt-cube_binary64_2179`
3×	`associate-l_binary64_2084` `cancel-sign-sub-inv_binary64_2109`
2×	`sum-log_binary64_2234` `unswap-sqr_binary64_2111`
1×	`+-commutative_binary64_2073` `diff-log_binary64_2235` `sub-neg_binary64_2136` `associate-+l-_binary64_2078` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192` `flip3-+_binary64_2146` `flip-+_binary64_2117` `*-commutative_binary64_2074`

Counts

2 → 39

Calls

2 calls:

8.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))
6.0ms	(*.f64 y (sqrt.f64 x))

series102.0ms (3.6%)

Counts

2 → 6

Calls

2 calls:

59.0ms	(*.f64 y (sqrt.f64 x))
43.0ms	(+.f64 (-.f64 1 x) (*.f64 y (sqrt.f64 x)))

simplify56.0ms (2%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5082	594

prune75.0ms (2.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	5	46

Merged error: 0.0b

Counts

46 → 5

Compiler

Compiled 1156 to 663 computations (42.6% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 x))
0.1b	(sqrt.f64 (sqrt.f64 x))
0.2b	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
0.3b	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

rewrite32.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`sqrt-prod_binary64_2159`
25×	`add-sqr-sqrt_binary64_2165`
18×	`associate-r_binary64_2083`
15×	`pow1_binary64_2204` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
11×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
8×	`sqrt-pow1_binary64_2161`
4×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `add-log-exp_binary64_2182` `cbrt-unprod_binary64_2176` `associate-l_binary64_2084` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192`
3×	`unswap-sqr_binary64_2111`
2×	`*-commutative_binary64_2074`

Counts

4 → 88

Calls

4 calls:

12.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))
8.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
2.0ms	(sqrt.f64 (sqrt.f64 x))
2.0ms	(sqrt.f64 (sqrt.f64 x))

series345.0ms (12%)

Counts

4 → 12

Calls

4 calls:

101.0ms	(sqrt.f64 (sqrt.f64 x))
100.0ms	(sqrt.f64 (sqrt.f64 x))
82.0ms	(*.f64 y (sqrt.f64 (sqrt.f64 x)))
60.0ms	(.f64 (.f64 y (sqrt.f64 (sqrt.f64 x))) (sqrt.f64 (sqrt.f64 x)))

simplify66.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5316	1029

prune95.0ms (3.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	99	6	105

Merged error: 0b

Counts

105 → 6

Compiler

Compiled 1943 to 807 computations (58.5% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 1 x) (.f64 (.f64 y (pow.f64 x 1/4)) (sqrt.f64 (sqrt.f64 x))))
0.1b	(sqrt.f64 (sqrt.f64 x))
0.2b	(*.f64 y (pow.f64 x 1/4))
0.3b	(.f64 (.f64 y (pow.f64 x 1/4)) (sqrt.f64 (sqrt.f64 x)))

rewrite35.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_2165`
19×	`add-exp-log_binary64_2181` `sqrt-prod_binary64_2159`
16×	`associate-r_binary64_2083`
13×	`add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
11×	`add-cbrt-cube_binary64_2179`
10×	`prod-exp_binary64_2192`
9×	`add-log-exp_binary64_2182`
8×	`pow1_binary64_2204`
4×	`unpow-prod-down_binary64_2222` `cbrt-unprod_binary64_2176` `associate-+l+_binary64_2076` `associate-l_binary64_2084` `sqrt-pow1_binary64_2161`
3×	`unswap-sqr_binary64_2111` `cancel-sign-sub-inv_binary64_2109`
2×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `pow-to-exp_binary64_2212` `sum-log_binary64_2234` `sqr-pow_binary64_2115` `*-commutative_binary64_2074` `pow-exp_binary64_2211`
1×	`+-commutative_binary64_2073` `diff-log_binary64_2235` `sub-neg_binary64_2136` `associate-+l-_binary64_2078` `pow-prod-down_binary64_2214` `flip3-+_binary64_2146` `flip-+_binary64_2117`

Counts

4 → 86

Calls

4 calls:

