Details

analyze20.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
74.9%	25%	0.1%	4
74.9%	25%	0.1%	5
87.4%	12.5%	0.1%	6
87.4%	12.5%	0.1%	7
93.7%	6.2%	0.1%	8
93.7%	6.2%	0.1%	9
96.8%	3.1%	0.1%	10
96.8%	3.1%	0.1%	11
98.3%	1.6%	0.1%	12
98.3%	1.6%	0.1%	13
99.1%	0.8%	0.1%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample12.0ms (0.3%)

Algorithm

1×

intervals

Results

6.0ms	251×	body	128	valid
0.0ms	3×	body	1024	valid
0.0ms	2×	body	512	valid

Compiler

Compiled 17 to 17 computations (0% saved)

simplify174.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	55	12
1	55	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: 0.0b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize7.0ms (0.2%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`add-log-exp_binary64_6179` `*-un-lft-identity_binary64_6143`
1×	`distribute-lft-out_binary64_6096` `add-exp-log_binary64_6178` `add-cube-cbrt_binary64_6175` `add-cbrt-cube_binary64_6176` `flip3-+_binary64_6146` `sum-log_binary64_6231` `+-commutative_binary64_6075` `add-sqr-sqrt_binary64_6164` `flip-+_binary64_6117` `pow1_binary64_6201`

Counts

1 → 12

Calls

1 calls:

8.0ms

(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

series40.0ms (1%)

Counts

1 → 3

Calls

1 calls:

39.0ms

(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

simplify67.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5380	259

prune19.0ms (0.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	4	16

Merged error: 0.0b

Counts

16 → 4

Compiler

Compiled 261 to 135 computations (48.3% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))
0.0b	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
0.0b	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
0.3b	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))

rewrite54.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64_6143` `sqrt-prod_binary64_6158`
28×	`add-sqr-sqrt_binary64_6164`
21×	`pow1_binary64_6201`
16×	`sqrt-div_binary64_6159`
14×	`add-cube-cbrt_binary64_6175`
11×	`swap-sqr_binary64_6110`
10×	`sqrt-pow1_binary64_6160` `pow1/2_binary64_6220`
9×	`distribute-lft-out_binary64_6096` `flip3-+_binary64_6146` `flip-+_binary64_6117`
7×	`associate-r_binary64_6085` `associate-l_binary64_6086`
6×	`add-log-exp_binary64_6179` `add-exp-log_binary64_6178` `add-cbrt-cube_binary64_6176`
5×	`pow-prod-up_binary64_6210`
4×	`frac-times_binary64_6153` `unswap-sqr_binary64_6111`
3×	`pow-sqr_binary64_6116` `pow-prod-down_binary64_6211`
2×	`associate-r/_binary64_6087` `rem-sqrt-square_binary64_6156` `associate-l/_binary64_6088`
1×	`rem-square-sqrt_binary64_6155` `cbrt-unprod_binary64_6173` `pow2_binary64_6221` `sqrt-unprod_binary64_6162` `prod-exp_binary64_6189` `pow-plus_binary64_6203` `sum-log_binary64_6231` `*-commutative_binary64_6076` `+-commutative_binary64_6075`

Counts

4 → 106

Calls

4 calls:

21.0ms	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
7.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
7.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
7.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

series339.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
125.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
51.0ms	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
37.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))

simplify84.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5801	2483

prune128.0ms (3.1%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	117	5	122

Merged error: 0.0b

Counts

122 → 5

Compiler

Compiled 2806 to 1427 computations (49.1% saved)

localize15.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
0.5b	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
0.5b	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
0.5b	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))

rewrite61.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`cbrt-prod_binary64_6171`
35×	`*-un-lft-identity_binary64_6143`
23×	`add-sqr-sqrt_binary64_6164`
18×	`cbrt-div_binary64_6172`
15×	`add-cube-cbrt_binary64_6175`
11×	`pow1_binary64_6201`
9×	`distribute-lft-out_binary64_6096` `swap-sqr_binary64_6110` `flip3-+_binary64_6146` `pow1/3_binary64_6222` `flip-+_binary64_6117`
7×	`associate-r_binary64_6085` `associate-l_binary64_6086`
6×	`add-exp-log_binary64_6178`
4×	`add-log-exp_binary64_6179` `frac-times_binary64_6153` `unswap-sqr_binary64_6111` `add-cbrt-cube_binary64_6176`
2×	`associate-r/_binary64_6087` `pow-sqr_binary64_6116` `pow-prod-up_binary64_6210` `pow-prod-down_binary64_6211` `associate-l/_binary64_6088`
1×	`cbrt-unprod_binary64_6173` `pow2_binary64_6221` `prod-exp_binary64_6189` `pow-plus_binary64_6203` `*-commutative_binary64_6076`

Counts

4 → 95

Calls

4 calls:

21.0ms	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
10.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
8.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
7.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))

series832.0ms (20.3%)

Counts

4 → 12

Calls

4 calls:

250.0ms	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))) (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
205.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
192.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))
185.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))

simplify68.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4991	3142
1	4991	3142

prune238.0ms (5.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	107	5	112

Merged error: 0.0b

Counts

112 → 5

Compiler

Compiled 5403 to 2930 computations (45.8% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
0.1b	(sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
0.2b	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))) 3))
0.5b	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))) 3)

rewrite85.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

121×	`sqrt-prod_binary64_6158`
74×	`add-sqr-sqrt_binary64_6164`
39×	`*-un-lft-identity_binary64_6143`
36×	`sqrt-div_binary64_6159`
29×	`unpow-prod-down_binary64_6219` `cube-prod_binary64_6168`
26×	`associate-r_binary64_6085`
25×	`add-cube-cbrt_binary64_6175`
24×	`unswap-sqr_binary64_6111`
12×	`sqrt-pow1_binary64_6160` `pow1_binary64_6201`
10×	`add-exp-log_binary64_6178` `associate-l_binary64_6086`
9×	`flip3-+_binary64_6146` `flip-+_binary64_6117`
8×	`cube-div_binary64_6169`
7×	`distribute-lft-out_binary64_6096` `add-cbrt-cube_binary64_6176`
6×	`pow1/2_binary64_6220`
5×	`sqr-pow_binary64_6115` `pow-pow_binary64_6212`
4×	`add-log-exp_binary64_6179` `frac-times_binary64_6153` `rem-sqrt-square_binary64_6156`
3×	`pow-unpow_binary64_6217` `prod-exp_binary64_6189`
2×	`associate-r/_binary64_6087` `unpow3_binary64_6206` `pow-to-exp_binary64_6209` `pow-exp_binary64_6208` `associate-l/_binary64_6088` `cube-mult_binary64_6170`
1×	`cbrt-unprod_binary64_6173` `rem-cube-cbrt_binary64_6165` `*-commutative_binary64_6076` `pow-prod-up_binary64_6210` `sqrt-pow2_binary64_6161`

Counts

4 → 169

Calls

4 calls:

34.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))) 3))
12.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))) 3)
8.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
8.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))

series929.0ms (22.7%)

Counts

4 → 12

Calls

4 calls:

464.0ms	(pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))) 3)
213.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
205.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2))))
47.0ms	(*.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))) (pow.f64 (sqrt.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2)))) 3))

simplify113.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

181 → 181

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4961	4645
1	4961	4645

prune262.0ms (6.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	1	0	1
Picked	1	0	1
Done	1	2	3
Total	182	4	186

Merged error: 0b

Counts

186 → 4

Compiler

Compiled 5174 to 2968 computations (42.6% saved)

regimes41.0ms (1%)

Compiler: Compiled 266 to 193 computations (27.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	12
1	19	12

end0.0ms (0%)

sample478.0ms (11.7%)

Algorithm

1×

intervals

Results

195.0ms	7721×	body	128	valid
10.0ms	87×	body	2048	valid
9.0ms	99×	body	1024	valid
4.0ms	58×	body	512	valid
2.0ms	35×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 99 to 74 computations (25.3% saved)

Details

analyze20.0ms (0.5%)

sample12.0ms (0.3%)

simplify174.0ms (4.2%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite9.0ms (0.2%)

series40.0ms (1%)

simplify67.0ms (1.6%)

prune19.0ms (0.5%)

localize9.0ms (0.2%)

rewrite54.0ms (1.3%)

series339.0ms (8.3%)

simplify84.0ms (2.1%)

prune128.0ms (3.1%)

localize15.0ms (0.4%)

rewrite61.0ms (1.5%)

series832.0ms (20.3%)

simplify68.0ms (1.7%)

prune238.0ms (5.8%)

localize11.0ms (0.3%)

rewrite85.0ms (2.1%)

series929.0ms (22.7%)

simplify113.0ms (2.8%)

prune262.0ms (6.4%)

regimes41.0ms (1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample478.0ms (11.7%)

Profiling