10.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (pow.f64 x 1/4)) (sqrt.f64 (sqrt.f64 x))))
10.0ms	(.f64 (.f64 y (pow.f64 x 1/4)) (sqrt.f64 (sqrt.f64 x)))
6.0ms	(*.f64 y (pow.f64 x 1/4))
2.0ms	(sqrt.f64 (sqrt.f64 x))

series385.0ms (13.4%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(.f64 (.f64 y (pow.f64 x 1/4)) (sqrt.f64 (sqrt.f64 x)))
105.0ms	(sqrt.f64 (sqrt.f64 x))
92.0ms	(*.f64 y (pow.f64 x 1/4))
80.0ms	(+.f64 (-.f64 1 x) (.f64 (.f64 y (pow.f64 x 1/4)) (sqrt.f64 (sqrt.f64 x))))

simplify92.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4854	1442
1	4854	1442

prune111.0ms (3.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	98	6	104

Merged error: 0b

Counts

104 → 6

Compiler

Compiled 2011 to 1193 computations (40.7% saved)

localize13.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (-.f64 1 x) (.f64 y (.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 x)))))
0.1b	(sqrt.f64 (sqrt.f64 x))
0.2b	(.f64 y (.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 x))))
0.5b	(*.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 x)))

rewrite39.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_2165`
28×	`sqrt-prod_binary64_2159`
19×	`add-exp-log_binary64_2181`
13×	`add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
11×	`add-cbrt-cube_binary64_2179`
10×	`associate-r_binary64_2083` `associate-l_binary64_2084` `prod-exp_binary64_2192`
9×	`pow1_binary64_2204` `add-log-exp_binary64_2182` `unswap-sqr_binary64_2111`
7×	`sqrt-pow1_binary64_2161`
6×	`unpow-prod-down_binary64_2222`
4×	`cbrt-unprod_binary64_2176` `associate-+l+_binary64_2076` `sqr-pow_binary64_2115`
3×	`pow1/2_binary64_2223` `cancel-sign-sub-inv_binary64_2109`
2×	`rem-sqrt-square_binary64_2156` `pow-to-exp_binary64_2212` `pow-prod-up_binary64_2213` `sum-log_binary64_2234` `*-commutative_binary64_2074` `pow-exp_binary64_2211`
1×	`+-commutative_binary64_2073` `diff-log_binary64_2235` `sub-neg_binary64_2136` `associate-+l-_binary64_2078` `pow-prod-down_binary64_2214` `flip3-+_binary64_2146` `flip-+_binary64_2117`

Counts

4 → 94

Calls

4 calls:

10.0ms	(+.f64 (-.f64 1 x) (.f64 y (.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 x)))))
10.0ms	(*.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 x)))
9.0ms	(.f64 y (.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 x))))
2.0ms	(sqrt.f64 (sqrt.f64 x))

series339.0ms (11.8%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(.f64 y (.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 x))))
92.0ms	(sqrt.f64 (sqrt.f64 x))
84.0ms	(+.f64 (-.f64 1 x) (.f64 y (.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 x)))))
46.0ms	(*.f64 (pow.f64 x 1/4) (sqrt.f64 (sqrt.f64 x)))

simplify130.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4853	1786
1	4853	1786

prune98.0ms (3.4%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	106	6	112

Merged error: 0b

Counts

112 → 6

Compiler

Compiled 1964 to 1116 computations (43.2% saved)

regimes44.0ms (1.5%)

Compiler: Compiled 260 to 208 computations (20% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	12
1	20	12

end0.0ms (0%)

sample519.0ms (18.1%)

Algorithm

1×

intervals

Results

244.0ms	7999×	body	128	valid
4.0ms	137×	body	128	nan
2.0ms	68×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 97 to 79 computations (18.6% saved)

Details

analyze51.0ms (1.8%)

sample14.0ms (0.5%)

simplify173.0ms (6%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite17.0ms (0.6%)

series102.0ms (3.6%)

simplify56.0ms (2%)

prune75.0ms (2.6%)

localize8.0ms (0.3%)

rewrite32.0ms (1.1%)

series345.0ms (12%)

simplify66.0ms (2.3%)

prune95.0ms (3.3%)

localize15.0ms (0.5%)

rewrite35.0ms (1.2%)

series385.0ms (13.4%)

simplify92.0ms (3.2%)

prune111.0ms (3.9%)

localize13.0ms (0.5%)

rewrite39.0ms (1.4%)

series339.0ms (11.8%)

simplify130.0ms (4.5%)

prune98.0ms (3.4%)

regimes44.0ms (1.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample519.0ms (18.1%)

Profiling